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A new deterministic technique is proposed for blind equalization of finite impulse response multiple-input multiple-output (FIR-MIMO) channels. The batch and adaptive algorithms are obtained by reformulating canonical correlation analysis (CCA) as a set of coupled least squares (LS) regression problems.

A new approach is presented for adaptive beamforming that has provided increased robustness against the mismatch problem as well as additional control over the sidelobe level. The computer simulations have shown an improved performance of the support vector machine (SVM)-based beamformer when compared with other robust beamforming methods.

A new criterion is described for effective channel order detection of single-input multiple-output (SIMO) channels. The straightforward combination of both cost functions attains its minimum at the correct channel order even for moderate signal-to-noise ratios (SNRs), while the proposed method works with small data sets, colored signals and channels with small head and tail taps.

A new generalized correlation function is developed that includes the information of both the distribution and that of the time structure of a stochastic process. An attempt is made to find out how this measure is interpreted from a kernel method as well as from information theoretic learning points of view, demonstrating some relevant properties.

A new blind equalization approach that aims to force the probability density function (PDF) at the equalizer output to match the known constellation PDF is presented. The proposed method relies on the Parzen window method to estimate the data PDF and is implemented by a stochastic gradient descent algorithm.

The problem of blind equalization of constant modulus (CM) signals, formulated within the support vector regression (SVR) framework is discussed. Simulation examples show that linear and nonlinear blind SV equalizers offer better performance than cumulant-based techniques, mainly in applications when only a small number of data samples is available.

The suitability of a class of Parzen-window-based entropy estimates, namely Renyi's entropy, as a criterion for blind deconvolution of linear channels are investigated. The results indicate that this nonparametric entropy estimation approach outperforms the standard Bell-Sejnowski and normalized kurtosis algorithms in blind deconvolution.

The application of error-entropy minimization algorithms to digital communications channel equalization is examined. A new optimization criterion, based on the Renyi's error entropy, is used.

This work presents a generalization of classical factor analysis (FA). Each of $M$ channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the $M$ multiple-input multiple-output (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar. [ABSTRACT FROM AUTHOR]

Improper Gaussian signaling is a well-known technique that has been shown to improve performance in different multi-user scenarios. In this paper, we analyze the benefit of improper signaling in underlay cognitive radio when users are equipped with multiple antennas. Specifically, we assume that the primary user is protected by the so-called interference temperature constraint, which guarantees a prescribed rate requirement. In this setting, we study how the maximum tolerable interference power changes when the interference is additionally constrained to be maximally improper (strictly noncircular, or rectilinear). We observe that the correlation structure of a maximally improper interference is an additional degree of freedom that can be exploited to improve the SU performance. Because of that, we propose two different protection strategies for the PU where this structure is either constrained or unconstrained, and derive the interference temperature threshold for both cases. We then focus on the secondary user and provide designs of the transmission parameters under the proposed protection strategies. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization–minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support. [ABSTRACT FROM AUTHOR]

This paper studies the existence of optimal invariant detectors for determining whether $P$ multivariate processes have the same power spectral density. This problem finds application in multiple fields, including physical layer security and cognitive radio. For Gaussian observations, we prove that the optimal invariant detector, i.e., the uniformly most powerful invariant test, does not exist. Additionally, we consider the challenging case of close hypotheses, where we study the existence of the locally most powerful invariant test (LMPIT). The LMPIT is obtained in the closed form only for univariate signals. In the multivariate case, it is shown that the LMPIT does not exist. However, the corresponding proof naturally suggests an LMPIT-inspired detector that outperforms previously proposed detectors. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-channel multiple-input multiple-output passive detection problem, in which there is a surveillance array and a reference array. The reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension, but unknown basis. The question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of the same dimension, but unknown basis, which is correlated with the subspace signal in the reference channel. We consider a second-order detection problem where these subspace signals are structured by an unknown, but common, $p$-dimensional random vector of symbols transmitted from sources of opportunity, and then received through unknown $M\times p$ matrices at each of the $M$ -element arrays. The noises in each channel have spatial correlation models ranging from arbitrarily correlated to independent with identical variances. We provide a unified framework to derive the generalized likelihood ratio test for these different noise models. In the most general case of arbitrary noise covariance matrices, the test statistic is a monotone function of canonical correlations between the reference and surveillance channels. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an algorithm to design interference alignment (IA) precoding and decoding matrices for arbitrary MIMO X networks. The proposed algorithm is rooted in the homotopy continuation techniques commonly used to solve systems of nonlinear equations. Homotopy methods find the solution of a target system by smoothly deforming the solution of a start system which can be trivially solved. Unlike previously proposed IA algorithms, the homotopy continuation technique allows us to solve the IA problem for both unstructured (i.e., generic) and structured channels such as those that arise when time or frequency symbol extensions are jointly employed with the spatial dimension. To this end, we consider an extended system of bilinear equations that include the standard alignment equations to cancel the interference, and a new set of bilinear equations that preserve the desired dimensionality of the signal spaces at the intended receivers. We propose a simple method to obtain the start system by randomly choosing a set of precoders and decoders, and then finding a set of channels satisfying the system equations, which is a linear problem. Once the start system is available, standard prediction and correction techniques are applied to track the solution all the way to the target system. We analyze the convergence of the proposed algorithm and prove that, for many feasible systems and a sufficiently small continuation parameter, the algorithm converges with probability one to a perfect IA solution. The simulation results show that the proposed algorithm is able to consistently find solutions achieving the maximum number of degrees of freedom in a variety of MIMO X networks with or without symbol extensions. Further, the algorithm provides insights into the feasibility of IA in MIMO X networks for which theoretical results are scarce. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

We consider the problem of blind identification and equalization of single-input multiple-output (SIMO) nonlinear channels. Specifically, the nonlinear model consists of multiple single-channel Wiener systems that are excited by a common input signal. The proposed approach is based on a well-known blind identification technique for linear SIMO systems. By transforming the output signals into a reproducing kernel Hilbert space (RKHS), a linear identification problem is obtained, which we propose to solve through an iterative procedure that alternates between canonical correlation analysis (CCA) to estimate the linear parts, and kernel canonical correlation (KCCA) to estimate the memoryless nonlinearities. The proposed algorithm is able to operate on systems with as few as two output channels, on relatively small data sets and on colored signals. Simulations are included to demonstrate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

This paper addresses the independent component analysis (ICA) of quaternion random vectors. In particular, we focus on the Gaussian case and therefore only consider the quaternion second-order statistics (SOS), which are given by the covariance matrix and three complementary covariance matrices. First, we derive the necessary and sufficient conditions for the identifiability of the quaternion ICA model, which are based on the definition of the properness profile of a quaternion random variable and more specifically on the concept of rotationally equivalent properness profiles. Second, we show that the maximum-likelihood (ML) approach to the quaternion ICA problem reduces to the approximated joint diagonalization (AJD) of the sample-mean estimates of the covariance and complementary covariance matrices. Unlike the complex case, these four matrices cannot be simultaneously diagonalized in general, and we have to resort to a particular AJD algorithm. The proposed technique, which can be seen as a quasi-Newton method, is based on the local approximation of the nonconvex ML-ICA cost function (a measure of the entropy loss due to the residual correlation among the estimated quaternion sources), and it provides a satisfactory solution of the quaternion ICA model. The performance of the proposed quaternion ML-ICA algorithm, as well as its relationship to the identifiability conditions, are illustrated by means of several numerical examples. [ABSTRACT FROM PUBLISHER]