Wireless powered communication networks (WPCNs) utilize the wireless energy transfer (WET) technique to facilitate the wireless information transmission (WIT) of nodes. We propose a two-step iterative algorithm to maximize the sum throughput of the users in a MIMO WPCN with discrete signal inputs. Firstly, the optimal solution of a convex power allocation problem can be found given a fixed time allocation; Secondly, a semi closed form solution for the optimal time allocation is obtained when fixing the power allocation matrix. By optimizing the power allocation and time allocation alternately, the two-step algorithm converges to a local optimal point. Simulation results show that the proposed algorithm outperforms the conventional schemes, which consider only Gaussian inputs.