Performance Enhancement of the Measure-transformed Music Algorithm via Mse Based Optimization

The measure-transformed (MT) MUltiple SIgnal Classification (MUSIC) algorithm is a robust MUSIC generalization that operates by applying a transform to the probability measure (distribution) of the data. In this paper, we first provide an asymptotic mean-squared-error (MSE) performance analysis of the MT-MUSIC algorithm. Under some mild assumptions, we show that the MT-MUSIC estimator is asymptotically normal and unbiased, and obtain an analytic expression for the asymptotic MSE matrix. We then proceed to develop a strongly consistent estimator for the asymptotic MSE matrix that is constructed from the same data samples being used for implementation of the MT-MUSIC. This paves the way for development of a data-driven procedure for optimal selection of the measure transformation parameters that minimizes an empirical estimate of the asymptotic average root MSE (RMSE). Simulation examples illustrate the performance advantage of the proposed MSE based optimization of the MT-MUSIC.