lp-Based complex approximate message passing with application to sparse stepped frequency radar

Compressed sensing exploits the sparsity of the signal to reduce the sampling rate while keeping the resolution fixed, and has been widely used. In this paper we propose a new algorithm called adaptive l(p)-CAMP and show its application in the sparse stepped frequency radar signal processing. Our algorithm is inspired by the complex approximate message passing algorithm (CAMP) that solves complex-valued LASSO. The following properties of the proposed algorithm make it superior to existing algorithms: (1) All the parameters of the algorithm are tuned dynamically and optimally. The algorithm does not require any information about the signal and is still capable of tuning the parameters as well as an oracle that has all the signal information. (2) Adaptive l(p)-CAMP is designed to solve the complex-valued l(p)-regularized least squares for 0 <= p <= 1. Hence, it can outperform CAMP. The performance of the proposed algorithm is verified by simulations and the data collected by a real radar system.