Publications

Paper

Copyright notice: The following material is presented here to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.

In this webpage you will find my publications: Book, Dissertations, Journal articles, Conference publications

Book:

D. Ramírez, I. Santamaría, and L. L. Scharf, Coherence: In Signal Processing and Machine Learning, 1st ed. Springer Nature, 2023.
```
@book{RamirezSantamariaScharf-2023-CoherenceInSignalProcessingand,
  author = {Ram{\'i}rez, D. and Santamar{\'i}a, I. and Scharf, L. L.},
  doi = {10.1007/978-3-031-13331-2},
  edition = {1st},
  publisher = {Springer Nature},
  title = {Coherence: In Signal Processing and Machine Learning},
  year = {2023}
}
```
This book organizes principles and methods of signal processing and machine learning into the framework of coherence. The book contains a wealth of classical and modern methods of inference, some reported here for the first time. General results are applied to problems in communications, cognitive radio, passive and active radar and sonar, multi-sensor array processing, spectrum analysis, hyperspectral imaging, subspace clustering, and related. The reader will find new results for model fitting; for dimension reduction in models and ambient spaces; for detection, estimation, and space-time series analysis; for subspace averaging; and for uncertainty quantification. Throughout, the transformation invariances of statistics are clarified, geometries are illuminated, and null distributions are given where tractable. Stochastic representations are emphasized, as these are central to Monte Carlo simulations. The appendices contain a comprehensive account of matrix theory, the SVD, the multivariate normal distribution, and many of the important distributions for coherence statistics. The book begins with a review of classical results in the physical and engineering sciences where coherence plays a fundamental role. Then least squares theory and the theory of minimum mean-squared error estimation are developed, with special attention paid to statistics that may be interpreted as coherence statistics. A chapter on classical hypothesis tests for covariance structure introduces the next three chapters on matched and adaptive subspace detectors. These detectors are derived from likelihood reasoning, but it is their geometries and invariances that qualify them as coherence statistics. A chapter on independence testing in space-time data sets leads to a definition of broadband coherence, and contains novel applications to cognitive radio and the analysis of cyclostationarity. The chapter on subspace averaging reviews basic results and derives an order-fitting rule for determining the dimension of an average subspace. These results are used to enumerate sources of acoustic and electromagnetic radiation and to cluster subspaces into similarity classes. The chapter on performance bounds and uncertainty quantification emphasizes the geometry of the Cramèr-Rao bound and its related information geometry.

Dissertations:

D. Ramírez, “Detection and Estimation of Time Series using a Multi-sensor Array (in Spanish),” PhD thesis, Universidad de Cantabria, 2011.

@phdthesis{Ramirez-2011-DetectionandEstimationofTime,
  author = {Ram{\'i}rez, D.},
  school = {Universidad de Cantabria},
  title = {Detection and Estimation of Time Series using a Multi-sensor Array (in Spanish)},
  year = {2011},
  local-url = {Ramirez_PhDThesis.pdf}
}

D. Ramírez, “Regularized detection techniques in VBLAST systems: Development of a 2x2 testbed at 2.4 GHz (in Spanish),” Master's thesis, Universidad de Cantabria, 2006.

@mastersthesis{Ramirez-2006-RegularizeddetectiontechniquesinVBLAST,
  author = {Ram{\'i}rez, D.},
  school = {Universidad de Cantabria},
  title = {Regularized detection techniques in VBLAST systems: Development of a 2x2 testbed at 2.4 GHz (in Spanish)},
  year = {2006},
  local-url = {Ramirez_PFC.pdf}
}

Journal articles:

D. Ramírez, I. Santamaría, and L. L. Scharf, “Passive detection of a random signal common to multi-sensor reference and surveillance arrays,” IEEE Trans. Vehicular Techn. (To appear), 2024.
```
@article{RamirezSantamariaScharf-2024-Passivedetectionofrandomsignal,
  author = {Ram{\'i}rez, D. and Santamar{\'i}a, I. and Scharf, L. L.},
  doi = {10.1109/TVT.2024.3366757},
  issn = {0018-9545},
  journal = {{IEEE} {T}rans.\ {V}ehicular {T}echn. (To appear)},
  arxiv = {2402.07583},
  title = {Passive detection of a random signal common to multi-sensor reference and surveillance arrays},
  year = {2024},
  local-url = {R34_TransVehTech_Rank_one.pdf}
}
```
This paper addresses the passive detection of a common rank-one subspace signal received in two multi-sensor arrays. We consider the case of a one-antenna transmitter sending a common Gaussian signal, independent Gaussian noises with arbitrary spatial covariance, and known channel subspaces. The detector derived in this paper is a generalized likelihood ratio (GLR) test. For all but one of the unknown parameters, it is possible to find closed-form maximum likelihood (ML) estimator functions. We can further compress the likelihood to only an unknown vector whose ML estimate requires maximizing a product of ratios in quadratic forms, which is carried out using a trust-region algorithm. We propose two approximations of the GLR that do not require any numerical optimization: one based on a sample-based estimator of the unknown parameter whose ML estimate cannot be obtained in closed-form, and one derived under low-SNR conditions. Notably, all the detectors are scale-invariant, and the approximations are functions of beamformed data. However, they are not GLRTs for data that has been pre-processed with a beamformer, a point that is elaborated in the paper. These detectors outperform previously published correlation detectors on simulated data, in many cases quite significantly. Moreover, performance results quantify the performance gains over detectors that assume only the dimension of the subspace to be known.
P.-W. Wu, L. Huang, D. Ramírez, Y.-H. Xiao, and and H. C. So, “One-bit spectrum sensing for cognitive radio,” IEEE Trans. Signal Process., vol. 72, pp. 549–564, 2024.
```
@article{WuHuangRamirez-2024-One-bitspectrumsensingforcognitive,
  arxiv = {2306.13558},
  author = {Wu, P.-W. and Huang, L. and Ram{\'i}rez, D. and Xiao, Y.-H. and and H. C. So},
  doi = {10.1109/TSP.2023.3343569},
  issn = {1053-587X},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  pages = {549--564},
  title = {One-bit spectrum sensing for cognitive radio},
  volume = {72},
  year = {2024},
  local-url = {R33_1_bit_spectrum_sensing.pdf}
}
```
Spectrum sensing for cognitive radio requires effective monitoring of wide bandwidths, which translates into high-rate sampling. Traditional spectrum sensing methods employing high-precision analog-to-digital converters (ADCs) result in increased power consumption and expensive hardware costs. In this paper, we explore blind spectrum sensing utilizing one-bit ADCs. We derive a closed-form detector based on Rao’s test and demonstrate its equivalence with the second-order eigenvalue-moment-ratio test. Furthermore, a near-exact distribution based on the moment-based method, and an approximate distribution in the low signal-to-noise ratio (SNR) regime based on the central limit theorem, are obtained. Theoretical analysis is then performed and our results show that the performance loss of the proposed detector is approximately 2 dB (\pi/2) compared to detectors employing ∞-bit ADCs when the SNR is low. This loss can be compensated for by using approximately 2.47 (\pi^2/4) times more samples. In addition, we unveil that the efficiency of incoherent accumulation in one-bit detection is the square root of that of coherent accumulation. Simulation results corroborate the correctness of our theoretical calculations.
P. Bonilla-Escribano, D. Ramírez, E. Baca-García, P. Courtet, A. Artés-Rodríguez, and J. López-Castromán, “Multidimensional variability in ecological assessments predicts two clusters of suicidal patients,” Scientific Reports, vol. 13, no. 3546, Mar. 2023.
```
@article{Bonilla-EscribanoRamirezBaca-Garcia-2023-Multidimensionalvariabilityinecologicalassessments,
  author = {Bonilla-Escribano, P. and Ram{\'i}rez, D. and Baca-Garc{\'i}a, E. and Courtet, P. and Art{\'e}s-Rodr{\'i}guez, A. and L{\'o}pez-Castrom{\'a}n, J.},
  doi = {10.1038/s41598-023-30085-1},
  issn = {2045-2322},
  journal = {{{S}}cientific {{R}}eports},
  month = {{M}arch},
  number = {3546},
  title = {Multidimensional variability in ecological assessments predicts two clusters of suicidal patients},
  volume = {13},
  year = {2023},
  local-url = {R31_Variability_Scientific_Reports.pdf}
}
```
The variability of suicidal thoughts and other clinical factors during follow-up has emerged as a promising phenotype to identify vulnerable patients through Ecological Momentary Assessment (EMA). In this study, we aimed to (1) identify clusters of clinical variability, and (2) examine the features associated with high variability. We studied a set of 275 adult patients treated for a suicidal crisis in the outpatient and emergency psychiatric departments of five clinical centers across Spain and France. Data included a total of 48,489 answers to 32 EMA questions, as well as baseline and follow-up validated data from clinical assessments. A Gaussian Mixture Model (GMM) was used to cluster the patients according to EMA variability during follow-up along six clinical domains. We then used a random forest algorithm to identify the clinical features that can be used to predict the level of variability. The GMM confirmed that suicidal patients are best clustered in two groups with EMA data: low- and high-variability. The high-variability group showed more instability in all dimensions, particularly in social withdrawal, sleep measures, wish to live, and social support. Both clusters were separated by ten clinical features (AUC=0.74), including depressive symptoms, cognitive instability, the intensity and frequency of passive suicidal ideation, and the occurrence of clinical events, such as suicide attempts or emergency visits during follow-up. Initiatives to follow up suicidal patients with ecological measures should take into account the existence of a high variability cluster, which could be identified before the follow-up begins.
Y.-H. Xiao, L. Huang, D. Ramírez, C. Qian, and H. C. So, “Covariance matrix recovery from one-bit data with non-zero quantization thresholds: Algorithm and performance analysis,” IEEE Trans. Signal Process., vol. 71, pp. 4060–4076, Nov. 2023.
```
@article{XiaoHuangRamirez-2023-Covariancematrixrecoveryfromone-bit,
  arxiv = {2303.16455},
  author = {Xiao, Y.-H. and Huang, L. and Ram{\'i}rez, D. and Qian, C. and So, H. C.},
  doi = {10.1109/TSP.2023.3325664},
  issn = {1053-587X},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  month = {{N}ovember},
  pages = {4060--4076},
  title = {Covariance matrix recovery from one-bit data with non-zero quantization thresholds: Algorithm and performance analysis},
  volume = {71},
  year = {2023},
  local-url = {R32_1_bit_covariance_reconstruction.pdf}
}
```
Covariance matrix recovery is a topic of great significance in the field of one-bit signal processing and has numerous practical applications. Despite its importance, the conventional arcsine law with zero threshold is incapable of recovering the diagonal elements of the covariance matrix. To address this limitation, recent studies have proposed the use of non-zero clipping thresholds. However, the relationship between the estimation error and the sampling threshold is not yet known. In this paper, we undertake an analysis of the mean squared error by computing the Fisher information matrix for a given threshold. Our results reveal that the optimal threshold can vary considerably, depending on the variances and correlation coefficients. As a result, it is inappropriate to adopt a constant threshold to encompass parameters that vary widely. To mitigate this issue, we present a recovery scheme that incorporates time-varying thresholds. Our approach differs from existing methods in that it utilizes the exact values of the threshold, rather than its statistical properties, to increase the estimation accuracy. Simulation results, including those of the direction-of-arrival estimation problem, demonstrate the efficacy of the developed scheme, especially in complex scenarios where the covariance elements are widely separated.
J. Pérez, J. Vía, L. Vielva, and D. Ramírez, “Online detection and SNR estimation in cooperative spectrum sensing,” IEEE Trans. Wireless Comm., vol. 21, no. 4, pp. 2521–2533, Apr. 2022.
```
@article{PerezViaVielva-2022-OnlinedetectionandSNRestimation,
  author = {P{\'e}rez, J. and V{\'i}a, J. and Vielva, L. and Ram{\'i}rez, D.},
  doi = {10.1109/TWC.2021.3113089},
  issn = {1536-1276},
  journal = {{IEEE} {T}rans.\ {W}ireless {C}omm.},
  month = {{A}pril},
  number = {4},
  pages = {2521--2533},
  title = {Online detection and {SNR} estimation in cooperative spectrum sensing},
  volume = {21},
  year = {2022},
  local-url = {R29_TWC_CSS.pdf}
}
```
Cooperative spectrum sensing has proved to be an effective method to improve the detection performance in cognitive radio systems. This work focuses on centralized cooperative schemes based on the soft fusion of the energy measurements at the cognitive radios (CRs). In these systems, the likelihood ratio test (LRT) is the optimal detection rule, but the sufficient statistic depends on the local signal-to-noise ratio (SNR) at the CRs, which are unknown in most practical cases. Therefore, the detection problem becomes a composite hypothesis test. The generalized LRT is the most popular approach in those cases. Unfortunately, in mobile environments, its performance is well below the LRT because the local energies are measured under varying SNRs. In this work, we present a new algorithm that jointly estimates the instantaneous SNRs and detects the presence of primary signals. Due to its adaptive nature, the algorithm is well suited for mobile scenarios where the local SNRs are time-varying. Simulation results show that its detection performance is close to the LRT in realistic conditions.
Y.-H. Xiao, D. Ramírez, P. J. Schreier, C. Qian, and L. Huang, “One-bit target detection in collocated MIMO Radar and performance degradation analysis,” IEEE Trans. Vehicular Techn., vol. 71, no. 9, pp. 9363–9374, Sep. 2022.
```
@article{XiaoRamirezSchreier-2022-One-bittargetdetectionincollocated,
  arxiv = {2012.10780v2},
  author = {Xiao, Y.-H. and Ram{\'i}rez, D. and Schreier, P. J. and Qian, C. and Huang, L.},
  doi = {10.1109/TVT.2022.3178285},
  issn = {0018-9545},
  journal = {{IEEE} {T}rans.\ {V}ehicular {T}echn.},
  month = {{S}eptember},
  number = {9},
  pages = {9363--9374},
  title = {One-bit target detection in collocated {MIMO} {R}adar and performance degradation analysis},
  volume = {71},
  year = {2022},
  local-url = {R30_TVT_1bit_detection.pdf}
}
```
Target detection is an important problem in multiple-input multiple-output (MIMO) radar. Many existing target detection algorithms were proposed without taking into consideration the quantization error caused by analog-to-digital converters (ADCs). This paper addresses the problem of target detection for MIMO radar with one-bit ADCs and derives a Rao’s test-based detector. The proposed method has several appealing features: 1) it is a closed-form detector; 2) it allows us to handle sign measurements straightforwardly; 3) there are closed-form approximations of the detector’s distributions, which allow us to theoretically evaluate its performance. Moreover, the closed-form distributions allow us to study the performance degradation due to the one-bit ADCs, yielding an approximate 2 dB loss in the low-signal-to-noise-ratio (SNR) regime compared to ∞-bit ADCs. Simulation results are included to showcase the advantage of the proposed detector and validate the accuracy of the theoretical results.
D. Ramírez, A. G. Marques, and S. Segarra, “Graph-signal reconstruction and blind deconvolution for structured inputs,” Signal Process. (Special issue on Processing and Learning over Graphs), vol. 188, p. 108180, Nov. 2021.
```
@article{RamirezMarquesSegarra-2021-Graph-signalreconstructionandblinddeconvolution,
  arxiv = {2105.14747},
  author = {Ram{\'i}rez, D. and Marques, A. G. and Segarra, S.},
  doi = {10.1016/j.sigpro.2021.108180},
  issn = {0165-1684},
  journal = {{S}ignal {P}rocess. ({S}pecial issue on {P}rocessing and {L}earning over {G}raphs)},
  month = {{N}ovember},
  pages = {108180},
  title = {Graph-signal reconstruction and blind deconvolution for structured inputs},
  volume = {188},
  year = {2021}
}
```
Key to successfully deal with complex contemporary datasets is the development of tractable models that account for the irregular structure of the information at hand. This paper provides a comprehensive view of several sampling, reconstruction, and recovery problems for signals defined on irregular domains that can be accurately represented by a graph. The workhorse assumption is that the (partially) observed signals can be modeled as the output of a graph filter to a structured (parsimonious) input graph signal. When either the input or the filter coefficients are known, this is tantamount to assuming that the signals of interest live on a subspace defined by the supporting graph. When neither is known, the model becomes bilinear. Upon imposing different priors and additional structure on either the input or the filter coefficients, a broad range of relevant problem formulations arise. The goal is then to leverage those priors, the structure of the supporting graph, and the samples of the signal of interest to recover: the signal at the non-sampled nodes (graph-signal interpolation), the input (deconvolution), the filter coefficients (system identification), or any combination thereof (blind deconvolution).
P. Moreno-Muñoz, D. Ramírez, and A. Artés-Rodríguez, “Change-point detection in hierarchical circadian models,” Pattern Recognition, vol. 113, p. 107820, May 2021.
```
@article{Moreno-MunozRamirezArtes-Rodriguez-2021-Change-pointdetectioninhierarchicalcircadian,
  arxiv = {1809.04197},
  author = {Moreno-Mu{\~n}oz, P. and Ram{\'i}rez, D. and Art{\'e}s-Rodr{\'i}guez, A.},
  doi = {10.1016/j.patcog.2021.107820},
  issn = {0031-3203},
  journal = {{P}attern {R}ecognition},
  month = {{M}ay},
  pages = {107820},
  title = {Change-point detection in hierarchical circadian models},
  volume = {113},
  year = {2021}
}
```
This paper addresses the problem of change-point detection in sequences of high-dimensional and heterogeneous observations, which also possess a periodic temporal structure. Due to the dimensionality problem, when the time between change points is of the order of the dimension of the model parameters, drifts in the underlying distribution can be misidentified as changes. To overcome this limitation, we assume that the observations lie in a lower-dimensional manifold that admits a latent variable representation. In particular, we propose a hierarchical model that is computationally feasible, widely applicable to heterogeneous data and robust to missing instances. Additionally, the observations’ periodic dependencies are captured by non-stationary periodic covariance functions. The proposed technique is particularly well suited to (and motivated by) the problem of detecting changes in human behavior using smartphones and its application to relapse detection in psychiatric patients. Finally, we validate the technique on synthetic examples and we demonstrate its utility in the detection of behavioral changes using real data acquired by smartphones.
P. Bonilla-Escribano, D. Ramírez, A. Porras-Segovia, and A. Artés-Rodríguez, “Assessment of variability in irregularly sampled time series: Applications to mental healthcare,” Mathematics (Special issue on Recent Advances in Data Science), vol. 9, no. 1, 2021.
```
@article{Bonilla-EscribanoRamirezPorras-Segovia-2021-Assessmentofvariabilityinirregularly,
  article-number = {71},
  author = {Bonilla-Escribano, P. and Ram{\'i}rez, D. and Porras-Segovia, A. and Art{\'e}s-Rodr{\'i}guez, A.},
  doi = {10.3390/math9010071},
  issn = {2227-7390},
  journal = {{M}athematics ({S}pecial issue on {R}ecent {A}dvances in {D}ata {S}cience)},
  number = {1},
  title = {Assessment of variability in irregularly sampled time series: Applications to mental healthcare},
  volume = {9},
  year = {2021},
  local-url = {R26_Variability_measures.pdf}
}
```
Variability is defined as the propensity at which a given signal is likely to change. There are many choices for measuring variability, and it is not generally known which ones offer better properties. This paper compares different variability metrics applied to irregularly (nonuniformly) sampled time series, which have important clinical applications, particularly in mental healthcare. Using both synthetic and real patient data, we identify the most robust and interpretable variability measures out of a set 21 candidates. Some of these candidates are also proposed in this work based on the absolute slopes of the time series. An additional synthetic data experiment shows that when the complete time series is unknown, as it happens with real data, a non-negligible bias that favors normalized and/or metrics based on the raw observations of the series appears. Therefore, only the results of the synthetic experiments, which have access to the full series, should be used to draw conclusions. Accordingly, the median absolute deviation of the absolute value of the successive slopes of the data is the best way of measuring variability for this kind of time series.
I. Santamaría, L. L. Scharf, and D. Ramírez, “Scale-invariant subspace detectors based on first- and second-order statistical models,” IEEE Trans. Signal Process., vol. 68, pp. 6432–6443, 2020.
```
@article{SantamariaScharfRamirez-2020-Scale-invariantsubspacedetectorsbasedon,
  author = {Santamar{\'i}a, I. and Scharf, L. L. and Ram{\'i}rez, D.},
  doi = {10.1109/TSP.2020.3036725},
  issn = {1053-587X},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  pages = {6432-6443},
  title = {Scale-invariant subspace detectors based on first- and second-order statistical models},
  volume = {68},
  year = {2020},
  local-url = {R25_TSP_First_Second.pdf}
}
```
The problem is to detect a multi-rank source transmitting an unknown sequence of complex-valued symbols to a multi-sensor array. In some cases the channel subspace is known, and in others only its dimension is known. Should the unknown transmissions be treated as unknowns in a first-order statistical model, or should they be assigned a prior distribution that is then used to marginalize a first-order model for a second-order statistical model? This question motivates the derivation of subspace detectors for cases where the subspace is known, and for cases where only the dimension of the subspace is known. For three of these four models the GLR detectors are known, and they have been reported in the literature. But the GLR detector for the case of a known subspace and a second-order model for the measurements is derived for the first time in this paper. When the subspace is known, second-order generalized likelihood ratio (GLR) tests outperform first-order GLR tests when the spread of subspace eigenvalues is large, while first-order GLR tests outperform second-order GLR tests when the spread is small. When only the dimension of the subspace is known, second-order GLR tests outperform first-order GLR tests, regardless of the spread of signal subspace eigenvalues. For a rank-1 source, first-order and second-order statistical models lead to equivalent GLR tests. This is a new finding.
S. Horstmann, D. Ramírez, and P. J. Schreier, “Two-channel passive detection of cyclostationary signals,” IEEE Trans. Signal Process., vol. 68, pp. 2340–2355, 2020.
```
@article{HorstmannRamirezSchreier-2020-Two-channelpassivedetectionofcyclostationary,
  author = {Horstmann, S. and Ram{\'i}rez, D. and Schreier, P. J.},
  doi = {10.1109/TSP.2020.2981767},
  issn = {1053-587X},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  pages = {2340-2355},
  title = {Two-channel passive detection of cyclostationary signals},
  volume = {68},
  year = {2020},
  local-url = {R24_TSP_TwoChannel_Detection.pdf}
}
```
This paper considers passive detection of a cyclostationary signal in two multiple-input multiple-output (MIMO) channels. The passive detection system consists of an illuminator of opportunity (IO), a reference array, and a surveillance array, each equipped with multiple antennas. As common transmission signals of the IO are cyclostationary, our goal is to detect the presence of cyclostationarity at the surveillance array, given observations from both channels. To this end, we analyze the existence of optimal invariant tests, and we derive an alternative and more insightful expression for a previously proposed generalized likelihood ratio test (GLRT). Since we show that neither the uniformly most powerful invariant test (UMPIT) nor the locally most powerful invariant test (LMPIT) exist, we propose an LMPIT-inspired detector that is given by a function of the cyclic cross-power spectral density. We show that the LMPIT-inspired detector outperforms the GLRT, and both detectors outperform state-of-the-art techniques.
D. Ramírez, I. Santamaría, L. L. Scharf, and S. V. Vaerenbergh, “Multi-channel factor analysis with common and unique factors,” IEEE Trans. Signal Process., vol. 68, pp. 113–126, 2020.
```
@article{RamirezSantamariaScharf-2020-Multi-channelfactoranalysiswithcommon,
  author = {Ram{\'i}rez, D. and Santamar{\'i}a, I. and Scharf, L. L. and Vaerenbergh, S. Van},
  doi = {10.1109/TSP.2019.2955829},
  issn = {1053-587X},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  pages = {113-126},
  title = {Multi-channel factor analysis with common and unique factors},
  volume = {68},
  year = {2020},
  local-url = {R23_TSP_MFA.pdf}
}
```
This work presents a generalization of classical factor analysis (FA). Each of M channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the M multiple-input multiple-output (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar.
V. Garg, I. Santamaría, D. Ramírez, and L. L. Scharf, “Subspace averaging and order determination for source enumeration,” IEEE Trans. Signal Process., vol. 67, no. 11, pp. 3028–3041, Jun. 2019.
```
@article{GargSantamariaRamirez-2019-Subspaceaveragingandorderdetermination,
  author = {Garg, V. and Santamar{\'i}a, I. and Ram{\'i}rez, D. and Scharf, L. L.},
  doi = {10.1109/TSP.2019.2912151},
  issn = {1053-587X},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  month = {{J}une},
  number = {11},
  pages = {3028--3041},
  title = {Subspace averaging and order determination for source enumeration},
  volume = {67},
  year = {2019},
  local-url = {R21_TSP_SA.pdf}
}
```
In this paper, we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in con- trast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization–minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support.
A. Eguizabal, C. Lameiro, D. Ramírez, and P. J. Schreier, “Source enumeration in the presence of colored noise,” IEEE Signal Process. Lett., vol. 26, no. 3, pp. 475–479, Mar. 2019.
```
@article{EguizabalLameiroRamirez-2019-Sourceenumerationinpresenceof,
  author = {Eguizabal, A. and Lameiro, C. and Ram{\'i}rez, D. and Schreier, P. J.},
  doi = {10.1109/LSP.2019.2895548},
  issn = {1070-9908},
  journal = {{IEEE} {S}ignal {P}rocess.\ {L}ett.},
  month = {{M}arch},
  number = {3},
  pages = {475--479},
  title = {Source enumeration in the presence of colored noise},
  volume = {26},
  year = {2019},
  local-url = {R20_PDM_SPL.pdf}
}
```
In array signal processing the detection of the number of sources is an important step. Most approaches assume the signals to be embedded in white noise. However, this assumption is unrealistic in many scenarios. In this paper, we propose a strategy that can handle colored noise. We model the source detection as a regression problem and apply information-theoretic criteria to determine the model order of the regression. We show simulations of different scenarios, where our approach outperforms traditional techniques.
P. Bonilla-Escribano, D. Ramírez, A. Sedano-Capdevila, J. J. Campaña-Montes, E. Baca-García, P. Courtet, and A. Artés-Rodríguez, “Assessment of e-social activity in psychiatric patients,” IEEE J. Biomedical and Health Informatics, vol. 23, no. 6, pp. 2247–2256, Nov. 2019.
```
@article{Bonilla-EscribanoRamirezSedano-Capdevila-2019-Assessmentofe-socialactivityin,
  author = {Bonilla-Escribano, P. and Ram{\'i}rez, D. and Sedano-Capdevila, A. and Campa{\~n}a-Montes, J. J. and Baca-Garc{\'i}a, E. and Courtet, P. and Art{\'e}s-Rodr{\'i}guez, A.},
  doi = {10.1109/JBHI.2019.2918687},
  issn = {2168-2194},
  journal = {{IEEE} {J}.\ {B}iomedical\ and {H}ealth {I}nformatics},
  month = {{N}ovember},
  number = {6},
  pages = {2247-2256},
  title = {Assessment of e-social activity in psychiatric patients},
  volume = {23},
  year = {2019},
  local-url = {R22_JBHI_PointProcesses.pdf}
}
```
This work introduces a novel method to assess the social activity maintained by psychiatric patients using information and communication technologies. In particular, we model the daily usage patterns of phone calls and social and communication apps using point processes. We propose a novel nonhomogeneous Poisson process model with periodic (circadian) intensity function using a truncated Fourier series expansion, which is inferred using a trust-region algorithm. We also extend the model using a mixture of periodic intensity functions to cope with the different daily patterns of a person. The analysis of the usage of phone calls and social and communication apps of a cohort of 259 patients reveals common patterns shared among patients with relatively high homogeneity and differences among patient pathologies.
S. Berrouiguet, D. Ramírez, M. L. Barrigón, P. Moreno-Muñoz, R. Carmona, E. Baca-García, and A. Artés-Rodríguez, “Combining continuous smartphone native sensors data capture and unsupervised data mining techniques for behavioral changes detection: A case series of the Evidence-Based Behavior (eB2) study,” JMIR mHealth and uHealth (Special issue on Computing and Mental Health), vol. 6, no. 12, p. e197, Dec. 2018.
```
@article{BerrouiguetRamirezBarrigon-2018-Combiningcontinuoussmartphonenativesensors,
  author = {Berrouiguet, S. and Ram{\'i}rez, D. and Barrig{\'o}n, M. L. and Moreno-Mu{\~n}oz, P. and Carmona, R. and Baca-Garc{\'i}a, E. and Art{\'e}s-Rodr{\'i}guez, A.},
  doi = {10.2196/mhealth.9472},
  issn = {2291-5222},
  journal = {{JMIR} {mHealth} and {uHealth} ({S}pecial issue on {C}omputing and {M}ental {H}ealth)},
  month = {{D}ecember},
  number = {12},
  pages = {e197},
  title = {Combining continuous smartphone native sensors data capture and unsupervised data mining techniques for behavioral changes detection: A case series of the {E}vidence-{B}ased {B}ehavior ({eB2}) study},
  volume = {6},
  year = {2018},
  local-url = {R17_JMU_eB2.pdf}
}
```
Background: The emergence of smartphones, wearable sensor technologies, and smart homes allows the non-intrusive collection of activity data. Thus, health-related events such as Activities of Daily Living (ADLs, e.g., mobility patterns, feeding, sleeping, ...) can be captured without the patient’s active participation. We designed a system able to detect changes in the mobility patterns based on the smartphone’s native sensors and advanced machine learning and signal processing techniques. Objective: The principal objective of this work was to assess the feasibility of detecting mobility patterns changes in a sample of outpatients suffering from depression using the smartphone’s sensors. The proposed method processed the data acquired by the smartphone using an unsupervised detection technique. Method: Thirty-eight outpatients from the Hospital Fundación Jiménez Díaz Psychiatry Department (Madrid, Spain) participated in the study. The eB2 app was downloaded by patients on the day of recruitment and configured with the assistance of the physician. The app captured the following data: inertial sensors, physical activity, phone calls and message logs, app usage, nearby Bluetooth and Wi-Fi connections, and location. We applied a change-point detection technique to location data on a sample of 9 outpatients recruited between April 6th, 2017 and December 14th, 2017. The change-point detection was based only on location information, but the eB2 platform allowed for an easy integration of additional data. The app remained running in the background on the patient’s smartphone during the study participation. Results: The principal outcome measure was the identification of mobility pattern changes based on an unsupervised detection technique applied to the smartphone’s native sensors data. Results from five patients’ records are presented as a case series . The eB2 system detected specific mobility pattern changes according to the patient’s activity, which may be used as indicators of behavioral and clinical state changes. Discussion: The proposed technique was able to automatically detect changes in the mobility patterns of the outpatients that took part in this study. Assuming these mobility pattern changes correlated with behavioral changes, we have developed a technique that may identify possible relapses or clinical changes. Nevertheless, it is important to point out that the detected changes are not always related to relapses and that some clinical changes cannot be detected by the proposed method.
A. Pries, D. Ramírez, and P. J. Schreier, “LMPIT-inspired tests for detecting a cyclostationary signal in noise with spatio-temporal structure,” IEEE Trans. Wireless Comm., vol. 17, no. 9, pp. 6321–6334, Sep. 2018.
```
@article{PriesRamirezSchreier-2018-LMPIT-inspiredtestsfordetectingcyclostationary,
  author = {Pries, A. and Ram{\'i}rez, D. and Schreier, P. J.},
  doi = {10.1109/TWC.2018.2859314},
  issn = {1536-1276},
  journal = {{IEEE} {T}rans.\ {W}ireless {C}omm.},
  month = {{S}eptember},
  number = {9},
  pages = {6321--6334},
  title = {{LMPIT}-inspired tests for detecting a cyclostationary signal in noise with spatio-temporal structure},
  volume = {17},
  year = {2018},
  local-url = {R16_TWC_LMPIT_inspired_Cyclo.pdf}
}
```
In spectrum sensing for cognitive radio, the presence of a primary user can be detected by making use of the cyclostationarity property of digital communication signals. For the general scenario of a cyclostationary signal in temporally colored and spatially correlated noise, it has previously been shown that an asymptotic generalized likelihood ratio test (GLRT) and locally most powerful invariant test (LMPIT) exist. In this paper, we derive detectors for the presence of a cyclostationary signal in various scenarios with structured noise. In particular, we consider noise that is temporally white and/or spatially uncorrelated. Detectors that make use of this additional information about the noise process have enhanced performance. We have previously derived GLRTs for these specific scenarios; here, we examine the existence of LMPITs. We show that these exist only for detecting the presence of a cyclostationary signal in spatially uncorrelated noise. For white noise, an LMPIT does not exist. Instead, we propose tests that approximate the LMPIT, and they are shown to perform well in simulations. Finally, if the noise structure is not known in advance, we also present hypothesis tests using our framework.
D. Ramírez, D. Romero, J. Vía, R. López-Valcarce, and I. Santamaría, “Testing equality of multiple power spectral density matrices,” IEEE Trans. Signal Process., vol. 66, no. 23, pp. 6268–6280, Dec. 2018.
```
@article{RamirezRomeroVia-2018-Testingequalityofmultiplepower,
  author = {Ram{\'i}rez, D. and Romero, D. and V{\'i}a, J. and L{\'o}pez-Valcarce, R. and Santamar{\'i}a, I.},
  doi = {10.1109/TSP.2018.2875884},
  issn = {1053-587X},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  month = {{D}ecember},
  number = {23},
  pages = {6268--6280},
  title = {Testing equality of multiple power spectral density matrices},
  volume = {66},
  year = {2018},
  local-url = {R19_PSD_equality_TSP.pdf}
}
```
This paper studies the existence of optimal invariant detectors for determining whether P multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i.e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the corresponding proof naturally suggests an LMPIT-inspired detector that outperforms previously proposed detectors.
S. Horstmann, D. Ramírez, and P. J. Schreier, “Joint detection of almost-cyclostationary signals and estimation of their cycle period,” IEEE Signal Process. Lett., vol. 25, no. 11, pp. 1695–1699, Nov. 2018.
```
@article{HorstmannRamirezSchreier-2018-Jointdetectionofalmost-cyclostationarysignals,
  author = {Horstmann, S. and Ram{\'i}rez, D. and Schreier, P. J.},
  doi = {10.1109/LSP.2018.2871961},
  issn = {1070-9908},
  journal = {{IEEE} {S}ignal {P}rocess.\ {L}ett.},
  month = {{N}ovember},
  number = {11},
  pages = {1695--1699},
  title = {Joint detection of almost-cyclostationary signals and estimation of their cycle period},
  volume = {25},
  year = {2018},
  local-url = {R18_ACS_detection_estimation.pdf}
}
```
We propose a technique that jointly detects the presence of almost-cyclostationary (ACS) signals in wide-sense stationary (WSS) noise and provides an estimate of their cycle period. Since the cycle period of an ACS process is not an integer, the approach is based on a combination of a resampling stage and a multiple hypothesis test, which deal separately with the fractional part and the integer part of the cycle period. The approach requires resampling the signal at many different rates, which is computationally expensive. For this reason we propose a filter bank structure that allows us to efficiently resample a signal at many different rates by identifying common interpolation stages among the set of resampling rates.
Y. Song, P. J. Schreier, D. Ramírez, and T. Hasija, “Canonical correlation analysis of high-dimensional data with very small sample support,” Signal Process., vol. 128, pp. 449–458, Nov. 2016.
```
@article{SongSchreierRamirez-2016-Canonicalcorrelationanalysisofhigh-dimensional,
  author = {Song, Y. and Schreier, P. J. and Ram{\'i}rez, D. and Hasija, T.},
  doi = {10.1016/j.sigpro.2016.05.020},
  issn = {0165-1684},
  journal = {{S}ignal {P}rocess.},
  month = {{N}ovember},
  pages = {449--458},
  title = {Canonical correlation analysis of high-dimensional data with very small sample support},
  volume = {128},
  year = {2016}
}
```
This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the data. In such a scenario, a principal component analysis (PCA) rank-reduction preprocessing step is commonly performed before applying canonical correlation analysis (CCA). We present simple, yet very effective approaches to the joint model-order selection of the number of dimensions that should be retained through the PCA step and the number of correlated signals. These approaches are based on reduced-rank versions of the Bartlett-Lawley hypothesis test and the minimum description length information-theoretic criterion. Simulation results show that the techniques perform well for very small sample sizes even in colored noise.
D. Ramírez, P. J. Schreier, J. Vía, I. Santamaría, and L. L. Scharf, “Detection of multivariate cyclostationarity,” IEEE Trans. Signal Process., vol. 63, no. 20, pp. 5395–5408, Oct. 2015.
```
@article{RamirezSchreierVia-2015-Detectionofmultivariatecyclostationarity,
  author = {Ram{\'i}rez, D. and Schreier, P. J. and V{\'i}a, J. and Santamar{\'i}a, I. and Scharf, L. L.},
  doi = {10.1109/TSP.2015.2450201},
  issn = {1053-587X},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  month = {{O}ctober},
  number = {20},
  pages = {5395--5408},
  title = {Detection of multivariate cyclostationarity},
  volume = {63},
  year = {2015},
  local-url = {R14_TSP_Cyclo.pdf}
}
```
This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman’s theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loève spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra.
J. Manco-Vásquez, M. Lázaro-Gredilla, D. Ramírez, J. Vía, and I. Santamaría, “A Bayesian approach for adaptive multiantenna sensing in cognitive radio networks,” Signal Process., vol. 96, Part B, pp. 228–240, Mar. 2014.
```
@article{Manco-VasquezLazaro-GredillaRamirez-2014-Bayesianapproachforadaptivemultiantenna,
  author = {Manco-V{\'a}squez, J. and L{\'a}zaro-Gredilla, M. and Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I.},
  doi = {10.1016/j.sigpro.2013.10.005},
  issn = {0165-1684},
  journal = {{S}ignal {P}rocess.},
  month = {{M}arch},
  pages = {228--240},
  title = {A {B}ayesian approach for adaptive multiantenna sensing in cognitive radio networks},
  volume = {96, Part B},
  year = {2014}
}
```
Recent work on multiantenna spectrum sensing in cognitive radio (CR) networks has been based on generalized likelihood ratio test (GLRT) detectors, which lack the ability to learn from past decisions and to adapt to the continuously changing environment. To overcome this limitation, in this paper we propose a Bayesian detector capable of learning in an efficient way the posterior distributions under both hypotheses. Our Bayesian model places priors directly on the spatial covariance matrices under both hypotheses, as well as on the probability of channel occupancy. Specifically, we use inverse-gamma and complex inverse-Wishart distributions as conjugate priors for the null and alternative hypotheses, respectively; and a binomial distribution as the prior for channel occupancy. At each sensing period, Bayesian inference is applied and the posterior for the channel occupancy is thresholded for detection. After a suitable approximation, the posteriors are employed as priors for the next sensing frame, which forms the basis of the proposed Bayesian learning procedure. The performance of the Bayesian detector is evaluated by simulations and by means of a CR testbed composed of universal radio peripheral (USRP) nodes. Both the simulations and experimental measurements show that the Bayesian detector outperforms the GLRT in a variety of scenarios.
D. Ramírez, P. J. Schreier, J. Vía, and I. Santamaría, “Testing blind separability of complex Gaussian mixtures,” Signal Process., vol. 95, pp. 49–57, Feb. 2014.
```
@article{RamirezSchreierVia-2014-Testingblindseparabilityofcomplex,
  author = {Ram{\'i}rez, D. and Schreier, P. J. and V{\'i}a, J. and Santamar{\'i}a, I.},
  doi = {10.1016/j.sigpro.2013.08.010},
  issn = {0165-1684},
  journal = {{S}ignal {P}rocess.},
  month = {{F}ebruary},
  pages = {49--57},
  title = {Testing blind separability of complex {G}aussian mixtures},
  volume = {95},
  year = {2014}
}
```
The separation of a complex mixture based solely on second-order statistics can be achieved using the Strong Uncorrelating Transform (SUT) if and only if all sources have distinct circularity coefficients. However, in most problems we do not know the circularity coefficients, and they must be estimated from observed data. In this work, we propose a detector, based on the generalized likelihood ratio test (GLRT), to test the separability of a complex Gaussian mixture using the SUT. For the separable case (distinct circularity coefficients), the maximum likelihood (ML) estimates are straightforward. On the other hand, for the non-separable case (at least one circularity coefficient has multiplicity greater than one), the ML estimates are much more difficult to obtain. To set the threshold, we exploit Wilks’ theorem, which gives the asymptotic distribution of the GLRT under the null hypothesis. Finally, numerical simulations show the good performance of the proposed detector and the accuracy of Wilks’ approximation.
S. C. Olhede, D. Ramírez, and P. J. Schreier, “Detecting directionality in random fields using the monogenic signal,” IEEE Trans. Inform. Theory, vol. 60, no. 10, pp. 6491–6510, Oct. 2014.
```
@article{OlhedeRamirezSchreier-2014-Detectingdirectionalityinrandomfields,
  author = {Olhede, S. C. and Ram{\'i}rez, D. and Schreier, P. J.},
  doi = {10.1109/TIT.2014.2342734},
  issn = {0018-9448},
  journal = {{IEEE} {T}rans.\ {I}nform.\ {T}heory},
  month = {{O}ctober},
  number = {10},
  pages = {6491-6510},
  title = {Detecting directionality in random fields using the monogenic signal},
  volume = {60},
  year = {2014},
  local-url = {R12_Monogenic_IT.pdf}
}
```
Detecting and analyzing directional structures in images is important in many applications since one-dimensional patterns often correspond to important features such as object contours or trajectories. Classifying a structure as directional or non-directional requires a measure to quantify the degree of directionality and a threshold, which needs to be chosen based on the statistics of the image. In order to do this, we model the image as a random field. So far, little research has been performed on analyzing directionality in random fields. In this paper, we propose a measure to quantify the degree of directionality based on the random monogenic signal, which enables a unique decomposition of a 2D signal into local amplitude, local orientation, and local phase. We investigate the second-order statistical properties of the monogenic signal for isotropic, anisotropic, and unidirectional random fields. We analyze our measure of directionality for finite-size sample images, and determine a threshold to distinguish between unidirectional and non-unidirectional random fields, which allows the automatic classification of images.
S. Ali, D. Ramírez, M. Jansson, G. Seco-Granados, and J. A. López-Salcedo, “Multi-antenna spectrum sensing by exploiting spatio-temporal correlation,” Eurasip J. Adv. Signal Process., vol. 160, 2014.
```
@article{AliRamirezJansson-2014-Multi-antennaspectrumsensingbyexploiting,
  author = {Ali, S. and Ram{\'i}rez, D. and Jansson, M. and Seco-Granados, G. and L{\'o}pez-Salcedo, J. A.},
  doi = {10.1186/1687-6180-2014-160},
  journal = {{E}urasip\ {J}.\ {A}dv. {S}ignal {P}rocess.},
  title = {Multi-antenna spectrum sensing by exploiting spatio-temporal correlation},
  volume = {160},
  year = {2014},
  local-url = {R13_EJASP_GLRT_ST.pdf}
}
```
In this paper, we propose a novel mechanism for spectrum sensing that leads us to exploit the spatio-temporal correlation present in the received signal at a multi-antenna receiver. For the proposed mechanism, we formulate the spectrum sensing scheme by adopting the generalized likelihood ratio test (GLRT). However, the GLRT degenerates in the case of limited sample support. To circumvent this problem, several extensions are proposed that bring robustness to the GLRT in the case of high dimensionality and small sample size. In order to achieve these sample-efficient detection schemes, we modify the GLRT-based detector by exploiting the covariance structure and factoring the large spatio-temporal covariance matrix into spatial and temporal covariance matrices. The performance of the proposed detectors is evaluated by means of numerical simulations, showing important advantages over existing detectors.
S. Dähne, V. V. Nikulin, D. Ramírez, P. J. Schreier, K.-R. Müller, and S. Haufe, “Finding brain oscillations with power dependencies in neuroimaging data,” NeuroImage, vol. 96, pp. 334–348, 2014.
```
@article{DahneNikulinRamirez-2014-Findingbrainoscillationswithpower,
  author = {D{\"a}hne, S. and Nikulin, V. V. and Ram{\'i}rez, D. and Schreier, P. J. and M{\"u}ller, K.-R. and Haufe, S.},
  doi = {10.1016/j.neuroimage.2014.03.075},
  issn = {1053-8119},
  journal = {NeuroImage},
  pages = {334--348},
  title = {Finding brain oscillations with power dependencies in neuroimaging data},
  volume = {96},
  year = {2014}
}
```
Phase synchronization among neuronal oscillations within the same frequency band has been hypothesized to be a major mechanism for communication between different brain areas. On the other hand, cross-frequency com- munications are more flexible allowing interactions between oscillations with different frequencies. Among such cross-frequency interactions amplitude-to-amplitude interactions are of a special interest as they show how the strength of spatial synchronization in different neuronal populations relates to each other during a given task. While, previously, amplitude-to-amplitude correlations were studied primarily on the sensor level, we present a source separation approach using spatial filters which maximize the correlation between the envelopes of brain oscillations recorded with electro-/magnetoencephalography (EEG/MEG) or intracranial multichannel re- cordings. Our approach, which is called canonical source power correlation analysis (cSPoC), is thereby capable of extracting genuine brain oscillations solely based on their assumed coupling behavior even when the signal-to- noise ratio of the signals is low. In addition to using cSPoC for the analysis of cross-frequency interactions in the same subject, we show that it can also be utilized for studying amplitude dynamics of neuronal oscillations across subjects. We assess the performance of cSPoC in simulations as well as in three distinctively different analysis sce- narios of real EEG data, each involving several subjects. In the simulations, cSPoC outperforms unsupervised state-of-the-art approaches. In the analysis of real EEG recordings, we demonstrate excellent unsupervised dis- covery of meaningful power-to-power couplings, within as well as across subjects and frequency bands.
D. Ramírez, J. Vía, I. Santamaría, and L. L. Scharf, “Locally most powerful invariant tests for correlation and sphericity of Gaussian vectors,” IEEE Trans. Inform. Theory, vol. 59, no. 4, pp. 2128–2141, Apr. 2013.
```
@article{RamirezViaSantamaria-2013-Locallymostpowerfulinvarianttests,
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I. and Scharf, L. L.},
  doi = {10.1109/TIT.2012.2232705},
  issn = {0018-9448},
  journal = {{IEEE} {T}rans.\ {I}nform.\ {T}heory},
  month = {{A}pril},
  number = {4},
  pages = {2128--2141},
  title = {Locally most powerful invariant tests for correlation and sphericity of {G}aussian vectors},
  volume = {59},
  year = {2013},
  local-url = {R8_LMPIT_TIT.pdf}
}
```
In this paper we study the existence of locally most powerful invariant tests (LMPIT) for the problem of testing the covariance structure of a set of Gaussian random vectors. The LMPIT is the optimal test for the case of close hypotheses, among those satisfying the invariances of the problem, and in practical scenarios can provide better performance than the typically used generalized likelihood ratio test (GLRT). The derivation of the LMPIT usually requires one to find the maximal invariant statistic for the detection problem and then derive its distribution under both hypotheses, which in general is a rather involved procedure. As an alternative, Wijsman’s theorem provides the ratio of the maximal invariant densities without even finding an explicit expression for the maximal invariant. We first consider the problem of testing whether a set of N-dimensional Gaussian random vectors are uncorrelated or not, and show that the LMPIT is given by the Frobenius norm of the sample coherence matrix. Second, we study the case in which the vectors under the null hypothesis are uncorrelated and identically distributed, that is, the sphericity test for Gaussian vectors, for which we show that the LMPIT is given by the Frobenius norm of a normalized version of the sample covariance matrix. Finally, some numerical examples illustrate the performance of the proposed tests, which provide better results than their GLRT counterparts.
V. Pichler, M. Homolák, W. Skierucha, M. Pichlerová, D. Ramírez, J. Gregor, and P. Jaloviar, “Variability of moisture in coarse woody debris from several ecologically important tree species of the temperate zone of Europe,” Ecohydrology, vol. 5, no. 4, pp. 424–434, Jul. 2012.
```
@article{PichlerHomolakSkierucha-2012-Variabilityofmoistureincoarse,
  author = {Pichler, V. and Homol{\'a}k, M. and Skierucha, W. and Pichlerov{\'a}, M. and Ram{\'i}rez, D. and Gregor, J. and Jaloviar, P.},
  doi = {10.1002/eco.235},
  journal = {{E}cohydrology},
  month = {{J}uly},
  number = {4},
  pages = {424--434},
  title = {Variability of moisture in coarse woody debris from several ecologically important tree species of the temperate zone of {E}urope},
  volume = {5},
  year = {2012}
}
```
Deadwood moisture affects multiple functions of downed logs in forest ecosystems. They include provision of habitats for xylobionts, additional water stores and organic carbon stocks. In contrast to Northern American forests, little is known about moisture variability in downed logs of important tree species within the Temperate Zone of Europe. Therefore, our study aimed at elucidating this variability according to species, site and decay class (DC). Measurements were taken by TDR during two vegetation periods in eight Carpathian natural forests representing distinct site conditions, ranging from xerothermophilous to subalpine. Downed logs of Quercus spp., Abies alba Mill., Fagus sylvatica L., and Picea abies L., belonging to various DCs, were selected and instrumented with TDR probes. Species and DC-specific TDR calibration showed the importance of intrinsic wood porosity. The course of deadwood moisture consisted of drying during the early decay stage, except for A. alba and F. sylvatica, and an intense water reabsorption at later decay stages. Average moisture for all species and sites displayed seasonal trends, reflecting the occurrence of precipitation clusters and dry periods, as well as short-term fluctuations. Cross-spectral analysis revealed that both sapwood and heartwood participated in wetting and drying processes, but only after reaching an advanced stage of decay. New findings can be applied in interpreting, modelling and predicting deadwood water stores, habitat properties and respiration.
D. Ramírez, G. Vazquez-Vilar, R. López-Valcarce, J. Vía, and I. Santamaría, “Detection of rank-P signals in cognitive radio networks with uncalibrated multiple antennas,” IEEE Trans. Signal Process., vol. 59, no. 8, pp. 3764–3774, Aug. 2011.
```
@article{RamirezVazquez-VilarLopez-Valcarce-2011-Detectionofrank-Psignalsin,
  author = {Ram{\'i}rez, D. and Vazquez-Vilar, G. and L{\'o}pez-Valcarce, R. and V{\'i}a, J. and Santamar{\'i}a, I.},
  doi = {10.1109/TSP.2011.2146779},
  issn = {1053-587X},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  month = {{A}ugust},
  number = {8},
  pages = {3764--3774},
  title = {Detection of {rank-$P$} signals in cognitive radio networks with uncalibrated multiple antennas},
  volume = {59},
  year = {2011},
  local-url = {R7_rankPdetection_TrSP.pdf}
}
```
Spectrum sensing is a key component of the Cognitive Radio paradigm. Primary signals are typically detected with uncalibrated receivers at signal-to-noise ratios (SNRs) well below decodability levels. Multiantenna detectors exploit spatial independence of receiver thermal noise to boost detection performance and robustness. We study the problem of detecting a Gaussian signal with rank-P unknown spatial covariance matrix in spatially uncorrelated Gaussian noise with unknown covariance using multiple antennas. The generalized likelihood ratio test (GLRT) is derived for two scenarios. In the first one, the noises at all antennas are assumed to have the same (unknown) variance, whereas in the second, a generic diagonal noise covariance matrix is allowed in order to accommodate calibration uncertainties in the different antenna frontends. In the latter case, the GLRT statistic must be obtained numerically, for which an efficient method is presented. Furthermore, for asymptotically low SNR, it is shown that the GLRT does admit a closed form, and the resulting detector performs well in practice. Extensions are presented in order to account for unknown temporal correlation in both signal and noise, as well as frequency-selective channels.
J. Gutiérrez, Ó. González, J. Pérez, D. Ramírez, L. Vielva, J. Ibáñez, and I. Santamaría, “Frequency-domain methodology for measuring MIMO channels using a generic test bed,” IEEE Trans. Instrum. Meas., vol. 60, no. 3, pp. 827–838, Apr. 2011.
```
@article{GutierrezGonzalezPerez-2011-Frequency-domainmethodologyformeasuringMIMO,
  author = {Guti{\'e}rrez, J. and Gonz{\'a}lez, {\'O}. and P{\'e}rez, J. and Ram{\'i}rez, D. and Vielva, L. and Ib{\'a}{\~n}ez, J. and Santamar{\'i}a, I.},
  doi = {10.1109/TIM.2010.2082432},
  journal = {{IEEE} {T}rans. {I}nstrum. {M}eas.},
  month = {{A}pril},
  number = {3},
  pages = {827--838},
  title = {Frequency-domain methodology for measuring {MIMO} channels using a generic test bed},
  volume = {60},
  year = {2011},
  local-url = {R5_MIMO_Channel_characterization_IEEE_TIM.pdf}
}
```
A multiple-input multiple-output (MIMO) frequency-domain channel measurement methodology is pre- sented. This methodology can be implemented in any transmit/receive hardware consisting of radio frequency modules and baseband digital processing units. It involves the transmission and reception of frequency and phase-optimized complex exponentials through antenna arrays, followed by an offline frequency estimation, which makes additional synchronization circuitry unnecesary. To test the feasibility of this method, a series of measurements is presented, employing a 4 \times 4 dual-band (2.4/5 GHz) MIMO test bed.
D. Ramírez, J. Vía, I. Santamaría, and L. L. Scharf, “Detection of spatially correlated Gaussian time series,” IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5006–5015, Oct. 2010.
```
@article{RamirezViaSantamaria-2010-DetectionofspatiallycorrelatedGaussian,
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I. and Scharf, L. L.},
  award = {https://www.youtube.com/watch?v=gCo_5zbF5lo},
  doi = {10.1109/TSP.2010.2053360},
  journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.},
  month = {{O}ctober},
  number = {10},
  pages = {5006--5015},
  title = {Detection of spatially correlated {G}aussian time series},
  volume = {58},
  year = {2010},
  local-url = {R4_GLRT_GCS_Detection_Spatially_TrSP.pdf}
}
```
This work addresses the problem of deciding whether a set of realizations of a vector-valued time series with unknown temporal correlation are spatially correlated or not. For wide sense stationary (WSS) Gaussian processes, this is a problem of deciding between two different power spectral density matrices, one of them diagonal. Specifically, we show that for arbitrary Gaussian processes (not necessarily WSS) the generalized likelihood ratio test (GLRT) is given by the quotient between the determinant of the sample space-time covariance matrix and the determinant of its block-diagonal version. Furthermore, for WSS processes, we present an asymptotic frequency-domain approximation of the GLRT which is given by a function of the Hadamard ratio (quotient between the determinant of a matrix and the product of the elements of the main diagonal) of the estimated power spectral density matrix. The Hadamard ratio is known to be the GLRT detector for vector-valued random variables and, therefore, what this paper shows is how frequency-dependent Hadamard ratios must be merged into a single test statistic when the vector-valued random variable is replaced by a vector-valued time series with temporal correlation. For bivariate time series, the derived frequency domain detector can be rewritten as a function of the well-known magnitude squared coherence (MSC) spectrum, which suggests a straightforward extension of the MSC spectrum to the general case of multivariate time series. Finally, the performance of the proposed method is illustrated by means of simulations.
J. Vía, D. Ramírez, and I. Santamaría, “Properness and widely linear processing of quaternion random vectors,” IEEE Trans. Inform. Theory, vol. 56, no. 7, pp. 3502–3515, Jul. 2010.
```
@article{ViaRamirezSantamaria-2010-Propernessandwidelylinearprocessing,
  author = {V{\'i}a, J. and Ram{\'i}rez, D. and Santamar{\'i}a, I.},
  doi = {10.1109/TIT.2010.2048440},
  issn = {0018-9448},
  journal = {{IEEE} {T}rans.\ {I}nform.\ {T}heory},
  month = {{J}uly},
  number = {7},
  pages = {3502--3515},
  title = {Properness and widely linear processing of quaternion random vectors},
  volume = {56},
  year = {2010},
  local-url = {R3_Trans_Info_Theory_2010_QuaternionWL.pdf}
}
```
In this paper, the second-order circularity of quater- nion random vectors is analyzed. Unlike the case of complex vectors, there exist three different kinds of quaternion properness, which are based on the vanishing of three different complemen- tary covariance matrices. The different kinds of properness have direct implications on the Cayley–Dickson representation of the quaternion vector, and also on several well-known multivariate statistical analysis methods. In particular, the quaternion exten- sions of the partial least squares (PLS), multiple linear regression (MLR) and canonical correlation analysis (CCA) techniques are analyzed, showing that, in general, the optimal linear processing is full-widely linear. However, in the case of jointly \mathbbQ-proper or \mathbbC^η-proper vectors, the optimal processing reduces, respectively, to the conventional or semi-widely linear processing. Finally, a measure for the degree of improperness of a quaternion random vector is proposed, which is based on the Kullback–Leibler diver- gence between two zero-mean Gaussian distributions, one of them with the actual augmented covariance matrix, and the other with its closest proper version. This measure quantifies the entropy loss due to the improperness of the quaternion vector, and it admits an intuitive geometrical interpretation based on Kullback–Leibler projections onto sets of proper augmented covariance matrices.
D. Ramírez, I. Santamaría, J. Pérez, J. Vía, J. A. García-Naya, T. M. Fernández-Caramés, H. Pérez-Iglesias, M. González-López, L. Castedo, and J. M. Torres-Royo, “A comparative study of STBC transmissions at 2.4 GHz over indoor channels using a 2 \times 2 MIMO testbed,” Wireless Comm. and Mobile Computing, vol. 8, no. 9, pp. 1149–1164, Nov. 2008.
```
@article{RamirezSantamariaPerez-2008-comparativestudyofSTBCtransmissions,
  author = {Ram{\'i}rez, D. and Santamar{\'i}a, I. and P{\'e}rez, J. and V{\'i}a, J. and Garc{\'i}a-Naya, J. A. and Fern{\'a}ndez-Caram{\'e}s, T. M. and P{\'e}rez-Iglesias, H. and Gonz{\'a}lez-L{\'o}pez, M. and Castedo, L. and Torres-Royo, J. M.},
  doi = {10.1002/wcm.558},
  journal = {{W}ireless {C}omm.\ and {M}obile {C}omputing},
  month = {{N}ovember},
  number = {9},
  pages = {1149--1164},
  title = {A comparative study of {STBC} transmissions at 2.4 {GHz} over indoor channels using a $2 \times 2$ {MIMO} testbed},
  volume = {8},
  year = {2008},
  local-url = {R2_Wireless_Communications_and_Mobile_Computing2008.pdf}
}
```
In this paper we employ a 2 \times 2 Multiple-Input Multiple-Output (MIMO) hardware platform to evaluate, in realistic indoor scenarios, the performance of different space-time block coded (STBC) transmissions at 2.4 GHz. In particular, we focus on the Alamouti orthogonal scheme considering two types of Channel State Information (CSI) estimation: a conventional pilot-aided supervised technique and a recently proposed blind method based on Second Order Statistics (SOS). For comparison purposes, we also evaluate the performance of a Differential (non-coherent) STBC (DSTBC). DSTBC schemes have the advantage of not requiring CSI estimation but they incur in a 3 dB loss in performance. The hardware MIMO platform is based on high-performance signal acquisition and generation boards, each one equipped with a 1 GB memory module that allows the transmission of extremely large data frames. Upconversion to RF is performed by two RF vector signal generators whereas downconversion is carried out with two custom circuits designed from commercial components. All the baseband signal processing is implemented off-line in Matlab, making the MIMO testbed very flexible and easily reconfigurable. Using this platform we compare the performance of the described methods in line-of-sight (LOS) and non-line-of-sight (NLOS) indoor scenarios.
D. Ramírez and I. Santamaría, “Regularised approach to detection of constant modulus signals in MIMO channels,” Electr. Lett., vol. 42, no. 3, pp. 184–186, Feb. 2006.
```
@article{RamirezSantamaria-2006-Regularisedapproachtodetectionof,
  author = {Ram{\'i}rez, D. and Santamar{\'i}a, I.},
  doi = {10.1049/el:20063870},
  journal = {{E}lectr. {L}ett.},
  month = {{F}ebruary},
  number = {3},
  pages = {184--186},
  title = {Regularised approach to detection of constant modulus signals in {MIMO} channels},
  volume = {42},
  year = {2006},
  local-url = {R1_Electronic_Letters_2006.pdf}
}
```
A new suboptimal algorithm for detection of constant modulus signals in multiple-input multiple-output (MIMO) channels is presented. The deviation of the solution from the desired constant modulus property is used as a penalty or regularization term in the conventional least squares cost function, and an iterative reweighted least squares (IRWLS) procedure is used to minimize the regularized functional.

Conference publications:

S. Horstmann, D. Ramírez, and P. J. Schreier, “Multistatic passive detection of cyclostationary signals,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Seoul, Korea, 2024.
```
@inproceedings{HorstmannRamirezSchreier-2024-Multistaticpassivedetectionofcyclostationary,
  address = {Seoul, Korea},
  author = {Horstmann, S. and Ram{\'i}rez, D. and Schreier, P. J.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP48485.2024.10447335},
  month = {{A}pril},
  title = {Multistatic passive detection of cyclostationary signals},
  year = {2024},
  local-url = {C52_ICASSP2024.pdf}
}
```
In this work we consider a multistatic passive detection problem, which is motivated by a multiple-input multiple-output (MIMO) passive radar application. Specifically, we consider a single illuminator of opportunity (IO) and several surveillance and reference arrays for the detection of a Gaussian cyclostationary signal in temporally colored and spatially correlated noise. Concretely, 1) we derive the generalized likelihood ratio test (GLRT) for this problem and 2) provide a stochastic representation of the test statistic under the null hypothesis, which allows us to set the threshold for a constant probability of false alarm. Monte Carlo simulations are carried out to investigate the performance of the proposed GLRT.
D. Ramírez, I. Santamaría, and L. L. Scharf, “Passive detection of rank-one Gaussian signals for known channel subspaces and arbitrary noise,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Rhodes, Greece, 2023.
```
@inproceedings{RamirezSantamariaScharf-2023-Passivedetectionofrank-oneGaussian,
  address = {Rhodes, Greece},
  author = {Ram{\'i}rez, D. and Santamar{\'i}a, I. and Scharf, L. L.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP49357.2023.10094671},
  month = {{J}une},
  title = {Passive detection of rank-one {G}aussian signals for known channel subspaces and arbitrary noise},
  year = {2023},
  local-url = {C50_ICASSP2023.pdf}
}
```
This paper addresses the passive detection of a common signal in two multi-sensor arrays. For this problem, we derive a detector based on likelihood theory for the case of one-antenna transmitters, independent Gaussian noises with arbitrary spatial structure, Gaussian signals, and known channel subspaces. The detector uses a likelihood ratio where all but one of the unknown parameters are replaced by their maximum likelihood (ML) estimates. The ML estimation of the remaining parameter requires a numerical search, and it is therefore estimated using a sample-based estimator. The performance of the proposed detector is illustrated by means of Monte Carlo simulations and compared with that of the detector for unknown channels, showing the advantage of this knowledge.
G. Stanton, H. Wang, D. Ramírez, I. Santamaria, and L. L. Scharf, “Identifiability of multi-channel factor analysis,” in Proc. Asilomar Conf. Signals, Syst. and Computers, Pacific Grove, USA, 2023.
```
@inproceedings{StantonWangRamirez-2023-Identifiabilityofmulti-channelfactoranalysis,
  address = {Pacific Grove, USA},
  author = {Stanton, G. and Wang, H. and Ram{\'i}rez, D. and Santamaria, I. and Scharf, L. L.},
  booktitle = {{P}roc.\ {A}silomar {C}onf.\ {S}ignals, {S}yst.\ and {C}omputers},
  doi = {10.1109/IEEECONF59524.2023.10476820},
  month = {{O}ctober},
  title = {Identifiability of multi-channel factor analysis},
  year = {2023},
  local-url = {C51_Identifiability_Asilomar.pdf}
}
```
The recently developed Multi-Channel Factor Analysis (MFA) is a promising method for extracting a latent signal that is present across multiple channels and corrupted by unobserved single-channel interference and idiosyncratic noise. In MFA, only the channel structure and dimensionality of the signal and interference subspaces are specified in advance, which raises the concern that the signal, interference, and noise covariances may not be uniquely determined by the observation model. This paper presents necessary and sufficient conditions on the channel sizes and subspace dimensions to guarantee the identifiability of MFA, ensuring that the second-order spatial properties of the latent components can, in principle, be recovered from the multi-channel observations. The dimension thresholds at which signal and interference subspaces can be separated and at which the noise variances can be isolated are given, and implications for practical application of MFA are discussed.
V. Garg, D. Ramírez, and I. Santamaría, “Sparse subspace averaging for order estimation,” in Proc. IEEE Work. Stat. Signal Process., Rio de Janeiro, Brazil, 2021.
```
@inproceedings{GargRamirezSantamaria-2021-Sparsesubspaceaveragingfororder,
  address = {Rio de Janeiro, Brazil},
  author = {Garg, V. and Ram{\'i}rez, D. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {IEEE} {W}ork.\ {S}tat.\ {S}ignal {P}rocess.},
  doi = {10.1109/SSP49050.2021.9513773},
  month = {{J}uly},
  title = {Sparse subspace averaging for order estimation},
  year = {2021},
  local-url = {C49_SSP2021_SSA.pdf}
}
```
This paper addresses the problem of source enumeration for arbitrary geometry arrays in the presence of spatially correlated noise. The method combines a sparse reconstruction (SR) step with a subspace averaging (SA) approach, and hence it is named sparse subspace averaging (SSA). In the first step, each received snapshot is approximated by a sparse linear combination of the rest of snapshots. The SR problem is regularized by the logarithm-based surrogate of the l0-norm and solved using a majorization-minimization approach. Based on the SR solution, a sampling mechanism is proposed in the second step to generate a collection of subspaces, all of which ap- proximately span the same signal subspace. Finally, the dimension of the average of this collection of subspaces provides a robust estimate for the number of sources. Our simulation results show that SSA provides robust order estimates under a variety of noise models.
P. Bonilla-Escribano, D. Ramírez, and A. Artés-Rodríguez, “Modeling phone call durations via switching Poisson processes with applications in mental health,” in Proc. IEEE Int. Work. Machine Learning for Signal Process., 2020.
```
@inproceedings{Bonilla-EscribanoRamirezArtes-Rodriguez-2020-Modelingphonecalldurationsvia,
  author = {Bonilla-Escribano, P. and Ram{\'i}rez, D. and Art{\'e}s-Rodr{\'i}guez, A.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {W}ork.\ Machine Learning for {S}ignal {P}rocess.},
  doi = {10.1109/MLSP49062.2020.9231856},
  month = {{S}eptember},
  title = {Modeling phone call durations via switching {P}oisson processes with applications in mental health},
  year = {2020},
  local-url = {C48_MLSP2020_PP.pdf}
}
```
This work models phone call durations via switching Poisson point processes. This kind of processes is composed by two intertwined intensity functions: one models the start of a call, whereas the other one models when the call ends. Thus, the call duration is obtained from the inverse of the intensity function of finishing a call. Additionally, to model the circadian rhythm present in human behavior, we shall use a (positive) truncated Fourier series as the parametric form of the intensities. Finally, the maximum likelihood estimates of the intensity functions are obtained using a trust region method and the performance is evaluated on synthetic and real data, showing good results.
P. Moreno-Muñoz, D. Ramírez, and A. Artés-Rodríguez, “Continual learning for infinite hierarchical change-point detection,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Barcelona, Spain, 2020.
```
@inproceedings{Moreno-MunozRamirezArtes-Rodriguez-2020-Continuallearningforinfinitehierarchical,
  address = {Barcelona, Spain},
  author = {Moreno-Mu{\~n}oz, P. and Ram{\'i}rez, D. and Art{\'e}s-Rodr{\'i}guez, A.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP40776.2020.9053853},
  month = {{M}ay},
  title = {Continual learning for infinite hierarchical change-point detection},
  year = {2020},
  local-url = {C47_ICASSP2020_CPD.pdf}
}
```
Change-point detection (CPD) aims to locate abrupt transitions in the generative model of a sequence of observations. When Bayesian methods are considered, the standard practice is to infer the posterior distribution of the change-point locations. However, for complex models (high-dimensional or heterogeneous), it is not possible to perform reliable detection. To circumvent this problem, we propose to use a hierarchical model, which yields observations that belong to a lower-dimensional manifold. Concretely, we consider a latent-class model with an unbounded number of categories, which is based on the chinese-restaurant process (CRP). For this model we derive a continual learning mechanism that is based on the sequential construction of the CRP and the expectation-maximization (EM) algorithm with a stochastic maximization step. Our numerical results show that the proposed method is able to recursively infer the number of underlying latent classes and perform CPD in a reliable manner.
Y.-H. Xiao, D. Ramírez, and P. J. Schreier, “A general test for the linear structure of covariance matrices of Gaussian populations,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Barcelona, Spain, 2020.
```
@inproceedings{XiaoRamirezSchreier-2020-generaltestforlinearstructure,
  address = {Barcelona, Spain},
  author = {Xiao, Y.-H. and Ram{\'i}rez, D. and Schreier, P. J.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP40776.2020.9053718},
  month = {{M}ay},
  title = {A general test for the linear structure of covariance matrices of {G}aussian populations},
  year = {2020},
  local-url = {C46_ICASSP2020_GeneralTest.pdf}
}
```
This paper addresses the problem of testing whether a covariance matrix can be expressed by an unknown linear combination of a set of known matrices or by another unknown linear combination of a set of different, but known, matrices. This problem is of interest in a wide range of real-world applications, such as radar, sonar, and spectrum sensing. We study the problem under the Gaussian assumption and derive the generalized likelihood ratio test (GLRT). Since there is no general closed-form solution for the maximum likelihood (ML) estimates of the covariance matrices, which are required for the GLRT, we resort to a powerful inverse iterative algorithm. Finally, an example, along with numerical results, is given to illustrate the methodology.
S. Horstmann, D. Ramírez, and P. J. Schreier, “Two-channel passive detection exploiting cyclostationarity,” in Proc. Eur. Signal Process. Conf., A Coruña, Spain, 2019.
```
@inproceedings{HorstmannRamirezSchreier-2019-Two-channelpassivedetectionexploitingcyclostationarity,
  address = {A Coru{\~n}a, Spain},
  author = {Horstmann, S. and Ram{\'i}rez, D. and Schreier, P. J.},
  booktitle = {{P}roc.\ {E}ur.\ {S}ignal {P}rocess.\ {C}onf.},
  doi = {10.23919/EUSIPCO.2019.8902989},
  month = {{S}eptember},
  title = {Two-channel passive detection exploiting cyclostationarity},
  year = {2019},
  local-url = {C43_EUSIPCO2019.pdf}
}
```
This paper addresses a two-channel passive detection problem exploiting cyclostationarity. Given a reference channel (RC) and a surveillance channel (SC), the goal is to detect a target echo present at the surveillance array transmitted by an illuminator of opportunity equipped with multiple antennas. Since common transmission signals are cyclostationary, we exploit this information at the detector. Specifically, we derive an asymptotic generalized likelihood ratio test (GLRT) to detect the presence of a cyclostationary signal at the SC given observations from RC and SC. This detector tests for different covariance structures. Simulation results show good performance of the proposed detector compared to competing techniques that do not exploit cyclostationarity.
S. Horstmann, D. Ramírez, P. J. Schreier, and A. Pries, “Two-channel passive detection of cyclostationary signals in noise with spatio-temporal structure,” in Proc. Asilomar Conf. Signals, Syst. and Computers, Pacific Grove, USA, 2019.
```
@inproceedings{HorstmannRamirezSchreier-2019-Two-channelpassivedetectionofcyclostationary,
  address = {Pacific Grove, USA},
  author = {Horstmann, S. and Ram{\'i}rez, D. and Schreier, P. J. and Pries, A.},
  booktitle = {{P}roc.\ {A}silomar {C}onf.\ {S}ignals, {S}yst.\ and {C}omputers},
  doi = {10.1109/IEEECONF44664.2019.9048746},
  month = {{N}ovember},
  title = {Two-channel passive detection of cyclostationary signals in noise with spatio-temporal structure},
  year = {2019},
  local-url = {C44_Asilomar2019.pdf}
}
```
In this work, we derive a two-channel passive detector for cyclostationary (CS) signals contaminated by noise with spatio-temporal structure. This problem is motivated by a passive radar system equipped with a reference and a surveillance antenna array. Since typical illuminators of opportunity (IO) transmit CS signals, we derive a generalized likelihood ratio test (GLRT) to detect the presence of cyclostationarity at the surveillance channel (SC) given observations of both SC and reference channel under different noise assumptions. Simulation results show that exploiting cyclostationarity on the one hand and the structure of the noise on the other hand increases the performance compared to the general case of temporally colored and spatially correlated noise. Our approach also outperforms other state-of-the-art competitors.
P. Bonilla-Escribano, D. Ramírez, and A. Artés-Rodríguez, “Mixtures of heterogeneous Poisson processes for the assessment of e-social activity in mental health,” in NeurIPS Workshop on Learning with Temporal Point Processes, 2019.
```
@inproceedings{Bonilla-EscribanoRamirezArtes-Rodriguez-2019-MixturesofheterogeneousPoissonprocesses,
  author = {Bonilla-Escribano, P. and Ram{\'i}rez, D. and Art{\'e}s-Rodr{\'i}guez, A.},
  booktitle = {NeurIPS Workshop on Learning with Temporal Point Processes},
  month = {{D}ecember},
  title = {Mixtures of heterogeneous {P}oisson processes for the assessment of e-social activity in mental health},
  year = {2019},
  local-url = {C45_NeuripsTPP2019.pdf}
}
```
This work introduces a novel method to assess the social activity maintained by psychiatric patients using information and communication technologies. In particular, we jointly model using point processes the e-social activity patterns from two heterogeneous sources: the usage of phone calls and social and communication apps. We propose a nonhomogeneous Poisson mixture model with periodic (circadian) intensity function using a truncated Fourier series expansion, which is inferred using a trust-region algorithm, and it is able to cope with the different daily patterns of a person. The analysis of the usage of phone calls and social and communication apps of a cohort of 164 patients reveals that 25 patterns suffice to characterize their daily behavior.
D. Ramírez, I. Santamaría, S. V. Vaerenbergh, and L. L. Scharf, “An alternating optimization algorithm for two-channel factor analysis with common and uncommon factors,” in Proc. Proc. Asilomar Conf. Signals, Syst. and Computers, Pacific Grove, USA, 2018.
```
@inproceedings{RamirezSantamariaVaerenbergh-2018-alternatingoptimizationalgorithmfortwo-channel,
  address = {Pacific Grove, USA},
  author = {Ram{\'i}rez, D. and Santamar{\'i}a, I. and Vaerenbergh, S. Van and Scharf, L. L.},
  booktitle = {{P}roc.\ {P}roc.\ {A}silomar {C}onf.\ {S}ignals, {S}yst.\ and {C}omputers},
  doi = {10.1109/ACSSC.2018.8645457},
  month = {{O}ctober},
  title = {An alternating optimization algorithm for two-channel factor analysis with common and uncommon factors},
  year = {2018},
  local-url = {C43_Asilomar2018.pdf}
}
```
An alternating optimization algorithm is presented and analyzed for identifying low-rank signal components, known in factor analysis terminology as common factors, that are correlated across two multiple-input multiple-output (MIMO) channels. The additive noise model at each of the MIMO channels consists of white uncorrelated noises of unequal variances plus a low-rank structured interference that is not correlated across the two channels. The low-rank components at each channel represent uncommon or channel-specific factors.
I. Santamaría, D. Ramírez, and L. L. Scharf, “Subspace averaging for source enumeration in large arrays,” in Proc. IEEE Work. Stat. Signal Process., Freiburg, Germany, 2018.
```
@inproceedings{SantamariaRamirezScharf-2018-Subspaceaveragingforsourceenumeration,
  address = {Freiburg, Germany},
  author = {Santamar{\'i}a, I. and Ram{\'i}rez, D. and Scharf, L. L.},
  booktitle = {{P}roc.\ {IEEE} {W}ork.\ {S}tat.\ {S}ignal {P}rocess.},
  doi = {10.1109/SSP.2018.8450837},
  month = {{J}une},
  title = {Subspace averaging for source enumeration in large arrays},
  year = {2018},
  local-url = {C41_SSP2018_SA.pdf}
}
```
Subspace averaging is proposed and examined as a method of enumerating sources in large linear arrays, under conditions of low sample support. The key idea is to exploit shift invariance as a way of extracting many subspaces, which may then be approximated by a single extrinsic average. An automatic order determination rule for this extrinsic average is then the rule for determining the number of sources. Experimental results are presented for cases where the number of array snapshots is roughly half the number of array elements, and sources are well separated with respect to the Rayleigh limit.
A. Eguizabal, P. J. Schreier, and D. Ramírez, “Model-order selection in statistical shape models,” in Proc. IEEE Int. Work. Machine Learning for Signal Process., Aalborg, Denmark, 2018.
```
@inproceedings{EguizabalSchreierRamirez-2018-Model-orderselectioninstatisticalshape,
  address = {Aalborg, Denmark},
  author = {Eguizabal, A. and Schreier, P. J. and Ram{\'i}rez, D.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {W}ork.\ Machine Learning for {S}ignal {P}rocess.},
  doi = {10.1109/MLSP.2018.8516941},
  month = {{S}eptember},
  title = {Model-order selection in statistical shape models},
  year = {2018},
  local-url = {C42_MLSP2018.pdf}
}
```
Statistical shape models enhance machine learning algorithms providing prior information about deformation. A Point Distribution Model (PDM) is a popular landmark-based statistical shape model for segmentation. It requires choosing a model order, which determines how much of the variation seen in the training data is accounted for by the PDM. A good choice of the model order depends on the number of training samples and the noise level in the training data set. Yet the most common approach for choosing the model order simply keeps a predetermined percentage of the total shape variation. In this paper, we present a technique for choosing the model order based on information-theoretic criteria, and we show empirical evidence that the model order chosen by this technique provides a good trade-off between over- and underfitting.
D. Ramírez, D. Romero, J. Vía, R. López-Valcarce, and I. Santamaría, “Locally optimal invariant detector for testing equality of two power spectral densities,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Calgary, Canada, 2018.
```
@inproceedings{RamirezRomeroVia-2018-Locallyoptimalinvariantdetectorfor,
  address = {Calgary, Canada},
  author = {Ram{\'i}rez, D. and Romero, D. and V{\'i}a, J. and L{\'o}pez-Valcarce, R. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2018.8462683},
  month = {{A}pril},
  title = {Locally optimal invariant detector for testing equality of two power spectral densities},
  year = {2018},
  local-url = {C39_ICASSPCalgary2018_PSD.pdf}
}
```
This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT does not exist. However, this proof suggests two LMPIT-inspired detectors, one of which outperforms previously proposed approaches, as computer simulations show.
F. J. Iglesias, S. Segarra, S. Rey-Escudero, A. G. Marques, and D. Ramírez, “Demixing and blind deconvolution of graph-diffused sparse signals,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Calgary, Canada, 2018.
```
@inproceedings{IglesiasSegarraRey-Escudero-2018-Demixingandblinddeconvolutionof,
  address = {Calgary, Canada},
  author = {Iglesias, F. J. and Segarra, S. and Rey-Escudero, S. and Marques, A. G. and Ram{\'i}rez, D.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2018.8462154},
  month = {{A}pril},
  title = {Demixing and blind deconvolution of graph-diffused sparse signals},
  year = {2018},
  local-url = {C40_ICASSP2018_demixing_GSP.pdf}
}
```
This paper generalizes the classical joint problem of signal demixing and blind deconvolution to the realm of graphs. We investigate a setup where a single observation formed by the sum of multiple graph signals is available. The main assumption is that each individual signal is generated by an originally sparse input diffused through the graph via the application of a graph filter. In this context, we address the related problems of: 1) separating the individual graph signals, 2) identifying the unknown input supports, and 3) estimating the coefficients of the diffusing graph filters. We first consider the case where each signal – prior to mixing – is diffused in a different graph. We then particularize the results for the more challenging case where all the signals are diffused in the same graph. The corresponding demixing and blind graph-signal deconvolution problems are formulated, convex relaxations are presented, and recovery conditions are discussed. Numerical experiments in both the single and multiple graph cases show the capabilities of demixing in synthetic and biology-inspired graphs.
S. Horstmann, D. Ramírez, and P. J. Schreier, “Detection of almost-cyclostationarity: An approach based on a multiple hypothesis test,” in Proc. Proc. Asilomar Conf. Signals, Syst. and Computers, Pacific Grove, USA, 2017.
```
@inproceedings{HorstmannRamirezSchreier-2017-Detectionofalmost-cyclostationarityapproachbased,
  address = {Pacific Grove, USA},
  author = {Horstmann, S. and Ram{\'i}rez, D. and Schreier, P. J.},
  booktitle = {{P}roc.\ {P}roc.\ {A}silomar {C}onf.\ {S}ignals, {S}yst.\ and {C}omputers},
  doi = {10.1109/ACSSC.2017.8335636},
  month = {{O}ctober},
  title = {Detection of almost-cyclostationarity: An approach based on a multiple hypothesis test},
  year = {2017},
  local-url = {C38_Asilomar_2017.pdf}
}
```
This work presents a technique to detect whether a signal is almost cyclostationary (ACS) or wide-sense stationary (WSS). Commonly, ACS (and also CS) detectors require a priori knowledge of the cycle period, which in the ACS case is not an integer. To tackle the case of unknown cycle period, we propose an approach that combines a resampling technique, which handles the fractional part of the cycle period and allows the use of the generalized likelihood ratio test (GLRT), with a multiple hypothesis test, which handles the integer part of the cycle period. We control the probability of false alarm based on the known distribution of the individual GLRT statistic, results from order statistics, and the Holm multiple test procedure. To evaluate the performance of the proposed detector we consider a communications example, where simulation results show that the proposed technique outperforms state-of-the-art competitors.
D. Ramírez, A. G. Marques, and S. Segarra, “Graph-signal reconstruction and blind deconvolution for diffused sparse inputs,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., New Orleans, USA, 2017.
```
@inproceedings{RamirezMarquesSegarra-2017-Graph-signalreconstructionandblinddeconvolution,
  address = {New Orleans, USA},
  author = {Ram{\'i}rez, D. and Marques, A. G. and Segarra, S.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2017.7952928},
  month = {{M}arch},
  title = {Graph-signal reconstruction and blind deconvolution for diffused sparse inputs},
  year = {2017},
  local-url = {C37_ICASSP_2017.pdf}
}
```
This paper investigates the problems of signal reconstruction and blind deconvolution for graph signals that have been generated by an originally sparse input diffused through the network via the application of a graph filter operator. Assuming that the support of the sparse input signal is unknown, and that the diffused signal is observed only at a subset of nodes, we address the related problems of: 1) identifying the input and 2) interpolating the values of the diffused signal at the non-sampled nodes. We first consider the more tractable case where the coefficients of the diffusing graph filter are known and then address the problem of joint input and filter identification. The corresponding blind identification problems are formulated, novel convex relaxations are discussed, and modifications to incorporate a priori information on the sparse inputs are provided.
T. Hasija, Y. Song, P. J. Schreier, and D. Ramírez, “Bootstrap-based detection of the number of signals correlated across multiple data sets,” in Proc. Proc. Asilomar Conf. Signals, Syst. and Computers, Pacific Grove, USA, 2016.
```
@inproceedings{HasijaSongSchreier-2016-Bootstrap-baseddetectionofnumberof,
  address = {Pacific Grove, USA},
  author = {Hasija, T. and Song, Y. and Schreier, P. J. and Ram{\'i}rez, D.},
  booktitle = {{P}roc.\ {P}roc.\ {A}silomar {C}onf.\ {S}ignals, {S}yst.\ and {C}omputers},
  doi = {10.1109/ACSSC.2016.7869115},
  month = {{N}ovember},
  title = {Bootstrap-based detection of the number of signals correlated across multiple data sets},
  year = {2016},
  local-url = {C36_Asilomar_Bootstrap.pdf}
}
```
In this work, a hypothesis-testing scheme using the bootstrap is presented for determining the number of signals common or correlated across multiple data sets. Handling multiple data sets is challenging due to the different possible correlation structures. For two data sets, the signals are either correlated or independent between the data sets. For multiple data sets, however, there are numerous combinations how the signals can be correlated. Prior studies dealing with multiple datasets all assume a particular correlation structure. In this paper, we present a technique based on the bootstrap that works for arbitrary correlation structure. Numerical results show that the proposed technique correctly detects the number of correlated signals in scenarios where the competition tends to overestimate.
T. Hasija, Y. Song, P. J. Schreier, and D. Ramírez, “Detecting the dimension of the subspace correlated across multiple data sets in the sample poor regime,” in Proc. IEEE Work. Stat. Signal Process., Majorca, Spain, 2016.
```
@inproceedings{HasijaSongSchreier-2016-Detectingdimensionofsubspacecorrelated,
  address = {Majorca, Spain},
  author = {Hasija, T. and Song, Y. and Schreier, P. J. and Ram{\'i}rez, D.},
  booktitle = {{P}roc.\ {IEEE} {W}ork.\ {S}tat.\ {S}ignal {P}rocess.},
  doi = {10.1109/SSP.2016.7551708},
  month = {{J}une},
  title = {Detecting the dimension of the subspace correlated across multiple data sets in the sample poor regime},
  year = {2016},
  local-url = {C34_SSP_2016.pdf}
}
```
This paper addresses the problem of detecting the number of signals correlated across multiple data sets with small sam- ple support. While there have been studies involving two data sets, the problem with more than two data sets has been less explored. In this work, a rank-reduced hypothesis test for more than two data sets is presented for scenarios where the number of samples is small compared to the dimensions of the data sets.
A. Pries, D. Ramírez, and P. J. Schreier, “Detection of cyclostationarity in the presence of temporal or spatial structure with applications to cognitive radio,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Shanghai, China, 2016.
```
@inproceedings{PriesRamirezSchreier-2016-Detectionofcyclostationarityinpresence,
  address = {Shanghai, China},
  author = {Pries, A. and Ram{\'i}rez, D. and Schreier, P. J.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2016.7472478},
  month = {{M}arch},
  title = {Detection of cyclostationarity in the presence of temporal or spatial structure with applications to cognitive radio},
  year = {2016},
  local-url = {C33_ICASSP_2016.pdf}
}
```
One approach to spectrum sensing for cognitive radio is the detection of cyclostationarity. We extend an existing multi- antenna detector for cyclostationarity proposed by Ramírez et al. [1], which makes no assumptions about the noise beyond being (temporally) wide-sense stationary. In special cases, the noise could be uncorrelated among antennas, or it could be temporally white. The performance of a general detector can be improved by making use of a priori structural information. We do not, however, require knowledge of the exact values of the temporal or spatial noise covariances. We develop an asymptotic generalized likelihood ratio test and evaluate the performance by simulations.
Y. Song, T. Hasija, P. J. Schreier, and D. Ramírez, “Determining the number of signals correlated across multiple data sets for small sample support,” in Proc. Eur. Signal Process. Conf., Budapest, Hungary, 2016.
```
@inproceedings{SongHasijaSchreier-2016-Determiningnumberofsignalscorrelated,
  address = {Budapest, Hungary},
  author = {Song, Y. and Hasija, T. and Schreier, P. J. and Ram{\'i}rez, D.},
  booktitle = {{P}roc.\ {E}ur.\ {S}ignal {P}rocess.\ {C}onf.},
  doi = {10.1109/EUSIPCO.2016.7760504},
  month = {{A}ugust},
  title = {Determining the number of signals correlated across multiple data sets for small sample support},
  year = {2016},
  local-url = {C35_Eusipco_2016.pdf}
}
```
This paper presents a detection scheme for de- termining the number of signals that are correlated across multiple data sets when the sample size is small compared to the dimensions of the data sets. To accommodate the sample-poor regime, we decouple the problem into several independent two- channel order-estimation problems that may be solved separately by a combination of principal component analysis (PCA) and canonical correlation analysis (CCA). Since the signals that are correlated across all data sets must be a subset of the signals that are correlated between any pair of data sets, we keep only the correlated signals for each pair of data sets. Then, a criterion inspired by a traditional information-theoretic criterion is applied to estimate the number of signals correlated across all data sets. The performance of the proposed scheme is verified by simulations.
D. Ramírez, P. J. Schreier, J. Vía, I. Santamaría, and L. L. Scharf, “An asymptotic LMPI test for cyclostationarity detection with application to cognitive radio (invited paper),” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Brisbane, Australia, 2015.
```
@inproceedings{RamirezSchreierVia-2015-asymptoticLMPItestforcyclostationarity,
  address = {Brisbane, Australia},
  author = {Ram{\'i}rez, D. and Schreier, P. J. and V{\'i}a, J. and Santamar{\'i}a, I. and Scharf, L. L.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2015.7179057},
  month = {{A}pril},
  title = {An asymptotic {LMPI} test for cyclostationarity detection with application to cognitive radio (invited paper)},
  year = {2015},
  local-url = {C32_ICASSP_2015.pdf}
}
```
We propose a new detector of primary users in cognitive radio networks. The main novelty of the proposed detector in comparison to most known detectors is that it is based on sound statistical principles for detecting cyclostationary signals. In particular, the proposed detector is (asymptotically) the locally most powerful invariant test, i.e. the best invariant detector for low signal-to-noise ratios. The derivation is based on two main ideas: the relationship between a scalar-valued cyclostationary signal and a vector-valued wide-sense stationary signal, and Wijsman’s theorem. Moreover, using the spectral representation for the cyclostationary time series, the detector has an insightful interpretation, and implementation, as the broadband coherence between frequencies that are separated by multiples of the cycle frequency. Finally, simulations confirm that the proposed detector performs better than previous approaches.
D. Ramírez, P. J. Schreier, J. Vía, I. Santamaría, and L. L. Scharf, “A regularized maximum likelihood estimator for the period of a cyclostationary process,” in Proc. Proc. Asilomar Conf. Signals, Syst. and Computers, Pacific Grove, USA, 2014.
```
@inproceedings{RamirezSchreierVia-2014-regularizedmaximumlikelihoodestimatorfor,
  address = {Pacific Grove, USA},
  author = {Ram{\'i}rez, D. and Schreier, P. J. and V{\'i}a, J. and Santamar{\'i}a, I. and Scharf, L. L.},
  booktitle = {{P}roc.\ {P}roc.\ {A}silomar {C}onf.\ {S}ignals, {S}yst.\ and {C}omputers},
  doi = {10.1109/ACSSC.2014.7094815},
  month = {{N}ovember},
  title = {A regularized maximum likelihood estimator for the period of a cyclostationary process},
  year = {2014},
  local-url = {C31_Asilomar_2014.pdf}
}
```
We derive an estimator of the cycle period of a univariate cyclostationary process based on an information- theoretic criterion. Transforming the univariate cyclostationary process into a vector-valued wide-sense stationary process allows us to obtain the structure of the covariance matrix, which is block-Toeplitz, and its block size depends on the unknown cycle period. Therefore, we sweep the block size and obtain the ML estimate of the covariance matrix, required for the information- theoretic criterion. Since there are no closed-form ML estimates of block-Toeplitz matrices, we asymptotically approximate them as block-circulant. Finally, some numerical examples show the good performance of the proposed estimator.
D. Ramírez, L. L. Scharf, J. Vía, I. Santamaría, and P. J. Schreier, “An asymptotic GLRT for the detection of cyclostationary signals,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Florence, Italy, 2014.
```
@inproceedings{RamirezScharfVia-2014-asymptoticGLRTfordetectionof,
  address = {Florence, Italy},
  author = {Ram{\'i}rez, D. and Scharf, L. L. and V{\'i}a, J. and Santamar{\'i}a, I. and Schreier, P. J.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2014.6854234},
  month = {{M}ay},
  title = {An asymptotic {GLRT} for the detection of cyclostationary signals},
  year = {2014},
  local-url = {C29_ICASSP_2014.pdf}
}
```
We derive the generalized likelihood ratio test (GLRT) for detecting cyclostationarity in scalar-valued time series. The main idea behind our approach is Gladyshev’s relationship, which states that when the scalar-valued cyclostationary sig- nal is blocked at the known cycle period it produces a vector- valued wide-sense stationary process. This result amounts to saying that the covariance matrix of the vector obtained by stacking all observations of the time series is block-Toeplitz if the signal is cyclostationary, and Toeplitz if the signal is wide- sense stationary. The derivation of the GLRT requires the maximum likelihood estimates of Toeplitz and block-Toeplitz matrices. This can be managed asymptotically (for large num- berofsamples)exploitingSzego ̈’stheoremanditsgeneraliza- tion for vector-valued processes. Simulation results show the good performance of the proposed GLRT.
S. Dähne, V. V. Nikulin, D. Ramírez, P. J. Schreier, K.-R. Müller, and S. Haufe, “Optimizing spatial filters for the extraction of envelope-coupled neural oscillations,” in Proc. Int. Work. Pattern Recognition In Neuroimaging, Tübingen, Germany, 2014.
```
@inproceedings{DahneNikulinRamirez-2014-Optimizingspatialfiltersforextraction,
  address = {T{\"u}bingen, Germany},
  author = {D{\"a}hne, S. and Nikulin, V. V. and Ram{\'i}rez, D. and Schreier, P. J. and M{\"u}ller, K.-R. and Haufe, S.},
  booktitle = {Proc.\ Int. Work. Pattern Recognition In Neuroimaging},
  doi = {10.1109/PRNI.2014.6858514},
  month = {{J}une},
  title = {Optimizing spatial filters for the extraction of envelope-coupled neural oscillations},
  year = {2014},
  local-url = {C30_PRNI_cSPoC.pdf}
}
```
Amplitude-to-amplitude interactions between neural oscillations are of a special interest as they show how the strength of spatial synchronization in different neuronal populations relates to each other during a given task. While, previously, amplitude-to-amplitude correlations were studied primarily on the sensor level, we present a source separation approach using spatial filters which maximize the correlation between the envelopes of brain oscillations recorded with electro-/magnetencephalography (EEG/MEG) or intracranial multichannel recordings. Our approach, which is called canonical source power correlation analysis (cSPoC), is thereby capable of extracting genuine brain oscillations solely based on their assumed coupling behavior even when the signal-to-noise ratio of the signals is low.
D. Ramírez, P. J. Schreier, J. Vía, and V. V. Nikulin, “Power-CCA: Maximizing the correlation coefficient between the power of projections,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Vancouver, Canada, 2013.
```
@inproceedings{RamirezSchreierVia-2013-Power-CCAMaximizingcorrelationcoefficientbetween,
  address = {Vancouver, Canada},
  author = {Ram{\'i}rez, D. and Schreier, P. J. and V{\'i}a, J. and Nikulin, V. V.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2013.6638864},
  month = {{M}ay},
  title = {Power-{CCA}: Maximizing the correlation coefficient between the power of projections},
  year = {2013},
  local-url = {C28_ICASSP_2013.pdf}
}
```
This work presents a variation of canonical correlation analysis (CCA), where the correlation coefficient between the instantaneous power of the projections is maximized, rather than between the projections themselves. The resulting optimization problem is not convex, and we have to resort to a sub-optimal approach. Concretely, we propose a two-step solution consisting of the singular value decomposition (SVD) of a "coherence" matrix followed by a rank-one matrix approximation. This technique is applied to blindly recovering signals in a model that is motivated by the study of neuronal dynamics in humans using electroencephalography (EEG) and magnetoencephalography (MEG). A distinctive feature of this model is that it allows recovery of amplitude-amplitude coupling between neuronal processes.
J. Manco-Vásquez, M. Lazaro-Gredilla, D. Ramírez, J. Vía, and I. Santamaría, “Bayesian multiantenna sensing for cognitive radio,” in Proc. IEEE Sensor Array and Multichannel Signal Process. Work., Hoboken, NJ, USA, 2012.
```
@inproceedings{Manco-VasquezLazaro-GredillaRamirez-2012-Bayesianmultiantennasensingforcognitive,
  address = {Hoboken, NJ, USA},
  author = {Manco-V{\'a}squez, J. and Lazaro-Gredilla, M. and Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {IEEE} {S}ensor {A}rray and {M}ultichannel {S}ignal {P}rocess. {W}ork.},
  doi = {10.1109/SAM.2012.6250566},
  month = {{J}une},
  title = {Bayesian multiantenna sensing for cognitive radio},
  year = {2012},
  local-url = {C25_SAM_2012_Bayesian.pdf}
}
```
In this paper, the problem of multiantenna spectrum sensing in cognitive radio (CR) is addressed within a Bayesian framework. Unlike previous works, our Bayesian model places priors directly on the spatial covariance matrices under both hypotheses, as well as on the probability of channel occupancy. Specifically, we use inverse-gamma and complex inverse-Wishart distributions as conjugate priors for the null and alternative hypotheses, respectively; and a Bernoulli distribution as the prior for channel occupancy. At each sensing period, Bayesian inference is applied and the posterior of channel occupancy is thresholded for detection. After a suitable approximation, the posteriors are employed as priors for the next sensing frame, which can be beneficial in slowly time-varying environments. By means of simulations, the proposed detector is shown to outperform the Generalized Likelihood Ratio Test (GLRT) detector.
D. Ramírez, J. Iscar, J. Vía, I. Santamaría, and L. L. Scharf, “The locally most powerful invariant test for detecting a rank-P Gaussian signal in white noise,” in Proc. IEEE Sensor Array and Multichannel Signal Process. Work., Hoboken, NJ, USA, 2012.
```
@inproceedings{RamirezIscarVia-2012-locallymostpowerfulinvarianttest,
  address = {Hoboken, NJ, USA},
  author = {Ram{\'i}rez, D. and Iscar, J. and V{\'i}a, J. and Santamar{\'i}a, I. and Scharf, L. L.},
  booktitle = {{P}roc.\ {IEEE} {S}ensor {A}rray and {M}ultichannel {S}ignal {P}rocess. {W}ork.},
  doi = {10.1109/SAM.2012.6250547},
  month = {{J}une},
  title = {The locally most powerful invariant test for detecting a {rank-$P$} {G}aussian signal in white noise},
  year = {2012},
  local-url = {C24_SAM_2012.pdf}
}
```
Spectrum sensing has become one of the main components of a cognitive transmitter. Conventional detectors suffer from noise power uncertainties and multiantenna detectors have been proposed to overcome this difficulty, and to improve the detection performance. However, most of the proposed multiantenna detectors are based on non-optimal techniques, such as the generalized likelihood ratio test (GLRT), or even heuristic approaches that are not based on first principles. In this work, we derive the locally most powerful invariant test (LMPIT), that is, the optimal invariant detector for close hypotheses, or equivalently, for a low signal-to-noise ratio (SNR). The traditional approach, based on the distributions of the maximal invariant statistic, is avoided thanks to Wijsman’s theorem, which does not need these distributions. Our findings show that, in the low SNR regime, and in contrast to the GLRT, the additional spatial structure imposed by the signal model is irrelevant for optimal detection. Finally, we use Monte Carlo simulations to illustrate the good performance of the LMPIT.
D. Ramírez, P. J. Schreier, J. Vía, and I. Santamaría, “GLRT for testing separability of a complex-valued mixture based on the strong uncorrelating transform,” in Proc. IEEE Int. Work. Machine Learning for Signal Process., Santander, Spain, 2012.
```
@inproceedings{RamirezSchreierVia-2012-GLRTfortestingseparabilityof,
  address = {Santander, Spain},
  author = {Ram{\'i}rez, D. and Schreier, P. J. and V{\'i}a, J. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {W}ork.\ Machine Learning for {S}ignal {P}rocess.},
  doi = {10.1109/MLSP.2012.6349785},
  month = {{S}eptember},
  title = {{GLRT} for testing separability of a complex-valued mixture based on the strong uncorrelating transform},
  year = {2012},
  local-url = {C26_MLSP2012.pdf}
}
```
The Strong Uncorrelating Transform (SUT) allows blind separation of a mixture of complex independent sources if and only if all sources have distinct circularity coefficients. In practice, the circularity coefficients need to be estimated from observed data. We propose a generalized likelihood ratio test (GLRT) for separability of a complex mixture using the SUT, based on estimated circularity coefficients. For distinct circularity coefficients (separable case), the maximum likelihood (ML) estimates, required for the GLRT, are straightforward. However, for circularity coefficients with multiplicity larger than one (non-separable case), the ML estimates are much more difficult to find. Numerical simulations show the good performance of the proposed detector.
S. C. Olhede, D. Ramírez, and P. J. Schreier, “The random monogenic signal,” in Proc. IEEE Int. Conf. Image Process., Orlando, Florida, USA, 2012.
```
@inproceedings{OlhedeRamirezSchreier-2012-randommonogenicsignal,
  address = {Orlando, Florida, USA},
  author = {Olhede, S. C. and Ram{\'i}rez, D. and Schreier, P. J.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {I}mage {P}rocess.},
  doi = {10.1109/ICIP.2012.6467404},
  month = {{S}eptember},
  title = {The random monogenic signal},
  year = {2012},
  local-url = {C27_ICIP2012.pdf}
}
```
The monogenic signal allows us to decompose a two-dimensional real signal into a local amplitude, a local orientation, and a local phase. In this paper, we introduce the random monogenic signal and study its second-order statistical properties. The monogenic signal may be represented as a quaternion-valued signal. We show that for homogeneous random fields, we need exactly two quaternion-valued covariance functions for a complete second-order description. We also introduce a stochastic model for unidirectional signals and a measure of unidirectionality.
D. Ramírez, J. Vía, and I. Santamaría, “The locally most powerful test for multiantenna spectrum sensing with uncalibrated receivers,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Kyoto, Japan, 2012.
```
@inproceedings{RamirezViaSantamaria-2012-locallymostpowerfultestfor,
  address = {Kyoto, Japan},
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2012.6288655},
  month = {{M}arch},
  title = {The locally most powerful test for multiantenna spectrum sensing with uncalibrated receivers},
  year = {2012},
  local-url = {C23_ICASSP_2012.pdf}
}
```
Spectrum sensing is a key component of the cognitive radio (CR) paradigm. Among CR detectors, multiantenna detectors are gaining popularity since they improve the detection performance and are robust to noise uncertainties. Traditional approaches to multiantenna spectrum sensing are based on the generalized likelihood ratio test (GLRT) or other heuristic detectors, which are not optimal in the Neyman-Pearson sense. In this work, we derive the locally most powerful invariant test (LMPIT), which is the optimal detector, among those preserving the problem invariances, in the low SNR regime. In particular, we apply Wijsman’s theorem, which provides us an alternative way to derive the ratio of the distributions of the maximal invariant statistic. Finally, numerical simulations illustrate the performance of the proposed detector.
D. Ramírez, J. Vía, I. Santamaría, and L. L. Scharf, “Multi-sensor beamsteering based on the asymptotic likelihood for colored signals,” in Proc. IEEE Work. Stat. Signal Process., Nice, France, 2011.
```
@inproceedings{RamirezViaSantamaria-2011-Multi-sensorbeamsteeringbasedonasymptotic,
  address = {Nice, France},
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I. and Scharf, L. L.},
  booktitle = {{P}roc.\ {IEEE} {W}ork.\ {S}tat.\ {S}ignal {P}rocess.},
  doi = {10.1109/SSP.2011.5967644},
  month = {{J}une},
  title = {Multi-sensor beamsteering based on the asymptotic likelihood for colored signals},
  year = {2011},
  local-url = {C19_SSPNice2011_ML_beamsteering.pdf}
}
```
In this work, we derive a maximum likelihood formula for beamsteering in a multi-sensor array. The novelty of the work is that the impinging signal and noises are wide sense stationary (WSS) time series with unknown power spectral densities, unlike in previous work that typically considers white signals. Our approach naturally provides a way of fusing frequency-dependent information to obtain a broadband beamformer. In order to obtain the compressed likelihood, it is necessary to find the maximum likelihood estimates of the unknown parameters. However, this problem turns out to be an ML estimation of a block-Toeplitz matrix, which does not have a closed-form solution. To overcome this problem, we derive the asymptotic likelihood, which is given in the frequency domain. Finally, some simulation results are presented to illustrate the performance of the proposed technique. In these simulations, it is shown that our approach presents the best results.
D. Ramírez, J. Vía, I. Santamaría, and L. L. Scharf, “Multiple-channel detection of a Gaussian time series over frequency-flat channels,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Prague, Czech Republic, 2011.
```
@inproceedings{RamirezViaSantamaria-2011-Multiple-channeldetectionofGaussiantime,
  address = {Prague, Czech Republic},
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I. and Scharf, L. L.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2011.5947194},
  month = {{M}ay},
  title = {Multiple-channel detection of a {G}aussian time series over frequency-flat channels},
  year = {2011},
  local-url = {C18_ICASSP2011Prague_GLRT_flat_fading.pdf}
}
```
This work addresses the problem of deciding whether a set of realizations of a vector-valued time series with unknown temporal correlation are spatially correlated or not. Specifically, the spatial correlation is induced by a colored source over a frequency-flat single-input multiple-output (SIMO) channel distorted by independent and identically distributed noises with temporal correlation. The generalized likelihood ratio test (GLRT) for this detection problem does not have a closed-form expression and we have to resort to numerical optimization techniques. In particular, we apply the successive convex approximations approach which relies on solving a series of convex problems that approximate the original (non-convex) one. The proposed solution resembles a power method for obtaining the dominant eigenvector of a matrix, which changes over iterations. Finally, the performance of the proposed detector is illustrated by means of computer simulations showing a great improvement over previously proposed detectors that do not fully exploit the temporal structure of the source.
D. Ramírez, G. Vazquez-Vilar, R. López-Valcarce, J. Vía, and I. Santamaría, “Multiantenna detection under noise uncertainty and primary user’s spatial structure,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Prague, Czech Republic, 2011.
```
@inproceedings{RamirezVazquez-VilarLopez-Valcarce-2011-Multiantennadetectionundernoiseuncertainty,
  address = {Prague, Czech Republic},
  author = {Ram{\'i}rez, D. and Vazquez-Vilar, G. and L{\'o}pez-Valcarce, R. and V{\'i}a, J. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2011.5946275},
  month = {{M}ay},
  title = {Multiantenna detection under noise uncertainty and primary user's spatial structure},
  year = {2011},
  local-url = {C17_ICASSP2011Prague_rankP_noIID.pdf}
}
```
Spectrum sensing is a challenging key component of the Cognitive Radio paradigm, since primary signals must be detected in the face of noise uncertainty and at signal-to-noise ratios (SNRs) well below decodability levels. Multiantenna detectors exploit spatial independence of receiver thermal noise to boost detection performance and robustness. Here, we study the problem of detecting Gaussian signals with unknown rank-P spatial covariance matrix when the noise at the receiver is independent across the antennas and with unknown power. A generic diagonal noise covariance matrix is allowed to model calibration uncertainties in the different antenna frontends. We derive the generalized likelihood ratio test (GLRT) for this detection problem. Although, in general, the corresponding statistic must be obtained by numerical means, in the low SNR regime the GLRT does admit a closed form. Numerical simulations show that the proposed asymptotic detector offers good performance even for moderate SNR values.
J. A. García-Naya, L. Castedo, Ó. González, D. Ramírez, and I. Santamaría, “Experimental evaluation of Interference Alignment under imperfect channel state information,” in Proc. Eur. Signal Process. Conf., Barcelona, Spain, 2011.
```
@inproceedings{Garcia-NayaCastedoGonzalez-2011-ExperimentalevaluationofInterferenceAlignment,
  address = {Barcelona, Spain},
  author = {Garc{\'i}a-Naya, J. A. and Castedo, L. and Gonz{\'a}lez, {\'O}. and Ram{\'i}rez, D. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {E}ur.\ {S}ignal {P}rocess.\ {C}onf.},
  month = {{S}eptember},
  title = {Experimental evaluation of {I}nterference {A}lignment under imperfect channel state information},
  year = {2011},
  local-url = {C20_Eusipco_2011.pdf}
}
```
Interference Alignment (IA) has been revealed as one of the most attractive transmission techniques for the K-user in- terference channel. In this work, we employ a multiuser Multiple-Input Multiple-Output (MIMO) testbed to analyze, in realistic indoor scenarios, the impact of channel state information errors on the sum-rate performance of IA. We restrict our study to a 3-user interference network in which each user transmits a single data stream using two transmit and two receive antennas. For this MIMO interference network, only two different IA solutions exist. We also evaluate the performance gain obtained in practice by using the IA solution that maximizes the sum-rate.
Ó. González, D. Ramírez, I. Santamaría, J. A. García-Naya, and L. Castedo, “Experimental validation of Interference Alignment techniques using a multiuser MIMO testbed,” in Proc. Int. ITG Work. on Smart Antennas, Aachen, Germany, 2011.
```
@inproceedings{GonzalezRamirezSantamaria-2011-ExperimentalvalidationofInterferenceAlignment,
  address = {Aachen, Germany},
  author = {Gonz{\'a}lez, {\'O}. and Ram{\'i}rez, D. and Santamar{\'i}a, I. and Garc{\'i}a-Naya, J. A. and Castedo, L.},
  booktitle = {Proc.\ Int.\ ITG Work.\ on Smart Antennas},
  doi = {10.1109/WSA.2011.5741921},
  month = {{F}ebruary},
  title = {Experimental validation of {I}nterference {A}lignment techniques using a multiuser {MIMO} testbed},
  year = {2011},
  local-url = {C16_WSA_2011.pdf}
}
```
Hardware platforms and testbeds are an essential tool to evaluate, in realistic scenarios, the performance of wireless communications systems. In this work we present a multiuser Multiple-Input Multiple-Output (MIMO) testbed made up of 6 nodes, each one with 4 antennas, which allows us to evaluate Interference Alignment (IA) techniques in indoor scenarios. We specifically study the performance of IA for the 3-user interference channel in the 5 GHz band. Our analysis identifies the main practical issues that potentially degrade the IA performance such as channel estimation errors or collinearity between the desired signal and interference subspaces.
G. Vazquez-Vilar, D. Ramírez, R. López-Valcarce, J. Vía, and I. Santamaría, “Spatial rank estimation in cognitive radio networks with uncalibrated multiple antennas (invited paper),” in Proc. Int. Conf. on Cognitive Radio and Advanced Spectrum Management, Barcelona, Spain, 2011.
```
@inproceedings{Vazquez-VilarRamirezLopez-Valcarce-2011-Spatialrankestimationincognitive,
  address = {Barcelona, Spain},
  author = {Vazquez-Vilar, G. and Ram{\'i}rez, D. and L{\'o}pez-Valcarce, R. and V{\'i}a, J. and Santamar{\'i}a, I.},
  booktitle = {Proc.\ Int. Conf. on Cognitive Radio and Advanced Spectrum Management},
  doi = {10.1145/2093256.2093291},
  month = {{O}ctober},
  title = {Spatial rank estimation in cognitive radio networks with uncalibrated multiple antennas (invited paper)},
  year = {2011},
  local-url = {C21_rankPestimation.pdf}
}
```
Spectrum sensing is a key component of the Cognitive Radio paradigm. Multiantenna detectors can exploit different spatial features of primary signals in order to boost detection performance and robustness in very low signal-to-noise ratios. However, in several cases these detectors require additional information, such as the rank of the spatial covariance matrix of the received signal. In this work we study the problem of estimating this rank under Gaussianity assumption using an uncalibrated receiver, i.e. with different (unknown) noise levels at each of the antennas.

G. Vazquez-Vilar, D. Romero, R. López-Valcarce, D. Ramírez, J. Vía, I. Santamaría, and J. Sala, “Recent advances in multiantenna spectrum sensing: complexity, noise uncertainty, and signal rank issues,” in Int. Work. COST Action IC0902, Barcelona, Spain, 2011.

@inproceedings{Vazquez-VilarRomeroLopez-Valcarce-2011-Recentadvancesinmultiantennaspectrum,
  address = {Barcelona, Spain},
  author = {Vazquez-Vilar, G. and Romero, D. and L{\'o}pez-Valcarce, R. and Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I. and Sala, J.},
  booktitle = {Int. Work. COST Action IC0902},
  month = {{O}ctober},
  note = {Extended abstract},
  title = {Recent advances in multiantenna spectrum sensing: complexity, noise uncertainty, and signal rank issues},
  year = {2011},
  local-url = {C22_CostBarcelona.pdf}
}

D. Ramírez, J. Vía, and I. Santamaría, “Multiantenna spectrum sensing: The case of wideband rank-one primary signals,” in Proc. IEEE Sensor Array and Multichannel Signal Process. Work., Israel, 2010.
```
@inproceedings{RamirezViaSantamaria-2010-Multiantennaspectrumsensingcaseof,
  address = {Israel},
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {IEEE} {S}ensor {A}rray and {M}ultichannel {S}ignal {P}rocess. {W}ork.},
  doi = {10.1109/SAM.2010.5606502},
  month = {{O}ctober},
  title = {Multiantenna spectrum sensing: The case of wideband rank-one primary signals},
  year = {2010},
  local-url = {C15_SAM2010_CR.pdf}
}
```
One of the key problems in cognitive radio (CR) is the detection of primary activity in order to determine which parts of the spectrum are available for opportunistic access. In this work, we present a new multiantenna detector which fully exploits the spatial and temporal structure of the signals. In particular, we derive the generalized likelihood ratio test (GLRT) for the problem of detecting a wideband rank-one signal under spatially uncorrelated noise with equal or different power spectral densities. In order to simplify the maximum likelihood (ML) estimation of the unknown parameters, we use the asymptotic likelihood in the frequency domain. Interestingly, for noises with different distributions and under a low SNR approximation, the GLRT is obtained as a function of the largest eigenvalue of the spectral coherence matrix. Finally, the performance of the proposed detectors is evaluated by means of numerical simulations, showing important advantages over previously proposed approaches.
J. Vía, D. Ramírez, I. Santamaría, and L. Vielva, “Improperness measures for quaternion random vectors,” in Proc. IEEE Int. Work. Machine Learning for Signal Process., Finland, 2010.
```
@inproceedings{ViaRamirezSantamaria-2010-Impropernessmeasuresforquaternionrandom,
  address = {Finland},
  author = {V{\'i}a, J. and Ram{\'i}rez, D. and Santamar{\'i}a, I. and Vielva, L.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {W}ork.\ Machine Learning for {S}ignal {P}rocess.},
  doi = {10.1109/MLSP.2010.5589225},
  month = {{A}ugust},
  title = {Improperness measures for quaternion random vectors},
  year = {2010},
  local-url = {C14_MLSP2010_QuaternionMeasures.pdf}
}
```
It has been recently proved that the two main kinds of quaternion improperness require two different kinds of widely linear process- ing. In this work, we show that these definitions satisfy some im- portant properties, which include the invariance to quaternion lin- ear transformations and right Clifford translations, as well as some clear connections with the case of proper complex vectors. More- over, we introduce a new kind of quaternion properness, which clearly relates the two previous definitions, and propose three mea- sures for the degree of improperness of a quaternion vector. The proposed measures are based on the Kullback-Leibler divergence between two zero-mean quaternion Gaussian distributions, one of them with the actual augmented covariance matrix, and the other with its closest proper version. These measures allow us to quan- tify the entropy loss due to the improperness of the quaternion vec- tor, and they admit an intuitive geometrical interpretation based on Kullback-Leibler projections onto sets of proper augmented co- variance matrices.
D. Ramírez, J. Vía, I. Santamaría, R. López-Valcarce, and L. L. Scharf, “Multiantenna spectrum sensing: Detection of spatial correlation among time-series with unknown spectra,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Dallas, USA, 2010.
```
@inproceedings{RamirezViaSantamaria-2010-MultiantennaspectrumsensingDetectionof,
  address = {Dallas, USA},
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I. and L{\'o}pez-Valcarce, R. and Scharf, L. L.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2010.5496151},
  month = {{M}arch},
  title = {Multiantenna spectrum sensing: Detection of spatial correlation among time-series with unknown spectra},
  year = {2010},
  local-url = {C13_ICASSP2010_CR_SpecSensing.pdf}
}
```
One of the key problems in cognitive radio (CR) is the detection of primary activity in order to determine which parts of the spectrum are available for opportunistic access. This detection task is challenging, since the wireless environment often results in very low SNR conditions. Moreover, calibration errors and imperfect analog components at the CR spectral monitor result in uncertainties in the noise spectrum, making the problem more difficult. In this work, we present a new multiantenna detector which is based on the fact that the observation noise processes are spatially uncorrelated, whereas any primary signal present should result inspatial correlation. In particular, we derive the generalized likelihood ratio test (GLRT) for this problem, which is given by the quotient between the determinant of the sample covariance matrix and the determinant of its block-diagonal version. For stationary processes the GLRT tends asymptotically to the integral of the logarithm of the Hadamard ratio of the estimated power spectral density matrix. Additionally, we present an approximation of the frequency domain detector in the low SNR regime, which results in computational savings. The performance of the proposed detectors is evaluated by means of numerical simulations, showing important advantages over existing detectors.
J. Vía, D. Ramírez, I. Santamaría, and L. Vielva, “Widely and semi-widely linear processing of quaternion vectors,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Dallas, USA, 2010.
```
@inproceedings{ViaRamirezSantamaria-2010-Widelyandsemi-widelylinearprocessing,
  address = {Dallas, USA},
  author = {V{\'i}a, J. and Ram{\'i}rez, D. and Santamar{\'i}a, I. and Vielva, L.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2010.5495787},
  month = {{M}arch},
  title = {Widely and semi-widely linear processing of quaternion vectors},
  year = {2010},
  local-url = {C12_ICASSP2010_QuaternionWL.pdf}
}
```
In this paper the two main definitions of quaternion properness (or second order circularity) are reviewed, showing their connection with the structure of the optimal quaternion linear processing. Specifically, we present a rigorous generalization of the most common multivariate statistical analysis techniques to the case of quaternion vectors, and show that the different kinds of quaternion improperness require different kinds of widely linear processing. In general, the optimal linear processing is full-widely linear, which requires the joint processing of the quaternion vector and its involutions over three pure unit quaternions. However, in the case of jointly \mathbbQ-proper and \mathbbC^η-proper vectors, the optimal processing reduces, respectively, to the conventional and semi-widely linear processing, with the latter only requiring to operate on the quaternion vector and its involution over the pure unit quaternion η. Finally, a simulation example poses some interesting questions for future research.
D. Ramírez, J. Vía, and I. Santamaría, “Coherent fusion of information for optimal detection in sensor networks,” in Proc. IEEE Work. Stat. Signal Process., Cardiff, UK, 2009.
```
@inproceedings{RamirezViaSantamaria-2009-Coherentfusionofinformationfor,
  address = {Cardiff, UK},
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {IEEE} {W}ork.\ {S}tat.\ {S}ignal {P}rocess.},
  doi = {10.1109/SSP.2009.5278473},
  month = {{S}eptember},
  title = {Coherent fusion of information for optimal detection in sensor networks},
  year = {2009},
  local-url = {C10_SSP_2009.pdf}
}
```
In this work, we consider the problem of centralized detection in wireless sensor networks when the sensors transmit coherently through a multiple access channel. We derive the optimal weighting at each sensor that maximizes the error exponent. Firstly, the noiseless case is considered and a closed-form solution to the problem is found. Secondly, we generalize the formulation to consider additive noise at the fusion center. For the noisy case, we propose a suboptimal approach which allows us to find a closed-form solution. Interestingly, the proposed approaches reduce to the extraction of a normalized eigenvector of a generalized eigenvalue problem. The performance of the proposed scheme is illustrated by means of numerical results, showing that the suboptimal approach has a similar performance to that of the optimal one; and that the proposed scheme outperforms other techniques, such as orthogonal transmissions or the maximization of the signal-to-noise ratio.
D. Ramírez, J. Vía, I. Santamaría, and P. Crespo, “Entropy and Kullback-Leibler divergence estimation based on Szegö’s Theorem,” in Proc. Eur. Signal Process. Conf., Glasgow, Scotland, 2009.
```
@inproceedings{RamirezViaSantamaria-2009-EntropyandKullback-Leiblerdivergenceestimation,
  address = {Glasgow, Scotland},
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I. and Crespo, P.},
  booktitle = {{P}roc.\ {E}ur.\ {S}ignal {P}rocess.\ {C}onf.},
  month = {{A}ugust},
  title = {Entropy and {K}ullback-{L}eibler divergence estimation based on {S}zeg\"o's Theorem},
  year = {2009},
  local-url = {C9_Eusipco_2009.pdf}
}
```
In this work, a new technique for the estimation of the Shannon’s entropy and the Kullback-Leibler (KL) divergence for one dimensional data is presented. The estimator is based on the Szegö’s theorem for sequences of Toeplitz matrices, which deals with the asymptotic behavior of the eigenvalues of those matrices, and the analogy between a probability density function (PDF) and a power spectral density (PSD), which allows us to estimate a PDF of bounded support using the well-known spectral estimation techniques. Specifically, an AR model is used for the PDF PSD estimation, and the entropy is easily estimated as a function of the eigenvalues of the autocorrelation Toeplitz matrix. The performance of the Szegö’s estimators is illustrated by means of Monte Carlo simulations and compared with previously proposed alternatives, showing a good performance.
D. Ramírez, J. Vía, and I. Santamaría, “A generalization of the magnitude squared coherence spectrum for more than two signals: Definition, properties and estimation,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Las Vegas, USA, 2008.
```
@inproceedings{RamirezViaSantamaria-2008-generalizationofmagnitudesquaredcoherence,
  address = {Las Vegas, USA},
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2008.4518473},
  month = {{A}pril},
  title = {A generalization of the magnitude squared coherence spectrum for more than two signals: Definition, properties and estimation},
  year = {2008},
  local-url = {C6_ICASSP_2008.pdf}
}
```
The coherence spectrum is a well-known measure of the linear statistical relationship between two time series. In this paper, we extend this concept to several processes and define the generalized magnitude squared coherence (GMSC) spectrum as a function of the largest eigenvalue of a matrix containing all the pairwise complex coherence spectra. The GMSC is bounded between zero and one, and attains its maximum when all the processes are perfectly correlated at a given frequency. Furthermore, three different GMSC spectrum estimators, extending those previously proposed for the MSC of two processes, are presented. Specifically, we compare the Welch method, the minimum variance distortionless response (MVDR) estimator and a new estimator based on canonical correlation analysis (CCA).
I. Santamaría, V. Elvira, J. Vía, D. Ramírez, J. Pérez, J. Ibáñez, R. Eickhoff, and F. Ellinger, “Optimal MIMO transmission schemes with adaptive antenna combining in the RF path,” in Proc. Eur. Signal Process. Conf., Lausanne, Switzerland, 2008.
```
@inproceedings{SantamariaElviraVia-2008-OptimalMIMOtransmissionschemeswith,
  address = {Lausanne, Switzerland},
  author = {Santamar{\'i}a, I. and Elvira, V. and V{\'i}a, J. and Ram{\'i}rez, D. and P{\'e}rez, J. and Ib{\'a}{\~n}ez, J. and Eickhoff, R. and Ellinger, F.},
  booktitle = {{P}roc.\ {E}ur.\ {S}ignal {P}rocess.\ {C}onf.},
  month = {{A}ugust},
  title = {Optimal {MIMO} transmission schemes with adaptive antenna combining in the {RF} path},
  year = {2008},
  local-url = {C8_Eusipco_UC_MIMAX.pdf}
}
```
In this paper we study space-time coding schemes for a novel MIMO transceiver which performs adaptive signal combining in radio-frequency (RF). The limitations of the RF circuitry make necessary to develop specific designs for this architecture. For instance, the space and time encoders must operate separately (the former works in the RF domain and the latter works in baseband), and at different time scales: the spatial encoder or RF beamformer must remain fixed dur- ing the transmission of a probably large number of symbols, whereas the time-encoder can work at the symbol rate. We show in the paper that although the multiplexing gain of the system is limited to one, we are still able to achieve the full spatial diversity of the MIMO channel as well as to increase the received signal-to-noise ratio through array gain. Specifically, when perfect channel state information (CSI) is available only at the receiver we propose to use a scheme referred to as orthogonal beam division multiplexing (OBDM). With this scheme the symbols are time-precoded with a unitary discrete Fourier transform (DFT) matrix, then they are successively transmitted through orthogonal direc- tions and, finally, we use a receiver comprising maximal ra- tio combining (MRC) followed by a minimum mean-square error (MMSE) decoder. The performance of the proposed techniques in terms of outage capacity and bit error rate is illustrated by means of several simulations examples.
D. Ramírez, J. Vía, and I. Santamaría, “Multiple-channel signal detection using the generalized coherence spectrum,” in Proc. IAPR Work. Cognitive Information Process., Santorini, Greece, 2008.
```
@inproceedings{RamirezViaSantamaria-2008-Multiple-channelsignaldetectionusinggeneralized,
  address = {Santorini, Greece},
  author = {Ram{\'i}rez, D. and V{\'i}a, J. and Santamar{\'i}a, I.},
  booktitle = {Proc.\ {IAPR} Work.\ Cognitive Information Process.},
  month = {{J}une},
  title = {Multiple-channel signal detection using the generalized coherence spectrum},
  year = {2008},
  local-url = {C7_CIP2008.pdf}
}
```
Recently, a generalization of the magnitude squared coherence (MSC) spectrum for more than two random processes has been proposed. The generalized MSC (GMSC) spectrum definition, which is based on the largest eigenvalue of a matrix containing all the pairwise complex coherence spectra, provides a frequency-dependent measure of the linear relationship among several stationary random processes. Moreover, it can be easily estimated by solving a generalized eigenvalue problem. In this paper we apply the GMSC spectrum for detecting the presence of a common signal from a set of linearly distorted and noisy observations. Specifically, the new statistic for the multiple-channel detection problem is the integral of the square root of the GMSC, which can be estimated as the sum of the P largest generalized canonical correlations (typically P=1 is enough in practice). Unlike previous approaches, the new statistic implicitly takes into account the spectral characteristics of the signal to be detected (e.g., its bandwidth). Finally, the performance of the proposed detector is compared in terms of its receiver operating characteristic (ROC) curve with the generalized coherence (GC) showing a clear improvement in most scenarios.
J. A. García-Naya, T. M. Fernández-Caramés, H. J. Pérez-Iglesias, M. González-López, L. Castedo, D. Ramírez, I. Santamaría, J. Pérez, J. Vía, and J. M. Torres-Royo, “Performance of STBC transmissions with real data,” in Proc. IST Mobile & Wireless Comms. Summit, Budapest, Hungary, 2007.
```
@inproceedings{Garcia-NayaFernandez-CaramesPerez-Iglesias-2007-PerformanceofSTBCtransmissionswith,
  address = {Budapest, Hungary},
  author = {Garc{\'i}a-Naya, J. A. and Fern{\'a}ndez-Caram{\'e}s, T. M. and P{\'e}rez-Iglesias, H. J. and Gonz{\'a}lez-L{\'o}pez, M. and Castedo, L. and Ram{\'i}rez, D. and Santamar{\'i}a, I. and P{\'e}rez, J. and V{\'i}a, J. and Torres-Royo, J. M.},
  booktitle = {Proc.\ IST Mobile $\&$ Wireless Comms.\ Summit},
  doi = {10.1109/ISTMWC.2007.4299296},
  month = {{J}uly},
  title = {Performance of {STBC} transmissions with real data},
  year = {2007},
  local-url = {C4_IST_Mobile_Summit_2007.pdf}
}
```
This paper presents a comparative study of three Space-Time Block Coding (STBC) techniques in realistic indoor scenarios. In particular, we focus on the Alamouti orthogonal scheme considering two types of Channel State Information (CSI) estimation: a conventional pilot-aided technique and a new blind method based on Second Order Statistics (SOS). We also considered a Differential (non-coherent) Space-Time Block code (DSTBC) that can be optimally decoded without CSI estimation, although it incurs in a 3 dB loss in performance. Experimental evaluation is carried out with a flexible and easy-to-use 2 \times 2 MIMO platform at 2.4 GHz. Results show the excellent performance of the blind channel estimation technique in either Line-Of-Sight (LOS) and Non-LOS (NLOS) indoor scenarios.
J. Vía, I. Santamaría, J. Pérez, and D. Ramírez, “Blind decoding of MISO-OSTBC systems based on principal component analysis,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Process., Toulouse, France, 2006.
```
@inproceedings{ViaSantamariaPerez-2006-BlinddecodingofMISO-OSTBCsystems,
  address = {Toulouse, France},
  author = {V{\'i}a, J. and Santamar{\'i}a, I. and P{\'e}rez, J. and Ram{\'i}rez, D.},
  booktitle = {{P}roc.\ {IEEE} {I}nt.\ {C}onf.\ {A}coustics, {S}peech and {S}ignal {P}rocess.},
  doi = {10.1109/ICASSP.2006.1661026},
  month = {{M}ay},
  title = {Blind decoding of {MISO-OSTBC} systems based on principal component analysis},
  year = {2006},
  local-url = {C1_icassp2006_OSTBC_pub.pdf}
}
```
In this paper, a new second-order statistics (SOS) based method for blind decoding of orthogonal space time block coded (OSTBC) systems with only one receive antenna is proposed. To avoid the in- herent ambiguities of this problem, the spatial correlation matrix of the source signals must be non-white and known at the receiver. In practice, this can be achieved by a number of simple linear preco- ding techniques at the transmitter side. More specifically, it is shown in the paper that if the source correlation matrix has different eigen- values, then the decoding process can be formulated as the problem of maximizing the sum of a set of weighted variances of the signal estimates. Exploiting the special structure of OSTBCs, this problem can be reduced to a principal component analysis (PCA) problem, which allows us to derive computationally efficient batch and adap- tive blind decoding algorithms. The algorithm works for any OSTBC (including the popular Alamouti code) with a single receive antenna. Some simulation results are presented to demonstrate the potential of the proposed procedure.
D. Ramírez, I. Santamaría, J. Pérez, J. Vía, A. Tazón, J. A. Garcia-Naya, T. M. Fernandez-Carames, M. G. Lopez, H. J. P. Iglesias, and L. Castedo, “A flexible testbed for the rapid prototyping of MIMO baseband modules,” in Proc. Int. Symp. on Wireless Comm. Systems, Valencia, Spain, 2006.
```
@inproceedings{RamirezSantamariaPerez-2006-flexibletestbedforrapidprototyping,
  address = {Valencia, Spain},
  author = {Ram{\'i}rez, D. and Santamar{\'i}a, I. and P{\'e}rez, J. and V{\'i}a, J. and Taz{\'o}n, A. and Garcia-Naya, J. A. and Fernandez-Carames, T. M. and Lopez, M. Gonzalez and Iglesias, H. J. P{\'e}rez and Castedo, L.},
  booktitle = {Proc.\ Int. Symp. on Wireless Comm. Systems},
  doi = {10.1109/ISWCS.2006.4362407},
  month = {{S}eptember},
  title = {A flexible testbed for the rapid prototyping of {MIMO} baseband modules},
  year = {2006},
  local-url = {C2_ISWCS_2006_b.pdf}
}
```
Hardware platforms and testbeds are an essential tool to evaluate, in realistic scenarios, the performance of Multiple-Input-Multiple-Ouput (MIMO) systems. In this work we present a simple and easily reconfigurable 2 \times 2 MIMO testbed for the rapid prototyping of the signal processing baseband functions. The signal generation module consists of a host PC equipped with a board that contains two high performance 100 MHz DACs and a 1 GB memory module that allows the transmission of extremely large frames of data. At the receiver side, we use another host PC equipped with two 105 MHz ADCs, another 1 GB memory module and a trigger that starts the acquisition process when the presence of signal is detected. The platform has been designed to operate at the ISM band of 2.4 GHz with a RF bandwidth of 20 MHz. In order to minimize the number of DAC and ADC circuits, signals are generated and acquired at an IF of 15 MHz. Upconversion to RF is performed with two RF vectorial signal generators (Agilent E4438C) and downconversion with two specific circuits designed from commercial components. Transmitter and receiver signal processing functions are implemented off-line in Matlab. To illustrate the performance and capabilities of the platform, we present the results of two experiments of a 2 \times 2 MIMO transmission with Alamouti coding.