Optimum equalization of multicarrier systems: a unified geometric approach

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