This paper presents novel moment generating function (MGF)- and characteristic function (CHF)-based frameworks for the EC performance analysis of a generic $L_{p}$ -norm diversity combining scheme under adaptive transmission policies. The considered system operates over generalized fading channels, a maximum delay constraint and under various channel state information (CSI) conditions. Depending upon the operational CSI, four policies are studied, namely: i) Constant power with optimal rate adaptation (ORA); ii) Optimal power and rate adaptation (OPRA); iii) Channel inversion with fixed rate (CIFR); and iv) Truncated CIFR (TIFR). The $L_{p}$ -norm diversity is a generic diversity structure which includes as special cases various well-known diversity schemes, such as equal gain combining (EGC), maximal ratio combining (MRC) and amplify-and-forward (AF) relaying. Under the ORA and OPRA policies, we derive single integral expressions for evaluating the EC of $L_{p}$ -norm diversity reception directly from the MGF or the incomplete MGF of the Signal-to-Noise-Ratio (SNR) at the receiver, respectively. For the EC performance evaluation of the EGC and AF relaying systems operating under the OPRA policy, a CHF-based approach, which is computationally more efficient as compared to the MGF-based approach, is further presented. It is shown that the EC for the CIFR and TIFR policies can be directly evaluated from the MGF or the CHF of the SNR at the receiver, respectively. For the ORA policy, a novel analytical approach for the asymptotic EC performance analysis is also developed and evaluated, revealing how important system operation parameters affect the overall system performance. The mathematical formalism is validated with selected numerical and equivalent simulation performance evaluation results, thus confirming the correctness of the proposed analytical methodology.

中文翻译：

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自适应传输方案下 Lp 范数分集接收器在广义衰落信道上的有效容量

本文提出了新的基于矩生成函数 (MGF) 和特征函数 (CHF) 的框架，用于通用的 EC 性能分析。 $L_{p}$ -自适应传输策略下的范数分集合并方案。所考虑的系统在广义衰落信道、最大延迟约束和各种信道状态信息 (CSI) 条件下运行。根据可操作的 CSI，研究了四种策略，即： i) 具有最佳速率自适应 (ORA) 的恒定功率；ii) 最佳功率和速率适配 (OPRA)；iii) 固定速率通道反转 (CIFR)；iv) 截断的 CIFR (TIFR)。这 $L_{p}$ -范数分集是一种通用分集结构，它包括作为特殊情况的各种众所周知的分集方案，例如等增益合并（EGC）、最大比合并（MRC）和放大转发（AF）中继。在 ORA 和 OPRA 政策下，我们推导出用于评估 EC 的单个积分表达式 $L_{p}$ - 标准分集接收直接来自 MGF 或接收器的信噪比 (SNR) 的不完整 MGF。对于在 OPRA 策略下运行的 EGC 和 AF 中继系统的 EC 性能评估，进一步提出了一种基于 CHF 的方法，该方法与基于 MGF 的方法相比计算效率更高。结果表明，CIFR 和 TIFR 策略的 EC 可以分别从接收端 SNR 的 MGF 或 CHF 直接评估。对于 ORA 策略，还开发和评估了一种新的渐近 EC 性能分析方法，揭示了系统运行参数对整体系统性能的影响程度。数学形式通过选定的数值和等效模拟性能评估结果进行验证，