The performance of MUSIC in white noise with limited samples and missing data

The Multiple Signal Classification (MUSIC) algorithm is widely used to estimate the direction of arrival (DOA) of signals impinging on a sensor array. In this work, we analyze the performance of the MUSIC algorithm in the presence of white noise, and when only a random, sample independent subset of the entries in the data matrix are observed, in both the sample rich and deficient regimes. We derive a simple, closed form expression for the mean-squared-error (MSE) performance of MUSIC for a single source system, in the asymptotic regime and validate our analysis with simulations.