Skip to main content
SpringerLink
Log in

A stochastic geometric programming approach for power allocation in wireless networks

  • Original Paper
  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

In this paper, we consider the power allocation problem for 5 G wireless networks using massive multiple input multiple output technologies. Two non-linear optimization models are considered to maximize the worst user signal-to-interference noise ratio and the total capacity of the network subject to power constraints. In particular, we transform the first one into a geometric programming (GP) problem. Whereas the second one leads to a signomial programming formulation. The main contributions of the paper are first to propose novel formulations for power allocation in wireless networks while using stochastic, geometric, and signomial programming frameworks altogether. We derive stochastic formulations for each GP model to deal with the uncertainty of wireless channels. Secondly, since solving optimally the stochastic models represents a challenging task, we obtain tight bounds using approximation solution methods. In particular, the piece-wise linear programming and the sequential approximation methods allow us to obtain tight intervals for the objective function values of the stochastic models. Notice that these intervals contain the optimal solutions. In particular, we propose an approximated GP model that allows obtaining lower bounds for the signomial problem. This is achieved by using the arithmetic–geometric mean inequality. Finally, we compare the deterministic and stochastic models and prove the robustness of the stochastic models. Notice that we solve all the instances and obtain near-optimal solutions for most of them.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Chiasserini, C., & Magnan, A. IEEE 5G for the Automotive Domain, https://futurenetworks.ieee.org/images/files/pdf/applications/5G-for-the-Automotive-Domain030518.pdf

  2. Somisetty, M. Big Data Analytics in 5G, https://futurenetworks.ieee.org/images/files/pdf/applications/Data-Analytics-in-5G-Applications030518.pdf

  3. Markakis, E., & Politis, I., 5G Emergency Communications, https://futurenetworks.ieee.org/images/files/pdf/applications/Emergency-Communications030518.pdf

  4. Orsino, A., Yilmaz, O. N.C., & Torsner, J. Ericsson Research, Factories of the Future Enabled by 5G Technology, https://futurenetworks.ieee.org/images/files/pdf/applications/Factories-of-the-Future-Enabled-by-5G-Technology_030518.pdf

  5. Rao, K. The Path to 5G for Health Care, https://futurenetworks.ieee.org/images/files/pdf/applications/5G--Health-Care030518.pdf

  6. Mangra, N., & Ghasempour, A. Smart Cities: Connected Ecosystem of Ecosystems, https://futurenetworks.ieee.org/images/files/pdf/applications/Smart-Cities_030518.pdf

  7. IEEE 5G and Beyond Technology Roadmap, https://futurenetworks.ieee.org/images/files/pdf/ieee-5g-roadmap-white-paper.pdf

  8. Boyd, S., Kim, S. J., Vandenberghe, L., & Hassibi, A. (2007). A tutorial on geometric programming. Optimization and Engineering, 8(67), 67–127.

    Article  MathSciNet  MATH  Google Scholar 

  9. Duffin, R., Peterson, E., & Zener, C. (1967). Geometric programming-theory and application. New York: Wiley.

    MATH  Google Scholar 

  10. Parsaeefard, S., Jumba, V., Shoaei, A. D., Derakhshani, M., & Le-Ngoc, T. (2021). User association in cloud RANs with massive MIMO. IEEE Transactions on Cloud Computing, 9(2), 821–833.

    Article  Google Scholar 

  11. Liu, J., Lisser, A., & Chen, Z. (2016). Stochastic geometric optimization with joint probabilistic constraints. Operations Research Letters, 44, 687–691.

    Article  MathSciNet  MATH  Google Scholar 

  12. Azizi, A., Parsaeefard, S., Javan, M. R., Mokari, N., & Yanikomeroglu, H. (2020). Profit maximization in 5G+ networks with heterogeneous aerial and ground base stations. IEEE Transactions on Mobile Computing, 19(10), 2445–2460.

    Article  Google Scholar 

  13. Bashar, M., Cumanan, K., Burr, A. G., Ngo, H. Q., Larsson, E. G., & Xiao, P. (2019). Energy efficiency of the cell-free massive mimo uplink with optimal uniform quantization. IEEE Transactions on Green Communications and Networking, 3(4), 971–987.

    Article  Google Scholar 

  14. Amani, N., Pedram, H., Taheri, H., & Parsaeefard, S. (2019). Energy-efficient resource allocation in heterogeneous cloud radio access networks via BBU offloading. IEEE Transactions on Vehicular Technology, 68(2), 1365–1377.

    Article  Google Scholar 

  15. Tweed, D., Derakhshani, M., Parsaeefard, S., & Le-Ngoc, T. (2017). Outage-constrained resource allocation in uplink NOMA for critical applications. IEEE Access, 5, 27636–27648.

    Article  Google Scholar 

  16. Parsaeefard, S., Dawadi, R., Derakhshani, M., Le-Ngoc, T., & Baghani, M. (2017). Dynamic resource allocation for virtualized wireless networks in massive-MIMO-Aided and Fronthaul-limited C-RAN. IEEE Transactions on Vehicular Technology, 66(10), 9512–9520.

    Article  Google Scholar 

  17. Lakani, S., & Gagnon, F. (2017). Optimal design and energy efficient binary resource allocation of interference-limited cellular relay-aided systems with consideration of queue stability. IEEE Access, 5, 8459–8474.

    Article  Google Scholar 

  18. Gao, H., Su, Y., Zhang, S., & Diao, M. (2019). Antenna selection and power allocation design for 5G massive MIMO uplink networks. China Communications, 16(4), 1–15.

    Google Scholar 

  19. Benmimoune, M., Driouch, E., Ajib, W., & Massicotte, D. (2015). Joint Transmit Antenna Selection and User Scheduling for Massive MIMO Systems, in IEEE Wireless Communications and Networking Conference (WCNC). https://ieeexplore.ieee.org/document/7127500

  20. Pedram, M., & Wang, L. (2020). Energy efficiency in 5G cellular network systems. IEEE Design and Test, 37(1), 64–78.

    Article  Google Scholar 

  21. Zhang, J., Zhang, Y., Xiang, L., Sun, Y., Kwan Ng, D. W., & Jo, M. (2021). Robust energy-efficient transmission for wireless-powered d2d communication networks. IEEE Transactions on Vehicular Technology, 70(8), 7951–7965.

    Article  Google Scholar 

  22. Le, A. T., Ha, N. D. X., Do, D. T., Silva, A., & Yadav, S. (2021). Enabling user grouping and fixed power allocation scheme for reconfigurable intelligent surfaces-aided wireless systems. IEEE Access, 9, 92263–92275.

    Article  Google Scholar 

  23. Lu, H., Jiang, X., & Chen, C. W. (2021). Distortion-aware cross-layer power allocation for video transmission over multi-user NOMA systems. IEEE Transactions on Wireless Communications, 20(2), 1076–1092.

    Article  Google Scholar 

  24. Chiang, M., Tan, C. W., Palomar, D. P., Ońeill, D., & Julian, D. (2007). Power control by geometric programming. IEEE Transactions on Wireless Communications, 6(7), 2640–2651.

    Article  Google Scholar 

  25. Cheng, J., Delage, E., & Lisser, A. (2014). Distributionally robust stochastic knapsack problem. SIAM Journal on Optimization, 24(3), 1485–1506.

    Article  MathSciNet  MATH  Google Scholar 

  26. Cheng, J., & Lisser, A. (2012). A second-order cone programming approach for linear programs with joint probabilistic constraints. Operations Research Letters, 40, 325–328.

    Article  MathSciNet  MATH  Google Scholar 

  27. Lobo, M., Vandenberghe, L., Boyd, S., & Lebret, H. (1998). Applications of second-order cone programming. Linear Algebra and its Applications, 284, 193–228.

    Article  MathSciNet  MATH  Google Scholar 

  28. Luedtke, J., Ahmed, S., & Nemhauser, G. (2010). An integer programming approach for linear programs with probabilistic constraints. Mathematical Programming, 122, 247–272.

    Article  MathSciNet  MATH  Google Scholar 

  29. Prékopa, A. (1995). Stochastic Programming, in: Mathematics and Its Applications, 324, Springer Netherlands.

  30. Prékopa, A. (1970). On probabilistic constrained programming Proceedings of the Princeton Symposium on Mathematical Programming. Princeton University Press, Princeton.

  31. Shapiro, A., Dentcheva, D., & Ruszczynski, A. (2009). Lectures on stochastic programming: Modeling and theory, 436. SIAM Philadelphia, Series on Optimization, 9 of MPS/SIAM, Philadelphia.

  32. Adasme, P., & Lisser, A. (2014). Stochastic and semidefinite optimization for scheduling in orthogonal frequency division multiple access networks. Journal of Scheduling, 17(5), 445–469.

    Article  MathSciNet  MATH  Google Scholar 

  33. Adasme, P., & Lisser, A. (2016). Uplink scheduling for joint wireless orthogonal frequency and time division multiple access networks. Journal of Scheduling, 19(3), 349–366.

    Article  MathSciNet  MATH  Google Scholar 

  34. Dupacová, J. Stochastic geometric programming: approaches and applications, In V. Brozová, R. Kvasnicka, eds., Proceedings of MME09, 2009, pp. 63-66.

  35. Rao, S. S. (1996). Engineering Optimization: Theory and Practice (3rd ed.). New York: Wiley- Interscience.

    Google Scholar 

  36. Liu, J., Peng, S., Lisser, A., & Chen, Z. (2020). Rectangular chance constrained geometric optimization. Optimization and engineering, 21, 537–566.

    Article  MathSciNet  MATH  Google Scholar 

  37. Haleem, M. A. (2018). On the Capacity and Transmission Techniques of Massive MIMO Systems. Wireless Communications and Mobile Computing. https://doi.org/10.1155/2018/9363515

    Article  Google Scholar 

  38. Adasme, P., Soto, I., Juan, E. S., Seguel, F., & Firoozabadi, A. D. (2020). Maximizing Signal to Interference Noise Ratio for Massive MIMO: A Mathematical Programming Approach, 2020 South American Colloquium on Visible Light Communications (SACVC), 1-6. https://ieeexplore.ieee.org/document/9129889

  39. Valduga, S., Deneire, L., Pardo, R., Almeida, A., Maciel, T., & Mota, J. (2018). Low complexity heuristics to beam selection and rate adaptation in sparse massive MIMO systems. Transactions on Emerging Telecommunication Technologies, 29(9), e3459.

    Article  Google Scholar 

  40. Diamond, S., & Boyd, S. (2016). CVXPY: A Python-embedded modeling language for convex optimization. The Journal of Machine Learning Research, 17(83), 1–5.

    MathSciNet  MATH  Google Scholar 

  41. Agrawal, A., Verschueren, R., Diamond, S., & Boyd, S. (2018). A rewriting system for convex optimization problems. Journal of Control and Decision, 5(1), 42–60.

    Article  MathSciNet  Google Scholar 

  42. MOSEK solver version 9.2.42, 2021, https://www.mosek.com/. MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constraint, conic and convex nonlinear mathematical optimization problems.

  43. Mohajer, A., Daliri, M. S., Mirzaei, A., Ziaeddini, A., Nabipour, M., & Bavaghar, M. (2022). Heterogeneous Computational Resource Allocation for NOMA: Toward Green Mobile Edge-Computing SystemsIEEE Transactions on Services Computing 1-14. https://doi.org/10.1109/TSC.2022.3186099

  44. Mohajer, A., Bavaghar, M., & Farrokhi, H. (2020). Mobility-aware load Balancing for Reliable Self-Organization Networks: Multi-agent Deep Reinforcement Learning, Reliability Engineering & System Safety, Volume 202, https://doi.org/10.1016/j.ress.2020.107056

  45. Mohajer, A., Sorouri, F., Mirzaei, A., Ziaeddini, A., Rad, K. J., & Bavaghar, M. (2022). Energy-Aware Hierarchical Resource Management and Backhaul Traffic Optimization in Heterogeneous Cellular Networks, in IEEE Systems Journal, 1-12. https://doi.org/10.1109/JSYST.2022.3154162

Download references

Acknowledgements

The authors acknowledge the financial support from Project: FONDECYT No. 11180107 and from Project Dicyt 062313AS.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Universidad de Santiago de Chile, Avenida Victor Jara 3519, Santiago, 9160000, Chile

    Pablo Adasme

  2. Laboratoire de Signaux & Systemes L2S, Centrale Supélec Bat. Breguet A 4.22 3, rue Joliot Curie, 91190, Gif-sur-Yvette, France

    Abdel Lisser

Authors
  1. Pablo Adasme
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdel Lisser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pablo Adasme.

Ethics declarations

Conflict of interest

The authors have no conficts of interest to declare that are relevant to the content of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 185 KB)

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Adasme, P., Lisser, A. A stochastic geometric programming approach for power allocation in wireless networks. Wireless Netw 29, 2235–2250 (2023). https://doi.org/10.1007/s11276-023-03295-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-023-03295-8

Keywords

Search

Navigation