Joint UAV Trajectory and Power Design in Energy‑Constrained Cognitive Radio Networks

Table of Links

Abstract and I. Introduction

II. System Model

III. Problem Formulation

IV. Proposed Algorithm for Problem P0

V. Numerical Results

VI. Conclusion

APPENDIX A: PROOF OF LEMMA 1 and References

Abstract—Unmanned aerial vehicles (UAVs) have been attracting significant attention because there is a high probability of line-of-sight links being obtained between them and terrestrial nodes in high-rise urban areas. In this work, we investigate cognitive radio networks (CRNs) by jointly designing three - dimensional (3D) trajectory, the transmit power of the UAV, and user scheduling. Considering the UAV’s onboard energy consumption, an optimization problem is formulated in which the average achievable rate of the considered system is maximized by jointly optimizing the UAV’s 3D trajectory, transmission power, and user scheduling. Due to the non-convex optimization problem, a lower bound on the average achievable rate is utilized to reduce the complexity of the solution. Subsequently, the original optimization problem is decoupled into four subproblems by using block coordinate descent, and each subproblem is transformed into manageable convex optimization problems by introducing slack variables and successive convex approximation. Numerical results validate the effectiveness of our proposed algorithm and demonstrate that the 3D trajectories of UAVs can enhance the average achievable rate of aerial CRNs.

I. INTRODUCTION

A. Background and Related Works

Unmanned aerial vehicles (UAVs) have become a revolutionary technology with extensive applications in various fields. UAVs were initially developed for military purposes and are now widely used in civilian and commercial sectors such as agriculture, disaster management, surveillance, and aerial photography, including surveillance and monitoring, aerial imaging, precision agriculture, intelligent logistics, law enforcement, disaster response, and prehospital emergency [1]. The rapid development of UAV technology, including the improvement of autonomy, payload capacity, and flight endurance, has promoted the widespread application of UAVs in various industries worldwide [2], [3]. The continuous development of UAV technology has brought new opportunities and challenges, requiring further exploration and research in areas such as regulation, security, and integration into existing infrastructure. Modifying the positioning or mapping out the flight path of UAVs can ensure a stable line-of-sight (LoS) connection to terrestrial nodes (TNs) with optimal reliability. Consequently, the altitude and lateral placement of UAVs play a crucial role in enhancing the efficiency of UAV communication systems. The trajectory designing has emerged as a critical challenge to address in the development of UAV assisted communication systems [4].

To enhance the performance of the Internet of Thing (IoT) systems, various schemes have been proposed in different scenarios. UAVs can play different roles in communication systems, such as serving as aerial base stations (BSs) to transmit information to ground users [5]-[8]. In [5], a multi-purpose UAV-enabled wireless network was considered. Specifically , user scheduling, UAV trajectories, and transmission power were jointly optimized to maximize the minimum average rate among all users. The results indicated that, compared t o traditional static base stations, the mobility of UAVs offers advantages in achieving better air-to-ground (A2G) channel conditions and providing additional flexibility for interference mitigation, thereby enhancing system throughput. Research on secure UAV-assisted downlink transmission in the presence of colluding eavesdroppers was presented in [6]. A single-antenna UAV served multiple ground users with imperfect location information, utilizing a power-splitting scheme to transmit confidential information and artificial noise. In [7], a scenario was considered where UAVs provide services to a group of TNs and maximize the minimum secrecy rate (SR) to ensure fairness between TNs. The results indicated that the minimum SR was significantly improved. A UAV-to-ground communication system operating in the presence of multiple potential Eves was investigated in [8] with incomplete information about the Eves’ locations. effectively.

Zeng et al. derived the closed-form expression of propulsion energy consumption for the fixed-wing UAVs in [9]. Their results demonstrated that UAVs must operate within specific speed and acceleration limits to conserve energy. The propulsion energy consumption for the fixed-wing UAVs is a function of the flying velocity and acceleration. Moreover, for level flight with fixed altitude, the UAV’s energy consumption only depends on the velocity and acceleration rather than it s actual location. Considering the propulsion energy constraint, the authors in [10] investigated the minimum average rate maximization and the energy efficiency (EE) maximization problems by jointly designing the trajectory, velocity, an d acceleration of the UAV and the transmit power of the TNs. Considering the UAV’s mobility constraints, the energy efficiency of the UAV-enabled communication system with multiple terrestrial jammer was maximized by designing the trajectory of the UAV in [11]. The EE of the UAV communication systems was also considered in [12]. To reduce the computational complexity, a new method based on receding horizon optimization was introduced to solve the formulated problem. The authors in [13] studied the max-min fairness problem of a system consisting of multiple UAVs and multiple TNs. The minimum achievable rate was maximized by jointly designing the UAVs’ trajectories, power allocation, and user scheduling.

Rotary-wing UAVs have the advantage of being able to take off and land vertically, as well as hover in a stationary position. Zeng et al. derived the closed-form expression of propulsion energy consumption models for the rotary-wing UAVs in [14]. Their results have shown that the propulsion power consumption of rotary-wing UAVs consists of three components: blade profile, induced, and parasite power. The first two parts increase with increasing speed, and the third part decreases with increasing speed. The authors in [15] minimized the maximum energy consumption of the rotary wing UAV-enabled IoT system by jointly designing the UAV’s trajectory, user scheduling, and power allocation. Considering the average and peak power constraints, the authors in [16] maximized the secrecy EE (SEE) of the full-duplex UAV communication systems by jointly designing the trajectory and the power allocation. Their results show that the SEE gains depended on the capability of the self-interference cancelation at the full-duplex UAV. In [17], the worst-case average SR and secrecy energy efficiency of the dual-UAV communication system were maximized, respectively. Their results demonstrated there is a tradeoff between maximizing the total information bits and minimizing the total propulsion energy consumption. The authors in [18] investigated the passive eavesdropping scenario without the eavesdropper’s instantaneous channel state information. Considering the constraints of connection outage probability, secrecy outage probability, and securely collected bits, the SEE was maximized by jointly optimizing the user scheduling and transmit power, UAV’s transmit power, trajectory, codeword rate, and redundancy rate. All the previous works utilized the deterministic LoS channel model which is usually a valid assumption for the scenarios without high and dense obstacles and the two-dimensional (2D) UAV trajectory was designed with a fixed altitude.

When the UAV flies at a relatively low altitude, the shadowing effect becomes more significant because obstacles will occasionally block the signal propagation between the UAV and the TN. The probabilistic LoS (PLoS) channel model was proposed in [19], and their results demonstrated that the probability of the LoS are functions of the elevation angle. Specifically, there are two states for the A2G channel, LoS and non-LoS (NLoS), and the probabilities of LoS/NLoS states depend on the relative position between the UAV and TN and the distributions of building density and height. Intuitively, the LoS probability increases with the elevation angle, by either moving the UAV horizontally closer to the ground node or increasing its altitude. In [20], a UAV was utilized to transmit jamming signals to enhance the terrestrial communication link. The expected SR was maximized by jointly optimizing the transmit power at the BS, the jamming power of the UAV, and the 2D trajectory of the UAV. In [21], the minimum average data collection rate was maximized by jointly optimizing the three-dimensional (3D) trajectory, the flying speed, and user scheduling. In [22], the authors considered an aerial wireless sensor network with a malicious terrestrial jammer and maximized the minimum expected rate by jointly optimizing the transmission scheduling and the 3D trajectory. In [23], a UAV was utilized as a relay to transmit signals to the TN; the EE was maximized by optimizing the 3D trajectory of the UAV considering the energy consumption of the UAV. In [24], the authors considered the fairness among the TNs and maximized the minimum expected sum throughput of the TNs by jointly designing the 3D trajectory of the UAV and the TN scheduling. In [25], the authors studied the problem of secure data collection problem in aerial communication systems with multiple location-uncertain terrestrial eavesdroppers. The bandwidth allocation and the 3D trajectory of the UAV were jointly designed to maximize the system’s overall fair SR subject to flight energy consumption, user fairness, and secure transmission constraints.

Cognitive radio technology is considered an advanced technology that can solve the problem of spectrum scarcity in UAV-assisted communication systems by using dynamic spectrum access techniques [26]. In [27], the authors considered the aerial underlay IoT systems with a single location-uncertainty eavesdropper. The cognitive UAV’s 2D trajectory, transmit power, and user scheduling were jointly designed to maximize the average SR of the cognitive users (CUs). The authors in [28] considered the aerial IoT systems with multiple locationuncertainty full-duplex eavesdroppers worked in colluding mode, and the cognitive UAV’s 2D trajectory and transmit power were jointly designed to maximize the worst average SR of the CUs. In [29], a UAV was utilized as a friendly jammer to transmit artificial noise for interrupting the eavesdropper in both scenarios with perfect and imperfect locations of the eavesdropper and TN. The average SR of the CU was maximized by jointly optimizing the transmit power and UAV’s 3D trajectory. In [30], a UAV was utilized as a cognitive relay to forward the signals to CUs and the sum throughput of the CUs was maximized by jointly optimizing the power allocation and 3D trajectory. It should be noted that LoS channel model was utilized in [29] and [30], although the 3D trajectory was designed. Based on the PLoS channel model, the authors in [31] considered both the quasi-stationary UAV scenario and mobile UAV scenario. The CU’s achievable rate was maximized by jointly designing the UAV’s 3D trajectory and power control, subject to the UAV’s altitude and power constraints and the interference temperature (IT) constraint for the primary user (PU). In [32], the SR of the UAV-enabled cognitive radio network (CRN) was maximized by optimizing UAV’s 3D trajectory, velocity, and acceleration considering the requirements location constraint, the speed constraint of UAV, and the IT constraint for all the PU.

B. Motivation and Contributions

The discussed works proved that the performance of aerial CRNs was significantly improved by designing the UAV’s

trajectory and transmit power. However, these outstanding works on aerial CRNs did not consider the propulsion energy constraint and PLoS channel model in designing the cognitive UAV’s trajectory. In this work, based on the PLoS channel model, we consider the limited onboard energy and jointly design the cognitive UAV’s 3D trajectory and transmission power and user scheduling to maximize the performance of the underlay IoT systems. The main contributions of this work are summarized as follows:

1. We consider an underlay aerial IoT system with multiple terrestrial cognitive users and a primary user on the ground. Based on the PLoS channel model, considering the UAV’s onboard energy consumption, the average achievable rate of the considered system is maximized by jointly optimizing the UAV’s 3D trajectory, transmission power, and user scheduling. The lower bound on the average achievable rate is utilized to reduce the complexity of the solution and the original optimization problem is decoupled into four subproblems by using the block coordinate descent (BCD). Each subproblem is transformed into manageable convex optimization problems by introducing slack variables and the successive convex approximation (SCA).

2. The simulation results of the proposed scheme are compared with benchmark schemes, demonstrating that the proposed trajectory scheme effectively improves the average achievable rate of CRN IoT systems. Moreover, in CRNs, IT threshold, flight altitude, and UAV energy consumption are very crucial for trajectory design.

3. Although the 3D trajectory design of UAVs was investigated in some outstanding works, such as [21] and [22], the energy consumption was ignored. Considering

the energy consumption, IT threshold, and transmitting power over 3D trajectory design in this work makes the formulated optimization problem more challenging to solve.

4. Relative to [29]-[31], wherein the 3D trajectory design in the CRNs was investigated based on the LoS channel model, the vertical position of the UAV only depends on the IT constraint. In the CRNs based on the PLoS channel model, optimizing the vertical position of the UAV must consider both the IT constraints and the loss probability. Although the 3D trajectory design based on the PLoS model was considered in [32], the elevation angle was assumed to be fixed to simplify the trajectory design. This work considers both the PLoS channel model and the energy consumption of the rotary-wing UAV in designing the 3D trajectory.