Determining Autocorrelation Matrix Size and Sampling Frequency for MUSIC Algorithm

• Published in: IEEE signal processing letters Vol. 22; no. 8; pp. 1016 - 1020
• Main Authors: Naha, Arunava, Samanta, Anik Kumar, Routray, Aurobinda, Deb, Alok Kanti
• Format: Journal Article
• Language: English
• Published: IEEE 01.08.2015
• Subjects: Algorithms; Autocorrelation; Autocorrelation matrix; closely spaced sinusoids; Correlation; detectability; Distortion; Eigenvalues and eigenfunctions; Exact solutions; Lobes; Mathematical analysis; matrix perturbation; Multiple signal classification; music; Noise; Sampling; Signal processing; Signal processing algorithms; Signal resolution; subspaces; Symmetric matrices
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2014.2366638

Detectability of closely spaced sinusoids in a noisy signal using MUltiple SIgnal Classifier (MUSIC) depends to a great extent on the sampling frequency (F s ) and the size of the autocorrelation matrix (N). Improper choice of any of these may result in increased computational burden and/or unresolved frequency components. This paper presents an analytical approach to determine expressions of lobe width using F s and N at lobe base (Δf b ) and half of the lobe height (Δf h ). The required values of F s and N can be derived from the expression of Δf b for distortion-less lobe heights of two closely spaced sinusoids. A tighter bound can be found using the expression of only Δf h to resolve two distinct peaks. Probability of resolution using reciprocal of MUSIC peaks is determined for various N and it's limit for full resolvability was verified with the derived analytical expressions.