Optimal Pulse Shaping for Pulse Position Modulation UWB Systems with Sparsity-Driven Signal Detection

In this paper, we study the problem of optimal pulse shaping for pulse position modulation (PPM) ultra-wideband (UWB) systems with a recently proposed sparsity-driven signal detection method. This signal detection method offers superior performance over traditional matched filter based detection through the representation of additive white Gaussian noise (AWGN) and the UWB pulses via atoms from a Hadamard Walsh matrix and a pulse constellation dictionary, respectively. Recognizing the possibility to further improve the performance with sparsity-driven signal detection through shaping the UWB pulses to be dissimilar to AWGN, we formulate an optimal pulse shaping problem considering the Federal Communication Commission (FCC) emission mask. We also develop a relaxation method to approximate the objective function, and solve the relaxed problem with classical nonlinear programming. Design examples are given to show the resulting pulse shape, its dissimilarity to the channel noise, and its compliance with the mandatory FCC emission mask