The accuracy of channel state information (CSI) available at the base station (BS) plays a very important role at increasing the overall downlink throughput of the communication systems. To facilitate this, the uplink channel must be consumed to feedback the CSI from the users and this CSI feedback should be limited.This dissertation first investigates the limited feedback problem in the classic orthogonal frequency division multiplexing (OFDM) system. Then focus is laid on the coordinated multi-point (CoMP) coordinated beamforming (CB) system as well as the CoMP joint transmission (JT) system. Some feedback algorithms and cooperative approaches are proposed, which improve the overall throughput of the system. The state of the art in the limited feedback problem in different systems is also reviewed.