Recurrent IQ Parameters of QAM Signal Estimation in a Digital System with Multi-Frequency Modulation of the DMT Standard

Instead of sequential processing of quadrature amplitude modulation symbols used in well-known narrowband modems, it is proposed to use parallel processing of symbols using fast Fourier transforms. An algorithm for optimal recurrent estimation of quadrature amplitude modulation symbols based on the known spectrum of the optimal finite signal taking into account observational noise based on minimizing empirical risk in the form of the Tikhonov regularizing functional is presented. The proposed approach can be used in digital data transmission systems with increased spectral efficiency and acceptable computational complexity based on the fast Fourier transform.