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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 Ts 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)/Ts, which is significantly higher than (log2 M/N)/Ts 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.