3D UAV placement and user association in software-defined cellular networks


With the onset of unexpected or temporary problems resulting in degraded user performance, the flexibility and elasticity requirements of future cellular networks may not be fully satisfied by fixed ground base stations. A promising solution for this deficiency is to establish drone cells, which are formed by quickly deploying unmanned aerial vehicles (UAVs) equipped with base stations. Consequently, a UAV placement and user association algorithm for future software-defined cellular networks (SDCN) is proposed in this study. In consideration of the optimal three-dimensional placement of UAVs and the optimal drone cell users’ associations, a utility maximization problem is formulated by utilizing a global view of the SDCN controller. Following mathematical manipulation, the intractable multidimensional problem is transformed into a two-phase algorithm involving the optimal UAV placement altitude-to-radius ratio and the optimal two-dimensional (2D) drone cell horizontal coverage combined with user association. Simulation results indicate the superiority of the proposed algorithm, which increases the average throughput and average utility of all users compared with random, center and 2D UAV placement schemes. By deploying the new design, the maximum average throughput gain can reach up to \(36.4\%\).

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11


  1. 1.

    \(L_2(o_{ij})\) is differentiable with respect to \(o_{ij}\) and the proof is shown in “Appendix D”.


  1. 1.

    Cisco. (2017). Cisco visual networking index: Global mobile data traffic forecast update. White Paper. http://www.cisco.com. Accessed Feb 2017.

  2. 2.

    Bleicher, A. (2013). A surge in small cell sites. IEEE Spectrum, 50(1), 38–39.

    Article  Google Scholar 

  3. 3.

    Bor-Yaliniz, I., & Yanikomeroglu, H. (2016). The new frontier in RAN heterogeneity: Multi-tier drone-cells. IEEE Communications Magazine, 54(11), 48.

    Article  Google Scholar 

  4. 4.

    Gupta, L., Jain, R., & Vaszkun, G. (2015). Survey of important issues in UAV communication networks. IEEE Communications Surveys and Tutorials, 18(2), 1123–1152.

    Article  Google Scholar 

  5. 5.

    Wu, Q., Zeng, Y., & Zhang, R. (2018). Joint trajectory and communication design for multi-UAV enabled wireless networks. IEEE Transactions on Wireless Communications, 17(3), 2109–2121.

    Article  Google Scholar 

  6. 6.

    Lyu, J., Zeng, Y., Zhang, R., & Lim, T. J. (2017). Placement optimization of UAV-mounted mobile base stations. IEEE Communications Letters, 21(3), 604–607.

    Article  Google Scholar 

  7. 7.

    Bor-Yaliniz, R. I., E1-Keyi, A., & Yanikomeroglu, H. (2016). Efficient 3-D placement of an aerial base station in next generation cellular networks. In: Proceedings of the 2016 IEEE international conference on communications (ICC) (pp. 1–5).

  8. 8.

    Open Networking Foundation. (2011). OpenFlow switch specification. http://archive.openflow.org/documents/openflow-spec-v1.1.0.pdf. Accessed Feb 2011.

  9. 9.

    Arslan, M. Y., Sundaresan, K., & Rangarajan, S. (2015). Software-defined networking in cellular radio access networks: Potential and challenges. IEEE Communications Magazine, 53(1), 150–156.

    Article  Google Scholar 

  10. 10.

    Li, L., Mao, Z. M., & Rexford, J. (2012). Toward software-defined cellular networks. In: Proceedings of the 2012 European workshop on software defined networking (EWSDN) (pp. 7–12).

  11. 11.

    Liyanage, M., Gurtov, A., & Ylianttila, M. (2015). Software defined mobile networks (SDMN): Beyond LTE architecture. Hoboken: Wiley.

    Google Scholar 

  12. 12.

    Yazici, V., Kozat, U. C., & Sunay, M. O. (2014). A new control plane for 5G network architecture with a case study on unified handoff, mobility, and routing management. IEEE Communications Magazine, 52(11), 76–85.

    Article  Google Scholar 

  13. 13.

    3GPP. (2012). Technical specification group services and system aspects; policy and charging control architecture. TS 23.203 ver.9.5.0. Technical report.

  14. 14.

    Pan, C., Yin, C., Beaulieu, N. C., & Yu, J. (2018). Distributed resource allocation in SDCN-based heterogeneous networks utilizing licensed and unlicensed bands. IEEE Transactions on Wireless Communications, 17(2), 711–721.

    Article  Google Scholar 

  15. 15.

    McKeown, N., Anderson, T., Balakrishnan, H., Parulkar, G., Peterson, L., & Rexford, J. (2008). OpenFlow: Enabling innovation in campus networks. ACM SIGCOMM Computer Communication Review, 38(2), 69–74.

    Article  Google Scholar 

  16. 16.

    Open Networking Foundation (ONF). (2013). OpenFlow\(^{\rm TM}\)-enabled mobile and wireless networks. ONF Solution Brief. https://www.opennetworking.org. Accessed Sept 2013.

  17. 17.

    Rappaport, T. S. (2002). Wireless communications: Principles and practice. Upper Saddle River, NJ: Prentice-Hall.

    Google Scholar 

  18. 18.

    Chen, M., Mozzaffari, M., Saad, W., Yin, C., Debbah, M., & Hong, C. S. (2017). Caching in the sky: Proactive deployment of cache-enabled unmanned aerial vehicles for optimized quality-of-experience. IEEE Journal on Selected Areas in Communications, 35(5), 1046–1061.

    Article  Google Scholar 

  19. 19.

    Hourani, A. A., Kandeepan, S., & Lardner, S. (2014). Optimal LAP altitude for maximum coverage. IEEE Wireless Communications Letters, 3(6), 569–572.

    Article  Google Scholar 

  20. 20.

    Challita, U., Saad, W., & Bettstetter C. (2018). Cellular-connected UAVs over 5G: Deep reinforcement learning for interference management. arxiv.org/abs/1801.05500.

  21. 21.

    K. Alexandris, N. Sapountzis, N. Nikaein, & Spyropoulos, T. (2016). Load-aware handover decision algorithm in next-generation HetNets. In Proceedings of the 2016 IEEE wireless communications and networking conference (WCNC) (pp. 1–6).

  22. 22.

    Ye, Q., Rong, B., Chen, Y., Al-Shalash, M., Caramanis, C., & Andrews, J. G. (2013). User association for load balancing in heterogeneous cellular networks. IEEE Transactions on Wireless Communications, 12(6), 2706–2716.

    Article  Google Scholar 

  23. 23.

    Mo, J., & Walrand, J. (2000). Fair end-to-end window-based congestion control. IEEE/ACM Transactions on Networking, 8(5), 555–567.

    Article  Google Scholar 

  24. 24.

    Tao, P. D., & An, L. T. H. (2005). The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Annals of Operations Research, 133(1–4), 23–46.

    MathSciNet  MATH  Google Scholar 

  25. 25.

    Yuille, A. L., & Rangarajan, A. (2001). The concave–convex procedure (CCCP). In Proceedings of the advances in neural information processing systems (pp. 1033–1040).

  26. 26.

    Lanckriet, G. R., & Sriperumbudur, B. K. (2009). On the convergence of the concave–convex procedure. In Proceedingds of the international conference on neural information processing systems (pp. 1759–1767).

  27. 27.

    Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge: Cambridge University Press.

    Google Scholar 

  28. 28.

    Liu, C., Samarakoon, S., & Bennis, M. (2016). Fronthaul-aware software-defined joint resource allocation and user scheduling for 5G networks. In Proceedings of the 2016 IEEE Globecom workshop on femtocell networks (pp. 1–6).

  29. 29.

    Liu, L., Chen, X., Bennis, M., Xue, G., & Han, Z. (2015). A distributed ADMM approach for mobile data offloading in software defined network. In Proceedings of the 2015 IEEE wireless communications and networking conference (WCNC) (pp. 1748–1752).

  30. 30.

    Liu, F., Bala, E., Erkip, E., Beluri, M., & Yang, R. (2015). Small cell traffic balancing over licensed and unlicensed bands. IEEE Transactions on Vehicular Technology, 64(12), 5850–5865.

    Article  Google Scholar 

  31. 31.

    Ma, Z., Wang, M., Brauer, & Fred, (2005). Fundamentals of advanced mathematics. Beijing: Higher Education Press.

    Google Scholar 

Download references


This work was supported in part by the National Natural Science Foundation of China under Grants 61671086, 61629101 and 61871041, in part by the 111 Project under Grant B17007.

Author information



Corresponding author

Correspondence to Chunyu Pan.


Appendix A


Define the midpoint of the domain as \(\mu _j(0)\), and denote the lower bound of the domain as LA and the upper bound as UA. Then, we have

$$\begin{aligned} \mu _j(0)=\frac{1}{2}(LA+UA). \end{aligned}$$

Bring \(\mu _j(0)\) into Eq. (14). If \(\frac{dF(\mu _j(0))}{d\mu _j(0)}=0\), then \(\mu _j(0)\) is the root of Eq. (14).

Otherwise, if \(\frac{dF(LA)}{dLA}\cdot \frac{dF(\mu _j(0))}{d\mu _j(0)}<0\), then \(\mu _j^*\in (LA, \mu _j(0))\), and we set \(\mu _j(1)=LA\), \(UA_1=\mu _j(0)\); if \(\frac{dF(\mu _j(0))}{d\mu _j(0)}\cdot \frac{dF(UA)}{dUA}<0\), then \(\mu _j^*\in (\mu _j(0), UA)\), and we set \(\mu _j(1)=\mu _j(0)\), \(UA_1=UA\).

Note that \([LA_1, UA_1]\) is a new domain of \(\mu _j\), and the length of the new domain is half that of the original one. Through this analogy, we obtain a series of domains according to

$$\begin{aligned}{}[LA, UA]\supset [LA_1, UA_1]\supset \ldots \supset [LA_n, UA_n]. \end{aligned}$$

Since each new domain is half the length of the previous one, the length of \([LA_n, UA_n]\) is

$$\begin{aligned} UA_n-LA_n=\frac{1}{2^n}(UA-LA). \end{aligned}$$

As \(n\rightarrow \infty\), the length of the domain \(UA_n-LA_n\rightarrow 0\).

Finally, we can conclude that the upper bound and the lower bound will converge to the point \(\mu _j^*\) as \(n\rightarrow \infty\).

Appendix B


Due the fact that \(f_{convex}\) is differentiable and strictly convex, \(f_{convex}\) must satisfy the first order condition [26, 27],

$$\begin{aligned} &f_{convex}\big (V(n+1)\big )\!\ge \! f_{convex}\big (V(n)\big )\nonumber \\ &\quad +\,\nabla f_{convex}\big (V(n)\big )\big (V(n\!+\!1)\!-\!V(n)\big )^{T}. \end{aligned}$$

To prove the monotonicity, we first assume that \(V(n+1)\ge V(n)\). We have

$$\begin{aligned} f\big (V(n+1)\big )&= {} f_{concave}\big (V(n+1)\big ) +f_{convex}\big (V(n+1)\big )\nonumber \\ & \ge\, {} f_{concave}\big (V(n+1)\big )+f_{convex}\big (V(n)\big )\nonumber \\&\quad +\,\!\nabla f_{convex}\big (V(n)\big )\big (V(n\!+\!1)\!-\!V(n)\big )^{T}. \end{aligned}$$

Based on Eq. (18), we have

$$\begin{aligned}&f_{concave}\big (V(n+1)\big )+\nabla f_{convex}\big (V(n) \big )*\big (V(n+1)\big )^T\nonumber \\& \ge\, {} f_{concave}\big ((V(n))\big )+\nabla f_{convex}\big (V(n)\big )*\big (V(n)\big )^Ts, \end{aligned}$$

and after transposition, we have

$$\begin{aligned} & f_{concave}\big (V(n+1)\big )\ge f_{concave}\big ((V(n))\big )\nonumber \\ &-\nabla f_{convex}\big (V(n)\big )*\Big (\big (V(n+1)-V(n)\big )\Big )^T. \end{aligned}$$

Combining Eqs. (22) with (20) yields

$$\begin{aligned} f\big (V(n+1)\big )\ge f_{concave}\big (V(n)\big )+f_{convex}\big (V(n)\big ), \end{aligned}$$

after which we have

$$\begin{aligned} f\big (V(n+1)\big )\ge f\big (V(n)\big ). \end{aligned}$$

Thus, Eq. (17) is strictly monotonically increasing on the generated sequence \(\{V(n)\}\).

If \({\mathcal {S}}_V\ne \varnothing\), it is easy to verify that \({\mathcal {S}}_V\) is closed and bounded from the constraints of (17). As shown in Remark 7 in [26], we can show that as \(n\rightarrow \infty\), \(||V_{n+1}-V_{n}||\rightarrow 0\), and \(\{V(n+1)\}\) converges (the limit points of \(\{V(n)\}\) are expressed as \(\overset{\infty }{V}\)).

Finally, we can conclude that the sequence of {\(V(n+1)\)} from the CCCP converges to \(\overset{\infty }{V}\).

Appendix C

Proof of Eq. 16

Note that \(F(V)=f_{concave}(V)+f_{convex}(V)\) and we define \(f_{concave}(V)\triangleq L_1(r_j)\) and \(f_{convex}(V)\triangleq -L_2(o_{ij})\) in the paper. To proof Eq. (), we just need to prove 16\(f_{convex}(V)\) is convex and \(f_{concave}(V)\) is concave. To do this, the proof is divided into two parts.

Part 1 (Prove that \(F_{convex}(V)\) is convex):

Choose any \(o_{ij}\), where \(o_{ij}\in\)dom\({{\mathcal {S}}}_V\), and dom\({{\mathcal {S}}}_V\) is convex (i.e., an interval).

Then, we have

$$\begin{aligned} {f_{convex}(o_{ij})}&{=-\sum _i\sum _j{\mathrm{U}}(\sum _i o_{ij})}\nonumber \\&{=-\sum _i\sum _j\log (o_{ij}).} \end{aligned}$$

The derivative of Eq. (2) is

$$\begin{aligned} {\nabla ^2 f_{convex}(o_{ij})}&{=(-\frac{1}{\sum _i\sum _j(o_{ij})})'}\nonumber \\&{=\frac{1}{\sum _i\sum _j(o_{ij})^2}\ge 0,} \end{aligned}$$

where \(\nabla ^2 f_{convex}(o_{ij})\) is the second derivative of \(f_{convex}(o_{ij})\).

Based on the second-order conditions [27], i.e. \(\nabla ^2 f_{convex}(o_{ij})\ge 0\), we conclude that \(f_{convex}(V)\) is convex.

Part 2 (Prove that \(F_{concave}(V)\) is concave):

Choose any \(r_{j}\), where \(r_{j}\in\)dom\({{\mathcal {S}}}_V\), and dom\({{\mathcal {S}}}_V\) is convex (i.e., an interval).

Then, we have

$$\begin{aligned} {f_{concave}(r_j)}&{=\sum _i\sum _j{\log }(B)+\sum _i\sum _j{\log } {\Bigg (}{\mathrm{{log}}}{\bigg (}\frac{P_{{T_D},j}}{\sigma ^2}{\bigg )}}\nonumber \\&\quad {-2{\log }{\bigg (}\frac{4\pi f_c}{c}{\bigg )}-2{\mathrm{{log}}}{\Big (}\sqrt{(1+\mu _j^{*2})r_j^2} {\Big )}}\nonumber \\&\quad {-\frac{1}{10}P_{\mu _j^*}\eta _{Los}-\frac{1}{10}{\Big (}1 -P_{\mu _j^*}{\Big )}\eta _{NLos}{\Bigg )}.} \end{aligned}$$

The derivative of Eq. (3) is

$$\begin{aligned} {\nabla ^2 f_{concave}(r_{j})=}&{-\frac{1}{\sum _jr^2_{j}{\Big (}\log {\Big (}\sqrt{(1+\mu _j^{*2})r_j^2}{\Big )}{\Big )}^2}}\nonumber \\&{-\frac{1}{\sum _jr_j^2\log {\Big (}\sqrt{(1+\mu _j^{*2})r_j^2}{\Big )}}.} \end{aligned}$$

We numerically construct the graph of Eq. (31) based on the interval domain \(d_{ij}^h\le r_j\le (F(\mu _j^*))^{\frac{1}{2}}\) in Fig. 12 for the high-rise urban environment, since we can not judge whether the Hessian is positive or not directly.

Fig. 12

The function of \(\nabla ^2 f_{concave}(r_{j})\) versus \(r_j\)

The results in Fig. 12 indicate that the second-order conditions [27] are satisfied, i.e. \(\nabla ^2 f_{concave}(r_{j})\le 0\), which means that \(F_{concave}(V)\) is concave.

Appendix D

Proof that \(L_2(o_{ij})\) is differentiable with respect to \(o_{ij}\)

From “Appendix C”, we know that function \(f_{convex}=-L_2(o_{ij})\) is differentiable at any point \(o_{ij}\) in dom\({{\mathcal {S}}}_V\). For simplicity, \(f_{o_{ij}}\) is used to represent the value of \(L_2(o_{ij})\). Thus, the increments \(\varDelta o_{ij}\) and \(\varDelta f_{o_{ij}}\) exist and satisfy

$$\begin{aligned} {\lim _{\varDelta o_{ij}\rightarrow 0}\frac{\varDelta f_{o_{ij}}}{\varDelta o_{ij}}=\nabla f_{convex}(o_{ij}),} \end{aligned}$$

where \(\varDelta\) is the incremental symbol and \(\nabla\) is the derivative symbol.

Theorem 1

The sufficient and necessary condition for the existence of the limitAof the functionf(x) is that\(f(x)=A+\alpha\), where\(\alpha\)is infinitesimal [31].

In our problem, Theorem 1 can be expressed as: The sufficient and necessary condition for the existence of the limit \(\overset{\infty }{o}_{ij}\) of function \(f_{convex}(o_{ij})\) is that \(f_{convex}(o_{ij})=\overset{\infty }{o}_{ij}+\alpha\), where \(\alpha\) is infinitesimal. Thus, Eq. (32) can be rewritten as

$$\begin{aligned} {\varDelta f_{o_{ij}}=\nabla f_{convex}(o_{ij})\varDelta o_{ij}+\alpha \varDelta o_{ij}.} \end{aligned}$$

Since \(\alpha \varDelta o_{ij}=0(\varDelta o_{ij})\), and \(\nabla f_{convex}(o_{ij})\) is independent of \(\varDelta o_{ij}\), Eq. (33) is equal to

$$\begin{aligned} {\varDelta f_{o_{ij}}=\nabla f_{convex}(o_{ij})\varDelta o_{ij}+0(\varDelta o_{ij}).} \end{aligned}$$

Thus, we conclude that \(f_{convex}\) is differentiable at any \(o_{ij}\) in dom\({{\mathcal {S}}}_V\), which means that \(L_2(o_{ij})\) is differentiable with respect to \(o_{ij}\).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Pan, C., Yin, C., Beaulieu, N.C. et al. 3D UAV placement and user association in software-defined cellular networks. Wireless Netw 25, 3883–3897 (2019). https://doi.org/10.1007/s11276-018-01925-0

Download citation


  • CCCP
  • Drone-cell
  • Software defined cellular networks
  • Unmanned aerial vehicles
  • UAV placement
  • User association