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In this paper we consider M-ary biorthogonal pulse shape modulation (BPSM) scheme, for an impulse radio ultra wideband (IR-UWB) system transmitting over lognormal fading channels. The receiver has RAKE structure which combines the signal energy scattered over several resolvable multipath components via maximum ratio combiner (MRC) or eual gain combiner (EGC). We derive closed form expressions for symbol error probability, for both MRC- and EGC-RAKE receivers, using Wilkinson's method (Cardieri and Rappaport, 2000). Furthermore, we examine the system performance with imperfect channel estimate, when (i) given the path delays, the receiver forms linear mean square error (LMMSE) estimate of fading coefficients, (ii) the receiver employs maximum likelihood (ML) estimator to find the path delays and fading coefficients. This performance examination enables us to find optimal number of training symbols that maximizes the system throughput via simulations. The numerical results are obtained using orthogonal waveforms of Prolate Spheroidal Wave Functions (PSWF).