Robust optimization for multi-antenna downlink transmission in cellular networks

In multi-cell networks where resources are aggressively reused and the cell sizes are shrinking to accommodate more users, eliminating interference is the key factor to reduce the system energy consumption. This growth in the demand of wireless services has urged the researchers to find new and efficient ways of increasing coverage and reliability, i.e., coordinated signal processing across base stations. The optimum exploitation of the benefits provided by coordinated signal processing can be achieved when a perfect channel state information at transmitter (CSIT) is available. The assumption of having perfect knowledge of the channel is, however, often unrealistic in practice. Noise-prone channel estimation, quantization effects, fast varying environment combined with delay requirements, and hardware limitations are some of the most important factors that cause errors. Providing robustness to imperfect channel state information (CSI) is, therefore, a task of significant practical interest. Current robust designs address the channel imperfections with the worstcase and stochastic approaches. In worst-case analysis, the channel uncertainties are considered as deterministic and norm-bounded, and the resulting design is a conservative optimization that guarantees a certain quality of service (QoS) for every allowable perturbation. The latter approach focuses on the average performance under the assumption of channel statistics, such as mean and covariance. The system performance could break down when persistent extreme errors occur. Thus, an outage probability-based approach is developed by keeping a low probability that channel condition falls below an acceptable level. Compared to the worst-case methods, this approach can optimize the average performance as well as consider the extreme scenarios proportionally. In existing literature, robust precoder designs for single-cell downlink transmissions have been extensively investigated, where inter-cell interference was treated as background noise. However, robust multi-cell signal processing has not been adequately explored. In this thesis, we focus on robust design of downlink beamforming vectors for multiple antenna base stations (BSs) in a multi-cell interference network. We formulate a robust distributed beamforming (DBF) to independently design beamformers for the local users of each BS. In DBF, the combination of each BS’s total transmit power and its resulting interference power toward other BSs’ users is minimized while the required signal-tointerference-plus-noise-ratios (SINRs) for its local users are maintained. In our first approach of solving the proposed robust downlink beamforming problem for multiple-input-single-output (MISO) system, we assume only imperfect knowledge of channel covariance is available at the base stations. The uncertainties in the channel covariance matrices are assumed to be confined in an ellipsoids of given sizes and shapes. We obtain exact reformulations of the worst-case quality of service (QoS) and inter-cell interference constraints based on Lagrange duality, avoiding the coarse approximations used by previous solutions. The final problem formulations are converted to convex forms using semidefinite relaxation (SDR). Through simulation results, we investigate the achievable performance and the impact of parameters uncertainty on the overall system performance. In the second approach, in contrast to the ‘average case’ and ‘worst-case’ estimation error scenarios in the literature, to provide the robustness against channel imperfections, the outage probability-based approach is proposed for the aforementioned optimization problem. The outages are due to the uncertainties that naturally emerge in the estimation of channel covariance matrices between a BS and its intra-cell local users as well as the other users of the other cells. We model these uncertainties using random matrices, analyze their statistical behavior and formulate a tractable probabilistic approach to the design of optimal robust downlink beamforming vectors by transforming the probabilistic constraints into a semidefinite programming (SDP) form with linear matrix inequality (LMI) constraints. The performance and power efficiency of the proposed probabilistic algorithm compare to the worst-case approach are assessed and demonstrated through simulation results. Finally, we shift to the case where imperfect channel state information is available both at transmitter and receiver sides; hence we adopt a bounded deterministic model for the error in instantaneous CSI and design the downlink beamformers. The robustness criterion is to minimize the transmitted power while guaranteeing a certain quality of service per user for every possible realization of the channel that is compatible with the available channel state information. To derive closed form solutions for the original nonconvex problem we transform the worst-case constraints into a SDP with LMI constraints using the standard rank relaxation and the S-procedure. Superiority of the proposed model is confirmed through simulation results.