Achievable Sum-rate of variants of QAM over Gaussian Multiple Access Channel with and without security

The performance of next generation wireless systems (5G/6G and beyond) at the physical layer is primarily driven by the choice of digital modulation techniques that are bandwidth and power efficient, while maintaining high data rates. Achievable rates for Gaussian input and some finite constellations (BPSK/QPSK/QAM) are well studied in the literature. However, new variants of Quadrature Amplitude Modulation (QAM) such as Cross-QAM (XQAM), Star-QAM (S-QAM), Amplitude and phase shift keying (APSK), and Hexagonal Quadrature Amplitude Modulation (H-QAM) are not studied in the context of achievable rates for meeting the demand of high data rates. In this paper, we study achievable rate region for different variants of M-QAM like Cross-QAM, H-QAM, Star-QAM and APSK. We also compute mutual information corresponding to the sum rate of Gaussian Multiple Access Channel (G-MAC), for hybrid constellation scheme, e.g., user 1 transmits using Star-QAM and user 2 by H-QAM. From the results, it is observed that S-QAM gives the maximum sum-rate when users transmit same constellations. Also, it has been found that when hybrid constellation is used, the combination of Star-QAM \& H-QAM gives the maximum rate. In the next part of the paper, we consider a scenario wherein an adversary is also present at the receiver side and is trying to decode the information. We model this scenario as Gaussian Multiple Access Wiretap Channel (G-MAW-WT). We then compute the achievable secrecy sum rate of two user G-MAC-WT with discrete inputs from different variants of QAM (viz, X-QAM, H-QAM and S-QAM).It has been found that at higher values of SNR, S-QAM gives better values of SSR than the other variants. For hybrid inputs of QAM, at lower values of SNR, combination of APSK and S-QAM gives better results and at higher values of SNR, combination of HQAM and APSK gives greater value of SSR.