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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不完善的 CSI 和收发器硬件噪声对 Nakagami-m 衰落信道上具有多天线终端的全双工测向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。与之前的工作不同，不完美的信道状态信息 (I-CSI)、收发器硬件噪声 (THN) 和残余自干扰 (RSI) 的影响都被考虑在内。我们在数学上推导出具有 I-CSI、THN 和 RSI 的 FD 中继系统的中断概率 (OP)、符号错误率 (SER) 和遍历容量 (EC) 的精确闭式表达式 - 百万美元 衰落的频道。从导出的表达式中，将考虑的系统在三个负面因素（I-CSI、THN 和 RSI）的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）），两个理想因子（P-CSI和P-TH，P-CSI和P-SIC，P-TH和P-SIC） ，或一种理想因子（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 有很强的影响，尤其是在系统的数据传输速率和信噪比 (SNR) 较高时。特别是，由于三个负面因素，OP、SER 和 EC 在高 SNR 状态下达到最低点。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，以在节省能源消耗的同时获得优异的性能。而且，当三个负面因素中的两个足够大时，其余因素的影响就变弱了，在某些情况下可以忽略不计。