Error rates in pulse position coding

An expression for the error rate in a system using a binary pulse position code is derived. In the system considered, the pulses amplitude modulate a carrier and the resultant signal is contaminated by additive Gaussian noise. At the receiver the pulses are recovered by an envelope detector. If synchronization errors and post-detection filtering are neglected, it is shown that the probability of a binary error is approximated well by , where is the peak input signal-to-noise power ratio. Finally, the error rate is derived for the case where the signal amplitude is subject to random fading. Some comparisons are made with error rates derived by Montgomery for other systems with and without carrier fading. It is found that when the signal is subject to fading the pulse position system is better than a comparable system using threshold detection.