Statistical characterization of the MUSIC null spectrum

Statistical characterization of the MUSIC sample null spectrum is presented for an arbitrary number of (possibly) correlated emitters observed by a general array. A remarkably simple expression is developed for the spectral covariance matrix in the vicinity of the emitters. The covariance result together with prior mean spectral results support a Gaussian characterization in the neighborhood of the emitters for many scenarios. It is shown that the sample spectrum is exactly Wishart distributed in the emitter directions. The results can be utilized to quantify a variety of performance metrics. As an illustration, models based on physical parameters are constructed for the curve of probability of resolution versus signal-to-noise ratio. The models predict the curve with a high degree of accuracy for example scenarios.<
>