Quadrature Compressive Sampling for Multiband Radar Echo Signals

Abstract

In multiband/multifunction radars, the received echoes are usually multiband signals consisting of several subbands with different carrier frequencies. Digital acquisition of the in-phase and quadrature ( ${I}$ and ${Q}$ ) components of each subband is important for the extraction of radar targets. However, the existing acquisition methods are inefficient because their sampling rates are at least twice of the effective bandwidth, also known as the Landau rate. In this paper, we merge the quadrature compressive sampling into the uniform sampling technique for multiband signals, and develop a multiband quadrature compressive sampling (MQuadCS) system. The MQuadCS system first applies the random modulation to generate a compressive multiband signal, and then utilizes the uniform sampling to output the samples of the compressive multiband signal at its Landau rate. As the Landau rate of the compressive multiband signal is much less than that of the received echo, the MQuadCS achieves the sub-Landau rate sampling. With the assumption of sparse targets, the $I$ and $Q$ components of each subband can be independently recovered by the corresponding samples separated from the compressive multiband samples. For the independent recovery, we establish the model of MQuadCS system parameters and provide a sufficient condition to ensure the existence of the system parameters. To guarantee successful recovery of each subband, we introduce the frequency domain representation of the MQuadCS and then derive the reconstructability condition via restricted isometry property analysis. Furthermore, we design a system parameter optimization scheme to improve the recovery performance. Theoretical analyses and simulations validate the efficiency of the MQuadCS system.