In this paper, the performance of a dual-hop relaying terahertz (THz) wireless communication system is investigated. In particular, the behaviors of the two THz hops are determined by three factors, which are the deterministic path loss, the fading effects, and pointing errors. Assuming that both THz links are subject to the $\alpha$-$\mu$ fading with pointing errors, we derive exact expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the end-to-end signal-to-noise ratio (SNR). Relying on the CDF and PDF, important performance metrics are evaluated, such as the outage probability, average bit error rate, and average channel capacity. Moreover, the asymptotic analyses are presented to obtain more insights. Results show that the dual-hop relaying scheme has better performance than the single THz link. The system's diversity order is $\min\left\{\frac{\phi_1}{2},\frac{\alpha_1\mu_1}{2},\phi_2,\alpha_2\mu_2\right\}$, where $\alpha_i$ and $\mu_i$ represent the fading parameters of the $i$-th THz link for $i\in(1,2)$, and $\phi_i$ denotes the pointing error parameter. In addition, we extend the analysis to a multi-relay cooperative system and derive the asymptotic symbol error rate expressions. Results demonstrate that the diversity order of the multi-relay system is $K\min\left\{\frac{\phi_1}{2},\frac{\alpha_1\mu_1}{2},\phi_2,\alpha_2\mu_2\right\}$, where $K$ is the number of relays. Finally, the derived analytical expressions are verified by Monte Carlo simulation.

中文翻译：

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具有指向误差的$α$-$μ$衰落信道上双跳太赫兹传输系统的性能分析

在本文中，研究了双跳中继太赫兹 (THz) 无线通信系统的性能。特别是，两个太赫兹跳频的行为由三个因素决定，即确定性路径损耗、衰落效应和指向错误。假设两个太赫兹链路都受到 $\alpha$-$\mu$ 衰落和指向错误的影响，我们推导出端到端信号的累积分布函数 (CDF) 和概率密度函数 (PDF) 的精确表达式噪声比 (SNR)。依靠 CDF 和 PDF，评估重要的性能指标，例如中断概率、平均误码率和平均信道容量。此外，提出渐近分析以获得更多见解。结果表明，双跳中继方案比单太赫兹链路具有更好的性能。系统的分集顺序为$\min\left\{\frac{\phi_1}{2},\frac{\alpha_1\mu_1}{2},\phi_2,\alpha_2\mu_2\right\}$，其中$\ alpha_i$和$\mu_i$代表$i\in(1,2)$的$i$-th THz链路的衰落参数，$\phi_i$表示指向误差参数。此外，我们将分析扩展到多中继协作系统并推导出渐近符号错误率表达式。结果表明多中继系统的分集顺序为$K\min\left\{\frac{\phi_1}{2},\frac{\alpha_1\mu_1}{2},\phi_2,\alpha_2\mu_2 \right\}$，其中 $K$ 是中继数。最后，通过蒙特卡罗模拟验证导出的解析表达式。其中$\alpha_i$和$\mu_i$代表$i\in(1,2)$的$i$-th THz链路的衰落参数，$\phi_i$表示指向误差参数。此外，我们将分析扩展到多中继协作系统并推导出渐近符号错误率表达式。结果表明多中继系统的分集顺序为$K\min\left\{\frac{\phi_1}{2},\frac{\alpha_1\mu_1}{2},\phi_2,\alpha_2\mu_2 \right\}$，其中 $K$ 是中继数。最后，通过蒙特卡罗模拟验证导出的解析表达式。其中$\alpha_i$和$\mu_i$代表$i\in(1,2)$的$i$-th THz链路的衰落参数，$\phi_i$表示指向误差参数。此外，我们将分析扩展到多中继协作系统并推导出渐近符号错误率表达式。结果表明多中继系统的分集顺序为$K\min\left\{\frac{\phi_1}{2},\frac{\alpha_1\mu_1}{2},\phi_2,\alpha_2\mu_2 \right\}$，其中 $K$ 是中继数。最后，通过蒙特卡罗模拟验证导出的解析表达式。结果表明多中继系统的分集顺序为$K\min\left\{\frac{\phi_1}{2},\frac{\alpha_1\mu_1}{2},\phi_2,\alpha_2\mu_2 \right\}$，其中 $K$ 是中继数。最后，通过蒙特卡罗模拟验证导出的解析表达式。结果表明多中继系统的分集顺序为$K\min\left\{\frac{\phi_1}{2},\frac{\alpha_1\mu_1}{2},\phi_2,\alpha_2\mu_2 \right\}$，其中 $K$ 是中继数。最后，通过蒙特卡罗模拟验证导出的解析表达式。