Iterative Refinement Methods for Time-Domain Equalizer Design

Abstract

Commonly used time domain equalizer (TEQ) design methods have been recently unified as an optimization problem involving an objective function in the form of a Rayleigh quotient. The direct generalized eigenvalue solution relies on matrix decompositions. To reduce implementation complexity, we propose an iterative refinement approach in which the TEQ length starts at two taps and increases by one tap at each iteration. Each iteration involves matrix-vector multiplications and vector additions with 2 × 2 matrices and two-element vectors. At each iteration, the optimization of the objective function either improves or the approach terminates. The iterative refinement approach provides a range of communication performance versus implementation complexity tradeoffs for any TEQ method that fits the Rayleigh quotient framework. We apply the proposed approach to three such TEQ design methods: maximum shortening signal-to-noise ratio, minimum intersymbol interference, and minimum delay spread.

Design of Sparse Filters for Channel Shortening

“…To design the optimum SSNR filter we need to design shortening equalizers for each value of ∈ Z + and perform an exhaustive search to select the equalizer candidate with the best shortening performance. In order to keep computational complexity in check, we first estimate a sub-optimal delay * [21] and then solve for the SSNR maximizing equalizer once. The heuristic used to estimate the sub-optimal * value is given as * = max…”

Maximum kurtosis estimation of the optimal filter and convergence step size parameter in blind adaptive TEQ for multicarrier systems

“…Blind solutions may also be obtained using DDLMS or CMA but convergence problems are encountered for Gaussian sources [10,11].…”

Tap Loading of Subcarrier Equalizers for Wireless Multicarrier Transceivers

“…Thus, the computational complexity of the proposed tap loading algorithm will be reduced and eventually approach that of other adaptive length equalization techniques found in the literature [15], [16].…”

“…For example, in single-carrier systems, there exist several implementations where the tap lengths of the equalizer vary depending on some cost function or metric [13]- [16]. Extending this notion to multicarrier transceivers, the idea of nonuniformly varying the multitap FEQ length across the subcarriers, using a subcarrier equalizer tap loading algorithm, has also been proposed in several designs [17], [18].…”