Invariant wideband spectrum sensing under unknown variances
IEEE Transactions on Wireless Communications
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We propose a computationally efficient algorithm for detection of multiple signals that also gives a rough estimation of their direction of arrivals (DOAs). The narrowband received signals from a uniform linear array are first filtered by a set of orthogonal filters, e.g., by a fast Fourier transformation, in order to separate the sources into multiple spatial intervals. This transformation converts the complicated multihypothesis problem of source detection and localization into multiple binary hypothesis testing problems. For an additive white Gaussian noise (AWGN) environment, the maximum-likelihood (ML) solution of these interrelated tests requires substantially less computational complexity than that of the multihypothesis problem. For each spatial interval, a binary test detects the presence of a single source and thus gives a rough localization. We employ generalized-likelihood ratio (GLR) tests as the detection criterion, assuming that the number of sources, their power, and the noise variance are all unknown. We also show that the optimal uniformly most powerful invariant (UMPI) detector does not exist. However, we derive a UMPI detector that uses some extra information and as a result provides an upper bound performance for evaluation of any invariant detector. Simulations illustrate that the proposed noniterative GLR test performs efficiently for various number of observed data snapshots and signal-to-noise-ratios (SNR)s, and its performance is comparable to the upper bound performance. We used the proposed algorithm for the initialization of the iterative implementation of the standard ML localization. This combination is a high-resolution localization algorithm with a low computational complexity