A comparison of least squares and gradient adaptive equalization for multipath fading in wideband digital mobile radio

The tracking behavior of least-mean-square (LMS) and exponentially weighted recursive least-squares (RLS) algorithms in adaptive equalizers for digital communications is examined. A simple multiple-ray model is employed to describe the channel characteristics, which vary in a deterministic fashion. The abilities of various equalizer structures (operating in reference-directed mode) to adaptively track the time-varying optimal channel equalizer are compared on the basis of squared error magnitude. It is found that, for the channel model considered, the least-squares techniques provide a tracking advantage over the gradient techniques, when the time variation of the optimal equalizer is rapid (with respect to the additive Gaussian noise in a specified sense). Also, while in the static channel case the extra parameters of a fractionally spaced equalizer often provide a significant performance advantage over a symbol-spaced structure, this is not necessarily the case in tracking applications