Block sparse representation and suppression of narrow-band interference signals for quadrature compressive sampling radar

The suppression of narrow-band interference (NBI) has received wide attention with Nyquist-sampling data. However, the developed techniques cannot be directly integrated into sub-Nyquist radar systems. In this paper, we study the NBI suppression for quadrature compressive sampling (QuadCS) radar having sub-Nyquist sampling rate. With slow time-varying property of the NBI envelope, we first define a short-time sinusoidal (STS) dictionary to represent the NBI signals and reveal that QuadCS NBI signals are not only sparse but also block sparse. Then we find that for sparse targets, QuadCS radar outputs a combined sparse signal consisting of sparse targets and block sparse NBI signals. Considering this structure and inherent property of the NBI signals, we finally develop a sparse reconstruction method for estimating both the target signals and the NBI signals. The proposed method is a cascade of the block sparse reconstruction and the sparse reconstruction with data-driven stopping conditions and therefore, it works without any a priori information on the sparsity and noise level. Computer simulations show that the STS dictionary approximates the NBI signals well and the cascade reconstruction derives high accurate estimation of the target signals with strong suppression of the NBI signals.