In this study, the authors present an analytical approach to evaluate the performance of a two-way multi-relay system with direct link using a three-phase analogue network coding and opportunistic relay selection scheme. Herein, the imperfect channel state information is considered over independent and non-identically distributed Nakagami- m fading channels with integer-valued fading parameter. For analysis, initially, the closed-form expressions of cumulative distribution function and moment generating function (MGF) for the considered system are derived. Further, by using the MGF-based approach, generalised expressions of average symbol error rate (ASER) for higher-order quadrature amplitude modulation (QAM) schemes such as hexagonal QAM, rectangular QAM, and cross QAM are derived. They then analyse the asymptotic behaviour of ASER expression to evaluate the system's diversity order. Furthermore, a comparative analysis of the ASER performance for various QAM constellations is illustrated and impact of the number of relays, fading parameter, relay location, and channel estimation error are highlighted on the system's performance. Finally, all the analytical results are validated through Monte-Carlo simulations.

中文翻译：

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CSI不完全的双向多重中继网络中高阶QAM方案的ASER性能

在这项研究中，作者提出了一种使用三相模拟网络编码和机会中继选择方案评估具有直接链接的双向多中继系统性能的分析方法。在此，不完整的信道状态信息是在独立且不相同分布的Nakagami- 米具有整数值衰落参数的衰落信道。为了进行分析，首先，得出了所考虑系统的累积分布函数和矩生成函数（MGF）的闭式表达式。此外，通过使用基于MGF的方法，可以导出用于六阶QAM，矩形QAM和交叉QAM的高阶正交幅度调制（QAM）方案的平均符号错误率（ASER）的通用表达式。然后，他们分析ASER表达的渐近行为，以评估系统的多样性顺序。此外，还对各种QAM星座的ASER性能进行了比较分析，并说明了中继数量，衰落参数，中继位置和信道估计误差对系统性能的影响。最后，