Shiftable representations and multipath processing

In multipath communications environments, the received signal is a superposition of delayed, possibly frequency shifted, and scaled replicas of a base signal s(t). For a known signal s(t), the optimal receiver is matched to the multipath signal s_M(t). In general, this requires the determination of the unknown parameters, a multidimensional optimization problem usually out of reach for most applications. By adapting the notion of shiftability to the multipath problem, the matched filter is found by inner products which are easier to implement than a multidimensional optimization. The paper introduces the concept of nearly shiftable and describes an explicit construction for designing increasingly nearly shiftable signals and demonstrating the improvement obtained in the context of the multipath problem