Constrained estimates of multipath covariance

When multipath propagation occurs, the covariance among signals traveling along rays emanating from a common source is expected to be larger than the covariance between signals generated by independent sources. Several data adaptive constrained estimates of the covariance are derived by the author as bilinear forms and some simulations are presented. The ability of a bilinear form to distinguish a 0-dB (relative to uncorrelated noise) correlated arrival pair from a 0-dB independent source is studied using an expected narrowband cross-spectral matrix corresponding to a simulated acoustic field with a 32-element line array at Nyquist spacing. An adaptive set of filter vectors obtained from the classical minimum variance problem are found to minimize sidelobe interference to 2 dB above the background noise level at the cost of reduced peaks having an 18-dB output above the uncorrelated background