Wireless Sensor Networks: An Information Processing Approach
Wireless Sensor Networks: An Information Processing Approach
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Toeplitz and circulant matrices: a review
Communications and Information Theory
Cognitive Wireless Communication Networks
Cognitive Wireless Communication Networks
Majorization and matrix-monotone functions in wireless communications
Foundations and Trends in Communications and Information Theory
Eigenvalue-based spectrum sensing algorithms for cognitive radio
IEEE Transactions on Communications
Correlation matching approach for spectrum sensing in open spectrum communications
IEEE Transactions on Signal Processing
Canonical coordinates and the geometry of inference, rate, andcapacity
IEEE Transactions on Signal Processing
Equalization Techniques for Distributed Space-Time Block Codes With Amplify-and-Forward Relaying
IEEE Transactions on Signal Processing
Wiener filters in canonical coordinates for transform coding,filtering, and quantizing
IEEE Transactions on Signal Processing
A geometric approach to multiple-channel signal detection
IEEE Transactions on Signal Processing
Cooperative diversity in wireless networks: Efficient protocols and outage behavior
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Testing blind separability of complex Gaussian mixtures
Signal Processing
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This work addresses the problem of deciding whether a set of realizations of a vector-valued time series with unknown temporal correlation are spatially correlated or not. For wide sense stationary (WSS) Gaussian processes, this is a problem of deciding between two different power spectral density matrices, one of them diagonal. Specifically, we show that for arbitrary Gaussian processes (not necessarily WSS) the generalized likelihood ratio test (GLRT) is given by the quotient between the determinant of the sample space-time covariance matrix and the determinant of its block-diagonal version. Furthermore, for WSS processes, we present an asymptotic frequency-domain approximation of the GLRT which is given by a function of the Hadamard ratio (quotient between the determinant of a matrix and the product of the elements of the main diagonal) of the estimated power spectral density matrix. The Hadamard ratio is known to be the GLRT detector for vector-valued random variables and, therefore, what this paper shows is how frequency-dependent Hadamard ratios must be merged into a single test statistic when the vector-valued random variable is replaced by a vector-valued time series with temporal correlation. For bivariate time series, the derived frequency domain detector can be rewritten as a function of the well-known magnitude squared coherence (MSC) spectrum, which suggests a straightforward extension of the MSC spectrum to the general case of multivariate time series. Finally, the performance of the proposed method is illustrated by means of simulations.