adaptive spatial filtering
evaluation of efficiency
limited volume of training sample data
perturbations of training sample data
perturbations of signal and noise subspaces of sample covariance matrix
The key indicator of adaptive spatial filtering system efficiency (and the one of a few, that can be evaluated experimentally) is the total power of outer jammers and inner antenna and receiver noise, being evaluated before and after adaptation. The result of the post adaptation power calculation turns out to be essentially dependent on what matrix of training samples (training packet) has been used for calculations – the same one from which the adaptive weight vector has been calculated (initial packet) or another one (independent packet).
It is proved that the difference depends on the spread of noise eigenvalues of sample covariance matrix (CM) of antenna array input signals. The spread does not depend on array configuration, but grows as the number N of array elements increases and as the ratio K/N decreases, where K is the number of training samples used for CM evaluation.
When calculated from independent packet the total power of jammers and noise (P2) corresponds to its real mean value, but the same power being calculated from initial packet (P1) result to be too small, thus the efficiency estimate result to be too great. The difference P2 – P1 for K = N may be as large as 20 to 30 dB and more, and no more than 1 dB for K/N 4.
For proper estimate of adaptive spatial filtering efficiency from residual total jammers and noise power to be obtained, the power either must be evaluated from independent packet, or when evaluated from initial packet the corresponding correction must be applied, evaluated for example by digital simulation.
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