Parameter estimation of multiple frequency-hopping signals based on space-time-frequency analysis by atomic norm soft thresholding with missing observations

In this paper, we address the problem of multiple frequency-hopping (FH) signal parameters estimation in the presence of random missing observations. A space-time matrix with random missing observations is acquired by a uniform linear array (ULA). We exploit the inherent incomplete data processing capability of atomic norm soft thresholding (AST) to analyze the space-time matrix and complete the accurate estimation of the hopping time and frequency of the received FH signals. The hopping time is obtained by the sudden changes of the spatial information, which is implemented as the boundary to divide the time domain signal so that each segment of the signal is a superposition of time-invariant multiple components. Then, the frequency of multiple signal components can be estimated precisely by AST within each segment. After obtaining the above two parameters of the hopping time and the frequency of signals, the direction of arrival (DOA) can be directly calculated by them, and the network sorting can be realized. Results of simulation show that the proposed method is superior to the existing technology. Even when a large portion of data observations is missing, as the number of array elements increases, the proposed method still achieves acceptable accuracy of multi-FH signal parameters estimation.