In this paper, we address the problem of spectrum estimation of multiple frequency-hopping (FH) signals in the presence of random missing observations. The signals are analyzed within the bilinear time-frequency (TF) representation framework, where a TF kernel is designed by exploiting the inherent FH signal structures. The designed kernel permits effective suppression of cross-terms and artifacts due to missing observations while preserving the FH signal auto-terms. The kernelled results are represented in the instantaneous autocorrelation function domain, which are then processed using a re-designed structure-aware Bayesian compressive sensing algorithm to accurately estimate the FH signal TF spectrum. The proposed method achieves high-resolution FH signal spectrum estimation even when a large portion of data observations is missing. Simulation results verify the effectiveness of the proposed method and its superiority over existing techniques.
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