Regularized estimate of the weight vector of an adaptive antenna array

We consider an adaptive antenna array (AAA) with the maximum signal-to-noise ratio (SNR) at the output. The antenna configuration is assumed to be arbitrary. A rigorous analytical solution for the optimal weight vector of the AAA is obtained if the input process is defined by the noise correlation matrix and the useful-signal vector. On the basis of this solution, the regularized estimate of the weight vector is derived by using a limited number of input noise samples, which can be either greater or smaller than the number of array elements. Computer simulation results of adaptive signal processing indicate small losses in the SNR compared with the optimal SNR value. It is shown that the computing complexity of the proposed estimate is proportional to the number of noise samples, the number of external noise sources, and the squared number of array elements.