The Improved-Sparsity Adaptive Matching Pursuit Algorithm for Pulse-Position-Modulation ADC Architecture

The emergency of compressed sensing breaks the bottleneck of traditional Nyquist theory and results in various sub-Nyquist sampling architectures. As a representative, the random pulse-position-modulation analog-to-digital converter (PPM ADC) combines compressed sensing techniques with time-domain signal processing to effectively leverage the power efficiency. For this frame, period random sampling reconstruction (PRSreco) algorithm is originally used to recover signal from sub-Nyquist samples. While PRSreco is restricted with the necessity of signal's prior sparsity information and has an unsatisfactory performance in low sub-sampling ratio. So we adopt sparsity adaptive matching pursuit (SAMP) algorithm to PPM ADC, which releases the condition of signals sparsity. What's more, we propose improved-SAMP by adding a denoising module to SAMP. The denoising module is based on the first significant jump point theory and eliminates the fake detected support set. Through numbers of simulations and discussions, we demonstrate that improved-SAMP augments the output SNR over whole sub-sampling ratio compared with PRSreco. Under noisy condition, improved-SAMP obtains the largest output SNR and corresponds to the least compression ratio satisfying a successful recovery.