A Physically Constrained Maximum-Likelihood Method for Snapshot-Deficient Adaptive Array Processing

This paper presents a physically constrained maximum-likelihood (PCML) method for spatial covariance matrix and power spectral density estimation as a reduced-rank adaptive array processing algorithm. The physical constraints of propagating energy imposed by the wave equation and the statistical nature of the snapshots are exploited to estimate the ldquotruerdquo maximum-likelihood covariance matrix that is full rank and physically realizable. The resultant matrix may then be used in adaptive processing for interference cancellation and improved power estimation in nonstationary environments where the amount of available data is limited. Minimum variance distortionless response (MVDR) power estimates are computed for a given environment at different levels of snapshot support using the PCML method and several other reduced-rank techniques. The MVDR power estimates from the PCML method are shown to have less bias and lower standard deviation at a given level of snapshot support than any of the other reduced-rank methods used. Furthermore, the estimated power spectral density from the PCML method is shown to offer better low-level source detection than the MVDR power estimates.