Least-Squares Algorithms for Adaptive Equalizers

Adaptive channel equalization is a widespread technique used in most high-speed digital data modems. Generally, a transversal filter with adjustable coefficients is used as the equalizer. It can be adjusted adaptively to compensate for the undesired intersymbol interference introduced by the channel. A large number of equalizer adjustment algorithms are conceivable, depending on the cost function. The currently prevailing technique is the so-called stochastic gradient algorithm. In the past years, three new rapidly converging algorithms were published, namely, the Kalman,1 fast Kalman,2 and adaptive lattice3"7 algorithms. Here, we consider algorithms which minimize the sum-of-error-squares cost function. Because these least-squares algorithms make better use of all the past available information than the stochastic gradient algorithms, their start-up is faster.8 Originally the Kalman, fast Kalman, and adaptive lattice algorithms for equalizer update procedures were published for real-valued signals. In this paper, we present extensions of these algorithms to complexvalued signals which facilitate the analysis of quadrature-amplitude1905