IR-UWB binary communications for sources with nonequal probabilities

Recently discovered optimal transmit energy allocation for binary sources with unequal probabilities is found not to be directly applicable to impulse radio ultra wideband (IR-UWB) transmitters. Such transmitters have a pulse generator producing pulses with equal energy, preventing full range optimal energy allocation. The optimum number of such equal energy pulses to transmit for each binary symbol are therefore determined in this paper for such UWB systems. The results are constrained by the maximum number of pulses per symbol N-s so as to maintain a certain data rate R. Results are obtained for both the popular pulse position and bipolar pulse amplitude modulation schemes (PPM and BPAM). Vast improvements in performance over a conventional system with equal energy per symbol (regardless of the source probability) are found. The proposal is also seen to outperform a system employing optimal source coding and compression with equiprobably symbols. It is also found that the greater the number of allowed pulses N-s, the closer the system performance is to the optimal energy allocation case, however acceptable results are found when N-s = 50.