Abstract
We consider the performance analysis of the multiple signal classification (MUSIC) algorithm for multiple incident signals when the uniform linear array (ULA) is adopted for estimation of the azimuth of each incident signal. We derive closed-form expression of the estimation error for each incident signal. After some approximations, we derive closed-form expression of the mean square error (MSE) for each incident signal. In the MUSIC algorithm, the eigenvectors of covariance matrix are used for calculation of the MUSIC spectrum. Our derivation is based on how the eigenvectors of the sample covariance matrix are related to those of the true covariance matrix. The main contribution of this paper is the reduction in computational complexity for the performance analysis of the MUSIC algorithm in comparison with the traditional Monte–Carlo simulation-based performance analysis. The validity of the derived expressions is shown using the numerical results. Future work includes an extension to performance analysis of the MUSIC algorithm for simultaneous estimation of the azimuth and the elevation.
Highlights
The multiple signal classification (MUSIC) algorithm [1] has been one of the most widely used direction-of-arrival (DOA) algorithms [2,3]
The ranging accuracy in terms of the mean square error can be obtained from (40) of this paper if the laser measurement noise can be modelled as an additive Gaussian noise
Based on some approximations and the Taylor series expansion, we have derived a few expressions of an approximation of estimate of the MUSIC algorithm
Summary
The multiple signal classification (MUSIC) algorithm [1] has been one of the most widely used direction-of-arrival (DOA) algorithms [2,3]. In this paper, the closed-form expression of the MSE of the azimuth estimate for the MUSIC DOA algorithm is presented. In this paper, the number of snapshots and the SNRs are explicitly taken into account in deriving the MSE in (40), implying that the empirical RMSEs for the MUSIC algorithm in Figures 4 and 5 of [19] can be analytically by taking the square root of the MSE value given by (40). If the MUSIC algorithm is used for the DOA estimation in the sound source experiment described in [20], the expression in Equation (40) of this paper can be employed to yield the performance of the MUSIC algorithm in terms of the MSE analytically, not empirically. The MSE of the estimated array design parameters can be evaluated by modification of the derivation leading to (40)
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