## 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: Dissertations, Journal articles, Conference publications

- 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.}, local-url = {Ramirez_PhDThesis.pdf}, school = {Universidad de Cantabria}, title = {Detection and Estimation of Time Series using a Multi-sensor Array (in Spanish)}, year = {2011} }

- 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.}, local-url = {Ramirez_PFC.pdf}, school = {Universidad de Cantabria}, title = {Regularized detection techniques in VBLAST systems: Development of a 2x2 testbed at 2.4 GHz (in Spanish)}, year = {2006} }

- 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, p. 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}, journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.}, local-url = {R14_TSP_Cyclo.pdf}, month = {{O}ctober}, number = {20}, pages = {5395--5408}, title = {Detection of multivariate cyclostationarity}, volume = {63}, year = {2015} }

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.

- 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}, journal = {{IEEE} {T}rans.\ {I}nform.\ {T}heory}, local-url = {R12_Monogenic_IT.pdf}, month = {{O}ctober}, number = {10}, pages = {6491-6510}, title = {Detecting directionality in random fields using the monogenic signal}, volume = {60}, year = {2014} }

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.

- 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. 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.

- 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. Applied 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}pplied {S}ignal {P}rocess.}, local-url = {R13_EJASP_GLRT_ST.pdf}, title = {Multi-antenna spectrum sensing by exploiting spatio-temporal correlation}, volume = {160}, year = {2014} }

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.

- 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}, journal = {{IEEE} {T}rans.\ {I}nform.\ {T}heory}, local-url = {R8_LMPIT_TIT.pdf}, 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} }

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 \emphQuercus spp., \emphAbies alba Mill., \emphFagus sylvatica L., and \emphPicea 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 \emphA. alba and \emphF. 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}, journal = {{IEEE} {T}rans.\ {S}ignal\ {P}rocess.}, local-url = {R7_rankPdetection_TrSP.pdf}, 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} }

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.}, local-url = {R5_MIMO_Channel_characterization_IEEE_TIM.pdf}, 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} }

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.

@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.}, local-url = {R4_GLRT_GCS_Detection_Spatially_TrSP.pdf}, month = {{O}ctober}, number = {10}, pages = {5006--5015}, title = {Detection of spatially correlated {G}aussian time series}, volume = {58}, year = {2010} }

- 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}, journal = {{IEEE} {T}rans.\ {I}nform.\ {T}heory}, local-url = {R3_Trans_Info_Theory_2010_QuaternionWL.pdf}, month = {{J}uly}, number = {7}, pages = {3502--3515}, title = {Properness and widely linear processing of quaternion random vectors}, volume = {56}, year = {2010} }

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 \emphfull-widely linear. However, in the case of jointly \mathbbQ-proper or \mathbbC^η-proper vectors, the optimal processing reduces, respectively, to the \emphconventional or \emphsemi-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}, local-url = {R2_Wireless_Communications_and_Mobile_Computing2008.pdf}, 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} }

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.}, local-url = {R1_Electronic_Letters_2006.pdf}, month = {{F}ebruary}, number = {3}, pages = {184--186}, title = {Regularised approach to detection of constant modulus signals in {MIMO} channels}, volume = {42}, year = {2006} }

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.

- 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.}, local-url = {C39_ICASSPCalgary2018_PSD.pdf}, month = {{A}pril}, title = {Locally optimal invariant detector for testing equality of two power spectral densities}, year = {2018} }

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.}, local-url = {C40_ICASSP2018_demixing_GSP.pdf}, month = {{A}pril}, title = {Demixing and blind deconvolution of graph-diffused sparse signals}, year = {2018} }

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. Asilomar Conf. Signals Syst. 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.\ {A}silomar {C}onf.\ {S}ignals {S}yst.\ {C}omputers}, local-url = {C38_Asilomar_2017.pdf}, month = {{O}ctober}, title = {Detection of almost-cyclostationarity: An approach based on a multiple hypothesis test}, year = {2017} }

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.}, local-url = {C37_ICASSP_2017.pdf}, month = {{M}arch}, title = {Graph-signal reconstruction and blind deconvolution for diffused sparse inputs}, year = {2017} }

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. Asilomar Conf. Signals Syst. 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.\ {A}silomar {C}onf.\ {S}ignals {S}yst.\ {C}omputers}, doi = {10.1109/ACSSC.2016.7869115}, local-url = {C36_Asilomar_Bootstrap.pdf}, month = {{N}ovember}, title = {Bootstrap-based detection of the number of signals correlated across multiple data sets}, year = {2016} }

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.

@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}, local-url = {C35_Eusipco_2016.pdf}, month = {{A}ugust}, title = {Determining the number of signals correlated across multiple data sets for small sample support}, year = {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}, local-url = {C34_SSP_2016.pdf}, month = {{J}une}, title = {Detecting the dimension of the subspace correlated across multiple data sets in the sample poor regime}, year = {2016} }

- 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}, local-url = {C33_ICASSP_2016.pdf}, month = {{M}arch}, title = {Detection of cyclostationarity in the presence of temporal or spatial structure with applications to cognitive radio}, year = {2016} }

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.

- 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}, local-url = {C32_ICASSP_2015.pdf}, month = {{A}pril}, title = {An asymptotic {LMPI} test for cyclostationarity detection with application to cognitive radio (invited paper)}, year = {2015} }

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. Asilomar Conf. Signals Syst. 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.\ {A}silomar {C}onf.\ {S}ignals {S}yst.\ {C}omputers}, doi = {10.1109/ACSSC.2014.7094815}, local-url = {C31_Asilomar_2014.pdf}, month = {{N}ovember}, title = {A regularized maximum likelihood estimator for the period of a cyclostationary process}, year = {2014} }

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.

- 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}, local-url = {C30_PRNI_cSPoC.pdf}, month = {{J}une}, title = {Optimizing spatial filters for the extraction of envelope-coupled neural oscillations}, year = {2014} }

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, 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}, local-url = {C29_ICASSP_2014.pdf}, month = {{M}ay}, title = {An asymptotic {GLRT} for the detection of cyclostationary signals}, year = {2014} }

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.

- 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}, local-url = {C28_ICASSP_2013.pdf}, month = {{M}ay}, title = {Power-{CCA}: Maximizing the correlation coefficient between the power of projections}, year = {2013} }

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.

- 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}, local-url = {C27_ICIP2012.pdf}, month = {{S}eptember}, title = {The random monogenic signal}, year = {2012} }

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, 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}, local-url = {C26_MLSP2012.pdf}, month = {{S}eptember}, title = {{GLRT} for testing separability of a complex-valued mixture based on the strong uncorrelating transform}, year = {2012} }

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.

- 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}, local-url = {C24_SAM_2012.pdf}, month = {{J}une}, title = {The locally most powerful invariant test for detecting a {rank-$P$} {G}aussian signal in white noise}, year = {2012} }

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.

- 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}, local-url = {C25_SAM_2012_Bayesian.pdf}, month = {{J}une}, title = {Bayesian multiantenna sensing for cognitive radio}, year = {2012} }

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. 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}, local-url = {C23_ICASSP_2012.pdf}, month = {{M}arch}, title = {The locally most powerful test for multiantenna spectrum sensing with uncalibrated receivers}, year = {2012} }

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.

- 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}, local-url = {C21_rankPestimation.pdf}, month = {{O}ctober}, title = {Spatial rank estimation in cognitive radio networks with uncalibrated multiple antennas (invited paper)}, year = {2011} }

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}, local-url = {C22_CostBarcelona.pdf}, month = {{O}ctober}, note = {Extended abstract}, title = {Recent advances in multiantenna spectrum sensing: complexity, noise uncertainty, and signal rank issues}, year = {2011} }

- 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.}, local-url = {C20_Eusipco_2011.pdf}, month = {{S}eptember}, title = {Experimental evaluation of {I}nterference {A}lignment under imperfect channel state information}, year = {2011} }

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.

- 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}, local-url = {C19_SSPNice2011_ML_beamsteering.pdf}, month = {{J}une}, title = {Multi-sensor beamsteering based on the asymptotic likelihood for colored signals}, year = {2011} }

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}, local-url = {C18_ICASSP2011Prague_GLRT_flat_fading.pdf}, month = {{M}ay}, title = {Multiple-channel detection of a {G}aussian time series over frequency-flat channels}, year = {2011} }

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}, local-url = {C17_ICASSP2011Prague_rankP_noIID.pdf}, month = {{M}ay}, title = {Multiantenna detection under noise uncertainty and primary user's spatial structure}, year = {2011} }

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.

- 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}, local-url = {C16_WSA_2011.pdf}, month = {{F}ebruary}, title = {Experimental validation of {I}nterference {A}lignment techniques using a multiuser {MIMO} testbed}, year = {2011} }

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.

- 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}, local-url = {C15_SAM2010_CR.pdf}, month = {{O}ctober}, title = {Multiantenna spectrum sensing: The case of wideband rank-one primary signals}, year = {2010} }

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}, local-url = {C14_MLSP2010_QuaternionMeasures.pdf}, month = {{A}ugust}, title = {Improperness measures for quaternion random vectors}, year = {2010} }

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.

- 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}, local-url = {C12_ICASSP2010_QuaternionWL.pdf}, month = {{M}arch}, title = {Widely and semi-widely linear processing of quaternion vectors}, year = {2010} }

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 \emphfull-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 \emphconventional and \emphsemi-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, 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}, local-url = {C13_ICASSP2010_CR_SpecSensing.pdf}, month = {{M}arch}, title = {Multiantenna spectrum sensing: Detection of spatial correlation among time-series with unknown spectra}, year = {2010} }

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.

- 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}, local-url = {C10_SSP_2009.pdf}, month = {{S}eptember}, title = {Coherent fusion of information for optimal detection in sensor networks}, year = {2009} }

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.}, local-url = {C9_Eusipco_2009.pdf}, month = {{A}ugust}, title = {Entropy and {K}ullback-{L}eibler divergence estimation based on {S}zeg\"o's Theorem}, year = {2009} }

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.

- 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.}, local-url = {C8_Eusipco_UC_MIMAX.pdf}, month = {{A}ugust}, title = {Optimal {MIMO} transmission schemes with adaptive antenna combining in the {RF} path}, year = {2008} }

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.}, local-url = {C7_CIP2008.pdf}, month = {{J}une}, title = {Multiple-channel signal detection using the generalized coherence spectrum}, year = {2008} }

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.

- 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}, local-url = {C6_ICASSP_2008.pdf}, month = {{A}pril}, title = {A generalization of the magnitude squared coherence spectrum for more than two signals: Definition, properties and estimation}, year = {2008} }

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).

- 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}, local-url = {C4_IST_Mobile_Summit_2007.pdf}, month = {{J}uly}, title = {Performance of {STBC} transmissions with real data}, year = {2007} }

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.

- 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}, local-url = {C2_ISWCS_2006_b.pdf}, month = {{S}eptember}, title = {A flexible testbed for the rapid prototyping of {MIMO} baseband modules}, year = {2006} }

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.

- 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}, local-url = {C1_icassp2006_OSTBC_pub.pdf}, month = {{M}ay}, title = {Blind decoding of {MISO-OSTBC} systems based on principal component analysis}, year = {2006} }

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.