Quantized Spectral Compressed Sensing: Cramer–Rao Bounds and Recovery Algorithms - 2018


Efficient estimation of wideband spectrum is of nice importance for applications like cognitive radio. Recently, sub-Nyquist sampling schemes based mostly on compressed sensing have been proposed to greatly scale back the sampling rate. But, the important issue of quantization has not been absolutely addressed, significantly, for prime resolution spectrum and parameter estimation. In this Project, we have a tendency to aim to recover spectrally sparse signals and also the corresponding parameters, such as frequency and amplitudes, from heavy quantizations of their noisy complex-valued random linear measurements, e.g., only the quadrant data. We have a tendency to initial characterize the Cramer-Rao certain beneath Gaussian noise, which highlights the trade-off between sample complexity and bit depth below completely different signal-to-noise ratios for a mounted budget of bits. Next, we propose a brand new algorithm based on atomic norm soft thresholding for signal recovery, which is akin to proximal mapping of properly designed surrogate signals with respect to the atomic norm that motivates spectral sparsity. The proposed algorithm can be applied to each the one measurement vector case, as well as the multiple measurement vector case. It is shown that below the Gaussian measurement model, the spectral signals will be reconstructed accurately with high chance, as the quantity of quantized measurements exceeds the order of K log n, where K is the level of spectral sparsity and n is that the signal dimension. Finally, numerical simulations are provided to validate the proposed approaches.

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