The goal of this paper is to describe a simple receiver with good performance for multipath communications channels. The new receiver is 'almost' invariant or robust to the multipath channel distortion. It preserves the simplicity of a traditional receiver-correlator receiver and at the same time approximates the computational intensive subspace receiver which is maximally invariant. The maximally invariant test statistic is the energy of the orthogonal projection of the received signal on the multipath signal subspace S. Calculating this orthogonal projection directly is a difficult multi-dimensional nonlinear optimization problem. Instead, we design a representation subspace G to approximate S. The gap metric is used as the measure between subspaces. The gap metric is closely related to the principle angles between subspaces. Wavelet multiresolution tools are called upon to facilitate the subspace design. Once we have designed the representation subspace G, we use the energy of the orthogonal projection of the received signal on G as the new test statistic. Simulation results demonstrate the robustness of the new receiver.
Jose M. F. Moura,
"Robust detection via subspace design", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); doi: 10.1117/12.255239; https://doi.org/10.1117/12.255239