Analog compressed sensing for multiband signals with non-modulated Slepian basis

Abstract

Recently, the recovery performance of analog Compressed Sensing (CS) has been significantly improved by representing multiband signals with the modulated and merged Slepian basis (MM-Slepian dictionary), which avoids the frequency leakage effect of the Discrete Fourier Transform (DFT) basis. However, the MM-Slepian dictionary has a very large scale and corresponds to a large-scale measurement matrix, which leads to high recovery computational complexity. This paper resolves the above problem by modulating and band-limiting the multiband signal rather than modulating the Slepian basis. Specifically, instead of using the MM-Slepian dictionary to represent the whole multiband signal, we propose to use the non-modulated Slepian basis to represent the modulated and band-limited version of the multiband signal based on the recently proposed Modulated Wideband Converter (MWC). Furthermore, based on the analytical derivation with the non-modulated Slepian basis, we propose an Interpolation Recovery (IR) algorithm to take full advantage of the Slepian basis, whereas the Direct Recovery (DR) algorithm using the Moore-Penrose pseudo-inverse cannot achieve this. Simulation results verify that, with low recovery computational load, the non-modulated Slepian basis combined with the IR algorithm improves the recovery SNR by up to 35 dB compared with the DFT basis in noise-free environment.