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Multichannel frequency estimation with incomplete data and miscellaneousnoises arises in array signal processing, modal analysis, wirelesscommunications, and so on. In this paper, we consider maximum-likelihood(-like)optimization methods for frequency estimation in which proper objectivefunctions are adopted subject to observed data patterns and noise types. Wepropose a universal signal-domain approach to solve the optimization problemsby embedding the noiseless multichannel signal of interest into a series oflow-rank positive-semidefinite block matrices of Hankel and Toeplitzsubmatrices and formulating the original parameter-domain optimization problemsas equivalent structured matrix recovery problems. The alternating directionmethod of multipliers (ADMM) is applied to solve the resulting matrix recoveryproblems in which both subproblems of ADMM are solved in (nearly) closed form.The proposed approach is termed as structured matrix embedding and recovery(StruMER). Extensive numerical simulations are provided to demonstrate thatStruMER has improved threshold performances in various challenging scenarios,e.g., limited data, low signal-to-noise ratio, impulsive noise, and closelyspaced frequencies, as compared with state-of-the-art methods.

Multichannel Frequency Estimation in Challenging Scenarios via Structured Matrix Embedding and Recovery (StruMER)