Bit error rate of TH-BPSK UWB receivers in multiuser interference

It is well known that the Gaussian distribution is not an accurate model for approximating the probability density function (PDF) of the multiple access interference (MAI) in time-hopping UWB (TH-UWB) systems. An exact theoretical model which explains the key features of the PDF of the MAI in TH-UWB systems is discussed. These features, which can be precisely anticipated by the proposed model include impulses, singularities, and the tail behaviour in the distribution of the MAI. The model reveals in quantitative terms why a Gaussian approximation for the MAI in TH-UWB systems is highly imprecise even in an environment with a large number of independent interferers. Based on the model obtained for the PDF of the MAI and exploiting the maximum a posteriori (MAP) receiver design rule, the optimal attainable BER performance of binary TH-UWB receivers in additive white Gaussian noise channels is numerically determined. The performances of some recently proposed UWB receivers are benchmarked against the optimal performance showing that some of them achieve near-optimal performance.