On the Sample Complexity of Multichannel Frequency Estimation via Convex Optimization
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The use of multichannel data in estimating a set of frequencies is common for improving the estimation accuracy in array processing, structural health monitoring, wireless communications, and more. Recently proposed atomic norm methods have attracted considerable attention due to their provable superiority in accuracy, flexibility and robustness compared with conventional approaches. In this paper, we analyze atomic norm minimization for multichannel frequency estimation from noiseless compressive data, showing that the sample size per channel required for exact frequency estimation decreases with the increase of the number of channels under mild conditions. In particular, given L channels, order K K (1+1/L N) samples per channel, selected randomly from N equispaced samples, suffice to guarantee with high probability exact estimation of K normalized frequencies that are mutually separated by at least 4/N. Numerical results are provided corroborating our analysis.
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