This article studies downlink subcarrier assignment problem to maximize rate-sum capacity subject to total power and proportional rate constraints in orthogonal frequency division multiplexing (OFDM) systems. Previous algorithms assume that the initial power is equally distributed over all subcarriers. The presence of path loss makes the assumption not correct any more. This article proposes a novel subcarrier assignment algorithm which makes full use of path loss and rate proportionality information to improve rate-sum capacity. The proposed algorithm determines optimal initial power allocation according to path losses and rate proportionalities of different users, assigns subcarriers to users in a greedy fashion, and then exchanges subcarriers between users to obtain fairer rate distribution. Simulation results show that the proposed algorithm approximately achieves double the capacity of static assignment schemes, such as fixed frequency band approach, and obtains better performance than previous subcarrier assignment algorithms in the presence of different path losses and proportional rate requirements.