On time-domain and frequency-domain MMSE-based TEQ designs for DMT transmission

We reconsider the MMSE-based time-domain equalizer (TEQ), bitrate maximizing TEQ (BM-TEQ) and per-tone equalizer design for DMT transmission. The MMSE-TEQ criterion can be formulated as a least-squares (LS) criterion that minimizes a time-domain (TD) error energy. Based on this LS-based TD-MMSE-TEQ, we derive new LS-based frequency-domain (FD) MMSE-TEQ criteria that are intermediate in terms of computational complexity and performance between the TD-MMSE-TEQ and the BM-TEQ. In addition, we show that the BM-TEQ design itself is equivalent to a so-called iteratively-reweighted separable nonlinear LS-based FD-MMSE-TEQ design. As a side result, the considered LS-based equalizer designs, although at first sight very different in nature- appear closely related when turning them into generalized eigenvalue problems.