ASER analysis of generalized hexagonal QAM schemes for NOMA systems over Nakagami‐m fading channels

Abstract

To achieve high data rates expected from beyond 5G communications, higherorder modulation techniques have been explored. The energy-efficient modulation technique with a high data rate has encouraged researches towards an optimum two-dimensional hexagonal-shaped constellation, namely, hexagonal quadrature amplitude modulation (HQAM). Thus, in this work, we analyze the average symbol error rate (ASER) of HQAM schemes by considering a two-user nonorthogonal multiple access (NOMA) pair. Closed-form expressions for ASER of HQAM schemes for users are derived over generalized Nakagami-m fading channels. Further, for the HQAM constellation feasibility in two-user downlink NOMA systems, the power allocation criterion for the users is presented. Furthermore, the impact of modulation order of the users over the systems ASER analysis is investigated and valuable insights are drawn.

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“…In [17], the authors derived the exact BER of downlink NOMA systems, considering imperfect SIC decoding over ordered Nakagami-m flat fading channels, for the two-user and three-user scenarios assuming QPSK modulation for all users, whereas they considered the analysis of JMLD in [18]. The authors of [19] derived expressions for the average SER in Rayleigh fading channels considering rectangular M n -QAM, whereas in [20], hexagonal M n -QAM was considered for deriving the average SER under Nakagami-m fading. Exact closed-form BER expressions for imperfect SIC decoding for a two-user downlink NOMA system considering rectangular M n -QAM transmission were derived in [21].…”

“…where this integral can be evaluated using Bernoulli's formula of integration to give the closed-form expression in (19) at the top of page 5. Likewise, the average unconditional probabilities of d 1 = 0 and d 1 = 2 √ 2 can be calculated using the same way to give closed-form expressions in (20) and (21), respectively, at the top of page 5. Consequently, the average BER of U 2 , given its channel g 2 2 , can be given as…”

“…, and the functions P s i , ∀i ∈ {1, 2, 3} are defined in (19), (20), and (21). Finally, by averaging (28) over the PDF of Z 3 = g 3 2 , which is identical to the PDF of Z 1 in (8), the average unconditional BER of U 3 can be given as In this section, we consider the analysis of a general Kuser scenario where every user uses any arbitrary rectangular M -QAM modulation.…”