Abstract
Unmanned aerial vehicles (UAVs), which enable both high flexibility and low cost, have been widely used in both military and civilian application scenarios. In this paper, we investigate a fixed-wing UAV relay system, where the fixed-wing UAV acts as a mobile relay with an elliptical trajectory between base station and ground users with broken communication links because of obstructions. Different time and power allocations are utilized to compute the outage probability among the Rician fading channel model. Due to the complexity of the formulated issue, we approximate the asymptotic solution using the first-order Maclaurin series convex optimization. Finally, we contrast the elliptical trajectory relay’s outage probability performance with that of the circular trajectory relay and the fixed relay. In the meanwhile, we examine the impact of the elliptical trajectory’s various long and short axis ratios on the outage probability of a relay system. The efficiency of the suggested elliptical trajectory relay method has been demonstrated in simulations.
Similar content being viewed by others
References
Zeng, Y., Zhang, R., & Lim, T. (2016). Wireless communications with unmanned aerial vehicles: Opportunities and challenges. IEEE Communications Magazine, 54(5), 36–42.
Khawaja, W., Guvenc, I., Matolak, D. W., Fiebig, U. C., & Schneckenburger, N. (2019). A survey of air-to-ground propagation channel modeling for unmanned aerial vehicles. IEEE Communications Surveys & Tutorials, 21(3), 2361–2391.
Gupta, L., Jain, R., & Vaszkun, G. (2016). Survey of important issues in UAV communication networks. IEEE Communications Surveys & Tutorials, 18(2), 1123–1152.
Zeng, Y., Xu, J., & Zhang, R. (2018). Rotary-wing UAV enabled wireless network: Trajectory design and resource allocation. In 2018 IEEE Global Communications Conference (GLOBECOM), pp. 1–6.
Zhang, S., Zhang, H., He, Q., Bian, K., & Song, L. (2018). Joint trajectory and power optimization for UAV relay networks. IEEE Communications Letters, 22(1), 161–164.
Zeng, Y., Zhang, R., & Lim, T. (2016). Throughput maximization for UAV-enabled mobile relaying systems. IEEE Transactions on Communications, 64(12), 4983–4996.
Ono, F., Ochiai, H., & Miura, R. (2016). A wireless relay network based on unmanned aircraft system with rate optimization. IEEE Transactions on Wireless Communications, 15(11), 7699–7708.
Van Der Meulen, E. C. (1971). Three-terminal communication channels. Advances in Applied Probability, 3(1), 120–154.
Sun, Z., Yang, D., Xiao, L., Cuthbert, L., Wu, F., & Zhu, Y. (2021). Joint energy and trajectory optimization for UAV-enabled relaying network with multi-pair users. IEEE Transactions on Cognitive Communications and Networking, 7(3), 939–954.
Zeng, Y., Xu, J., & Zhang, R. (2019). Energy minimization for wireless communication with rotary-wing UAV. IEEE Transactions on Wireless Communications, 18(4), 2329–2345.
Wu, G., Gao, X., Fu, X., Wan, K., & Di, R. (2019). Mobility control of unmanned aerial vehicle as communication relay in airborne multi-user systems. Chinese Journal of Aeronautics, 32(6), 1520–1529.
Xiao, L., Xu, Y., Yang, D., & Zeng, Y. (2020). Secrecy energy efficiency maximization for UAV-enabled mobile relaying. IEEE Transactions on Green Communications and Networking, 4(1), 180–193.
Song, K., Zhang, J., Ji, Z., Jiang, J., & Li, C. (2020). Energy-efficiency for IoT system with cache-enabled fixed-wing UAV relay. IEEE Access: Practical Innovations, Open Solutions, 8, 117503–117512.
Wang, L., Hu, B., Chen, S., & Cui, J. (2020). UAV-enabled reliable mobile relaying based on downlink NOMA. IEEE Access: Practical Innovations, Open Solutions, 8, 25237–25248.
Abu Al Haija, A., & Vu, M. (2015). Outage analysis for coherent decode-forward relaying over Rayleigh fading channels. IEEE Transactions on Communications, 63(4), 1162–1177.
Zeng, S., Zhang, H., Bian, K., & Song, L. (2018). UAV relaying: Power allocation and trajectory optimization using decode-and-forward protocol. In 2018 IEEE International Conference on Communications Workshops (ICC Workshops), pp. 1–6.
Jiang, X., Yin, Z., Wu, Z., Yang, Z., & Sun, L. (2019). Outage probability optimization for UAV-enabled wireless relay networks in fading channels. Physical Communication, 33, 35–45.
Jeganathan, A., Mitali, G., Jayakody, D., & Muthuchidambaranathan, P. (2021). Outage and throughput performance of half/full-duplex UAV-assisted co-operative relay networks over Weibull fading channel. Wireless Personal Communications, 120, 2389–2407.
Hoang, T., Nguyen, B., Dung, L., & Kim, T. (2020). Outage performance of multi-antenna mobile UAV-assisted NOMA relay systems over Nakagami-m fading channels. IEEE Access: Practical Innovations, Open Solutions, 8, 215033–215043.
Sagduyu, Y., Shi, Y., Ponnaluri, S., Soltani, S., Li, J., Riley, R., Banner, C., & Heinen, G. (2018). Optimal network-centric planning for airborne relay communications. IEEE Systems Journal, 12(4), 3450–3460.
Sun, C., Hu, Z., Wen, X., Lu, Z., & Qi, H. (2019). Spectrum efficiency maximization with trajectory design in UAV-enabled mobile relaying. Journal of China Posts and Telecommunications Universities (English Edition), 26(4), 17–24.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
As for formula (22), the objective function is a function of the variables \(\lambda\) and \(\beta\).We define
The objective function can be demonstrated to be a convex function using the convexity criterion if \({f_1}(\lambda ,\beta )\) and \({f_2}(\lambda ,\beta )\) are convex functions. By obtaining the function’s Hessian matrix, we may determine if it is a convex function. The second order partial derivatives of the function \({f_1}(\lambda ,\beta )\) can be expressed as
According to the above partial derivatives, the determinant of the Hessian matrix can be obtained as
Similarly, the second order partial derivatives of the function \({f_2}(\lambda ,\beta )\) can be expressed as
The determinant of the Hessian matrix can be obtained as
The simplification and derivation of \({H_1}(\lambda ,\beta )\) and \({H_2}(\lambda ,\beta )\) show that both of them are bigger than zero. As a result, the sum of them is a convex function, while the objective function is also a convex function. The optimization problem (formula) of the above interruption probability is an inequality-constrained convex optimization problem. The interior point method in the convex programming method finds the numerical solution.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Pan, W., Lyu, N., Miao, J. et al. Outage probability optimization of UAV relay system based on elliptical trajectory. Wireless Netw 29, 3285–3294 (2023). https://doi.org/10.1007/s11276-023-03387-5
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11276-023-03387-5