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Detection of Rank $P$ Signals in Cognitive Radio Networks With Uncalibrated Multiple Antennas

Detection of Rank $P$ Signals in Cognitive Radio Networks With Uncalibrated Multiple Antennas,10.1109/TSP.2011.2146779,IEEE Transactions on Signal Pro

Detection of Rank $P$ Signals in Cognitive Radio Networks With Uncalibrated Multiple Antennas  
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Spectrum sensing is a key component of the cognitive radio paradigm. Primary signals are typically detected with un- calibrated receivers at signal-to-noise ratios (SNRs) well below de- codability levels. Multiantenna detectors exploit spatial indepen- denceof receiverthermalnoiseto boostdetectionperformanceand robustness. We study the problem of detecting a Gaussian signal with rank- unknown spatial covariance matrix in spatially un- correlated Gaussian noise with unknown covariance using mul- tiple antennas. The generalized likelihood ratio test (GLRT) is de- rived 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 ordertoaccommodatecalibrationuncertaintiesinthedifferentan- tenna frontends. In the latter case, the GLRT statistic must be ob- tainednumerically,forwhichanefficientmethodispresented.Fur- thermore, 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 un- known temporal correlation in both signal and noise, as well as frequency-selective channels.
Journal: IEEE Transactions on Signal Processing - TSP , vol. 59, no. 8, pp. 3764-3774, 2011
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