Minimum Symbol-Error-Rate Equalisation

The equalisation topic is well researched and a variety of solutions are available. The MAP sequence detector provides the lowest symbol error rate (SER) attainable, and the MLSE offers a near optimal solution. However, these optimal techniques are not yet practical for high-level modulation schemes, due to their computational complexity. Linear equaliser or linear-combiner DFE are practical schemes for high-level modulation systems, as they readily meet realtime computation requirements. This research re-visits the linear equaliser and conventional DFE. Classically, the minimum mean square error (MMSE) solution is regarded as the “optimal” solution for the linear equaliser or DFE. For the MMSE to be optimal, the probability distribution of the equaliser soft output must be Gaussian. As the PDF of the equaliser output is clear non-Gaussian (a sum of mixed Gaussians), the MMSE solution can be far away from the optimal solution. Adopting the non-Gaussian approach naturally leads to the optimal minimum SER (MSER) equaliser.