Performance of Amplitude Probabilistic Shaping Based on Modified Multi-Repeat Mapping in Wireless Fading Channels

Probabilistic Amplitude Modulation (PAS) is one of the techniques that has attracted significant and increasing interest in recent years in improving system performance, bringing the data rate achievable to the Shannon limit, improving spectral efficiency, and reducing constellation power. This paper will analyse the average symbol error rate performance of Probability Amplitude Shaping (PAS). The discussion is based on a Modified Multi-Repeat Distribution Matcher (PASMMRDM) used for wireless communications in Gaussian and fading channels. The analysis includes four different fading models: Rayleigh channels, Log-normal fading channels, Nakagami-m channels, and Composite Log-Normal shadowing/Nakagami-m fading channels. Simulation supported and compared the results with input symbols for high-order modulation schemes such as uniform Quadrature Amplitude Modulation (QAM). It will also be noted that PAS based on MMRDM provides a significant improvement in the average symbol error rate at a certain Signal-to-Noise Ratio (SNR) or a significant decrease in the SNR wanted to perform specific symbol error probability compared to uniform QAM for different cases of channels, for example, the improvement in the net shaping gain of about 1.21, 1.64, and 1.81 dB at Symbol Error Rate (SER) with entropy rate 4, 6, and 8 bits/symbol, all cases at Symbol Error Ratio (SER)= 10−4 when compared with uniformly distributed symbols of QAM.