Numerical Validation of UAV‑CRN Optimization: Improved Rates Under Energy and PLoS Constraints

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

V. NUMERICAL RESULTS

In this section, extensive simulations are conducted to validate the effectiveness and the convergence of the proposed algorithm. To illustrate the advantages of the proposed algorithm, the following three benchmark schemes are compared.

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1. Benchmark I: B transmit signals with the average power and both 3D trajectory of B and user scheduling are jointly optimized based on the PLoS model, which is denoted by ‘NPC’.

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2. Benchmark II: The 2D trajectory of B, the transmission power of B, and user scheduling are jointly optimized based on the LoS model, which is denoted by ‘2D-LoS’.

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3. Benchmark III: B works with fixed vertical trajectory and its horizontal and transmission power of B, and user scheduling are jointly optimized based on the PLoS model, which is denoted by ‘2D-PLoS’.

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\ Figs. 4(a) and 4(b) provide the 3D trajectory of B with the different schemes and in the scenarios with different propulsion power limitations, respectively. From Fig. 4(a), it can be observed that compared with the scenarios with the 2D-PLoS scheme, B in the 2D-LoS scheme must keep away from D to meet IT constraints. This requirement for B to keep away from D in the 2D-LoS scheme is due to the exaggerated probability of LoS for the A2G link. The results in Fig. 4(b) show that different propulsion power limitation results in different vertical trajectories

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VI. CONCLUSION

This work investigated the achievable rate of the underlay IoT system with an energy-constrained UAV under PLoS channels. The achievable rate of the considered systems was maximized by jointly considering the UAV’s 3D trajectory, transmission power, and user scheduling, which is a nonlinear mixed-integer non-convex problem. The lower bound of the average achievable rate was utilized and the original nonconvex problem was transformed into several solvable convex subproblems by using BCD and SCA techniques, and an efficient iterative algorithm was proposed. The numerical results not only verified the convergence and effectiveness of the algorithm but also illustrated the impact of propulsion power and interference thresholds on the average achievable rate

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APPENDIX A

PROOF OF LEMMA 1

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\ \ From the above Jacobian matrix, we can obtain the Hessian matrix of f(x, y) as

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\ \ According to (33) and (34), for any given A ≥ 0, We can determine that the determinant of the cofactor matrix of the Hessian matrix of function f(x, y) is greater than or equal to 0. Therefore, the Hessian matrix of f(x, y) is a semi-positive definite matrix, so f(x, y) is a convex function.

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:::info Authors:

(1) Hongjiang Lei, School of Communications and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China (leihj@cqupt.edu.cn);

(2) Xiaqiu Wu, School of Communications and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China (cquptwxq@163.com);

(3) Ki-Hong Park, CEMSE Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia (kihong.park@kaust.edu.sa);

(4) Gaofeng Pan, School of Cyberspace Science and Technology, Beijing Institute of Technology, Beijing 100081, China (gaofeng.pan.cn@ieee.org).

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:::info This paper is available on arxiv under CC BY 4.0 DEED license.

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