M.V. Ratynsky, A.A. Komov

When Capon algorithm uses true covariance matrix (CM) of array input signals, the heights of space spectrum (SS) signal peak and background are determined by signal and noise eigenvalues (EV) of CM correspondingly. If the algorithm uses sample CM under limited number K of training samples, the heights of SS peak and background decrease, and for K = N, where N is the number of antenna array elements, decrease amounts to 15-30 dB and more. The decrease on average is the same for peak and background if measured at logarithmic scale (peak and background decrease by the same factor). The decrease does not depend on antenna array configuration and grows slightly as N increases. The peak and background decrease analysis is carried out by digital simulation and analytically. In analytical estimation the published results on largest noise EV of sample CM distribution (Tracy-Widom distribution) and on signal and noise subspaces of sample CM perturbations have been utilized. It is proved that the background decrease is a consequence of the spread of noise EV of sample CM of array input signals, the spread is the greater the smaller is the volume of training sample data. The peak decrease is a consequence of the same noise EV spread in combination with nonorthogonality of hypothesis vector for desired signal source and CM noise eigenvectors, the nonorthogonality becomes greater as the volume of training sample data reduces.