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This paper presents a closed-form expression for the signal to noise ratio (SNR) of a pulse position modulated (PPM) signal in an ultra-wideband (UWB) channel with multiple transmit and receive antennas. We consider a generalized fading channel model that can capture the cluster property and the highly dense multipath effect. Through simulations, we demonstrate that the derived analytical model can accurately estimate the PPM signals of the UWB system in such a frequency selective fading channel. Furthermore, we investigate to what extend the performance of the PPM based UWB system can be further enhanced by exploiting the advantage of the multiple antenna systems. Our results show that the synergy of combining the time-switched transmit diversity (TSTD) scheme with a template-based detection can be further exploited to improve the UWB system performance.