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Resource allocation in future HetRAT networks: a general framework

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Abstract

Aggregation of resources in space, spectrum, and so on, is the fundamental idea behind many technology building blocks of 5G networks, such as massive multi-input multi-output and carrier aggregation, among others. In this respect, another important dimension for parallelism is the aggregation of diverse radio access technologies (RATs), such as WiFi, LTE, and 5G, in heterogeneous networks (HetRAT networks). Simultaneous multiple RAT connectivity facilitates both users and network operators in achieving even higher data rates and in balancing the traffic load, respectively. In this paper, we review the technological supports for the realization of the multi-RAT connectivity and focus on a general framework for resource allocation in HetRAT systems. Specifically, a distributed algorithm is proposed to allocate, with minimal overhead signaling, the bandwidths of available RATs among users considering both the system operator’s objective and the users’ demands and constraints. The optimality of the proposed distributed algorithm is further proved, and its convergence is investigated. Finally a test case is introduced in which users are power constrained and the system operator enforces capacity limits and motivates users for a fair load balancing over RATs. Numerical results shows the efficiency of the proposed algorithm and its fast convergence in few iterations.

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Notes

  1. In practice this assumption can be realized by inserting slack variables and barrier terms to the problem [33].

References

  1. ITU-R M.[IMT.VISION]. IMT Vision—Framework and Overall Objectives of the Future Development of IMT for 2020 and Beyond. ITU Working Document 5D/TEMP/224-E, July 2013.

  2. NGMN Alliance. (Feb. 2015). 5G White Paper. [Online]. Available: http://www.3gpp.org/technologies/presentations-white-papers.

  3. 3GPP. (2015) Architecture enhancements for non-3GPP accesses. 3GPP Mobile Competence Centre c/o ETSI, Sophia Antipolis Cedex, France, Tech. Specification TS 23.402.

  4. Bangerter, B., Talwar, S., Arefi, R., & Stewart, K. (2014). Networks and devices for the 5G era. IEEE Communications Magazine, 52, 90–96.

    Article  Google Scholar 

  5. Project RAN evolution: Multi-RAT joint radio operation (MRJRO), NGMN alliance, Reading, MA, USA, Technical Report, Marce 2015.

  6. Irmer, R., Droste, H., Marsch, P., Grieger, M., Fettweis, G., Brueck, S., et al. (2011). Coordinated multipoint: Concepts, performance, and field trial results. IEEE Communications Magazine, 49, 102–111.

    Article  Google Scholar 

  7. Lim, G., Xiong, C., Cimini, L. J., & Li, G. Y. (2014). Energy-efficient resource allocation for OFDMA-based multi-RAT networks. IEEE Transactions on Wireless Communications, 13, 2696–2705.

    Article  Google Scholar 

  8. Andrews, M., Kumaran, K., Ramanan, K., Stolyar, A., Whiting, P., & Vijayakumar, R. (2001). Providing quality of service over a shared wireless link. IEEE Communications Magazine, 39, 150–154.

    Article  Google Scholar 

  9. Eryilmaz, A., & Srikant, R. (2007). Fair resource allocation in wireless networks using Queue-length-based scheduling and congestion control. IEEE/ACM Transactions on Networking, 15, 1333–1344.

    Article  Google Scholar 

  10. Stanczak, S., Wiczanowski, M., & Boche, H. (2008). Fundamentals of resource allocation in wireless networks: Theory and algorithms. Berlin: Springer.

    Book  Google Scholar 

  11. Damnjanovic, A., Montojo, J., Wei, Y., Ji, T., Luo, T., Vajapeyam, M., et al. (2011). A survey on 3GPP heterogeneous networks. IEEE Wireless Communications, 18, 10–21.

    Article  Google Scholar 

  12. Dai, H., Huang, Y., & Yang, L. (2015). Game theoretic max-logit learning approaches for joint base station selection and resource allocation in heterogeneous networks. IEEE Journal on Selected Areas in Communications, 33, 1068–1081.

    Article  Google Scholar 

  13. Lopez-Perez, D., Valcarce, A., de la Roche, G., & Zhang, J. (2009). OFDMA femtocells: A roadmap on interference avoidance. IEEE Communications Magazine, 47, 41–48.

    Article  Google Scholar 

  14. Andrews, J. G., Singh, S., Ye, Q., Lin, X., & Dhillon, H. S. (2014). An overview of load balancing in HetNets: Old myths and open problems. IEEE Transactions on Wireless Communications, 21, 18–25.

    Article  Google Scholar 

  15. Chen, Q., Yu, G., Shan, H., Maaref, A., Li, G. Y., & Huang, A. (2016). Cellular meets WiFi: Traffic offloading or resource sharing? IEEE Transactions on Wireless Communications, 15, 3354–3367.

    Article  Google Scholar 

  16. Wang, K., Yang, K., & Magurawalage, C. S. (2018). Joint energy minimization and resource allocation in C-RAN with mobile cloud. IEEE Transactions on Mobile Computing, 6, 760–770.

    Google Scholar 

  17. Moshref, M., Yu, M., Govindan, R., & Vahdat, A. (2014). DREAM: Dynamic resource allocation for software-defined measurement. In SIGCOMM

  18. Wang, L., Lu, Z., Wen, X., Knopp, R., & Gupta, R. (2016). Joint optimization of service function chaining and resource allocation in network function virtualization. IEEE Access, 4, 8084–8094.

    Article  Google Scholar 

  19. Yu, F., & Krishnamurthy, V. (2007). Optimal joint session admission control in integrated WLAN and CDMA cellular networks with vertical handoff. IEEE Transactions on Mobile Computing, 6, 126–139.

    Article  Google Scholar 

  20. Niyato, D., & Hossain, E. (2009). Dynamics of network selection in heterogeneous wireless networks: An evolutionary game approach. IEEE Transactions on Vehicular Technology, 58, 2008–2017.

    Article  Google Scholar 

  21. Naghavi, P., Rastegar, S. H., Shah-Mansouri, V., & Kebriaei, H. (2016). Learning rat selection game in 5G heterogeneous networks. IEEE Communications Letters, 5, 52–55.

    Article  Google Scholar 

  22. Galinina, O., Pyattaev, A., Andreev, S., Dohler, M., & Koucheryavy, Y. (2015). 5G Multi-RAT LTE-WiFi ultra-dense small cells: Performance dynamics, architecture, and trends. IEEE Journal on Selected Areas in Communications, 33, 1224–1240.

    Article  Google Scholar 

  23. Gerasimenko, M., Moltchanov, D., Andreev, S., Koucheryavy, Y., Himayat, N., Yeh, S. P., et al. (2017). Adaptive resource management strategy in practical multi-radio heterogeneous networks. IEEE Access, 5, 219–235.

    Article  Google Scholar 

  24. Singh, S., Yeh, S. P., Himayat, N., & Talwar, S. (2016, May). Optimal traffic aggregation in multi-rat heterogeneous wireless networks. In IEEE International Conference on Communication, Workshops (ICC) (pp. 626–631).

  25. OMA Device Management Protocol, v. 1.3, OMA-TS-DM-Protocol-V1-3, Open Mobile Alliance, May 2016.

  26. Stewart, R. (2007, September). Stream Control Transmission Protocol. RFC 4960, IETF Network Working Group.

  27. Ford, A., Raiciu, C., Handley, M., & Bonaventure, O. (2013, January). TCP extensions for multipath operation with multiple addresses. RFC 6824, IETF.

  28. Gundavelli, S., Leung, K., Devarapalli, V., Chowdhury, K., & Patil, B. (2008, August). Proxy Mobile IPv6. RFC 5213, IETF Network Working Group.

  29. Kelly, F., Maulloo, A., & Tan, D. (1998). Rate control for communication networks: Shadow prices, proportional fairness and stability. Operational Research Society, 49, 237–252.

    Article  Google Scholar 

  30. Qiu, Y., & Marbach, P. (2003, March). Bandwidth allocation in ad hoc networks: A price-based approach. In IEEE INFOCOM (Vol. 2, pp. 797–807).

  31. Altman, E., Boulogne, T., El-Azouzi, R., Jimenez, T., & Wynter, L. (2006). A survey on networking games in telecommunications. Computers & Operations Research, 33(2), 286–311.

    Article  MathSciNet  Google Scholar 

  32. Osborne, M. J. (2003). An introduction to game theory. London: Oxford University Press.

    Google Scholar 

  33. Bertsekas, D. P. (1995). Nonlinear programming. Bertsekas: Athena Scientific.

    MATH  Google Scholar 

  34. 3GPP, Radio Frequency (RF) system scenarios. Technical Specification Group Radio Access Network, Technical Report TR 25.942 (2017).

  35. 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, 2706–2716.

    Article  Google Scholar 

  36. 3GPP. (2017). Radio Frequency (RF) system scenarios. Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA), Technical Report TR 36.942

  37. Huang, J., Qian, F., Gerber, A., Mao, Z. M., Sen, S., & Spatscheck, O. (2012, June). A close examination of performance and power characteristics of 4G LTE networks. In ACM MobiSys.

  38. Conejo, A., Nogales, F., & Prieto, F. (2002). A decomposition procedure based on approximate Newton directions. Mathematical Programming, Series A. New York: Springer.

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Correspondence to Mohammad Hossein Manshaei.

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Appendices

Appendix 1: Proof of Proposition 1

A feasible strategy profile \(\varvec{s}^*=\{\varvec{s}^*_i\}_{i=1}^{Q}\) is an NE of the \(\mathcal {G}\) if

$$\begin{aligned} \Gamma _i(\varvec{s}^{*}_i,\varvec{s}^{*}_{-i})\le \Gamma _i(\varvec{s}_i,\varvec{s}^*_{-i})\quad \forall \varvec{s}_i\in \mathcal {S}_i, i=1,\ldots , Q, \end{aligned}$$
(16)

This means that, for \(i=1,\ldots ,Q\), \(({\varvec{s}}^*_i,s^*_{-i})\) solves the optimization problem of the ith UE given in (4). As a result, the strategy profile \(({\varvec{s}}^*_i,{\varvec{s}}^*_{-i})\) satisfies in the Karush-Kuhn-Tucker (KKT) conditions in the form of

$$\begin{aligned}&0\le s^*_{i,n} {{\perp }} \left( \frac{\partial ( u_i({\varvec{s}}^*_i)+ f({\varvec{s}}^*,{\varvec{r}}))}{\partial s_{i,n}} - \sum _{m=1}^{c_i}\lambda _{i,m}\frac{\partial g_{i,m}({\varvec{s}}^*_i)}{\partial s_{i,n}}\right) \ge 0;\nonumber \\&\quad n=1,\ldots ,N, \end{aligned}$$
(17)
$$\begin{aligned}&0\le \lambda _{i,m} {{\perp }} g_{i,m}({\varvec{s}}^*_i)\ge 0;\quad m=1,\ldots ,c_i, \end{aligned}$$
(18)

where \(\{\lambda _{i,m}\}_{m=1}^{c_i}\) are the Lagrange multipliers and the operator \({{\perp }}\) means the orthogonality of the operands. On the other hand, if the KKT optimality conditions of every UE’s problem in (17)–(18) (\(i=1,\ldots ,Q\)) are put together, it can be readily verified that they are identical to the first-order optimality conditions of the global problem in (5).

Appendix 2: Proof of Proposition 2

The first order method is given by

$$\begin{aligned} \bar{\varvec{s}}\leftarrow \bar{\varvec{s}}+\alpha \nabla _{\varvec{s}}\mathcal {L}(\bar{\varvec{s}},\bar{\varvec{\lambda }}),\quad \bar{\varvec{\lambda }}\leftarrow \bar{\varvec{\lambda }}+\alpha \varvec{g(\bar{\varvec{s}}),} \end{aligned}$$
(19)

where the operator \(\nabla _{\varvec{s}}\) gives the vector of first derivatives (gradient) of its operand with respect to \(\varvec{s}\), \(\varvec{g(\bar{\varvec{s}})}=[g_{1,1}(\bar{\varvec{s}}_1),\ldots ,g_{Q,c_Q}(\bar{\varvec{s}}_Q)]\) and \(\alpha >0\) is a scalar stepsize. On the other hand, (19) can be re-written as

$$\begin{aligned} \bar{\varvec{s}}_i\leftarrow \bar{\varvec{s}}_i+\alpha \nabla _{\varvec{s}_i}\mathcal {L}(\bar{{\varvec{s}}}, \bar{\varvec{\lambda }}),\quad \bar{\varvec{\lambda }}_i\leftarrow \bar{\varvec{\lambda }}_i+\alpha \varvec{g_i(\bar{\varvec{s}}),} \end{aligned}$$
(20)

for \(i=1,\ldots ,Q,\) where \(\varvec{g_i(\bar{\varvec{s}})}=[g_{i,1}(\bar{\varvec{s}}_1),\ldots ,g_{i,c_i}(\bar{\varvec{s}}_Q)].\) Equations in (20) show that distributed implementation of the first order method is equivalent to the centralized implementation.

Appendix 3: Proof of Proposition 3

Newton’s method for solving the Lagrangian system is

$$\begin{aligned} \bar{\varvec{s}}\leftarrow \bar{\varvec{s}}+\Delta \bar{\varvec{s}},\quad \bar{\varvec{\lambda }}\leftarrow \bar{\varvec{\lambda }}+\Delta \bar{\varvec{\lambda }}, \end{aligned}$$
(21)

where \(\Delta \bar{\varvec{s}}\) and \(\Delta \bar{\varvec{\lambda }}\) are given by solving the system of equations

$$\begin{aligned} \underbrace{\nabla ^2\mathcal {L}(\bar{{\varvec{s}}},\bar{\varvec{\lambda }})}_{\mathbf {K}}\left( \begin{array}{c} \Delta \bar{\varvec{s}} \\ \Delta \bar{\varvec{\lambda }} \end{array}\right) =-\nabla \mathcal {L}(\bar{{\varvec{s}}},\bar{\varvec{\lambda }}). \end{aligned}$$
(22)

Without loss of generality, consider the case in which two single constrained UEs compete for resource allocation. Under this assumption, we have

$$\begin{aligned}&\mathbf {K} =\left( \begin{array}{l l} \mathbf {K}_1&{} \mathbf {K}_{1,2}\\ \mathbf {K}_{2,1}&{}\mathbf {K}_2 \end{array}\right) , \quad \nabla \mathcal {L}(\bar{{\varvec{s}}},\bar{\varvec{\lambda }})= \left( \begin{array}{c} \nabla _{\varvec{s}_1}\mathcal {L}(\bar{{\varvec{s}}},\bar{\varvec{\lambda }})\\ g_{1,1}(\bar{\varvec{s}}_1) \\ \nabla _{\varvec{s}_2}\mathcal {L}(\bar{{\varvec{s}}},\bar{\varvec{\lambda }})\\ g_{2,1}(\bar{\varvec{s}}_2) \end{array}\right) , \end{aligned}$$
(23)

where

$$\begin{aligned}&\mathbf {K}_1=\left( \begin{array}{l l} \nabla ^2_{\varvec{s}_1,\varvec{s}_1}\mathcal {L}(\bar{{\varvec{s}}},\bar{\varvec{\lambda }})&{} \nabla _{\bar{{\varvec{s}}}_1} g_{1,1}(\bar{{\varvec{s}}}_1)\\ {\nabla _{\bar{{\varvec{s}}}_1} g_{1,1}(\bar{{\varvec{s}}}_1)}^T&{}\mathbf {0} \end{array}\right) ,\nonumber \\&\mathbf {K}_2=\left( \begin{array}{l l} \nabla ^2_{\varvec{s}_2,\varvec{s}_2}\mathcal {L}(\bar{{\varvec{s}}},\bar{\varvec{\lambda }})&{} \nabla _{\bar{{\varvec{s}}}_2} g_{2,1}(\bar{{\varvec{s}}}_2)\\ {\nabla _{\bar{{\varvec{s}}}_2} g_{2,1}(\bar{{\varvec{s}}}_2)}^T&{}\mathbf {0} \end{array}\right) ,\nonumber \\&\mathbf {K}_{1,2}=\left( \begin{array}{l l} \nabla ^2_{\varvec{s}_1,\varvec{s}_2}\mathcal {L}(\bar{{\varvec{s}}},\bar{\varvec{\lambda }})&{} \mathbf {0}\\ \mathbf {0}&{}\mathbf {0} \end{array}\right) ,\nonumber \\&\mathbf {K}_{2,1}=\mathbf {K}_{1,2}^T. \end{aligned}$$
(24)

The coupling submatrices \(\mathbf {K}_{1,2}\) and \(\mathbf {K}_{2,1}\) hinder the distributed implementation of the Newton step. This problem is resolved if the matrix \(\mathbf {K}\) is replaced by \(\mathbf {K}_0\) given by

$$\begin{aligned} \mathbf {K}_0 =\left( \begin{array}{l l} \mathbf {K}_1&{} \mathbf {0}\\ \mathbf {0}&{}\mathbf {K}_2 \end{array}\right) . \end{aligned}$$
(25)

On the other hand, based on [38], we can conclude that using \(\mathbf {K}_0\) instead of \(\mathbf {K}\) does not affect the convergence to the optimal solution if coupling is below a specific threshold, mathematically described as \(\rho (\mathbf {I}-\mathbf {K}_0^{*^{-1}}\mathbf {K}^*)<1\).

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Heidarpour, M.R., Manshaei, M.H. Resource allocation in future HetRAT networks: a general framework. Wireless Netw 26, 2695–2706 (2020). https://doi.org/10.1007/s11276-019-02006-6

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