Complexity Reduction of Finite-Length MMSE Equalization Using FFT

In this paper, the task of performing finite-length minimum mean square error (MMSE) equalization is considered for single carrier communication systems. A detailed mathematical derivation of the finite-length MMSE equalizer is presented where the MMSE equalizer coefficients are described using linear convolution instead of the matrix form representation, which is commonly found in literature. The linear convolution is then transformed into circular convolution by performing frequency-domain sampling while avoiding time-domain aliasing. The computation of the circular convolution naturally lends itself to employing FFT and IFFT operations, which leads to a significant complexity reduction compared to the traditional approaches of computing the MMSE equalizer coefficients using matrix inversion.