Double-Sparsity Recovery for ADC-Distorted Compressive Sensing

In practical compressive sensing (CS) communication system, Analog to Digital Converter (ADC) is a necessary component to convert analog signals into digital ones. However, nonlinear distortion in ADC is unavoidable and definitely affects the reception accuracy. Though recent works have studied various methods to combat the negative effect of ADC nonlinear distortion, few of them discuss the solution in communication system with CS. This paper studies the CS recovery method when compressive measurements suffer from ADC nonlinear distortion. A double-sparsity model is first formulated, where the original signal and the ADC nonlinear distortion are both sparse. Then, for the type of clipping ADC, we propose a corresponding algorithm based on the Alternating Direction Method of Multipliers (ADMM) strategy to solve the double-sparsity (DS) problem, named as DS-ADMM. For the type of self-reset (SR) ADC, we explore its essence of rounding operation to design an integer constraint based feedback updating (ICFU) strategy, and accordingly propose the DS-ADMM-ICFU recovery algorithm. Experiment results show that the DS-ADMM algorithm for the double-sparsity problem improves the recovery performance compared with the existing counterpart, and DS-ADMM-ICFU for SR ADC exhibits preferable advantage in typical communication systems.