Impact of Number of Noise Eigenvectors Used on the Resolution Probability of MUSIC

The MUltiple SIgnal Classification (MUSIC) algorithm is a well-known eigenanalysis technique and has been studied extensively. The algorithm relies on accurate partitioning of the eigenvectors of the spatial correlation matrix between the signal (i.e., signal subspace) and noise eigenvectors (i.e., noise subspace). In this paper, we present a novel statistical framework for analyzing the resolution performance of the MUSIC algorithm in resolving closely spaced sources. The statistical framework is based on the first-order approximation of the perturbations in the noise subspace eigenvectors. Using this framework, we derive an analytical expression for the probability of resolution of the MUSIC algorithm according to the number of noise eigenvectors used in the spectrum computation. Such an investigation cannot be carried out with the existing probability of resolution expressions of the MUSIC algorithm. Using the analytical tools presented in this paper, it is possible to predict the resolution performance with respect to many important system parameters, i.e., signal-to-noise ratio (SNR), the number of samples, and the number of noise eigenvectors. For example, we found that the resolution threshold in terms of SNR is independent of the number of noise eigenvectors used. The simulation results are presented to verify the accuracy of the analytical expressions. More importantly, real radio-frequency experiments with a 24-GHz radar platform are carried out to demonstrate the resolution performance of MUSIC to support our findings in practical settings.