Generalized Approximate Message Passing for Unlimited Sampling of Sparse Signals

Abstract: In this paper we consider the generalized approximate message passing (GAMP) algorithm for recovering a sparse signal from modulo samples of randomized projections of the unknown signal. The modulo samples are obtained by a self-reset (SR) analog to digital converter (ADC). Additionally, in contrast to previous work on SR ADC, we consider a scenario where the compressed sensing (CS) measurements (i.e., randomized projections) are sent through a communication channel, namely an additive white Gaussian noise (AWGN) channel before being quantized by a SR ADC. To show the effectiveness of the proposed approach, we conduct Monte-Carlo (MC) simulations for both noiseless and noisy case. The results show strong ability of the proposed algorithm to fight the nonlinearity of the SR ADC, as well as the possible additional distortion introduced by the AWGN channel.