Abstract: Equalizing inter\|symbol interference (ISI) quickly and effectively is one of keys for satellite
high\|speed broadband digital transmission. A kind of S\|type function (Sigmoid function and hyperbolic tangent function) variable step LMS algorithms is discussed in this paper. These algorithms have flaws that μ(n) changes a lot when error e(n) is close to zero and high complexity. Therefore, an improved variable step LMS adaptive equalization algorithm is proposed. Through simplifying the complexity of step formula update, increasing the amount of error information, optimizing the structure of modified S\|type functions and building new nonlinear relations between step factor μ(n) and error function e(n), the step of new algorithm changes not only smoothly and slowly when error e(n) is close to zero, but also eliminates the impact of uncorrelated noise sequences. The complexity of the new algorithm is smaller than other similar modified algorithms. Simulation results show that the performance of new algorithm is superior to other modified algorithms. The satellite high\|speed broadband digital transmission system simulation model is also given in this paper. When the new algorithm is applied to the adaptive equalizer of system model, the system bit error rate (BER) performance is improved
greatly.

Key words: Satellite high-speed broadband digital transmission, Adaptive equalization, Variable tap-lenGth, LMS algorithm