Detection of multipath random signals by multiresolution subspace design

In our earlier work, 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 of Chaung He et al. (see ICASSP, p.V-2650-53, 1996 and IEEE Trans. Signal Processing, 1996) 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 modified deflection 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 modified deflection sense. Wavelet multiresolution tools are used to facilitate the design