Soft-thresholding for spectrum sensing with coprime samplers

Coprime Sampling has been recently proposed to efficiently estimate the spectrum of wideband signals, using sampling rates which can be significantly lower than the Nyquist rate. While the method has been shown to work well when large number of samples are available for estimating the autocorrelation, the effect of fewer samples on the performance of coprime spectrum estimation has not been addressed so far. This paper addresses this issue by employing a denoising scheme on the spectral estimates, as a l₁ norm penalized quadratic program. The solution to this problem results in the so-called soft thresholding operator on the spectral estimates, which inherently promotes sparsity. It also helps to combat the effect of spurious peaks resulting from the finite sample averaging. The probabilities of detecting active and inactive bands are also explicitly characterized and they converge to unity by increasing the number (L) of sub Nyquist samples available to compute the estimates. The effectiveness of the proposed method is demonstrated through numerical examples.