The study of the effects of Nakagami-$m$ fading channels with both integer and non-integer $m$ plays an important role in the design of practical wireless systems. In this paper, we investigate a dual-hop cooperative communication system, where source node communicates with destination node through direct and relaying paths. Partial relay selection (PRS) scheme is used to select the best relay among $N$ relays which are capable of harvesting energy from radio frequency (RF) signals. At the destination, selection combining (SC) technique is employed to combine the signals of the direct path and the relaying path. We consider two relaying protocols, i.e. amplify-and-forward (AF) and decode-and-forward (DF). For both AF and DF protocols, we derive the tight lower-bound closed-form approximate expression and the exact closed-form expression of the outage probability (OP) over Nakagami-$m$ fading channels with both integer and non-integer $m$. Moreover, the optimal energy harvesting duration which minimizes the OP is also determined. Numerical results show that, the OP of DF protocol and its minimum value is lower than those of AF protocol for the same parameter settings. Moreover, the time switching ratio which gives the smallest OP in the case without direct path is larger than the case with direct path.

中文翻译：

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具有整数和非整数 m 的 Nakagami-m 衰落信道上射频能量收集协作通信系统的中断分析

Nakagami-的影响研究百万美元 具有整数和非整数的衰落信道 百万美元在实际无线系统的设计中起着重要作用。在本文中，我们研究了一个双跳协作通信系统，其中源节点通过直接和中继路径与目的节点通信。部分继电器选择 (PRS) 方案用于选择最佳继电器$N$能够从射频 (RF) 信号中收集能量的继电器。在目的地，采用选择合并（SC）技术来合并直接路径和中继路径的信号。我们考虑两种中继协议，即放大转发（AF）和解码转发（DF）。对于 AF 和 DF 协议，我们导出了 Nakagami 上的中断概率（OP）的紧下界封闭形式近似表达式和精确封闭形式表达式。百万美元 具有整数和非整数的衰落信道 百万美元. 此外，还确定了最小化 OP 的最佳能量收集持续时间。数值结果表明，在相同的参数设置下，DF协议的OP及其最小值低于AF协议。此外，在没有直接路径的情况下给出最小OP的时间切换比大于有直接路径的情况。