Abstract
The development of the theory of adaptive arrays (AAs) is proposed based on the representation of the inverse covariance matrix (CM) of a noise in the AA channels as a finite power series expansion using the direct CM and by representation of a weight vector of the AA as a finite series expansion of the power vectors. The dimension of the power CM basis is equal to the power of the minimum polynomial of the CM. In the case when the number of external interference sources is less than the number of AA channels, such polynomials have the same fundamental role as the characteristic polynomial of the CM in an opposite case. Proofs for the existence of the above mentioned polynomials of the CM are given. A new method for the calculation of the polynomial coefficients is presented, and the physical properties of the power vector basis are studied. It is shown that the power vectors are correlated and that there are two stages of AA signal processing.
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