Two methods for estimating the weight vector of an adaptive antenna array (AAA) when receiving a signal against the background of external noise sources are proposed. Rigorous analytical solutions are derived for the regular weight vector in the basis of power vectors. On the basis of these solutions, regularized weighting vector estimates are found. The methods are applicable for a short sample of noise, when the noise correlation matrix is singular. The computational complexity of these methods is proportional to the number of noise samples, the number of external noise sources and the number of AAA elements.
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