Symbol error probability of time spread PPM signals in the presence of interference

Time spread (TS) pulse position modulation (PPM) signals have been proposed for CDMA applications, where envelope detection is employed instead of coherent detection for easier synchronization of PPM. A new method of deriving the symbol error probability (SEP) of TS PPM signals in the presence of interference is introduced. The analysis is based on the moment technique. The maximum entropy criterion for estimating an unknown probability density function (PDF) from its moments is applied to the evaluation of the PDF of the envelope detector output. Numerical results of the SEP are shown for 4, 8 and 16 PPM in the practical range of signal-to-noise power ratio (SNR) and signal-to-interference power ratio (SIR) of 5, 10 and 20 dB. The SEP obtained by the union bound is also given for comparison. From the results it is noted that when the PPM multilevel number is small, the union bound goes near to the SEP obtained by the proposed method, but when it increases the difference of the SEP obtained by the bound and proposed method becomes larger