Gridless Quadrature Compressive Sampling with Interpolated Array Technique

TL;DR

This paper introduces a novel gridless quadrature compressive sampling method that accurately reconstructs continuous delay parameters in radar signals by decoupling delay and gain estimation, using an interpolated array technique.

Contribution

It proposes a gridless reconstruction approach for continuous delay parameters in QuadCS, utilizing a beamspace DOA formulation and an interpolated array for improved accuracy.

Findings

Superior reconstruction accuracy demonstrated in simulations

Effective decoupling of delay and gain estimation

Conditions established for successful delay estimation

Abstract

Quadrature compressive sampling (QuadCS) is a sub-Nyquist sampling scheme for acquiring in-phase and quadrature (I/Q) components in radar. In this scheme, the received intermediate frequency (IF) signals are expressed as a linear combination of time-delayed and scaled replicas of the transmitted waveforms. For sparse IF signals on discrete grids of time-delay space, the QuadCS can efficiently reconstruct the I/Q components from sub-Nyquist samples. In practice, the signals are characterized by a set of unknown time-delay parameters in a continuous space. Then conventional sparse signal reconstruction will deteriorate the QuadCS reconstruction performance. This paper focuses on the reconstruction of the I/Q components with continuous delay parameters. A parametric spectrum-matched dictionary is defined, which sparsely describes the IF signals in the frequency domain by delay parameters and gain coefficients, and the QuadCS system is reexamined under the new dictionary. With the inherent structure of the QuadCS system, it is found that the estimation of delay parameters can be decoupled from that of sparse gain coefficients, yielding a beamspace direction-of-arrival (DOA) estimation formulation with a time-varying beamforming matrix. Then an interpolated beamspace DOA method is developed to perform the DOA estimation. An optimal interpolated array is established and sufficient conditions to guarantee the successful estimation of the delay parameters are derived. With the estimated delays, the gain coefficients can be conveniently determined by solving a linear least-squares problem. Extensive simulations demonstrate the superior performance of the proposed algorithm in reconstructing the sparse signals with continuous delay parameters.