A New Super-Resolution Technique for Direction (and Time) of Arrival Detection

A new technique for resolving different directions (or times) of arrival beyond the Rayleigh diffraction limit is presented. It is based on the Euclidean Algorithm for polynomial factorization and is implemented as a simple polynomial division (deconvolution) followed by a polynomial-root search. Similar to other super-resolution techniques, it reflects the exchangeability between bandwidth and signal-to-noise ratio governed by Shannon information-capacity concept. The core idea of the technique is borrowed from the error correction analysis of the Generalized Reed-Solomon codes used in channel coding. Both noiseless and noisy synthetic measurements of the output signals of a uniform linear antenna array are used for verifying the technique.

I. Introduction

For a long time, the term “resolution” was related to optics and, in particular, to the diffraction limitation described by Rayleigh criterion. Optical apertures with finite dimensions feature point-spread functions of finite extension. The relation between the aperture size and the extension of the related point-spread function is governed by the Heisenberg uncertainty principle featuring any Fourier transform pair. The same applies to observation time windows of finite duration and the related spectral purity as well as band limited spectral data and the related temporal resolution.