Compressed sensing-based FH-BPSK signals'digital domain compressive sampling and reconstruction

In order to effectively solve the problem of dealing pressure in ultra wideband, ultra high frequency, high bit rate, and high sampling rate of frequency hopping signal in military satellite communications and aerospace TT& C communication system, the present paper focuses on the study of the digital domain compressive sampling and reconstruction algorithm of frequency hopping signal by taking the basic principles and methods of compressed sensing. It first discusses the compressive sampling model, FH-BPSK (frequency hopping binary phase-shiftkeying) modulation signal model and its sparsity. Then, it focuses on the RIP (Restricted Isometry Property) and incoherent properties of measurement matrix in digital domain compressive sampling, as well as noise folding caused by compressive sampling. After that, it compares the reconstruction algorithm of FH-BPSK signals of compressive sampling and sparsity. It also discusses the reconstruction algorithm and its improvement of SL0 (Smoothed L0 Norm) and compares it with the classical OMP (Orthogonal Matching Pursuit) algorithm. Finally, the simulative experiments illustrate the performance and conclusion, exploring the relationship among the SNR (Signal to Noise Ratio), compression ratio, relative error and run time in the reconstruction of the FH-BPSK signal under certain conditions. The results show that provided the original information be retained, the digital sampling rate will drop significantly, providing new possibilities for subsequent compressed domain information processing.