Design of Sub-Nyquist Receiver for Sparse and Localized UWB Signals

Abstract

Commonly used Gaussian and Bernoulli distributed measurement matrices are sub-optimum for sparse and localized (SaL) signals. In this paper, we propose a measurement matrix design to enhance the sub-Nyquist rate-based receiver’s performance by exploiting the SaL characteristics of the received signal. The proposed measurement matrix exploits the covariance matrix structure of the underlying received signal and can be optimized off-line or adaptively. Effectiveness of the proposed measurement matrix is verified on ultra-wideband (UWB) signals, since the UWB signals are both sparse and localized. Proposed matrix yields approx 2 dB gain as compared to the conventional Gaussian random matrix for the UWB system over the standardized IEEE 802.15.4a multipath channel.