On Optimal Scheduling for Joint Spatial Division and Multiplexing Approach in FDD Massive MIMO

Massive multiple-input and multiple-output is widely considered as a key enabler of the next generation 5G networks. With a large number of antennas at the base station, both spectral and energy efficiencies can be enhanced. Unfortunately, the down-link channel estimation overhead scales linearly with the number of antennas. This burden is easily mitigated in time division duplex systems by the use of the channel reciprocity property. However, this is unfeasible for frequency division duplex systems, and the method of two-stage beamforming was therefore developed to reduce the amount of channel state information feedback. The performance of this scheme being highly dependent on the users grouping and scheduling mechanisms, we introduce in this paper a new similarity measure coupled with a novel clustering procedure to achieve the appropriate users grouping. We also proceed to formulate the optimal users scheduling policy in joint spatial division and multiplexing (JSDM) and prove that it is NP-hard. This result is of paramount importance since it suggests that, unless P = NP, there are no polynomial time algorithms that solve the general scheduling problem to global optimality and the use of sub-optimal scheduling strategies is more realistic in practice. We, therefore, use graph theory to develop a sub-optimal users scheduling scheme that runs in polynomial time and outperforms the scheduling schemes previously introduced in the literature for JSDM in both sum-rate and throughput fairness.