Gold-MUSIC: A Variation on MUSIC to Accurately Determine Peaks of the Spectrum

Abstract

This paper presents a new way of accurately determining peaks of the MUSIC (“Multiple emitter location and signal parameter estimation,” R. O. Schmidt, IEEE Trans. Antennas and Propagation, vol. AP-34, no. 3, pp. 276-280, Mar. 1986) spectrum, here considered from the point of view of estimating the directions of arrival (DOAs) of narrowband signals. It can be used, with any smart antenna geometry and for any purpose where MUSIC is applicable. The MUSIC algorithm for DOA estimation evaluates the MUSIC spectrum for various angles and chooses the maxima or peaks as the angles of arrival. The values obtained depend on the interval at which the spectrum is evaluated. The coarser the interval, the less accurate are the results in case of MUSIC. To improve accuracy and not depend on the interval, Root-MUSIC (“Direction finding for diversely polarized signals using polynomial rooting,” A. J. Weiss and B. Friedlander, IEEE Trans. Signal Processing, vol. 41, no. 5, pp. 1893-1905, May 1993), which involves finding the roots of a polynomial, is available. However, Root-MUSIC is applicable, in its original form, only to uniform linear arrays (ULA). The gold-MUSIC algorithm proposed in this paper is a two-stage process. The first stage evaluates the objective function at coarse intervals and determines peaks followed by an iterative approach based on gold-section univariate (GSU) minimization (Algorithms for Minimization Without Derivatives, R. Brent, Englewood Cliffs, NJ, USA: Prentice-Hall, 1983) to find accurate values of the peaks. If the number of peaks found so far is equal to the number of estimated peaks, the algorithm stops with this first stage. The second stage is an iterative step for fine resolution using finer intervals around the peaks found so far for finding peaks that were missing in previous iterations. This paper, also presents a method, based on a partitioning algorithm for estimating the number of emitters. The performance of gold-MUSIC is described, including its advantages and comparison of time complexities for MUSIC, Root-MUSIC and gold-MUSIC. The proposed algorithm gives good results even when the number of snapshots is small. This gives it an additional computational advantage. It does not compromise on the resolving power of MUSIC.