On the complexity of wireless uplink scheduling with successive interference cancellation

In this paper, we study the problem of uplink scheduling in wireless networks with successive interference cancellation (SIC). With SIC, concurrent transmissions, if properly scheduled, can be successfully decoded at a receiver. The scheduler decides: (i) in which time- slot, and (ii) in what order in a time-slot to decode each transmission in order to maximize the system utility. These two scheduling decisions effectively determine the rates allocated to concurrent transmissions, which in turn determine the throughput and fairness of the system. We consider two scheduling problems, namely Maximum Throughput Scheduling and Proportional Fair Scheduling. We prove the first problem is NP-hard, while the second seemingly harder problem can be solved in polynomial time.