An Alternating Optimization Algorithm for Energy Efficiency in Heterogeneous Networks

This paper studies the problems of precoding designs to achieve the energy efficiency (EE) in the uplink heterogeneous networks in which the multiple small cells are deployed in a macro-cell.  We consider two design problems which maximize either the total system energy efficiency (SEE) or the minimum energy efficiency (MinEE) among users subject to the transmit power constraints at each user and interference constraints caused to the macro base station. Since the optimization problems are non-convex fractional programming in matrix variables, it cannot be straightforward to obtain the optimal solutions. To tackle with the non-convexity challenges of the design problems, we adopt the relationships between the minimum mean square error (MMSE) and achievable data rate to recast the EE problems into ones more amenable. Then, we employ the block coordinate ascent (BCA) and the Dinkelbach methods to develop efficient iterative algorithms in which the closed form solutions are obtained or the semi-definite programming (SDP) problems are solved at each iteration. Simulation results are provided to investigate the EE performance of the EE optimization as compared to those of the spectral efficiency (SE) optimization.