A novel variable step size adaptive filtering algorithm based on logarithmic function

In wireless communication, due to the complexity and variability of the transmission channel, the signal transmission process will be affected by many factors and interference, noise as a disturbance factor has a huge impact on the transmission of the signal, how to remove the noise, so that the signal is not distorted during transmission, while maintaining system stability, was a significant issue of study in signal processing. As the improvement of information technology, adaptive signal processing technology has been widely used as an important technology in signal processing of wireless communication. In traditional LMS algorithm, the fixed step factor cannot reach the optimum both in the convergence speed and steady-state error at the same time. The variable step size LMS algorithm solves this problem that the traditional algorithm cannot change step factor. However, noise can affect the performance of the variable-step LMS algorithm. In the fundament of the classical fixed-step LMS algorithm, this paper constructed a new adaptive filtering algorithm by using the variable-step LMS algorithm changed by the logarithmic function through the multiscale wavelet transform, and it is known that the new algorithm can achieve lower steady-state error and faster convergence speed through MATLAB software simulation. To a certain extent, it can better remove the noise and keep the system stable.