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High Resolution
Beamforming for Closely
Spaced, Highly Correlated
Sources: The delta-MUSIC

Randy K. Howell and R. L. Kirlin
Department of Electrical and Computer Engineering
University of Victoria
Victoria, B. C., Canada, V8W 3P6
email: howell@sirius.uvic.ca, kirlin@ece.uvic.ca

High resolution algorithms such as MUSIC were crafted for the special problem of resolving the bearing of closely spaced sources. As with all such algorithms, there is a resolution threshold below which the sources within a cluster are too closely spaced to be resolved. In addition to this problem, the sources may be unresolvable if they are highly correlated. Combined, these two problems present a serious obstacle to high resolution beamforming.

This presentation introduces the delta-MUSIC or derivative-MUSIC algorithm, which may be considered to be a simple adaptation of the standard MUSIC algorithm, with the difference that it not only utilizes the signal space information of the correlation matrix R, but its spatial derivative R' as well. It will be demonstrated that the signal space information contained in both R and R' can be expressed in terms of a common vector set. Hence, the signal space information of both matrices may be utilized to resolve the sources. As the difference pattern in sum/difference beamforming is closely related to the spatial derivative of a beamformer response, the delta-MUSIC method may be considered an example of a high resolution sum/difference beamformer. To the best of the authors' knowledge, this is the first known example of such a beamformer.

Not only does the proposed algorithm have a resolution threshold far superior to that of the standard MUSIC algorithm, it is also relatively insensitive to the problem of source correlation, with very little change in performance occurring even if the sources are fully coherent. Such a method would be ideal for multipath problems which suffer from a high degree of correlation between the direct and reflected signals. A full discussion of the algorithm is presented along with a number of test results.



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