General performance analysis of TR UWB systems

A new analytical method for evaluating the bit error rate performance of a transmitted reference ultra-wide bandwidth system with an arbitrary front-end filter is derived. The method is based on expanding the received signal using the Karhunen-Loeve expansion and then evaluating the characteristic function of the receiver decision metric. This new method puts no restriction on the front-end filter type, is suitable for any arbitrary value of receiver time-bandwidth product and is highly accurate for evaluating bit error rates as small as 10^-9 in both additive white Gaussian noise and fading multipath channels. The method is also extended to the case of correlated message and reference noises. The results indicate that the effect of this cross-correlation is not negligible in evaluating the bit error rate. It is found that differences in the front-end filter can lead to significant differences in the system bit error rate.