Optimum equalization of multicarrier systems via projection onto convex set

This paper presents a new, iterative equalization algorithm that maximizes capacity for discrete multitone (DMT) systems. The research modifies a previously proposed criterion and applies an appropriate transformation to map the constraint set into a proper region. The resulting constraint set exhibits an identifiable geometric characteristic, which provides an efficient method for obtaining the optimal solution. Using the gradient projection method in conjunction with projection onto convex sets (POCS) provides us with an iterative search algorithm which facilitates the search direction. We also generalize the approach to two important subclasses of equalizers, namely linear phase and unit tap filters. An fundamental limit on the performance of the approach is also derived. In comparison with the previous methods, the proposed equalization algorithm is less computationally complex, more robust, and geometrically intuitive. Simulation experiments confirm the validity of the proposed method for practical purposes.