Determining Autocorrelation Matrix Size and Sampling Frequency for MUSIC Algorithm

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.