Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems

Abstract

Absrracrxonventional equalization and carrier recovery algorithms for minimizing mean-square error in digital communication systems generally require an initial training period during which a known data sequence is transmitted and properly synchronized at the receiver. This paper solves the general problem of adaptive channel equalization without resorting to a known training sequence or to conditions of limited distortion. The criterion for equalizer adaptation is the minimization of a new class of nonconvex cost functions which are shown to characterize intersymbol interference independently of carrier phase and of the data symbol constellation used in the transmission system. Equalizer convergence does not require carrier recovery, so that carrier phase tracking can be carried out at the equalizer output in a decision-directed mode. The convergence properties of the self-recovering algorithms are analyzed mathematically and confirmed by computer simulation.

Asymptotic properties of the algebraic constant modulus algorithm

“…We have just shown that as , the beamformers provided by ACMA converge to the Wiener receivers (8). In general, this is a very attractive property.…”

“…First derived as LMS-type adaptive equalizers by Godard [8] and Treichler et al [24], [25], CMAs are straightforward to implement, robust, and computationally of modest complexity. Quite soon, the algorithms were also applied to blind beamforming (spatial source separation), which gave rise to the similar constant modulus array [21].…”

Fractionally Spaced Constant Modulus Algorithm for Wireless Channel Equalization

“…Convergence analysis of fractional spaced equalizers draws two important conclusions, 1. a finite length channel satisfying a length & zero condition allows CMA-FSE to be globally convergent [2,[5][6][7] and 2. The linear FSE filter length need not be longer than the channel delay spread.…”

“…The convergence of equalizer parameter vector under CMA can be viewed as a transverse of the CMA cost surface [2,5,6,8] with average movement in the direction of steepest descent, so from the Fig. 6 dynamical behavior of CMA can be estimated.…”

An analysis of constant modulus algorithm for array signal processing

“…Since the inception of the constant modulus algorithm (CMA) in 1980, proposed first by Godard [3] and later independently by Treichler and Agee [11], CMA has been successfully implemented in various applications including equalization for microwave radio links and blind beamforming in array signal processing. Although originally invented for the equalization of a single-user intersymbol interference (ISI) channel, it has been recognized, first by Gooch and Lundell [4], that CMA applies also to the multiuser beamforming problem where the objective is to estimate one or all the source signals from an array of receivers.…”