A General Framework for UAV-Aided THz Communications Subject to Generalized Geometric Loss

In this article, we develop a general framework for the performance analysis of unmanned aerial vehicle (UAV) aided terahertz (THz) communications under generalized geometric loss, which considers the fluctuations of the UAV's position and orientation alongside the non-orthogonality of the THz beam with respect to the detector plane. In particular, we derive general and novel analytical expressions for the probability density function and the cumulative distribution function of the instantaneous signal-to-noise ratio (SNR) under generalized fading channels subject to generalized geometric loss. Consequently, novel, general, and accurate analytical expressions for the outage probability, average symbol error rate, and average channel capacity are derived. Furthermore, approximate asymptotic expressions in the high SNR regime are also derived. Moreover, A very accurate approximate expression for the channel capacity is also provided in the low SNR regime. As an example, the system performance under the $\alpha$-$\mu$ fading channel model is analyzed in terms of the above-mentioned performance metrics.

I. Introduction

The compound annual growth rate (CAGR) of global mobile data traffic (MDT) over the last five years has indeed been 46%, resulting in overall MDT of 77 and 1589.7 Exabytes (EB, i.e. Terabyte (TB)) per month in 2022 and 2030, respectively [1]. In particular, the Asia Pacific region accounts for 56% of all traffic. Furthermore, with a device CAGR of 7%, it is predicted to have more than 20.6 billion connected devices by 2030. Because of the tremendous expansion of both MDT and users, there is a strong need to broaden the bandwidth to several Terahertz (THz) and increase the average channel capacity to Terabits per second [2]. To that purpose, the wavelength range ( mm) or, more accurately, the THz frequency band ( THz) began to garner significant attention in the scientific community. Millimeter wave (mmWave) and optical frequency gaps are filled by THz communications, which can enable faster speed data rates compared to mmWave communications. Outdoor THz communication is not affected by the effects of the atmosphere like optical communications are. However, the THz beam may be traced more easily indoors than optical beams, which reduces the mobility of wireless communication devices. Additionally, the reflected pathways in THz communication can be effectively used to improve system performance. THz can also provide UAV services like video surveillance, hotspot seamless coverage, and emergency communications. Nevertheless, despite its appealing properties, THz communication experiences a number of losses, including path-loss, molecular absorption loss, and antenna misalignment loss. TABLE IMathematical Notations and Function Definitions

Notation	Explanation
	Transmit-antenna gain
	Receive-antenna gain
	Speed of light
	Operating frequency
	Transmitter-receiver distance
	Detector radius
	Beam-waist radius
	Refractive-index structure parameter
	Wave-number
	Beam-width
	Coherence length
	I-function [11, eq. (3.1)]
	Gamma function [12, eq. (8.310.1)]
	Modified Bessel function of the first kind with zero-order [12, eq. (8.406.1)]
	Error function [12, eq. (8.250.1)]
	Meijer's G-function [12, eq. (9.301)]
	Logarithmic function
	Digamma function [12, eq. (8.36)]