Theoretical performance prediction of the MUSIC algorithm

The expected value of the MUSIC `spectrum¿ is investigated for two situations. First we investigate the case when there are very few data samples available. The paper performs a second-order perturbation analysis, using the assumption that the data comes from a complex Gaussian distribution. The final expression which is obtained is shown to be very simple to compute, and gives very good agreement with results obtained by simulation. The paper also investigates the performance of the MUSIC algorithm when it is necessary to perform some pre-whitening. In practical situations, it is often necessary to estimate the background noise statistics from noise samples. The paper obtains analytic expressions for the expected value of the MUSIC spectrum under these conditions. Good agreement is obtained between the predicted spectra and results obtained by simulation.