Compressive sampling based differential detection for UWB impulse radio signals

Noncoherent detectors significantly contribute to the practical realization of the ultra-wideband (UWB) impulse-radio (IR) concept, in that they allow avoiding channel estimation and provide highly efficient reception capabilities. Complexity can be reduced even further by resorting to an all-digital implementation, but Nyquist-rate sampling of the received signal is still required. The current paper addresses this issue by proposing a novel differential detection (DD) scheme, which exploits the compressive sampling (CS) framework to reduce the sampling rate much below the Nyquist-rate. The optimization problem is formulated to jointly recover the sparse received signal as well as the differentially encoded data symbols, and is compared with both the separate approach and the scheme using the compressed received signal directly, i.e., without reconstruction. Finally, a maximum a posteriori based detector using the compressed symbols is developed for a Laplacian distributed channel, as a reference to compare the performance of the proposed approaches. Simulation results show that the proposed joint CS-based DD brings the considerable advantage of reducing the sampling rate without degrading the performance, compared with the optimal MAP detector.