In many signal processing applications one must invert an estimated correlation matrix which can be ill-conditioned. Ill-conditioning arises in adaptive beamforming when the number of sensors in an array is greater than the number of point sources. Ill-conditioning amplifies estimation, arithmetic, and other system errors. It is well known in the numerical analysis literature, that singular value decomposition is the only reliable method for detection and correction of ill-conditioning. This paper shows how ill-conditioning arises in adaptive beam processing, derives optimum array weights in terms of generalized matrix inverse, and applies an eigenvalue preprocessor to correct the ill-conditioning. The eigenvalue preprocessor can be considered to be a beamformer that reduces the dimensionality of the array processing problem to the dimensions required to effectively process independent point sources.
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