  Multichannel frequency estimation with incomplete data and miscellaneous
noises arises in array signal processing, modal analysis, wireless
communications, and so on. In this paper, we consider maximum-likelihood(-like)
optimization methods for frequency estimation in which proper objective
functions are adopted subject to observed data patterns and noise types. We
propose a universal signal-domain approach to solve the optimization problems
by embedding the noiseless multichannel signal of interest into a series of
low-rank positive-semidefinite block matrices of Hankel and Toeplitz
submatrices and formulating the original parameter-domain optimization problems
as equivalent structured matrix recovery problems. The alternating direction
method of multipliers (ADMM) is applied to solve the resulting matrix recovery
problems 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 that
StruMER has improved threshold performances in various challenging scenarios,
e.g., limited data, low signal-to-noise ratio, impulsive noise, and closely
spaced frequencies, as compared with state-of-the-art methods.
