Parameter estimation of multiple frequency-hopping signals based on Bayesian compressive sensing and atomic norm soft thresholding with missing observations

In this study, the problem of estimating multiple frequency-hopping (FH) signal parameters in situations in which random observations are missing is addressed. A uniform linear array (ULA) is utilized to receive FH signals, and the missing observations are considered to be equivalent to randomly missing elements in the space-time matrix obtained from the ULA. Bayesian compressed sensing (BCS) estimates the hopping time of received FH signals by the spatial information from the space-time matrix and restores the missing observations. The estimated hopping time is implemented as the boundary to divide the signals such that each segment contains a superposition of time-invariant multiple components. Then, the instantaneous frequency (IF) of multiple components can be estimated precisely by atomic norm soft thresholding (AST) within each segment. After estimating the hopping time and IF, the direction of arrival (DOA) of multiple signals is directly calculated using these two parameters. The simulation results show that the proposed method is superior to existing approaches. Provided that sufficient array elements are available, multi-FH signal parameters can be estimated with satisfactory accuracy even when a large portion of observations is missing.