Analysis of a PCM System Employing a PPM Vernier

The upper limit to the output SNR of sampled-data PCM systems is set by the quantization noise. The present study is concerned with a method of overcoming this limitation by employing time shifting of the PCM pulse groups so as to constitute an analog encoding of the difference between the sample amplitude and the nearest quantization level. Thus PCM is introduced to serve as a vernier to PPM. For this Vernier system the optimum values are found of 1) the number of pulses per pulse group for a given time-bandwidth per pulse group and 2) the detection threshold. An SNR analysis is then carried out, comparing this system with conventional doublepolarity PCM and with conventional single-polarity PPM. This comparison is made on the basis of equal energy and time-bandwidth per pulse group and a simplified model of the channel and detection scheme. The analysis shows that the Vernier system's threshold of channel SNR required for reliable detection is about 6 db higher than that for pure PCM, but that, near and beyond this threshold, the Vernier system's performance exceeds that of pure PCM and of pure PPM consistently and considerably. This improvement in performance can be realized as an increase in output SNR, as a decrease in time-bandwidth occupancy, or as a combination of these advantages.