Effect of spatial smoothing on the performance of MUSIC and the minimum-norm method

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Abstract
The effect of using a spatially smoothed forward-backward covariance matrix on the performance of MUSIC and the minimum-norm method for estimating the direction of arrival of plane waves in white noise using a uniformly spaced linear array (ULA) is analysed. In particular, asymptotic results for the mean squared error in the estimates of the signal zeros and the direction of arrival are derived. It is shown that in general for subspace methods a forward-backward smoothing approach is preferable to a forward smoothing approach. An important outcome of this analysis is that for MUSIC, the error in the signal zeros is shown to exhibit a different trend compared to the error in the DOA estimates and this leads to difficulty in interpreting the spatial spectrum. For instance, when smoothing is used, the peaks in the spatial spectrum become sharper, giving the impression of higher resolution, whereas in reality the estimates of the DOA may in fact have deteriorated compared with the ones obtained using minimal or no smoothing. With regard to the minimum-norm method, the errors in the signal zeros exhibit the same trend as the DOA estimates so that no such problem is created. As to the relative comparison of the methods, it is shown that proper spatial smoothing enables the performance of the minimum-norm method to be made comparable to MUSIC.

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