Error Performance of Pulse Shape Modulation for UWB Communication with MRC and EGC RAKE Receivers

In this paper we propose an M-ary biorthogonal pulse shape modulation (BPSM) scheme for an impulse radio ultra wideband (IR-UWB) system transmitting over lognormal fading channels. Our proposed modulation scheme enables different transmission rates for a fixed number of orthogonal pulses M/2, while the symbol period T_s is constant. In our scheme information bits are mapped into N pulses (N symbols), using M/2 orthogonal pulses and their negates. The N generated pulses are superimposed to form one pulse that will be transmitted over the channel. The transmission rate provided by this scheme is N(log₂ M/N)/T_s, which is significantly higher than (log₂ M/N)/T_s provided by the conventional biorthogonal signaling. The RAKE receiver demodulates the N symbols. For the proposed modulation scheme we derive closed form expressions for symbol error probability, for both maximum ratio combining (MRC) and equal gain combining (EGC)-RAKE receivers, using Wilkinson´s method. Furthermore, we numerically evaluate performances of the proposed transceiver, assuming perfect and imperfect channel estimation at the receiver, and compare them with our analytical expressions.