In underlay heterogeneous networks (HetNets), the distance between a macro base station (MBS) and a macro user (MU) is crucial for a small-cell based station (SBS) to control the interference to the MU and achieve the coexistence. To obtain the distance between the MBS and the MU, the SBS needs a backhaul link from the macro system, such that the macro system is able to transmit the information of the distance to the SBS through the backhaul link. However, there may not exist any backhaul link from the macro system to the SBS in practical situations. Thus, it is challenging for the SBS to obtain the distance. To deal with this issue, we propose a median based (MB) estimator for the SBS to obtain the distance between the MBS and the MU without any backhaul link. Numerical results show that the estimation error of the MB estimator can be as small as 4%.

Next generation wireless networks face the challenge of increasing energy consumption while satisfying the unprecedented increase in the data rate demand. To address this problem, we propose a utility-based energy-efficient resource allocation algorithm for the downlink transmissions in heterogeneous networks (HetNets). We consider the fractional frequency reuse (FFR) method in order to mitigate the intraand inter-cell interference. The proposed algorithm divides the resource allocation problem into frequency and power assignment problems and sequentially solves them. The proposed power control algorithm uses the gradient ascent method to control the transmit power of macrocell base stations (MeNBs) as most of the power in the network is consumed there. We present the optimality conditions of the resource allocation problem and the convergence of the proposed algorithm. In order to mitigate the inter-cell interference further, we study the interference pricing mechanisms and obtain an upper bound to the maximum energy efficiency problem including the inter-cell interference contributions. The performance of the proposed algorithm is studied in a Long Term Evolution (LTE) system. Our simulation results demonstrate that the proposed algorithm provides substantial improvements in the energy efficiency and throughput of the network. It is also shown that interference pricing provides only marginal improvements over the proposed algorithm.

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Abstract-In this paper, we aim to maximize the energy efficiency of cellular wireless networks. Specifically, we address the power allocation problem in multi-cell multi-carrier systems. Considering realistic base station power consumption models, we formulate a network-wide energy efficiency maximization problem. Using tools from fractional programming, we cast this problem in the framework of bi-criterion optimization where rate maximization and power minimization are weighted accordingly. Interference pricing mechanism is applied to reduce the intercell interference and to achieve a higher network performance. We decompose the main problem into subproblems via dual decomposition. These subproblems are independently solved per sector using limited information exchange between base stations. We first derive our expressions and present algorithms for the single-tier networks. Then, we extend our analysis to two-tier networks where picocell base stations are deployed to improve the network performance and reduce the link distances. Lastly, we extend our framework and include the quality-of-service constraints. We obtain closed-form expressions for the power level updates which are determined by the multi-level water-filling algorithm, or, as it is sometimes called as, the modified waterfilling algorithm. Based on our simulation results, we demonstrate that the proposed algorithms can outperform the benchmark approaches in terms of energy efficiency by a factor of 2.7.