Fast constant modulus algorithm in the DFT domain

In this paper, a novel fast CMA employing fast convolution in the DFT domain is proposed. It is similar to the FBLMS (frequency domain block LMS) which is used for the conventional linear adaptive filtering. However, the FBLMS can not be applied to the CMA, since the CMA has no reference signal and it should minimize the nonlinear cost function. Thus, in this paper, a new nonlinear adaptation rule minimizing the CMA cost function in the DFT domain is proposed. The computer simulation results reveal that the proposed algorithm shows comparable performance to the conventional CMA, while requiring much less computation. The multiplications required for the conventional CMA and the proposed algorithm are in the order of O(N²) and O(NlogN), respectively.