The sum-rate maximization rule can find an optimal user set that maximizes the sum capacity in multiple input multiple output (MIMO) broadcast channels (BCs), but the search space for finding the optimal user set becomes prohibitively large as the number of users increases. The proposed algorithm selects a user set of the largest effective channel norms based on statistical channel state information (CSI) for reducing the computational complexity, and uses Tomlinson-Harashima precoding (THP) for minimizing the interference between selected users in time-varying MIMO BCs.