Performance analysis of G-MUSIC based DOA estimator with random linear array : A single source case

We analyze the performance of direction-of-arrival (DOA) estimation based on the G-MUSIC algorithm for a single source using a random linear array, i.e., only a random subset of sensor array is in operation. The classical asymptotic analysis assumes that the number of snapshots tends to infinity whereas the number of sensors remains fixed. In contrast, this work studies the scenario where both quantities tend to infinity at the same rate. This general asymptotic regime provides a more accurate description of the practical situation where these two quantities are finite and comparable. We prove the consistency of the DOA estimator and derive an analytic expression for the mean square error (MSE) performance in the general asymptotic situation. The asymptotic MSE turns out to be a function of signal-to-noise ratio, probability of operating sensors and ratio of number of sensors to number of snapshots. Numerical results are presented to confirm the effectiveness of our theoretical calculations.