Adaptive algorithms based on exact gradients

Adaptive algorithms with the update direction based on the gradient of the sum of squared error (SSE) cost function are investigated. The step sizes are optimized each iteration in a least-squares sense. Some simplifications (constant step sizes) and special cases (instantaneous squared error cost function) are also proposed, to reduce the complexity. For comparison of the algorithms, simulation results from an equalizer application are given. The performance of the fastest algorithm (least squares multiple update) is almost as good as that of the RLS (recursive least squares) algorithm, but the complexity is also of the same order. Another algorithm (normalized least mean squares algorithm) is shown to have better performance than the LMS algorithm, while the complexity is only slightly increased