FiWi enhanced LTE-A HetNet comprising hybrid fiber-wireless networks as its backhaul and LTE-A heterogeneous networks as its wireless front end, is considered to be a promising technique for 5G radio access network (RAN) to host large-scale mobile data transmission with high energy efficiency. Offloading is generally used as the method to improve energy consumption and packet delay, where user equipment traffic of lightly loaded BSs is offloaded to other BSs and these lightly loaded BSs are switched into sleep state so as to reduce overall energy consumption. On the other hand, to provide data transmission for more UEs active BSs should be as more as possible. Thus, there is a tradeoff between energy consumption minimization and UE connection maximization. However, contemporary research works either focused on energy consumption minimization or focused on UE connection maximization, and few of them integrate these two parts together and gives an optimal solution. Toward this end, our paper aims to study the issues of energy consumption minimization with UE connection constraint in the wireless front end of FiWi enhanced LTE-A HetNets, and present two algorithms, i.e., a brute force algorithm and a heuristic greedy algorithm, to find the state list of all BSs and the associated UE list of each active BS that minimize the overall energy consumption while satisfying the UE connection constraint. Additionally, we also present some numerical results and validate that the heuristic greedy algorithm not only has a high efficiency but also is able to find out the optimal solution as well as the brute force algorithm.