In this paper, we investigate the performance of a full-duplex (FD) relay system where multi-antennas are exploited at source and destination. Unlike previous works, the impacts of imperfect channel state information (I-CSI), transceiver hardware noise (THN), and residual self-interference (RSI) are taken into account. We mathematically derive the exact closed-form expressions of the outage probability (OP), symbol error rate (SER), and ergodic capacity (EC) of the FD relay system with I-CSI, THN, and RSI over Nakagami- $m$ fading channels. From the derived expressions, the performance of the considered system under the effects of three negative factors (I-CSI, THN, and RSI) is compared with that system in the case of all ideal factors (perfect channel state information (P-CSI), perfect transceiver hardware (P-TH) and perfect self-interference cancellation (P-SIC)), two ideal factors (P-CSI and P-TH, P-CSI and P-SIC, P-TH and P-SIC), or one ideal factor (P-CSI or P-TH or P-SIC). Numerical results show a strong impact of three negative factors on the OP, SER, and EC of the considered FD relay system, especially when the data transmission rate of the system and signal-to-noise ratio (SNR) are high. In particular, OP, SER, and EC go to the floors in the high SNR regime due to the three negative factors. Therefore, when I-CSI, THNs, and RSI exist in the FD relay system, we should use suitable source and relay transmission power to obtain excellent performance while saving energy consumption. Moreover, when two of the three negative factors are large enough, the remaining factor’s impact becomes weaker and may be neglected in certain circumstances.

中文翻译：

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不完美的 CSI 和收发器硬件噪声对 Nakagami-m 衰落信道上多天线终端全双工 DF 中继系统性能的影响


在本文中，我们研究了在源和目的地使用多天线的全双工（FD）中继系统的性能。与以前的工作不同，它考虑了不完善的信道状态信息（I-CSI）、收发器硬件噪声（THN）和残余自干扰（RSI）的影响。我们通过数学推导了 FD 中继系统的中断概率 (OP)、符号错误率 (SER) 和遍历容量 (EC) 的精确封闭式表达式，其中 I-CSI、THN 和 RSI 在 Nakagami-$m$ 上衰落通道。根据导出的表达式，将所考虑的系统在三个负面因素（I-CSI、THN 和 RSI）影响下的性能与所有理想因素（完美信道状态信息（P-CSI））情况下的系统进行了比较，完美的收发器硬件（P-TH）和完美的自干扰消除（P-SIC）），两个理想因素（P-CSI和P-TH，P-CSI和P-SIC，P-TH和P-SIC） ，或一个理想因子（P-CSI 或 P-TH 或 P-SIC）。数值结果表明，三个负面因素对所考虑的 FD 中继系统的 OP、SER 和 EC 产生强烈影响，特别是当系统的数据传输速率和信噪比 (SNR) 高时。特别是，由于这三个负面因素，OP、SER 和 EC 处于高 SNR 状态下。因此，当FD中继系统中存在I-CSI、THN和RSI时，我们应该使用合适的源和中继传输功率，以获得优异的性能，同时节省能耗。而且，当三个负面因素中有两个足够大时，其余因素的影响就会变弱，在某些情况下可以忽略不计。