Detection of multipath random signals by multiresolution subspace design

In our earlier work [1, 2], we developed a robust detector for multipath constrained environments when the transmitted signal is known. In this paper, we extend these results to the case where the transmitted signal is a random process. The approach in [1, 2] is to replace the orthogonal projection on the multipath signal subspace S by the orthogonal projection on a representation subspace G, such that G and S are close in the gap metric sense. When the signal is random, S is no longer a linear subspace but a set with a given structure. The gap metric applies only when S and G are subspaces. In this paper, we introduce the modied de ection as the appropriate measure to be used in the random signal case. We design the representation subspace G to match the multipath signal set S in the modi ed de ection sense. Wavelet multiresolution tools are used to facilitate the design.