Conference Proceeding

# Multiantenna spectrum sensing: Detection of spatial correlation among time-series with unknown spectra.

Commun. Eng. Dept., Univ. of Cantabria, Santander, Spain

Acoustics, Speech, and Signal Processing, 1988. ICASSP-88., 1988 International Conference on (Impact Factor: 4.63). 01/2010; DOI:10.1109/ICASSP.2010.5496151 In proceeding of: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010, 14-19 March 2010, Sheraton Dallas Hotel, Dallas, Texas, USA Source: IEEE Xplore

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**ABSTRACT:**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.IEEE Transactions on Signal Processing 11/2010; · 2.81 Impact Factor - [show abstract] [hide abstract]

**ABSTRACT:**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.IEEE Transactions on Signal Processing 09/2011; · 2.81 Impact Factor

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