Abstract— A user association algorithm with optimal bandwidth allocation for optimizing the energy efficiency of HetNet is presented in this paper. The energy efficiency of the network was formulated as a non-convex optimization problem due to the binary nature of the user association indicator. The Lagrangian dual decomposition and sub-gradient method were used to maximize energy efficiency. The performance of the developed algorithm was compared with Maximum Reference Signal Received Power (MaxRSRP) and Maximum Signal-to-Interference-Noise Ratio (MaxSINR) user associations which are the benchmark user association algorithms as specified by 3rd Generation Partnership Project. The results show that the proposed algorithm has network energy efficiency performance improvement of 9.94% and 5.45% with respect to MaxRSRP and MaxSINR user association respectively, for increasing number of macro BSs antennas. Also, the proposed algorithm has network energy efficiency performance improvement of 11.33% and 6.65% over MaxRSRP and MaxSINR user association respectively, for increasing number of pico BSs per macro cell. Lastly, the proposed algorithm has network energy efficiency performance improvement of 11.00% and 7.35% over MaxRSRP and MaxSINR user association, respectively, for increasing number of femto BSs per macro cell. This implies that the developed algorithm outperforms the existing algorithms in terms of network energy efficiency.