Collision model for performance analysis of coded transmission in time hopping impulse radio over multipath nakagami-m channels

Time hopping is the strategy employed in impulse radio systems to increase the communication reliability by spreading the multiple access interference (MAI) over numerous time intervals. This results in a non-stationary interference that makes the error probability performance to be dominated by the worst-case. In this paper we employ a collision model analysis for this time-varying interference that is ruled by the system loading in term of the corresponding MAI collision probability. The model proves to be simple and accurate to characterize the decision variable conditioned to the collision events. This provides a reliable framework for evaluating the error probability in multipath faded channels with RAKE receiver either for coded and uncoded systems. In this paper we derive closed form approximations of the bit-error-rate for multipath channels with exponential power delay profile and Nakagami-m fading. Validations by numerical analysis show that the collision model provides an accurate framework to evaluate also performance of realistic channel models.