Adaptive detection in subspaces

Considers subspace based adaptive detection in the context of the likelihood ratio test studied by Kelly (1986). The probability of false alarm for this test depends only on the subspace dimension while the probability of detection is a function of the subspace. The authors propose choosing the transformation onto the subspace to maximize the probability of detection over a likely class of noise and interference scenarios. An approximate solution to this optimization problem is described. The approach can lead to dramatic increases in the probability of detection given a fixed number of data observations due to a large gain in the statistical stability associated with the reduced dimension subspace. The relationship between subspace design for adaptive detection and partially adaptive beamformer design is explored. Simulations verify the analysis.<>