Energy- and spectral-efficiency tradeoff in massive MIMO systems with inter-user interference

In this paper, the power allocation problem for downlink massive multiple-input multiple-output (MIMO) systems with inter-user interference is investigated considering the tradeoff between energy efficiency (EE) and spectral efficiency (SE). The minimum mean-square-error channel estimate and the rigorous closed-form expression of achievable downlink rate are first derived. Then, the multi-objective optimization problem (MOP) is formulated subject to maximum total transmission power constrain, where conflicting EE and SE are maximized simultaneously. To obtain the solution set characterized as a Pareto set, the MOP is transformed into a single-objective problem (SOP) using weighted sum method. We further convert the SOP into a convex optimization problem by adding an additional interference constraint, and the optimal power allocation algorithm is proposed by using dual method to balance EE and SE efficiently. Simulation results demonstrate the effectiveness of the proposed algorithm and illustrate the fundamental tradeoff between EE and SE for different parameter settings.