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UAV-Assisted and Intelligent Reflecting Surfaces-Supported Terahertz Communications

Yijin Pan, Kezhi Wang, Cunhua Pan, Huiling Zhu, Jiangzhou Wang

arXiv:2010.14223v2eess.SP

TL;DR

The paper addresses joint design for UAV-supported, IRS-assisted THz communications, targeting the minimum average rate across users. It jointly optimizes trajectory, IRS phase shifts, sub-band allocation, and power control using an iterative approximation-based approach with a closed-form phase-shift solution. Simulations report that the proposed algorithm achieves the best minimum average UE rate and increasing gaps over other algorithms.

  • Problem

    Joint optimization of UAV trajectory, IRS phase shifts, THz sub-band allocation, and power control for maximizing the minimum average UE rate had not been studied for this setting.

  • Method

    The optimization is decoupled into subproblems, using successive convex approximation with rate-constraint penalties for trajectory optimization and a closed-form IRS phase-shift solution with pricing factors.

  • Results

    The proposed algorithm achieves the best minimum average UE rate, with performance gaps over other algorithms considerable and increasing.

  • Takeaways & Limitations

    The proposed scheme significantly enhances the rate performance of the IRS-assisted and UAV-supported THz communication system.

Abstract

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In this paper, unmanned aerial vehicles (UAVs) and intelligent reflective surface (IRS) are utilized to support terahertz (THz) communications. To this end, the joint optimization of UAV's trajectory, the phase shift of IRS, the allocation of THz sub-bands, and the power control is investigated to maximize the minimum average achievable rate of all the users. An iteration algorithm based on successive Convex Approximation with the Rate constraint penalty (CAR) is developed to obtain UAV's trajectory, and the IRS phase shift is formulated as a closed-form expression with introduced pricing factors. Simulation results show that the proposed scheme significantly enhances the rate performance of the whole system.

I. INTRODUCTION

The paper motivates combining UAVs and IRSs for multi-user THz communications, where distance-dependent path loss and frequency-selective sub-bands complicate aerial transmission. It jointly optimizes UAV trajectory, IRS phase shifts, sub-band allocation, and power control to maximize the minimum average UE rate.

  • Motivation: THz communications offer abundant bandwidth but are vulnerable to blockage, motivating flexible UAV deployment and IRS-assisted propagation reconfiguration.IRS reflecting-element phase shifts can improve propagation conditions for UEs with poor channels.
  • Research gap: Existing terrestrial IRS-assisted THz approaches cannot be directly applied to aerial scenarios with flexibly deployed UAVs.Prior IRS-assisted UAV work also considered only single-sub-band scenarios.
  • Research gap: Distance-dependent THz path-loss peaks make sub-band selection important because peak locations vary with communication distance.The UAV trajectory affects transmission distance, while multiple UEs require intelligent sub-band assignment to avoid path-loss peaks.
  • Contributions: The paper jointly optimizes UAV trajectory, IRS phase shifts, THz sub-band allocation, and power control, targeting the maximum minimum average rate among UEs.The paper identifies this joint optimization as previously unstudied in the cited literature.
  • Contributions: The proposed algorithm uses successive convex approximation with rate-constraint penalties for trajectory optimization and a closed-form IRS phase-shift solution with pricing factors.The optimization is decoupled into trajectory, phase-shift, sub-band allocation, and power-control subproblems.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system models a UAV serving ground UEs at a fixed altitude while an IRS is deployed as a uniform planar array on a wall. Transmission is discretized into time slots with fixed UAV position and channels within each slot.

  • System model: The UAV serves U ground UEs over a total transmission time divided into T time slots.The UAV location and all channels are assumed unchanged within each time slot.
  • System model: The UAV flies at fixed altitude H, with time-slot position l(t) = [X(t), Y(t), H]^T.The ground location of UE u is denoted by l_u = [x_u, y_u, 0]^T.
  • IRS model: The IRS is mounted on a wall parallel to the XOZ plane and modeled as a uniform planar array.N_x and N_z denote the element counts along the X- and Z-axes, giving N = N_xN_z total reflecting elements.
  • IRS model: The IRS’s first reflecting element is at l_0 = [a, 0, c]^T, and element locations follow the specified X- and Z-axis spacings.Each reflecting element has unit amplitude and an individually adjustable phase shift φ_n(t).

A. Direct Transmission Links

The direct UAV-to-UE THz link is modeled with distance-dependent spreading loss and molecular absorption across multiple sub-bands. The formulation also establishes distance and phase quantities used in the IRS-assisted channel model.

  • Direct transmission links: The UAV-to-UE transmission distance is d_u(t) = |l(t) − l_u|.This distance depends on the UAV’s time-slot position and the UE location.
  • Direct transmission links: THz transmission is affected by free-space spreading loss and molecular absorption.The absorption coefficient K(f_i) depends on the sub-band’s central frequency f_i.
  • Direct transmission links: The total THz bandwidth is divided into sub-bands to confront frequency-selective fading.f_i denotes the central frequency of sub-band i, and I is the total number of sub-bands.
  • IRS-assisted channel quantities: The UAV-to-IRS relative phase difference depends on the UAV position, IRS element spacing, and sub-band frequency.The model defines the relative phase between the first IRS element and element (n_x, n_z) using the UAV-to-IRS distance.
  • IRS-assisted channel quantities: The cascaded UAV-IRS-UE channel combines the UAV-to-IRS and IRS-to-UE transmission vectors with the IRS reflection matrix.The reflection matrix is diagonal, with entries exp(jφ_n(t)) representing element reflection coefficients.

C. Problem Formulation

The problem formulation jointly optimizes UAV trajectory, IRS phase shifts, THz sub-band allocation, and power allocation to maximize the minimum average UE rate under system constraints.

  • Each sub-band i has bandwidth Bi, and UE transmission rates depend on sub-band assignment, transmit power, channel gain, and noise.
  • The UAV trajectory is constrained by a fixed start point, return to its initial location by Ts, and a maximum per-slot travel distance determined by Vmax.
  • Binary variables αi,u indicate sub-band assignment, with each sub-band allocated to at most one UE, while total transmit power and IRS phase shifts are constrained.
  • The formulation defines Ru as the average rate of UE u and introduces Rth and auxiliary variables to reformulate the optimization problem.
  • The objective is to maximize the minimum average rate among all UEs by jointly optimizing trajectory, sub-band allocation, IRS phase shifts, and power allocation.

III. SOLUTION ANALYSIS

Because the joint optimization is non-convex, the solution separates it into trajectory, IRS phase-shift, sub-band allocation, and power-control subproblems.

  • The formulated problem is non-convex and is therefore decoupled into three optimization subproblems.
  • The decomposed optimization covers UAV trajectory, IRS phase shift, THz sub-band allocation, and power control.

A. Trajectory Optimization

Trajectory optimization addresses complicated, non-convex THz channel gains using successive convex approximation and rate-constraint penalties within the CAR algorithm.

  • Periodic cosine patterns across sub-bands and UEs make the overall THz channel gain difficult to handle.
  • With a sufficiently short time slot, channel-gain terms Ci,u(l(t)) and Di,u(l(t)) are treated as constants because UAV position changes only slightly.
  • The trajectory subproblem uses first-order Taylor approximations of convex functions fi(x) and qi(x,y) to reformulate non-convex constraints.
  • If a trajectory update decreases a UE’s average rate, stricter rate constraints are introduced for affected UEs to preserve Ru ≥ Rth.
  • The updated problem may be infeasible when the UAV’s movement constraint prevents finding a new position that improves Rth, in which case it stays at the current position.
  • The resulting successive-convex-approximation procedure with rate-constraint penalties is summarized as CAR Algorithm 1 for UAV trajectory optimization.

B. Phase Shift Optimization

IRS phase-shift optimization uses convex reformulation and pricing factors after fixing sub-band allocation, power control, and UAV trajectory.

  • Given sub-band allocation, power control, and UAV trajectory, the IRS phase shift is optimized through a sequence of problems.
  • Defining si,u(t) = vi,u(t)φ(t) allows the relevant expression to be formulated as a convex function and approximated at a given point.
  • Although the resulting phase-shift problem remains non-convex, its globally optimal solution can be obtained according to the cited result.
  • The phase-shift formulation introduces pricing factors through an objective penalty and updates them using sub-gradient descent.

C. THz Sub-Band Allocation and Power Control

Given the UAV trajectory and IRS phase shift, the paper addresses THz sub-band allocation and power control through a transformed optimization problem and dual-based solution. Algorithm 2 summarizes the resulting procedure.

  • THz sub-band allocation and power control are optimized given the UAV’s trajectory and IRS phase shift.
  • The transformation x_u,i(t) = α_u,i p_i(t) is introduced before solving the resulting problem.
  • The transformed problem can be solved using a dual-based method.
  • Algorithm 2 is proposed to solve the overall problem based on the preceding analysis.

IV. SIMULATION RESULTS

The simulations evaluate the proposed scheme under specified THz communication and UAV settings, comparing it with fixed or randomly selected design components. The optimized trajectory balances distances to UEs and the IRS, while the proposed algorithm achieves the best minimum average rate and increasing performance gaps over iterations.

  • Simulation settings: The IRS is positioned at height 2 m with N_x = 8, N_z = 10, and element spacings δ_x = δ_z = 5 mm.
  • Compared algorithms: The comparison includes randomly selected sub-band allocation and power control, randomly generated IRS phase shifts, and a fixed initialized UAV trajectory.
  • Trajectory results: The optimized UAV trajectory compromises between distances to UEs and the IRS and requires a much smaller movement than the initial trajectory.
  • Trajectory results: The reduced movement is attributed to jointly optimized IRS phase shifts, THz channel allocation, and power control, implying flight-energy savings.
  • Rate convergence: The proposed algorithm achieves the best minimum average UE rate, with performance gaps over other algorithms increasing with iterations.

V. CONCLUSION

The paper investigates IRS-assisted and UAV-supported THz communications by jointly optimizing UAV trajectory, IRS phase shifts, THz sub-band allocation, and power control. Simulations validate the effectiveness of the proposed algorithm for maximizing the minimum average UE rate.

  • The study investigates IRS-assisted and UAV-supported THz communications.
  • The minimum average UE rate is maximized by optimizing the UAV’s trajectory, IRS phase shifts, THz sub-band allocation, and power control.
  • Simulation results validate the effectiveness of the proposed algorithm.
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