Adaptive signal processing as a new subject, is widely used to telecommunication, radar, industrial control, earthquake detection , biomedicine and electronics field,etc.. In recent years, the great progress has been made in the theory, method and application of adaptive signal processing. The application of adaptive signal processing to mobile telecommunication is researched in the paper, The basic algorithms for adaptive wireless signal processing, i.e. Least Mean Square(LMS),Sequence Regression(SER),Recursion Least Square(RLS) and Random Search(RS),etc. are mainly analyzed and the performance of these algorithms are compared in the paper. It is propitious to choice and amelioration of the adaptive algorithms for different surroundings and condition in reason.