Robust Beamforming Designs For Multi-cell Wireless Cellular Systems

In cellular networks,universal frequency reuse is adopted to enhance cell converge and offer ubiquitous high date-rate in the future wireless systems.However,signals from different base stations(BSs)may interfere and as a result,inter-cell interference is a major source of performance degradation.For mitigating inter-cell interference,multi-cell cooperation among BSs has been emerged as a promising solution.A typical multi-cell coordinated transmission strategy is called coordinated beamforming,where only channel state information(CSI)is shared for signal processing to improve the capacity of the inter-cell interference mitigation.In practice,however,a base station can acquire only imperfect CSI which is contaminated with some unknown errors.As a result,robust optimization is a critical investigation by considering different CSI error models for the coordinated multi-cell transmission.In this paper,we assume a few communication scenarios,and consider the beamforming designs for different optimization objectives for the multi-cell system.This paper considers a two-cell multiple-input single-output(MISO)interference channel,where the Pareto boundary of the achievable rate region is computed through linear beamforming design.A distributed beamforming strategy is provided by solving the signal-to-leakageplus-noise ratio(SLNR)maximization problem with per base station power constraints.After some conversion,a single real-valued parameter per BS is derived to achieve all points on the Pareto boundary with local CSI,where the points on the Pareto boundary corresponds to beamforming vectors that are linear combinations of the zero forcing(ZF)and maximum-ratio transmission(MRT)beamformers.The proposed algorithm can be extended to multi-cell MISO interference channels.Simulation results demonstrate that the proposed distributed algorithm is Pareto optimal and has lower computational complexity than the iterative algorithms.To mitigate the inter-cell interference in multicell downlink systems,this paper considers the robust precoder design for multicell cooperation where the knowledge of channel state available at the base station is imperfect.Assuming that imperfect CSI can be exchanged among cells but with no data sharing,we investigate the worst-case performance optimization problem with bounded CSI error.Our objective is to minimize the weighted sum mean-square-error(MSE)subject to per-base-station power constraints in multi-cell MISO interference channels.A distributed solution is obtained by reformulating the upper bound of MSE and exploiting the Lagrangian method for the optimal problem.Simulation results demonstrate that the proposed algorithm is robust to guarantee the worst-case sum rate performance and has lower computational complexity than the signal-to-interference-plus-noise ratio(SINR)-based design.Furthermore,we consider the worst-case performance optimization problem in multi-cell MISO interference broadcast channels.According to the leakage-based schemes,the sum-MSE minimization problem is reformulated as a series of parallel sub-problems that can be recast as a semidefinite programming(SDP)problem,and solved in a distributed manner.Moreover,a modified cost function is proposed to get a distributed solution for the min-max MSE optimization problem.In the modified MSE,inter-cell leakage is introduced to replace intercell interference in the traditional MSE.Simulation results indicate that the inter-cell leakage is comparable to the inter-cell interference for each user and demonstrate the robustness of the distributed precoder designs through the bit error rate(BER)performance.This paper considers multi-cell multiple-input multiple-output(MIMO)interference channels,where robust transceivers are designed under imperfect CSI.First,we focus on robust beamforming designs for MIMO interference channels with imperfect channel state information(CSI)which is described as a bounded CSI error model.With all transmissions restricted to single data stream,the problem of maximizing the minimum SINR subject to individual power constraint at each transmitter is considered as the max-min fairness transceiver design.Specifically,we propose a robust beamforming algorithm named as block diagonalization assisted(BDA)approach for solving the max-min problem.Firstly,block diagonalization precoding is applied to simplify the original max-min SINR problem.Then,an iterative algorithm is proposed with alternating process to solve the simplified problem,and the convergence behavior and computational complexity are analyzed.Simulation results show the convergence of the BDA algorithm and demonstrate the robustness of the proposed transceiver design through the BER and the minimum SINR.In addition,assuming bounded CSI error,we recast this max-min SINR problem as a worst-case fairness problem with linear matrix inequalities(LMIs)constraints.Due to its nonconvexity,we propose an iterative algorithm in which the transmit and the receive beamformers are obtained alternately to solve the worst-case max-min fairness transceiver design problem.The transceivers generated by the proposed algorithm monotonically improve the min-SINR utility and guarantee to converge to a local optimal solution.Simulation results demonstrate the convergence behavior and the robustness of the proposed algorithm.Then,we consider robust transceiver designs for the MIMO interference channel with statistical CSI errors.For the user fairness,we design a robust beamforming strategy by maximizing the minimum SINR utility,subject to individual power constraints at each transmitter under CSI mismatch.According to the alternating schemes,the max-min fairness problem is reformulated as a series of parallel subproblems with fixed transmit beamforming vectors.While,the max-min fairness problem can be recast as a second order cone programming(SOCP)problem with fixed receive beamforming vectors.As a result,an adaptive alternating algorithm is proposed for the max-min SINR problem.Simulation results show the convergence behavior of the proposed algorithm,and demonstrate the robustness of the adaptive alternating algorithm through the BER performance.Another objective is to minimize the sum-MSE subject to per-transmitter power constraints.An iterative algorithm is proposed to solve the optimization problem.The analysis shows that the optimal equalizer is equivalent to the minimum MSE(MMSE)receiver,while the optimal precoder is obtained distributively by exploiting the Lagrangian method.Simulation results verifies the effectiveness of the proposed algorithm under CSI mismatch.