High-Accuracy Compressed Sensing Decoder Based on Adaptive $(\ell_{0},\ell_{1})$ Complex Approximate Message Passing: Cross-layer Design

Compressed sensing (CS) allows a signal that is sparse in certain domain to be acquired and reconstructed accurately with only a small number of samples. In this paper, we propose an adaptive (ℓ
₀
, ℓ
₁
) complex approximate message passing (CAMP) algorithm and its hardware implementation for complex-valued sparse signal recovery. Compared with the existing CAMP algorithm which solves ℓ
₁
-regularized least squares problems, our proposed algorithm adaptively switches between ℓ
₀
and ℓ
₁
-regularized least squares and therefore significantly outperforms the original CAMP. We implement the architecture in a medium-sized field-programmable gate array (FPGA) chip. For a sparse stepped frequency waveform radar application, we perform experiments on the simulated data and the data collected by a real radar system. According to the result, the decoder design achieves 7.2 dB improvement over the conventional CAMP architecture with less than 27.4% extra hardware cost.