Luxi Yang

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.

Distributed Multicell Beamforming With Limited Intercell Coordination

This paper studies distributed optimization schemes for multicell joint beamforming and power allocation in time-division-duplex (TDD) multicell downlink systems where only limited-capacity intercell information exchange is permitted. With an aim to maximize the worst-user signal-to-interference-and-noise ratio (SINR), we devise a hierarchical iterative algorithm to optimize downlink beamforming and intercell power allocation jointly in a distributed manner. The proposed scheme is proved to converge to the global optimum. For fast convergence and to reduce the burden of intercell parameter exchange, we further propose to exploit previous iterations adaptively. Results illustrate that the proposed scheme can achieve near-optimal performance even with a few iterations, hence providing a good tradeoff between performance and backhaul consumption. The performance under quantized parameter exchange is also examined.

Optimal pilot sequence design for channel estimation in MIMO OFDM systems

In orthogonal frequency division multiplexing (OFDM) systems, since virtual subcarriers are not used for transmission, approach of conventional uniformly placed pilot tones is not applicable in some situations. In this letter, based on nonuniform pilot tone placement, we derive optimal pilot sequences, which can achieve the minimum mean square error of the least squares estimate for multiple-input multiple-output (MIMO) OFDM systems. Simulation results demonstrate the effectiveness of the proposed approach.

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.

Distributed Multicell Beamforming Design Approaching Pareto Boundary with Max-Min Fairness

This paper addresses coordinated downlink beamforming optimization in multicell time division duplex (TDD) systems where a small number of parameters are exchanged between cells but with no data sharing. With the goal to reach the point on the Pareto boundary with max-min rate fairness, we first develop a two-step centralized optimization algorithm to design the joint beamforming vectors. This algorithm can achieve a further sum-rate improvement over the max-min optimal performance, and is shown to guarantee max-min Pareto optimality for scenarios with two base stations (BSs) each serving a single user. To realize a distributed solution with limited intercell communication, we then propose an iterative algorithm by exploiting an approximate uplink-downlink duality, in which only a small number of positive scalars are shared between cells in each iteration. Simulation results show that the proposed distributed solution achieves a fairness rate performance close to the centralized algorithm while it has a better sum-rate performance, and demonstrates a better tradeoff between sum-rate and fairness than the Nash Bargaining solution especially at high signal-to-noise ratio.

A Limited Feedback Joint Precoding for Amplify-and-Forward Relaying

This paper deals with the practical precoding design for a dual hop downlink with multiple-input multiple-output (MIMO) amplify-and-forward relaying. First, assuming that full channel state information (CSI) of the two hop channels is available, a suboptimal dual hop joint precoding scheme, i.e., precoding at both the base station and relay station, is investigated. Based on its structure, a scheme of limited feedback joint precoding using joint codebooks is then proposed, which uses a distributed codeword selection to concurrently choose two joint precoders such that the feedback delay is considerably decreased. Finally, the joint codebook design for the limited feedback joint precoding system is analyzed, and results reveal that independent codebook designs at the base station and relay station using the conventional Grassmannian subspace packing method is able to guarantee that the overall performance of the dual hop joint precoding scheme improves with the size of each of the two codebooks. Simulation results show that the proposed dual hop joint precoding system using distributed codeword selection scheme exhibits a rate or BER performance close to the one using the optimal centralized codeword selection scheme, while having lower computational complexity and shorter feedback delay.

A Joint Source and Relay Power Allocation Scheme for a Class of MIMO Relay Systems

A joint power allocation (PA) scheme for a class of MIMO relay systems is presented in this paper. Based on the maximization of the capacity or minimization of the mean-square error (MSE), two joint PA optimization problems are first formulated. Since the cost functions thus obtained are in general not convex, a tight lower bound of the capacity and a similar upper bound of the MSE are derived, and employed to modify the two cost functions so as to obtain a convex optimization problem. It is confirmed through computer simulations that the proposed PA scheme outperforms the existing method in terms of both the capacity and the MSE of MIMO relay systems.

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 limited feedback precoding system with hierarchical codebook and linear receiver

In this paper, the conventional Grassmannian codebook for precoding is first analyzed, showing that the performance loss caused by linear receivers was not taken into account. To tackle the performance loss issue, a novel hierarchical codebook consisting of a Grassmannian subcodebook and a perturbation subcodebook is then proposed for precoding systems with linear receivers. A two-step codeword selection scheme that uses the product of two codewords selected from the subcodebooks as the precoder is also presented. Our analysis shows that the perturbation subcodebook is able to compensate for the performance loss from linear receivers. Compared with the Grassmannian codebook, the superiority of the proposed codebook in terms of search complexity as well as throughput/ BER is further confirmed by computer simulations.

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.