Oskari Tervo

Optimal Energy-Efficient Transmit Beamforming for Multi-User MISO Downlink

This paper studies beamforming techniques for energy efficiency maximization (EEmax) in multiuser multiple-input single-output (MISO) downlink system. For this challenging nonconvex problem, we first derive an optimal solution using branch-and-reduce-and-bound (BRB) approach. We also propose two low-complexity approximate designs. The first one uses the well-known zero-forcing beamforming (ZFBF) to eliminate inter-user interference so that the EEmax problem reduces to a concave-convex fractional program. Particularly, the problem is then efficiently solved by closed-form expressions in combination with the Dinkelbachs approach. In the second design, we aim at finding a stationary point using the sequential convex approximation (SCA) method. By proper transformations, we arrive at a fast converging iterative algorithm where a convex program is solved in each iteration. We further show that the problem in each iteration can also be approximated as a second-order cone program (SOCP), allowing for exploiting computationally efficient state-of-the-art SOCP solvers. Numerical experiments demonstrate that the second design converges quickly and achieves a near-optimal performance. To further increase the energy efficiency, we also consider the joint beamforming and antenna selection (JBAS) problem for which two designs are proposed. In the first approach, we capitalize on the perspective reformulation in combination with continuous relaxation to solve the JBAS problem. In the second one, sparsity-inducing regularization is introduced to approximate the JBAS problem, which is then solved by the SCA method. Numerical results show that joint beamforming and antenna selection offers significant energy efficiency improvement for large numbers of transmit antennas.

Achieving Energy Efficiency Fairness in Multicell MISO Downlink

We investigate the fairness of achievable energy efficiency in a multicell multiuser multiple-input single-output (MISO) downlink system, where a beamforming scheme is designed to maximize the minimum energy efficiency among all base stations. The resulting optimization problem is a nonconvex max-min fractional program, which is generally difficult to solve optimally. We propose an iterative beamformer design based on an inner approximation algorithm which aims at locating a Karush-Kuhn-Tucker solution to the nonconvex program. By novel transformations, we arrive at a convex problem at each iteration of the proposed algorithm, which is amendable for being approximated by a second order cone program. The numerical results demonstrate that the proposed algorithm outperforms the existing schemes in terms of the convergence rate and processing time.

Decentralized coordinated beamforming for weighted sum energy efficiency maximization in multi-cell MISO downlink

We study energy-efficient decentralized coordinated beam-forming in multi-cell multiuser multiple-input single-output system. The problem of interest is to maximize the weighted sum energy efficiency subject to user-specific quality of service constraints. The original problem is iteratively approximated as a convex program according to successive convex approximation (SCA) principle. The convex problem at each iteration is then formulated as a general global consensus problem, which is solved via alternating direction method of multipliers (ADMM). This enables base stations to independently and in parallel optimize their beamformers relying only on local channel state information and limited backhaul information exchange. In addition to waiting for the ADMM to converge as conventionally when solving the approximate convex program, we propose a method where only one ADMM iteration is performed after each SCA update step. Numerical results illustrate the fast convergence of the proposed methods and show that performing only one ADMM iteration per each convex problem can significantly improve the convergence speed.

Energy-Efficient Beam Coordination Strategies With Rate-Dependent Processing Power

This paper proposes energy-efficient coordinated beamforming strategies for multicell multiuser multiple-input single-output system. We consider a practical power consumption model, where part of the consumed power depends on the base station or user specific data rates due to coding, decoding, and backhaul. This is different from the existing approaches where the base station power consumption has been assumed to be a convex or linear function of the transmit powers. Two optimization criteria are considered, namely network energy efficiency maximization and weighted sum energy efficiency maximization. We develop successive convex approximation-based algorithms to tackle these difficult nonconvex problems. We further propose decentralized implementations for the considered problems, in which base stations perform parallel and distributed computation based on local channel state information and limited backhaul information exchange. The decentralized approaches admit closed-form solutions and can be implemented without invoking a generic external convex solver. We also show an example of the pilot contamination effect on the energy efficiency using a heuristic pilot allocation strategy. The numerical results are provided to demonstrate that the rate dependent power consumption has a large impact on the system energy efficiency, and, thus, has to be taken into account when devising energy-efficient transmission strategies. The significant gains of the proposed algorithms over the conventional low-complexity beamforming algorithms are also illustrated.

Energy-efficient coordinated beamforming with rate dependent processing power

This paper studies energy-efficient coordinated beamforming in multi-cell multi-user multiple-input single-output (MISO) system. On contrary to the existing approaches where the power consumption of a base station is modeled as a convex or linear function, we consider a more practical model where part of the processing power depends on the rate provided by the base stations. Two optimization criteria are considered, namely network energy efficiency maximization and weighted sum energy efficiency maximization. We develop successive convex approximation based algorithms to tackle these difficult nonconvex problems. The numerical results illustrate that the rate dependent power consumption has a large impact on the energy efficiency, and, thus, has to be taken into account when devising energy-efficient transmission strategies.

Energy-efficient coordinated multi-cell multi-group multicast beamforming with antenna selection

This paper studies energy-efficient coordinated beamforming in multi-cell multi-user multigroup multicast multiple-input single-output systems. We aim at maximizing the network energy efficiency by taking into account the fact that some of the radio frequency chains can be switched off in order to save power. We consider the antenna specific maximum power constraints to avoid non-linear distortion in power amplifiers and user-specific quality of service (QoS) constraints to guarantee a certain QoS levels. We first introduce binary antenna selection variables and use the perspective formulation to model the relation between them and the beamformers. Subsequently, we propose a new formulation which reduces the feasible set of the continuous relaxation, resulting in better performance compared to the original perspective formulation based problem. However, the resulting optimization problem is a mixed-Boolean non-convex fractional program, which is difficult to solve. We follow the standard continuous relaxation of the binary antenna selection variables, and then reformulate the problem such that it is amendable to successive convex approximation. Thereby, solving the continuous relaxation mostly results in near-binary solution. To recover the binary variables from the continuous relaxation, we switch off all the antennas for which the continuous values are smaller than a small threshold. Numerical results illustrate the superior convergence result and significant achievable gains in terms of energy efficiency with the proposed algorithm.

Energy-efficient transmit beamforming for MISO downlink via sequential convex approximation

We study the problem of energy efficiency maximization (EEmax) with user-specific quality of service constraints in multiple-input single-output broadcast channels with transmit beamforming. For this challenging nonconvex problem, we propose an efficient approximate design based on sequential convex approximation (SCA). By proper reformulations we arrive at a fast converging iterative algorithm where a convex program is solved at each iteration. We further show that the problem in each iteration can also be approximated as a second-order cone program (SOCP), allowing for exploiting computationally efficient state-of-the-art SOCP solvers. Numerical results show that compared to existing two-layer iterative Dinkelbach based algorithms, the SCA-based method can yield a solution within a few iterations and is insensitive to initial points. We also demonstrate that the superior performance to existing scheme is achieved with lower computational complexity.

Joint transmit beamforming and antenna selection for energy efficiency maximization in MISO downlink

We study the joint beamforming and antenna selection problem for energy efficiency maximization in multi-user multiple-input single-output (MISO) downlink channel. By viewing antenna selection as finding a sparse solution, we first introduce a sparsity-inducing regularization term to the design problem. Since the resulting problem is nonconvex, it is difficult to find an optimal solution, and we apply a local optimization method based on the concept of sequential convex approximation (SCA) to solve this problem. By proper reformulations we arrive at a fast converging iterative algorithm, where a convex program is solved at each iteration. In the first design, we simply ignore antennas of which the associated beamformers are nearly zero and select the remaining ones. In the second design, we further perform the search over the selected antennas of the first design to improve the energy efficiency. Numerical results demonstrate remarkable performance gains of the proposed approaches in terms of energy efficiency over the solution without antenna selection.

Distributed Optimization for Coordinated Beamforming in Multicell Multigroup Multicast Systems: Power Minimization and SINR Balancing

This paper considers coordinated multicast beamforming in a multicell multigroup multiple-input single-output system. Each base station (BS) serves multiple groups of users by forming a single beam with common information per group. We propose centralized and distributed beamforming algorithms for two different optimization targets. The first objective is to minimize the total transmission power of all the BSs while guaranteeing the user-specific minimum quality-of-service targets. The semidefinite relaxation (SDR) method is used to approximate the nonconvex multicast problem as a semidefinite program (SDP), which is solvable via centralized processing. Subsequently, two alternative distributed methods are proposed. The first approach turns the SDP into a two-level optimization via primal decomposition. At the higher level, intercell interference powers are optimized for fixed beamformers, whereas the lower level locally optimizes the beamformers by minimizing BS-specific transmit powers for the given intercell interference constraints. The second distributed solution is enabled via an alternating direction method of multipliers, where the intercell interference optimization is divided into a local and a global optimization by forcing the equality via consistency constraints. We further propose a centralized and a simple distributed beamforming design for the signal-to-interference-plus-noise ratio (SINR) balancing problem in which the minimum SINR among the users is maximized with given per-BS power constraints. This problem is solved via the bisection method as a series of SDP feasibility problems. The simulation results show the superiority of the proposed coordinated beamforming algorithms over traditional noncoordinated transmission schemes, and illustrate the fast convergence of the distributed methods.

Energy-efficient transmission strategies for CoMP downlink—overview, extension, and numerical comparison

This paper focuses on energy-efficient coordinated multi-point (CoMP) downlink in multi-antenna multi-cell wireless communications systems. We provide an overview of transmit beamforming designs for various energy efficiency (EE) metrics including maximizing the overall network EE, sum weighted EE, and fairness EE. Generally, an EE optimization problem is a nonconvex program for which finding the globally optimal solutions requires high computational effort. Consequently, several low-complexity suboptimal approaches have been proposed. Here, we sum up the main concepts of the recently proposed algorithms based on the state-of-the-art successive convex approximation (SCA) framework. Moreover, we discuss the application to the newly posted EE problems including new EE metrics and power consumption models. Furthermore, distributed implementation developed based on alternating direction method of multipliers (ADMM) for the provided solutions is also discussed. For the sake of completeness, we provide numerical comparison of the SCA based approaches and the conventional solutions developed based on parametric transformations (PTs). We also demonstrate the differences and roles of different EE objectives and power consumption models.