Performance Analysis of Dual-Hop THz Transmission Systems over $α$-$μ$ Fading Channels with Pointing Errors

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.