To deal with the future high demands of wireless traffic and energy consumption, one type of heterogeneous deployments is to distribute the base station antennas throughout the entire cell, which is called remote radio head (RRH). In view of radio resource management, the joint resource allocation in broadband orthogonal frequency division multiple access RRH (OFDMA-RRH) has not been thoroughly studied, which includes the antenna port selection, subcarrier assignment and power allocation under the power constraints per antenna port. This article focuses on the downlink resource allocation in OFDMA-RRH, where the coherent transmitter with phase steering is used. The problem to maximize the system spectrum efficiency (SE) is formulated, and solved by a dual decomposition method, where the decomposed sub-problems in the dual domain are solved by analytic geometry. In the optimal solution, the system power is always exhaustively used. As another contribution, this article further proposes that in the optimal solution, there is a considerable part of system power which makes little contribution to the SE and thus should be saved. Specifically, the energy efficiency is analyzed for an individual subcarrier transmission. A proportional power allocation (PPA) method is proposed to achieve a local optimality for each subcarrier. By applying the PPA to every subcarrier in order to maximize the system SE, a new resource allocation problem is formulated and solved. Discussions are also presented for the proposed algorithms on the computational complexity and feasibility in multi-cell cases. Simulation results show that the optimal algorithm consumes all the system power and has good convergence. The algorithm applying PPA can effectively improves the system power efficiency while achieving the SE optimality.