1. A wireless communication system for a communication between a transmitter and a receiver each having a plurality of antennas, by multiplexing a signal, the system comprising: a channel information acquirer which obtains channel information representing a characteristic of a channel linking the transmitter and the receiver based on a reference signal sent to the transmitter from the receiver; a first matrix determiner which determines a weighting coefficient matrix for the antennas of the transmitter based on the obtained channel information; a weight calculator which calculates a weight to be assigned to each of components of the signal multiplexed at the transmitter; a training signal sender which sends training signals for the respective components of the multiplexed signal to the receiver, the training signals being weighted by the weights calculated by the weight calculator; and a second matrix determiner which determines a weighting coefficient matrix for the antennas of the receiver based on the received training signals, wherein the wireless communications system employs a RTS/CTS function where the transmitter sends a transmission requesting packet RTS (Request To Send) and the receiver sends a confirmation packet CTS (Clear To Send) in response to the RTS, so that the data transfer is initiated when the transmitter receives the CTS, the receiver sends the CTS packet with reference signals included in the CTS packet, and the transmitter calculates a weight to be assigned to each of components of the multiplexed signal based on the channel information which is obtained based on the reference signals included in the CTS packet, and sends data packet including training signals for respective signal components sent in a multiplexed fashion.