Statistical Analysis of the MUSIC Algorithm in the Presence of Modeling Errors, Taking Into Account the Resolution Probability

This paper considers the statistical performance of the MUSIC method under the condition that two closely spaced sources impinging on an array of sensors are effectively resolved, i.e., the spectrum exhibits two peaks in the neighborhood of the true directions-of-arrival (DOA). The MUSIC algorithm is known to have an infinite resolution power in theory. However, in the presence of modeling errors, sources can not be resolved with certainty, even if the array correlation matrix is perfectly known. The focus of this paper is to predict the bias and variance of the DOA estimates taking into account the possible resolution failure of MUSIC. This performance prediction, based on our recent mathematical investigation, is new to the best of our knowledge. A general mathematical framework to derive closed form expressions of the bias and variance versus the model mismatch, conditioned on a general statistical resolution test is proposed. In order to illustrate our mathematical approach, statistical tests with one and two conditions, respectively, are investigated. The accuracy of the performance prediction is illustrated in a simulation study. It is found that the proposed approach outperforms the "classical" technique, which ignores the possible resolution failure of the MUSIC algorithm. Therefore, our results provide better tools for determining the necessary antenna calibration accuracy to achieve some targeted specifications on the estimator performance