Characterising the Pareto frontier of multiple access rate region: a study on the effect of decoding order on achievable performance
For a multiple access channel, each user has its own power constraint. However, when a multiple access channel is being considered as the dual of a broadcast channel, it must exploit the additional freedom in power allocation and the constraint should be a sum power constraint. Duality helps us to transform the non-convex problems in a broadcast channel to convex problems in a multiple access channel. This helps to solve sum-rate optimisation problems with linear power constraints. However, maximising the sum-rate does not completely characterise the entire rate region boundary, formally called as the Pareto frontier. This work first reviews some of the existing results of polymatroid formulation from the Pareto optimality perspective and then proposes a complete characterisation of the Pareto frontier to show its relationship with the sum-rate optimisation problem. The significance of decoding order on the achievable rate region is considered. The work also shows some of the decoding orders to be suboptimal in Pareto sense and proposes an algorithm to find the correct decoding order based on power allocation. Simulation results are presented to support the theoretical arguments.
KeywordsDuality Interference management Multiple access channel Pareto optimality Resource allocation
The work was supported by the Ministry of Education, Singapore Government Project Number RG42/12. The authors express their gratitude to editor Prof. Edmundo Monteiro and the reviewers for their advices to improve the work.
- 3.Boyd, S., & Vandenberghe, L. (2004). Convex optimization (2nd ed.). New York: Cambridge University Press. doi: 10.1016/B978-012428751-8/50019-7.
- 4.Brehmer, J., Bai, Q., & Utschick, W. (2008). Time sharing solutions in MIMO broadcast channel utility maximization. In ITG Workshop on Smart Antennas (pp. 153–156). Wien.Google Scholar
- 5.Edmonds, J. (1969). Submodular functions, matroids, and certain polyhedra. In International Conference on Combinatorial Structures and Applications (pp. 69–87). Calgary. http://link.springer.com/chapter/10.1007/3-540-36478-1_2
- 9.Grant, M. C. (2004). Disciplined convex programming. Ph.D. thesis, Stanford University. http://www.stanford.edu/boyd/papers/pdf/mcg_thesis
- 10.Huh, H., Papadopoulos, H., & Caire, G. (2009). MIMO broadcast channel optimization under general linear constraints. In International Symposium on Information Theory (pp. 2664–2668). Seoul. doi: 10.1109/ISIT.2009.5205911
- 11.Jafar, S. A., Foschini, G. J., & Goldsmith, A. J. (2004). PhantomNet: Exploring optimal multicellular multiple antenna systems. EURASIP Journal on Advances in Signal Processing (5), 591–604. doi: 10.1155/S1110865704312072. http://asp.eurasipjournals.com/content/2004/5/691857