Probability of Resolution of G-MUSIC: An Asymptotic Approach

In this paper, the outlier production mechanism of the G-MUSIC Direction-of-Arrival estimation technique is investigated using tools from Random Matrix Theory. The G-MUSIC Direction-of-Arrival estimation technique is an improved version of the conventional MUSIC method that provides superior performance in low sample size scenarios. The stochastic behavior of the G-MUSIC cost function is analyzed in the asymptotic regime where both the number of snapshots and the number of antennas increase without bound at the same rate. The finite dimensional distribution of the G-MUSIC cost function is shown to be asymptotically jointly Gaussian. Furthermore, the probability of resolution of the G-MUSIC Direction-of-Arrival estimator is characterized by means of the derived asymptotic probability density function of the G-MUSIC cost function.