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We propose a compressive sampling (CS) based MVDR spectrum estimator, which estimates the wideband spectrum from the compressed signals with sub-Nyquist-rate sampling. To analyze detection performance, we derive the statistics of the estimated CS MVDR spectrum considering finite samples. We also show that different compression matrices produce different levels of signal leakage and influence the computation of detection thresholds.
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Wang et al. (2010) studied this question.