Passive detection of rank-one Gaussian signals for known channel subspaces and arbitrary noise

This paper addresses the passive detection of a common signal in two multi-sensor arrays. For this problem, we derive a detector based on likelihood theory for the case of one-antenna transmitters, independent Gaussian noises with arbitrary spatial structure, Gaussian signals, and known channel subspaces. The detector uses a likelihood ratio where all but one of the unknown parameters are replaced by their maximum likelihood (ML) estimates. The ML estimation of the remaining parameter requires a numerical search, and it is therefore estimated using a sample-based estimator. The performance of the proposed detector is illustrated by means of Monte Carlo simulations and compared with that of the detector for unknown channels, showing the advantage of this knowledge.