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.

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.

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.

Fitting a multivariate Gaussian mixture to data represents an attractive, as well as challenging problem, in especial when sparsity in the solution is demanded. Achieving this objective requires the concurrent update of all parameters (weight, centers, and precisions) of all multivariate Gaussian functions during the learning process. Such is the focus of this paper, which presents a novel method founded on the minimization of the error of the generalized logarithmic utility function (GLUF). This choice, which allows us to move smoothly from the mean square error (MSE) criterion to the one based on the logarithmic error, yields an optimization problem that resembles a locally convex problem and can be solved with a quasi-Newton method. The GLUF framework also facilitates the comparative study between both extremes, concluding that the classical MSE optimization is not the most adequate for the task. The performance of the proposed novel technique is demonstrated on simulated as well as realistic scenarios.

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 signal 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 number of samples) exploiting Szegö's theorem and its generalization for vector-valued processes. Simulation results show the good performance of the proposed GLRT.

Physical-layer authentication techniques exploit the unique properties of the wireless medium to enhance traditional higher-level authentication procedures. We propose to reduce the higher-level authentication overhead by using a state-of-the-art multi-target tracking technique based on Gaussian processes. The proposed technique has the additional advantage that it is capable of automatically learning the dynamics of the trusted user's channel response and the time-frequency fingerprint of intruders. Numerical simulations show very low intrusion rates, and an experimental validation using a wireless test bed with programmable radios demonstrates the technique's effectiveness.

This paper considers the problem of distilling a secret key in a Gaussian multiple-input multiple-output (MIMO) scenario with two legitimate nodes and an eavesdropper. Focusing on the realistic case without perfect knowledge of the eavesdropper channel, and following a conservative practical approach based on the maximization of the worst case secret key capacity (SKC), the problem of designing the optimal transmit covariance matrix is reformulated as a convex optimization problem. In the limiting case in which the eavesdropper channel can not be estimated, or when the estimate is highly unreliable, the optimal covariance matrix can be obtained by means of waterfilling or matched filtering like algorithms. Additionally, we illustrate the benefits of allowing time sharing between transmissions of the two legitimate nodes, and provide an efficient algorithm for obtaining the optimal transmit covariance matrices and time-sharing factor.

In this paper we provide an efficient procedure to compute the total number of degrees of freedom (DoF), achievable by linear beamforming, of the K-user multiple-input multiple-output (MIMO) interference channel with an arbitrary number of Tx-Rx antennas at each link. Firstly, we derive an analytical outer bound that generalizes the results that exist for the symmetric K-user M × N interference channel. Secondly, we obtain a tighter bound by solving a convex optimization problem that includes as constraints the DoF characterizations for point-to-point MIMO links and for 2-user interference channels. The solution to this convex problem admits an interesting waterfilling interpretation. Finally, exploiting this outer bound and using a recently proposed feasibility test, we show that it is possible to obtain the DoF for any interference channel in an efficient way. Some simulations results are included to illustrate the tightness of the derived bounds, as well as to study the DoF achievable for the 4-user channel when we distribute the total number of antennas among users and between transmitters and receivers in different ways.

Negative co-occurrence is a common phenomenon in many signal processing applications. In some cases the signals involved are sparse, and this information can be exploited to recover them. In this paper, we present a sparse learning approach that explicitly takes into account negative co-occurrence. This is achieved by adding a novel penalty term to the LASSO cost function based on the cross-products between the reconstruction coefficients. Although the resulting optimization problem is non-convex, we develop a new and efficient method for solving it based on successive convex approximations. Results on synthetic data, for both complete and overcomplete dictionaries, are provided to validate the proposed approach.

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.

We describe two formulations of the kernel canonical correlation analysis (KCCA) problem for multiple data sets. The kernel-based algorithms, which allow one to measure nonlinear relationships between the data sets, are obtained as nonlinear extensions of the classical maximum variance (MAX-VAR) and minimum variance (MINVAR) canonical correlation analysis (CCA) formulations. We then show how adaptive versions of these algorithms can be obtained by reformulating KCCA as a set of coupled kernel recursive least-squares algorithms. We illustrate the performance of the proposed algorithms on a nonlinear identification application and a cognitive radio detection problem.

This paper presents a novel method for fitting a sparse Gaussian mixture on a non-negative function of reference. Despite this problem is well known to be highly non-linear, the use of the logarithmic utility function seems to alleviate such an undesired situation. Moreover, sparsity measures related to the Gaussian precision can be integrated in such a way that the numerical algorithm turns out easy to implement, it is numerically efficient, and presents stable convergence. The method has been originally thought for the parameterization of power spectra, but it can also be useful in different scenarios.

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 ofN-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.

An alternating optimization algorithm was recently proposed for the K-user multiple-input multiple-output (MIMO) interference channel. For flat-fading channels and feasible problems, this algorithm successfully aligns the interfering signals exploiting the spatial dimensions. In this paper, we consider the case in which all pairwise MIMO channels are frequency-selective (convolutive), and the users transmit broadband signals using a single-carrier scheme. Unlike the flat-fading case, for frequency-selective channels it is necessary to add a spectral mask in the frequency response of the precoders and decoders to avoid trivial solutions. We show in the paper that each step of the alternating minimization algorithm can be reformulated as a convex optimization problem in which the autocorrelation function of the precoders or decoders is obtained. Upon convergence, a final spectral factorization stage must be applied to obtain the precoders and decoders from their autocorrelation functions. Simulation results are provided to illustrate the performance of the proposed algorithm.

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.

The goal of this paper consists in characterizing the capacity region of a broadcast system based on analog antenna combining and orthogonal frequency division multiplexing (OFDM). In particular, we consider the maximization of a weighted sum of the rates, which results in a highly non-convex optimization problem. The proposed iterative approach is based on the alternative optimization of the beamformers, and the power and subcarrier allocation. Finally, our experiments show that in most practical situations, the complexity of the optimal approaches (subcarrier sharing and power allocation) is not justified by the marginal gains in the capacity region.

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.

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.

This paper considers the problem of joint blind source separation (J-BSS), which appears in many practical problems such as blind deconvolution or functional magnetic resonance imaging (fMRI). In particular, we establish the necessary and sufficient conditions for the solution of the J-BSS problem by exclusively exploiting the second-order statistics (SOS) of the observations. The identifiability analysis is based on the idea of equivalently distributed sets of latent variables, that is, latent variables with covariance matrices related by means of a diagonal matrix. Interestingly, the identifiability analysis also allows us to introduce a measure of the identifiability degree based on Kullback-Leibler projections. This measure is clearly correlated with the performance of practical SOS-based J-BSS algorithms, which is illustrated by means of numerical examples.

This work considers the independent component analysis (ICA) of quaternion random vectors. In particular, we focus on the Gaussian case, and therefore the ICA problem is solved by exclusively exploiting the second-order statistics (SOS) of the observations. In the quaternion case, the SOS of a random vector are given by the covariance matrix and three complementary covariance matrices. Thus, quaternion ICA amounts to jointly diagonalizing these four matrices. Following a maximum likelihood (ML) approach, we show that the ML-ICA problem reduces to the minimization of a cost function, which can be interpreted as a measure of the entropy loss due to the correlation among the estimated sources. In order to solve the non-convex ML-ICA problem, we propose a practical quasi-Newton algorithm based on quadratic local approximations of the cost function. Finally, the practical performance and potential application of the proposed technique is illustrated by means of numerical examples.

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 in spatial 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.

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 ℚ-proper and ℂη-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.

Society demands access to high capacity wireless communications and to the services that can be provided on top of them. To satisfy these demands, engineers are constantly developing new technologies. These developments have to be selectively transferred to the university curricula. The student has to be familiar not only with the basic theory and techniques, but also with those of the more advanced techniques that provide a more profound insight. One of these techniques is based on Multiple-Input Multiple-Output (MIMO) systems. In this paper we show how to build a web platform for learning advanced digital communications based on a MIMO testbed. Using as starting point a 4 × 4 flexible dual band (2.4/5 GHz), we first develop a webservice interface to provide remote access to the services offered by the testbed and then implement a virtual laboratory where the students can parameterize and perform advanced experiments.

In this paper, we propose a general beamforming criterion for pre-FFT processing in orthogonal frequency division multiplexing (OFDM) systems with multiple transmit and receive antennas. The proposed criterion depends on a single parameter α, which establishes a tradeoff between the energy of the equivalent SISO channel (after Tx-Rx beamforming) and its spectral flatness. The proposed cost function embraces most reasonable criteria for designing Tx-Rx pre-FFT beamformers. Hence, for particular values of α the proposed criterion reduces to the minimization of the mean square error (MSE), the maximization of the system capacity, or the maximization of the received signal-to-noise ratio (SNR). In general, the proposed criterion results in a non convex optimization problem. However, we show that the problem can be approximately solved by semidefinite relaxation (SDR) techniques. Additionally, since the computational cost of SDR for this problem is rather high, we propose a simple yet efficient gradient search algorithm which provides satisfactory solutions with a moderate computational cost for OFDM-based WLAN standards such as 802.11a. Finally, the good performance of the proposed technique is illustrated by means of some numerical results.

In this paper, the second-order circularity of quaternion 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 complementary 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 extensions 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 Q-proper or Cη-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 divergence 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.

Abstract In this paper, a new technique for the blind estimation of frequency and/or time‐selective multiple‐input multiple‐output (MIMO) channels under space‐time block coding (STBC) transmissions is presented. The proposed method relies on a basis expansion model (BEM) of the MIMO channel, which reduces the number of parameters to be estimated, and includes many practical STBC‐based transmission scenarios, such as STBC‐orthogonal frequency division multiplexing (OFDM), space‐frequency block coding (SFBC), time‐reversal STBC, and time‐varying STBC encoded systems. Inspired by the unconstrained blind maximum likelihood (UML) decoder, the proposed criterion is a subspace method that efficiently exploits all the information provided by the STBC structure, as well as by the reduced‐rank representation of the MIMO channel. The method, which is independent of the specific signal constellation, is able to blindly recover the MIMO channel within a small number of available blocks at the receiver side. In fact, for some particular cases of interest such as orthogonal STBC‐OFDM schemes, the proposed technique blindly identifies the channel using just one data block. The complexity of the proposed approach reduces to the solution of a generalized eigenvalue (GEV) problem and its computational cost is linear in the number of sub‐channels. An identifiability analysis and some numerical examples illustrating the performance of the proposed algorithm are also provided. Copyright © 2009 John Wiley & Sons, Ltd.

In this paper, we study transmission schemes for a novel OFDM-based MIMO system which performs adaptive signal combining in radio-frequency (RF). Specifically, we consider the problem of selecting the linear precoder and the transmit and receive RF weights (or beamformers) for minimizing the bit error rate (BER) under the assumption of perfect channel knowledge and linear receivers. Firstly, it is shown that the optimal precoder amounts to uniformly distribute the overall mean square error (MSE) among the information symbols. Secondly, we propose a gradient search algorithm to obtain the optimal pair of beamformers. Interestingly, in the case of low signal to noise ratios (SNR), the proposed beamforming criterion is equivalent to the maximization of the received SNR. However, for moderate and high SNRs, part of the received SNR is sacrificed in order to improve the channel response of the worst subcarriers, which translates into significant advantages over other previously proposed approaches. Finally, the performance of the proposed scheme is illustrated by means of some numerical examples.

In this paper, we study beamforming schemes for a novel MIMO transceiver, which performs adaptive signal combining in the radio-frequency domain. Assuming perfect channel knowledge at both the transmit and receive sides, we consider the problem of selecting the transmit and receive RF beamformers that maximize the capacity (MaxCAP criterion) of the system under orthogonal frequency division multiplexing (OFDM) transmissions. This problem is non-convex and has no closed-form solution, therefore the maximum capacity beamformers are found using a gradient search algorithm. Furthermore, it is shown in the paper that, for low signal-to-noise ratios (SNR), the MaxCAP criterion is equivalent to maximizing the received SNR (MaxSNR criterion). However, for moderate and high SNRs, the maximum capacity beamformers sacrifice part of the received SNR in order to improve the worst subcarriers and, in this way, they increase the overall capacity of the multicarrier channel. Finally, by means of numerical examples we show that the MaxCAP criterion significantly outperforms the MaxSNR criterion in terms of bit error rate and outage probability.

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).

In this paper, the conditions for blind identifiability from second-order statistics (SOS) of multiple-input multiple-output (MIMO) channels under orthogonal space-time block coded (OSTBC) transmissions are studied. The main contribution of the paper consists in the proof that, assuming more than one receive antenna, any OSTBC with a transmission rate higher than a given threshold, which is inversely proportional to the number of transmit antennas, permits the blind identification of the MIMO channel from SOS. Additionally, it has been proven that any real OSTBC with an odd number of transmit antennas is identifiable, and that any OSTBC transmitting an odd number of real symbols permits the blind identification of the MIMO channel regardless of the number of receive antennas, which extends previous identifiability results and suggests that any nonidentifiable OSTBC can be made identifiable by slightly reducing its code rate. The implications of these theoretical results include the explanation of previous simulation examples and, from a practical point of view, they show that the only nonidentifiable OSTBCs with practical interest are the Alamouti codes and the real square orthogonal design with four transmit antennas. Simulation examples and further discussion are also provided.

Abstract In this paper we employ a 2 × 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) space‐time block coding (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. Copyright © 2007 John Wiley & Sons, Ltd.

In this paper, a new technique for the estimation of the magnitude squared coherence (MSC) spectrum is proposed. The method is based on the relationship between the MSC and the canonical correlation analysis (CCA) of stationary time series. Particularly, the canonical correlations coincide asymptotically with the squared roots of the MSC, which is exploited in the paper to obtain an estimate of the MSC based on a reduced-rank version of the estimated coherence matrix. The proposed technique provides a higher spectral resolution than the well-known Welch's method, and it also avoids the signal mismatch problem associated to the minimum variance distortionless response (MVDR) based approach. Finally, the performance of the proposed method is evaluated by means of some numerical examples.

In this paper, the conditions for blind identifiability from second order statistics (SOS) of multiple-input multiple-output (MIMO) channels under orthogonal space-time block coded (OSTBC) transmissions are studied. The main contribution of the paper is to show that, assuming more than one receive antenna, any OSTBC with a transmission rate higher than a given threshold, which is inversely proportional to the number of transmit antennas, permits the blind identification of the MIMO channel from SOS. Additionally, some previous identifiability results have been extended. The implications of these theoretical results include the explanation of previous simulation examples found in the literature and, from a practical point of view, they show that the only non-identifiable OSTBC codes with practical interest are the Alamouti codes and the real square orthogonal design with four transmit antennas. Further discussion and empirical analysis are also provided.

In this paper we apply the structural risk minimization (SRM) principle to derive a blind single-input multiple-output (SIMO) channel estimation algorithm, which is robust to channel order overestimation. Specifically, the blind estimation is formulated as a support vector regression (SVR) problem in which the channel coefficients are the Lagrange multipliers of the dual problem. In this paper, we show that the SRM principle pushes to zero the small leading and trailing terms of the channel impulse response even when its order is highly overestimated. The main drawback of this approach is the high computational cost of the resulting quadratic programming (QP) problem. To alleviate this, in this paper we propose to use a simple and fast algorithm called the Adatron to solve the QP problem. Simulation results are provided to demonstrate the performance of our channel estimator.

In this paper we propose a new kernel-based version of the recursive least-squares (RLS) algorithm for fast adaptive nonlinear filtering. Unlike other previous approaches, we combine a sliding-window approach (to fix the dimensions of the kernel matrix) with conventional L2-norm regularization (to improve generalization). The proposed kernel RLS algorithm is applied to a nonlinear channel identification problem (specifically, a linear filter followed by a memoryless nonlinearity), which typically appears in satellite communications or digital magnetic recording systems. We show that the proposed algorithm is able to operate in a time-varying environment and tracks abrupt changes in either the linear filter or the nonlinearity

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 inherent 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 precoding techniques at the transmitter side. More specifically, it is shown in the paper that if the source correlation matrix has different eigenvalues, 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 adaptive 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

We consider the application of kernel canonical correlation analysis (K-CCA) to the supervised equalization of Wiener systems. Although a considerable amount of research has been carried out on identification/equalization of Wiener models, in this paper we show that K-CCA is a particularly suitable technique for the inversion of these nonlinear dynamic systems. Another contribution of this paper is the development of an online K-CCA algorithm which combines a sliding-window approach with a recently proposed reformulation of CCA as an iterative regression problem. This online algorithm permits fast equalization of time-varying Wiener systems. Simulation examples are added to illustrate the performance of the proposed method.

Canonical correlation analysis (CCA) is a classical tool in statistical analysis that measures the linear relationship between two data sets. In this paper we show that CCA can be reformulated as a pair of coupled least squares (LS) problems. By exploiting this idea, we first present an iterative batch procedure to extract all the canonical vectors through a regression procedure. Then, we derive a recursive least squares (RLS) algorithm for on-line CCA. This algorithm can be further improved to increase its robustness against outliers and impulsive noise. The proposed algorithm is applied to blind identification of multichannel FIR systems, and its performance is illustrated through simulations.

A novel technique for blind identification of multichannel FIR systems is derived from the learning paradigm of support vector machines (SVMs). Specifically, blind identification is formulated as a support vector regression problem and an iterative procedure, which avoids a trivial solution, is proposed to solve it. The SVM-based approach can be viewed as a regularized version of the least squares method for blind identification. We show that minimizing the complexity of the solution, as suggested by the structural risk minimization (SRM) principle, increases the robustness of the proposed SVM-based technique to channel order overestimation as well as to poor diversity channels (i.e., when a pair of subchannels have close zeros). The performance of the method is demonstrated through some simulation examples.

Recent work has shown how the support vector machine (SVM) framework can be used for blind equalization of constant modulus (CM) signals. The basic idea consists of exploiting the CM property of the input signals to reformulate the blind equalization problem as a regression problem. We extend this idea to encompass the problem of separating and estimating multiple CM signals mixed through an unknown matrix (i.e., blind beamforming). The quadratic inequalities derived from the CM property are transformed into linear ones, thus yielding a quadratic programming (QP) problem. Then an iterative reweighted procedure is proposed to blindly restore the CM property. Once a signal is recovered, its contribution to the original observations is removed and the iterative procedure can be applied again to extract another CM signal. Simulation results show that this SVM-based algorithm offers better performance than the algebraic constant modulus algorithm (ACMA), mainly when only a small number of snapshots is available.