[en] This paper studies hybrid precoding (HP) for mmWave multi-user OFDMA systems with sub-carrier allocation (SA) consideration. Constrained by a computation limit on the total number of data streams that can be processed, we aim to jointly optimize the SA and HP design to maximize the system sum-rate. This optimization is first formulated as a computation sparsity-constrained HP design problem, which is non-convex and challenging to solve. We then propose two-stage solution approach to tackle the problem. In stage one, we optimize the fully digital precoding (FDP) considering the computation sparsity constraint. In the second stage, we exploit an alternating MMSE minimization algorithm to reconstruct the HP's based on the achieved FDP. A novel analog precoding design, namely “Projected-Gradient-Descent based”, is then proposed to optimize the analog part of the HP's.