Optimum space-time processing for semi-stationary signals in spatially correlated noise

The problem of optimum space-time processing for multiple Gaussian source signals transmitted through a slowly-varying linear channel and monitored with a passive array of sensors in the presence of spatially correlated noise is addressed. To solve this problem, a new class of linear systems (LS), referred to as semistationary, is introduced. These LS are characterized by time-frequency representations whose variations in time occur over intervals much larger than the corresponding system correlation time. The general conditions under which semistationary LS can be used in array processing are investigated and shown to be satisfied in many applications. By modeling the slowly varying linear channel as a semistationary LS and using the factorization properties of the optimum processor, closed form expressions are obtained for the log-likelihood function of the array output and for the associated Cramer-Rao lower bound on estimator variance