A General Sub-Nyquist Sampling System for Pulse Streams

Abstract

The recent finite rate of innovation (FRI) framework has shown that pulse streams can be sampled at the rate of innovation and recovered from a set of Fourier coefficients. However, due to the individual variation of the pulse frequency spectrum, previous FRI sampling systems vary owing to different pulse shapes. In this paper, we propose a general sub-Nyquist sampling and recovery method for pulse streams that is available for many kinds of pulses. The proposed scheme exploits the spread-spectrum technique from a random demodulator (RD), in which an analog mixing front end aliases the spectrum. Such a technique allows for recovery of an arbitrary pulse with the baseband of the frequency spectrum, which greatly improves the flexibility of the sampling system. But unlike the fast switching rate of the mixing signal in RD, the proposed method has a lower rate requirement and is simpler to implement in practice. To recover the unknown parameters of the pulse streams from the obtained aliased Fourier coefficients, we quantize the analog time axis with a fit number of uniform bins and propose a sparsity-based recovery algorithm. Finally, simulation results demonstrate the effectiveness and robustness of the proposed method.