Joint downlink beamforming and discrete resource allocation using missed-integer programming

Multi-antenna processing is widely adopted as one of the key enabling technologies for current and future cellular networks. Particularly, multiuser downlink beamforming (also known as space-division multiple access), in which multiple users are simultaneously served with spatial transmit beams in the same time and frequency resource, achieves high spectral efficiency with reduced energy consumption. To harvest the potential of multiuser downlink beamforming in practical systems, optimal beamformer design shall be carried out jointly with network resource allocation. Due to the specifications of cellular standards and/or implementation constraints, resource allocation in practice naturally necessitates discrete decision makings, e.g., base station (BS) association, user scheduling and admission control, adaptive modulation and coding, and codebook-based beamforming (precoding). This dissertation focuses on the joint optimization of multiuser downlink beamforming and discrete resource allocation in modern cellular networks. The problems studied in this thesis involve both continuous and discrete decision variables and are thus formulated as mixed-integer programs (MIPs). A systematic MIP framework is developed to address the problems. The MIP framework consists of four components: (i) MIP formulations that support the commercial solver based approach for computing the optimal solutions, (ii) analytic comparisons of the MIP formulations, (iii) customizing techniques for speeding up the MIP solvers, and (iv) low-complexity heuristic algorithms for practical applications. We consider first joint network topology optimization and multi-cell downlink beamforming (JNOB) for coordinated multi-point transmission. The objective is to minimize the overall power consumption of all BSs while guaranteeing the quality-of-service (QoS) requirements of the mobile stations (MSs). A standard mixed-integer second-order cone program (MISOCP) formulation and an extended MISOCP formulation are developed, both of which support the branch-and-cut (BnC) method. Analysis shows that the extended formulation admits tighter continuous relaxations (and hence less computational complexity) than that of the standard formulation. Effective strategies are proposed to customize the BnC method in the MIP solver CPLEX when applying it to the JNOB problem. Low-complexity inflation and deflation procedures are devised for large-scale applications. The simulations show that our design results in sparse network topologies and partial BS cooperation. We study next the joint optimization of discrete rate adaptation and downlink beamforming (DRAB), in which rate adaptation is carried out via modulation and coding scheme (MCS) assignment and admission control is embedded in the MCS assignment procedure. The objective is to achieve the maximum sum-rate with the minimum transmitted BS power. As in the JNOB problem, a standard and an extended MISOCP formulations are developed, and analytic comparisons of the two formulations are carried out. The analysis also leads to efficient customizing strategies for the BnC method in CPLEX. We also develop fast inflation and deflation procedures for applications in large-scale networks. Our numerical results show that the heuristic algorithms yield sum-rates that are very close to the optimal ones. We then turn our attention to codebook-based downlink beamforming. Codebook-based beamforming is employed in the latest cellular standards, e.g., in long-term evolution advanced (LTE-A), to simplify the signaling procedure of beamformers with reduced signaling overhead. We consider first the standard codebook-based downlink beamforming (SCBF) problem, in which precoding vector assignment and power allocation are jointly optimized. The objective is to minimize the total transmitted BS power while ensuring the prescribed QoS targets of the MSs. We introduce a virtual uplink (VUL) problem, which is proved to be equivalent to the SCBF problem. A customized power iteration method is developed to solve optimally the VUL problem and hence the SCBF problem. To improve the performance of codebook-based downlink beamforming, we propose a channel predistortion mechanism that does not introduce any additional signalling overhead or require modification of the mobile receivers. The joint codebook-based downlink beamforming and channel predistortion (CBCP) problem represents a non-convex MIP. An alternating optimization algorithm and an alternating feasibility search algorithm are devised to approximately solve the CBCP problem. The simulation results confirm the efficiency of the channel predistortion scheme, e.g., achieving significant reductions of the total transmitted BS power. We study finally the worst-case robust codebook-based downlink beamforming when only estimated channel covariance matrices are available at the BS. Similar to the DRAB problem, user admission control is embedded in the precoding vector assignment procedure. In the robust codebook-based downlink beamforming and admission control (RCBA) problem, the objective is to achieve the maximum number of admitted MSs with the minimum transmitted BS power. We develop a conservative mixed-integer linear program (MILP) approximation and an exact MISOCP formulation of the RCBA problem. We further propose a low-complexity inflation procedure. Our simulations show that the three approaches yield almost the same average number of admitted MSs, while the MILP based approach requires much more transmitted BS power than the other two to support the admitted MSs. The MIP framework developed in this thesis can be applied to address various discrete resource allocation problems in interference limited cellular networks. Both optimal solutions, i.e., performance benchmarks, and low-complexity practical algorithms are considered in our MIP framework. Conventional approaches often did not adopt the exact discrete models and approximated the discrete variables by (quantized) continuous ones, which could lead to highly suboptimal solutions or infeasible problem instances.