Duality Based Energy-Efficient Beamforming Design for Multiuser Downlink Systems

In this letter, we consider energy efficient beamforming for the broadcast multiple antenna channel. The optimization problem is formulated as maximizing the ratio of the achievable sum-rate to the total power consumption subject to given power and SINR constraints, which is non-convex and hard to tackle. In contrast to existing approaches, we first derive a virtual uplink problem that is dual to the primal downlink problem, which extends the conventional uplink-downlink duality into energy efficiency region. Owing to the fact that the optimal receive beamforming vectors in the uplink have analytical solutions, we then propose an efficient algorithm to solve the dual problem and convert its solution to the primal problem. Our complexity analysis shows that the proposed algorithm has much lower complexity than the existing solutions. Numerical results finally confirm the effectiveness of our proposed algorithm and illustrate its advantage over the conventional approaches.