Determining Autocorrelation Matrix Size and Sampling Frequency for MUSIC Algorithm

Abstract

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 ( $\Delta {f_b}$ ) and half of the lobe height ( $\Delta {f_h}$ ). The required values of ${F_s}$ and $N$ can be derived from the expression of $\Delta {f_b}$ for distortion-less lobe heights of two closely spaced sinusoids. A tighter bound can be found using the expression of only $\Delta {f_h}$ 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.