Low-complexity equalizers - Rank versus order reduction

Reduced-rank approximations of finite impulse response equalizers in Krylov subspaces, e. g., the conjugate gradient algorithm, can be used to decrease computational complexity involved in calculating the filter coefficients. However, an alternative approach would be to reduce the order of the corresponding full-rank filter or to even combine rank and order reduction. In this paper, we compare both reduction methods based on (G,D)-charts where we analyze the mean square error of the reduced-rank equalizers on complexity isosets, i. e., for tuples of the filter length G and its rank D resulting in a certain number of floating point operations. The application of (G,D)-charts to a coded system with an iterative receiver (turbo equalization) reveals the superiority of rank reduction, especially, if one is interested in low-complexity implementations.