Broad-band DOA estimation and beamforming in multipath environment

It is shown that the effective dimension of the signal subspace collapses in the presence of multipath and may be recovered with subarray averaging. The F-norm (Frobenius norm) of the cross-correlation matrix is proposed as a measure of the correlation between the impinging signals, and an upper bound on this norm, which depicts all the essential features of the true F-norm, is derived. Using this bound, how the correlation between the direct and multipath signals falls with progressive smoothing and how the rate is which it falls depends on the spacing and directions of the sources are studied. Computer simulations are provided to support theoretical predictions. To keep the notation and the analysis simple, the analysis was restricted to two-source models; however, the results extend to signal models with more than two sources