Conventionally, if equalization is carried out in time domain, matrix inversion is involved. However, if the channel has long impulse response, the computational complexity of calculation matrix inversion is very high, making it impossible for practical applications. We recall that the received signal is the linear convolution of transimitted signal and channel gains. Furthermore, according to digital signal processing theory, curcular convolution in time domain corresponds to wise-product of their DFTs. Thus, equalization can be efficiently implemented in frequency domain.
In order to do so, at the transmitter, a special data transmission format must be utilized to make data periodic.