Statistical analysis of “superresolving” methods for direction-of-arrival estimation of noise radiation sources under finite size of training sample

• We analyze the resolution-detection potentialities of noisy quasi-harmonic signals.
• We compare the resolution by statistical criteria of some “superresolving” methods.
• We perform statistical analysis of these methods’ resolution by Rayleigh criterion.
• Under finite sample size, resolution by any criterion is worse than asymptotic one.
• Real efficiency of “superresolving” methods could be opposite to the asymptotic one.

This paper addresses a detailed comparative study of operational performances of a family of the most prominent in the literature so-called “superresolution” methods for the estimation of spatial spectrum of Gaussian noise radiation sources impinging on an antenna array. Real-world operational scenarios are considered, in which small size samples are used for maximum likelihood estimation of the data correlation matrices. We perform an analysis of exact analytically derived and empirically evaluated distribution laws of random operational parameters that determine the resolution performances of the compared direction-of-arrival (DoA) superresolution estimation methods evaluated by statistical and non-statistical criteria. Our study reveals that in realistic scenarios with small size sample data these distribution laws may manifest a behavior significantly different from that theoretically predicted for asymptotic assumptions of “infinitely large” sample data recordings. The addressed detailed analysis of changes in behavior of such distribution laws provides the remedies for improvement of the convergence rates and robustness performances of the proposed modified superresolution procedures for feature-enhanced DoAs estimation of multiple noise radiation sources. The reported simulations corroborate the effectiveness of the proposed modified superresolution DoA estimation techniques.