Analytical framework for multiuser uplink MIMO space-time scheduling design with convex utility functions

In this paper, we derive a novel analytical framework for designing optimal multiple-input multiple-output (MIMO) uplink space-time scheduling algorithms with respect to general convex utility functions. The novel approach we take is to discretize the search space and apply integer-programming techniques. We assume that mobile terminal has n_T transmit antennas while the base station has n_R receive antennas. With multiple antennas at the transmitter and the receiver, joint beam-forming has to be considered. In order that our proposed framework is practicable and can be implemented with a reasonable cost in a real environment, we impose a linear spatial processing constraint at the physical layer of the base station. We apply the framework to two commonly used system utility functions, namely, maximal throughput and proportional fair. We devise an optimal scheduling algorithm based on our framework as a performance reference and observe that transmit antennas and receive antennas have different roles in the system performance. On the other hand, we study how far we are from the optimal performance on a widely used heuristic called the greedy algorithm in 3G1x and Universal Mobile Terrestrial Service (UMTS) systems. We found that it is optimal when n_R=1 but there is quite a large performance penalty when n_R>1 compared with the optimal reference. We further propose another heuristic algorithm [called the genetic algorithm(GA)] and found that the GA is quite promising in terms of performance complexity tradeoff, especially for large K (number of mobile users), n_T, and n_R.