Multi-sensor kernel design for time-frequency analysis of sparsely sampled nonstationary signals

In this paper, we examine the sparsity-based time-frequency signal representation (TFSR) of randomly thinned nonstationary signals in a multi-sensor platform to yield improved performance with reduced number of samples in each sensor. The property that different sensors share identical auto-term time-frequency regions renders the TFSR a group sparse reconstruction problem, which is effectively solved using the compressive sensing techniques for high-fidelity TFSR reconstruction. We exploit the adaptive optimal kernel (AOK) to effectively preserve signal auto-terms and mitigate cross-terms. High level of noise and artifacts due to missing samples, however, may render AOK ineffective if designed for each sensor separately. We develop a robust multi-sensor AOK design based on data fusion across all sensors so as to enhance the signal auto-terms while effectively mitigating artifacts, cross-terms, and noise. The superior performance of the proposed multi-sensor AOK design is demonstrated through the comparison with its single-antenna counterpart and data-independent kernels.

I. Introduction

A large class of nonstationary signals, particularly those characterized by their instantaneous frequencies (IFs), are often encountered in practice, including radar, sonar, communications and biomedical applications [1]–[6]. In particular, by exploiting multiple sensors, array processing of nonstationary signals finds broad applications, such as direction finding, source separation, jammer suppression, and source localization [7]–[14].