Performance of a multi-hop UWB transmitted reference system using decode-and-forward relays

In this paper, end-to-end average bit error rate (ABER) of a multi-hop decode-and-forward relay system is evaluated using ultra-wideband transmitted reference (TR) receiver over a multi-path fading channel. Distribution of individual hop signal to noise ratio (SNR) is approximated by a log-normal distribution and corresponding ABER is evaluated by Gauss-Hermite Quadrature rule. These individual hop ABERs are then used to find the end-to-end ABER performance analytically which is faster than the simulation method available in the literatures. Performances of three variants of non-coherent TR receivers: simple transmitted reference, average transmitted reference and differential transmitted reference (DTR) receivers are compared assuming same total transmit power for a fixed end-to-end distance in line-of-sight (LOS) and non line-of-sight (NLOS) channel model. It is observed that the end-to-end ABER performance using DTR receivers is the best and multi-hop relaying is also most effective using these receivers to improve the performance. It is also found that the laws of diminishing returns hold for performance gain in average transmit SNR per bit at a particular ABER in LOS channel i.e. performance improvement in terms of transmit SNR is not equal as the number of hop increases. It decreases with increase in hop number but the reverse trend can be found in NLOS channel.