Gap detector for multipath

In a multipath communication channel, the optimal receiver is matched to the maximum likelihood (ML) estimate of the multipath signal. In general, this leads to a computationally intensive multi-dimensional nonlinear optimisation problem. We develop a detection algorithm that avoids the ML estimation while still achieving good performance. Our approach is based on a geometric interpretation of the problem. The ML estimate of the multipath signal is the orthogonal projection of the received signal on a suitable signal subspace S. We design a second subspace G, the representation subspace, that is close to S, but whose orthogonal projection is easily computed. The "closeness" is measured by the gap metric. The subspace G is designed by using wavelet multiresolution analysis tools coupled with a reshaping algorithm in the Zak transform domain. We show an example where our approach significantly outperforms the correlator receiver and an alternative suboptimal approach.