On the Performance of THz Wireless Systems over $\alpha$-$\mathcal{F}$ Channels with Beam Misalignment, Mobility and Hardware Impairments

Technical Summary: Performance of THz Wireless Systems over $\alpha$-F Channels with Beam Misalignment, Mobility, and Hardware Impairments

Problem Statement
Terahertz (THz) wireless systems are critical enablers for sixth-generation (6G) networks due to their ultra-wide bandwidths and high data rates. However, accurate performance analysis is complicated by the simultaneous influence of multiple physical phenomena: multipath fading, shadowing, beam misalignment, transceiver hardware impairments, user mobility, path loss, and atmospheric molecular attenuation. Existing literature often addresses these factors in isolation or relies on models that only partially capture the physical characteristics of THz channels. Specifically, there is a lack of unified frameworks that jointly evaluate the non-linearity of the propagation medium, shadowing, multipath, beam misalignment, mobility, and hardware impairments. This paper addresses this gap by investigating the performance of THz wireless systems over $\alpha$-F fading channels under these combined practical effects.

Methodology
The authors develop a comprehensive analytical framework based on the following modeling assumptions:

• Channel Model: The composite fading is modeled using the $\alpha$-$F$ distribution, which characterizes multipath fading, shadowing, and the non-linearity of the propagation medium. This model generalizes other distributions (e.g., Fisher-Snedecor $F$ and $\alpha$-$\mu$).
• Beam Misalignment: A pointing error model suitable for high-directional antenna arrays is adopted, accounting for unstable transmitter and receiver orientations relative to the antenna pattern.
• Mobility: User mobility is modeled using the Random Waypoint (RWP) model, treating the distance between the base station and the user as a continuous random variable with specific probability density functions for 1D, 2D, and 3D topologies.
• Hardware Impairments: Transceiver imperfections are modeled as additive noise terms dependent on the signal power, characterized by impairment levels $k_t$ and $k_r$.
• Propagation Effects: The model incorporates distance-dependent path loss and frequency-dependent atmospheric molecular absorption (based on ITU-R recommendations).

The system model derives the instantaneous Signal-to-Noise Ratio (SNR), conditioned on distance and hardware impairments. The authors then derive exact closed-form expressions for the Probability Density Function (PDF), Cumulative Distribution Function (CDF), and higher-order moments of the instantaneous SNR. These derivations utilize the Fox H-function and Gauss-Legendre quadrature to handle the complex integrals arising from the composite model.

Key Contributions
The paper makes the following technical contributions:

1. Unified Statistical Framework: It presents the first work, to the authors' knowledge, to jointly evaluate the effects of $\alpha$-F fading, beam misalignment, mobility, and hardware impairments within a single framework.
2. Exact Statistical Expressions: New closed-form expressions are derived for the PDF, CDF, and higher-order moments of the instantaneous SNR.
3. Performance Metrics: Novel formulas are extracted for Outage Probability (OP), Average Symbol Error Probability (ASEP), and Average Channel Capacity.
4. Asymptotic Analysis: Asymptotic expressions are derived for the high-SNR regime, providing insights into the diversity gain and the limiting effects of system parameters.
5. Capacity Bounds: An upper bound on the average channel capacity is obtained using Jensen's inequality, and an asymptotic capacity limit is derived.

Results
Numerical results, validated by Monte Carlo simulations, reveal several key behaviors:

• Impact of Hardware Impairments: Hardware impairments impose a strict upper bound on the achievable SNR ($1/k^2$). Consequently, in the high-SNR regime, the system performance saturates. The OP and ASEP converge to irreducible error floors, and the channel capacity approaches a limit of $\log_2(1 + 1/k^2)$, regardless of further increases in transmit power.
• Beam Misalignment: Misalignment significantly degrades performance. The study shows that ASEP can increase by more than an order of magnitude when comparing ideal alignment ($\beta \to \infty$) to a scenario with moderate misalignment ($\beta = 3$).
• Path Loss and Mobility: Severe path loss conditions (higher path loss exponents) and longer link distances lead to significant performance degradation in terms of OP and ASEP. The diversity order in the high-SNR regime is shown to depend on the number of multipath clusters, channel non-linearity, and pointing error parameters.
• Frequency Dependence: Average capacity decreases with increasing frequency due to higher path losses and atmospheric absorption peaks (e.g., around 184 GHz, 327 GHz, 380 GHz, and 447 GHz).

Significance and Claims
The paper claims that its primary significance lies in providing a unified analytical framework that captures the complex interplay of multiple practical impairments in THz systems. The authors assert that their derived expressions offer new insights into system behavior, particularly regarding the saturation effects caused by hardware impairments, which prevent performance gains in the high-SNR regime. The work demonstrates that while THz systems offer high potential, their practical realization is heavily constrained by the combined effects of mobility, misalignment, and hardware non-idealities. The analytical results are shown to be accurate through rigorous comparison with simulations, offering a reliable tool for system design and optimization in future 6G networks.

The paper modestly suggests that future work could extend this framework to physical layer security metrics and multi-user scenarios with multiple antennas, but does not propose specific experimental implementations or applications beyond the scope of the derived analytical models.