We study the joint subcarrier allocation and pre-coder design (JSAPD) problem to maximize the sum rate of downlink orthogonal frequency division multiple access (OFDMA) systems under a sum power constraint. Naturally, this problem belongs to a class of combinatorial optimization problems which are difficult to solve in general. Based on the concept of big-M formulation, and by exploiting its specific structure, we can transform the JSAPD problem into a mixed integer second order cone program (MI-SOCP), which then offers two advantages. Firstly, when the number of subcarriers/users is small, the design problem can be solved to global optimum in reasonable time by dedicated solvers. Secondly, when the number of subcarriers/users is large, near-optimal solutions of the JSAPD problem can be found by considering the continuous convex relaxation of the MI-SOCP. Numerical experiments are carried out to demonstrate the improved performance of the proposed designs compared to known solutions.