Shiwen He

Coordinated Beamforming for Energy Efficient Transmission in Multicell Multiuser Systems

In this paper we study energy efficient joint power allocation and beamforming for coordinated multicell multiuser downlink systems. The considered optimization problem is in a non-convex fractional form and hard to tackle. We propose to first transform the original problem into an equivalent optimization problem in a parametric subtractive form, by which we reach its solution through a two-layer optimization scheme. The outer layer only involves one-dimension search for the energy efficiency parameter which can be addressed using the bi-section search, the key issue lies in the inner layer where a non-fractional sub-problem needs to tackle. By exploiting the relationship between the user rate and the mean square error, we then develop an iterative algorithm to solve it. The convergence of this algorithm is proved and the solution is further derived in closed-form. Our analysis also shows that the proposed algorithm can be implemented in parallel with reasonable complexity. Numerical results illustrate that our algorithm has a fast convergence and achieves near-optimal energy efficiency. It is also observed that at the low transmit power region, our solution almost achieves the optimal sum rate and the optimal energy efficiency simultaneously; while at the middle-high transmit power region, a certain sum rate loss is suffered in order to guarantee the energy efficiency.

Coordinated Multicell Multiuser Precoding for Maximizing Weighted Sum Energy Efficiency

Energy efficiency optimization of wireless systems has become urgently important due to its impact on the global carbon footprint. In this paper we investigate energy efficient multicell multiuser precoding design and consider a new criterion of weighted sum energy efficiency, which is defined as the weighted sum of the energy efficiencies of multiple cells. This objective is more general than the existing methods and can satisfy heterogeneous requirements from different kinds of cells, but it is hard to tackle due to its sum-of-ratio form. In order to address this non-convex problem, the user rate is first formulated as a polynomial optimization problem with the test conditional probabilities to be optimized. Based on that, the sum-of-ratio form of the energy efficient precoding problem is transformed into a parameterized polynomial form optimization problem, by which a solution in closed form is achieved through a two-layer optimization. We also show that the proposed iterative algorithm is guaranteed to converge. Numerical results are finally provided to confirm the effectiveness of our energy efficient beamforming algorithm. It is observed that in the low signal-to-noise ratio (SNR) region, the optimal energy efficiency and the optimal sum rate are simultaneously achieved by our algorithm; while in the middle-high SNR region, a certain performance loss in terms of the sum rate is suffered to guarantee the weighed sum energy efficiency.

Leakage-Aware Energy-Efficient Beamforming for Heterogeneous Multicell Multiuser Systems

Energy-efficient communications has attracted much interest in the research of 5G cellular systems. In this paper, we study energy-efficient coordinated beamforming design for heterogeneous multicell multiuser downlink systems. The considered problem is formulated as maximizing the weighted sum per-cell energy efficiencies (WSPEEMax) subject to predefined per-user target rate demands, maximum leakage interference power constraints, and per-BS transmit power constraints. This formulation is more general than the conventional EE optimization problem and provides a unified way to consider the EE of heterogeneous networks. However, it is hard to tackle due to the weighted sum-of-ratios form of the objective function and the non-convex nature of per-user target rate constraints. To address it, we propose to first transform the original problem into a polynomial form optimization by introducing some auxiliary variables and then further reveal their equivalence in finding the solution. Then, an efficient block coordinate ascent optimization algorithm is developed to solve the equivalent problem by exploiting the concave nature of the considered problem with respect to each optimization variable. To further improve the network EE, we also develop an energy-efficient transmission method for each small-cell network. Finally, extensive numerical results are provided to verify the effectiveness of the proposed schemes and show that both the EE and spectral efficiency (SE) of heterogeneous network can be significantly improved by energy-efficient coordinated multiple-input multiple-output (MIMO) transmission.

A Multi-Cell Beamforming Design by Uplink-Downlink Max-Min SINR Duality

In this paper, we address the problem of the coordinated beamforming design for multi-cell multiple input single output (MISO) downlink system subject to per-BS power constraints. The objective is taken as the maximization of the minimum signal-to-interference plus noise ratio (SINR), while a complete analysis of the duality between the multi-cell downlink and the virtual uplink optimization problems is provided. A hierarchical iterative scheme is proposed to solve the virtual uplink optimization problem, whose solution is then converted to derive the one of the multi-cell downlink beamforming problem. The proposed algorithm is proved to converge to a stable point. Additional, the complexity of the proposed algorithm is analyzed. Simulation results show that, in contrast to existing multi-cell beamforming schemes, the proposed algorithm achieves better performance in terms of both rate per energy (RPE) and the worst-user rate.

Max-Min Energy Efficient Beamforming for Multicell Multiuser Joint Transmission Systems

Energy efficient communication technology has attracted much attention due to the explosive growth of energy consumption in current wireless communication systems. In this letter we focus on fairness-based energy efficiency and aim to maximize the minimum user energy efficiency in the multicell multiuser joint beamforming system, taking both dynamic and static power consumptions into account. This optimization problem is a non-convex fractional programming problem and hard to tackle. In order to find its solution, the original problem is transformed into a parameterized polynomial subtractive form by exploiting the relationship between the user rate and the minimum mean square error, and using the fractional programming theorem. An iterative algorithm with proved convergence is then developed to achieve a near-optimal performance. Numerical results validate the effectiveness of the proposed solution and show that our algorithm significantly outperforms the max-min rate optimization algorithm in terms of maximizing the minimum energy efficiency.

Decentralized Energy-Efficient Coordinated Beamforming for Multicell Systems

Energy-efficient transmission is crucial for future wireless communication systems and has attracted much attention. In this paper, we study coordinated beamforming optimization for multicell multiple-input-single-output (MISO) downlink systems using energy efficiency as a criterion, which is still an open problem to the best of our knowledge. The optimization problem of interest is nonconvex and in a fractional form. To solve it, we first reveal that finding the solution of the problem is equivalent to searching for a particular point on the Pareto boundary of the newly defined energy-efficiency rate tuples. Then, we propose to use a set of interference temperature (IT)-constrained beamforming optimization problems to characterize the energy-efficiency rate Pareto boundary. Based on that, two efficient iterative algorithms are developed to reach the Pareto optimality and thus to solve the primary problem. We show that the proposed algorithms can be carried out in a decentralized manner and are guaranteed to converge. Then, these algorithms are extended to consider imperfect channel state information (CSI) using the worst-case design. Numerical results are finally provided to verify the effectiveness of the proposed schemes and they exhibit the great potential of the coordinated beamforming optimization in improving the energy efficiency of the cellular network. In particular, the results also illustrate that our proposed algorithms achieve most of the achievable performance gain with a small number of iterations and thereby with limited backhaul overhead in a time-division duplexing (TDD) system.

On Optimal Power Allocation for Downlink Non-Orthogonal Multiple Access Systems

Non-orthogonal multiple access (NOMA) enables power-domain multiplexing via successive interference cancellation (SIC) and has been viewed as a promising technology for 5G communication. The full benefit of NOMA depends on resource allocation, including power allocation and channel assignment, for all users, which, however, leads to mixed integer programs. In the literature, the optimal power allocation has only been found in some special cases, while the joint optimization of power allocation and channel assignment generally requires exhaustive search. In this paper, we investigate resource allocation in downlink NOMA systems. As the main contribution, we analytically characterize the optimal power allocation with given channel assignment over multiple channels under different performance criteria. Specifically, we consider the maximin fairness, weighted sum rate maximization, sum rate maximization with quality of service (QoS) constraints, and energy efficiency maximization with weights or QoS constraints in NOMA systems. We also take explicitly into account the order constraints on the powers of the users on each channel, which are often ignored in the existing works, and show that they have a significant impact on SIC in NOMA systems. Then, we provide the optimal power allocation for the considered criteria in closed or semi-closed form. We also propose a low-complexity efficient method to jointly optimize channel assignment and power allocation in NOMA systems by incorporating the matching algorithm with the optimal power allocation. Simulation results show that the joint resource optimization using our optimal power allocation yields better performance than the existing schemes.

Energy Efficient Coordinated Beamforming Design in Multi-Cell Multicast Networks

In this letter, we study energy efficient physical layer multicasting in multi-cell networks where each base station is equipped with multiple antennas, and transmits a common message using a single beamformer to multiple users in the same cell. The goal of our coordinated beamforming design is to maximize the worst case system energy efficiency while guaranteeing that received signal-to-interference-plus-noise ratio (SINR) at each user is above a predetermined threshold. The considered optimization problem is in a non-convex fractional form and hard to tackle. We propose to first transform the original problem into a tractable optimization problem which is then solved by developing an iterative optimization algorithm with provable convergence. Numerical results further validate the effectiveness of our proposed algorithm and show that the developed algorithm converges to a stable point in a limited number of iterations.

Codebook-Based Hybrid Precoding for Millimeter Wave Multiuser Systems

In millimeter-wave (mmWave) systems, antenna architecture limitations make it difficult to apply conventional fully digital precoding techniques but call for low-cost analog radio frequency (RF) and digital baseband hybrid precoding methods. This paper investigates joint RF-baseband hybrid precoding for the downlink of multiuser multiantenna mmWave systems with a limited number of RF chains. Two performance measures, maximizing the spectral efficiency and the energy efficiency of the system, are considered. We propose a codebook-based RF precoding design and obtain the channel state information via a beam sweep procedure. Via the codebook-based design, the original system is transformed into a virtual multiuser downlink system with the RF chain constraint. Consequently, we are able to simplify the complicated hybrid precoding optimization problems to joint codeword selection and precoder design (JWSPD) problems. Then, we propose efficient methods to address the JWSPD problems and jointly optimize the RF and baseband precoders under the two performance measures. Finally, extensive numerical results are provided to validate the effectiveness of the proposed hybrid precoders.

Energy-Efficient Transceiver Design for Hybrid Sub-Array Architecture MIMO Systems

Millimeter-wave (mmWave) communication operated in frequency bands between 30 and 300 GHz has attracted extensive attention due to the potential ability of offering orders of magnitude greater bandwidths combined with further gains via beamforming and spatial multiplexing from multi-element antenna arrays. mmwave system may exploit the hybrid analog and digital precoding to achieve simultaneously the diversity, array and multiplexing gain with a lower cost of implementation. Motivated by this, in this paper, we investigate the design of hybrid precoder and combiner with sub-connected architecture, where each radio frequency chain is connected to only a subset of base station antennas from the perspective of energy efficient transmission. The problem of interest is a non-convex and NP-hard problem that is difficult to solve directly. In order to address it, we resort to design a two-layer optimization method to solve the problem of interest by exploiting jointly the interference alignment and fractional programming. First, the analog precoder and combiner are optimized via the alternating-direction optimization method where the phase shifter can be easily adjusted with an analytical structure. Then, we optimize the digital precoder and combiner based on an effective multiple-input multiple-output channel coefficient. The convergence of the proposed algorithms is proved using the monotonic boundary theorem and fractional programming theory. Extensive simulation results are given to validate the effectiveness of the presented method and to evaluate the energy efficiency performance under various system configurations.