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; 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.