The SNR Threshold in PPM Reception

The signal-to-noise-ratio (SNR) performance of a pulse-position-modulation (PPM) receiver is well understood when the input SNR exceeds the threshold, but below it the output SNR deteriorates on account of false pulses due to noise. The calculation of their effect, which determines the threshold, has been considered a difficult problem. However, the use of Rice´s 1948 result concerning the rate of occurrence of noise peaks permits a very simple analysis of this effect. Thus, a formula is obtained for the output SNR as a function of the input SNR that is valid somewhat below as well as near and above the threshold. From it the threshold is easily determined, and it is found to be higher than has sometimes been indicated. The paper includes a new, simpler derivation of Rice´s result as well as a resolution of the demodulator output into its various com ponents which should also prove useful in other applications.