Compressed sensing for bandwidth constrained systems

This paper considers compressed sensing (CS) of time varying signals with quantized innovations (QI). Recently, an MMSE optimal Kalman like particle filter (KLPF) for systems with QI was proposed in. We first present a low complexity sequential implementation of the KLPF algorithm for multiple observations, and then adapt the algorithm to the CS scenario. Three algorithms (SKLPF1, SKLPF2 and SKLPF3) are presented and their performance is compared to the full innovation Kalman filter CS (FIKFCS). The simulation results demonstrate that SKLPF1 and SKLPF2 achieve performance comparable to that of the FIKFCS even for the single-bit quantization scheme.