Energy Efficient Power Control and Beamforming in Multi-Antenna enabled Femtocells K.B. Shashika Manosha, S. Joshi, N. Rajatheva, and M. Latva-aho Centre for Wireless Communications, University of Oulu, P.O. Box 4500, FIN-90014, Oulu, Finland. {manosha, sjoshi, rrajathe, matti.latva-aho}@ee.oulu.fi Abstract— Energy efficient beamforming and power control problem is considered for a MISO (multiple input single output) network. We consider an active femtocell within the coverage area of a macrocell. The femto base station is equipped with multi antennas and the users are considered to be single antenna users. A beamforming and power control problem is formulated in order to minimize the energy consumption per bit in the downlink transmission in the femtocell. The objective function is introduced as sum power/sum rate which has the unit J/bit to measure the energy efficiency of the network. The problem is non- convex. We introduce a novel method to solve this problem with an approximation. We show that the problem can be solved with convex optimization techniques which has more practical interest even though the solution is suboptimal. In order to measure the energy efficiency we apply an existing power model which considers the total energy consumption of a base station. Thus we expect that our solution indicates realistic energy consumption measurements. Then we introduce a beamforming and power control algorithm which minimizes the energy consumption per bit transmission. Finally, the behavior of the objective function was observed in different antenna configurations by varying the user density in different channel environments. I. I NTRODUCTION The increasing demand for higher data rates has been the focus in wireless research. Implementing new base stations can increase the aggregate data rates while serving additional amount of subscribers. On the other hand, it has been identified that by analyzing the network load that most of the requests for high data rates are coming from indoor users. Femtocells (FC) appeared as a plausible solution to serve the indoor users while preserving more resources for the outdoor users. Another significant issue these days is the energy efficiency (EE) of wireless networks. Whether the FCs contribute to this is not yet fully investigated. There is a strong collaboration between industry and acad- emic through several large scale projects to improve EE [1]. EARTH (Energy Aware Radio and neTworking tecHnologies), is one such project funded by European Union with the objectives to reduce the energy consumption, stopping energy wastage without compromising QoS (quality of service) of a user etc [2]. It is important to define proper metrics to evaluate the EE of a network. This is also is one of the main tasks in EARTH [3]. This research has been funded in part by the EARTH Project EU, the LOCON project. The EE of a network is measured in terms of J/bit or bit/J which indicates that the objective function to be considered is sum power/sum rate or the other way round. Optimal power allocation for maximizing the EE using bit/J metric is considered in [4], [5]. In [6], they argue that the optimal solution for the EE problem is not necessarily the answer we get by minimizing sum power under rate constraint or maximizing sum rate under sum power constraint. All these works are focused mainly on single input single output (SISO) systems. In addition several also considered the weighted sum rate maximization and sum power minimization in MISO networks [7]. However, only a few addressed directly the EE of MISO networks. In this paper, our approach is to find a method for power allocation and beamforming direction to minimize the energy consumption per bit in a FC for a fixed interference power generated by the macrocell. We use the J/bit metric to evaluate the EE of the network by formulating the objective function as sum power/sum rate. This objective function is non-convex and has no practical relevance in terms of finding the global optimal solution due to the high complexity (NP- hard [8]). Thus, here we introduce an upper bound for the objective function and by further using an approximation we reformulate it as a convex objective function. The problem is solved in two steps. In first step we consider one sub set of variables (signal to interference plus noise ratio (SINR) and power) and solve the problem using geometric programming. In the second step we consider another sub set of variables (power and beamformers) and solve the problem using second order cone programming. Then we solve the problem by iterating between these two problems. The rest of the paper is organized as follows. In section II, we describe the system model and the problem formulation. In section III, we introduce necessary steps needed for algorithm derivation and section IV summarizes the numerical results. Finally, conclusions are presented in section V. Notations: All boldface lower and upper case letters rep- resent vectors and matrices respectively. C nt denotes set of complex n t vectors (n t × 1 matrices). The absolute value of scalar x is defined by ‖x‖ and the ‖x‖ 2 is the Euclidean norm. (.) H is used to denote the Hermitian transpose of a vector. (.) ∗ is the optimum value. ≻ denotes the component wise inequality of a vector.