Sparsity analysis of FH-BPSK signals via K-SVD dictionary learning

Compressed sensing provides a new method to meet the processing requirements of the ultra wideband, high frequency band, high data rate and high sampling rate of frequency hopping signals in the communication system of military satellites and TT&C. Moreover, sparsity is an important prerequisite for the application of compressed sensing. Firstly, this paper studies the sparsity of frequency hopping signals by sparse representation theory and algorithm which via compressed sensing. Then we establish Frequency hopping Binary Phase Shift Keying (FH-BPSK) modulation signal model. In addition, analyze the time-frequency characteristics of frequency hopping signals. Lastly, we build k iteration singular value decomposition (K-SVD) learning basis dictionary for the FH-BPSK signal according to the idea of dictionary learning. The simulation results show that the FH-BPSK signals have a strong sparsity in the learning basis dictionary. In addition, the learning basis dictionary has robustness to noise, which establishes the foundation for processing of frequency hopping signals via compressed sensing.