The communication process of digital binary pulse-position modulation with additive white Gaussian noise

Digital pulse-position modulation (PPM) is a time-domain version of frequency-shift keying that encodes each variable pulse to a particular position within a period. Although numerous essays have researched PPM applied to optical fiber, the PPM process with additive white Gaussian noise (AWGN) was not mentioned. In this paper, a relatively simple model was constructed for 2-bit message signals passing through the AWGN channel. While encoding the baseband signals, Gray Code was adopted to encode them in each period separated into four equal parts. Afterward, they all passed through the AWGN channel, and the constellation of baseband signals and received signals was performed in MATLAB. Then we applied the minimum distance identification method to find the estimated baseband signals. Finally, the PPM signal-tonoise ratio (SNR) was obtained based on previous probability errors. Executing the codes in MATLAB, we got the baseband signals, constellation, and SNR function that can all be directly shown in the figure. In general, our work filled the gap of the PPM method sending over the AWGN channel. This can also become the preliminary foundation for a broader range of applications using PPM to implement the whole communication process with AWGN.