  This paper studies downlink energy efficiency (EE) of a cellular massive
Multiple Input Multiple Output (MIMO) system with massive number of antennas at
both base station (BS) and relay considering cell-edge users which is less
investigated in the literature. Some improving methods for base station (BS)
and relay power allocation under quality of service constraints are proposed.
The EE optimization problem is provided over BS and relay power variables
(power dimensions). Considering the quasi-concavity property of the EE function
relative to each power variable, we propose to use a power bisection algorithm
(PBA) in one dimension, followed by the exhaustive search in the other
dimension (ODS algorithm) which is called PBODS algorithm and also a method to
limit the range of power variables. The results show that the performance of
the PBODS algorithm approaches the performance of optimal solution which is
exhaustive search in both dimensions while it has a lower complexity. In
addition to that we suggest to use the PBA in two dimensions alternatively as
the sub-optimal alternative optimization (AOP) algorithm. The complexity can
highly be reduced using the AOP algorithm with a slight but acceptable
degradation in performance which makes the algorithm much suitable for
practical use.
