Exact Solutions for Certain Weighted Sum-Rate and Common-Rate Maximization Problems
Koosha Pourtahmasi Roshandeh, Masoud Ardakani, Chintha Tellambura · IEEE Communications Letters · 2018
Weighted sum-rate and common-rate optimization Σi=1Nαilog2(1 + γi) and max mini(γi), respectively, where γirepresents the signal to noise ratio (SNR) of user i and aiis a constant weight. In general, these problems are non-deterministic polynomial-time-hard problems. In this letter, we propose an optimal solution framework for a selected class of such problems. Subject to some conditions on the region of feasible SNRs, we thus derive the optimal solutions utilizing the inequality of arithmetic and geometric means. We show that these solutions apply to several practical scenarios. For example, we derive optimal closed-form power allocations for a two-way relay network with a large antenna array relay. Numerical results and simulations verify the optimality of the analytical approach.