To maximize the spectral e±ciency of a Decode-and-forward (DF) cooperative Orthogonal fre- quency division multiplexing (OFDM) system, we ¯rst pro- pose the optimal power allocation algorithm when per- fect Channel state information (CSI) feedback is available. Since perfect CSI feedback is unrealistic, we further pro- pose a power allocation scheme using limited feedback, where the power allocation vectors for the source and re- lay are limited in two ¯nite power allocation tables respec- tively. In this scheme, the destination chooses the power allocation vectors for the source and relay, and feeds the indices of the vectors back. The power allocation tables are designed by using the Lloyd algorithm. Simulation re- sults show that the perfect CSI feedback power allocation scheme achieves the best performance, and that the per- formance of the limited feedback scheme lies between the perfect CSI scheme and the scheme with no CSI.