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 /spl Sscr/ by the orthogonal projection on a representation subspace /spl Gscr/, such that /spl Gscr/ and /spl Sscr/ are close in the gap metric sense. When the signal is random, /spl Sscr/ is no longer a linear subspace but a set with a given structure. The gap metric applies only when /spl Sscr/ and /spl Gscr/ 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 /spl Gscr/ to match the multipath signal set /spl Sscr/ in the modified deflection sense. Wavelet multiresolution tools are used to facilitate the design.