There are several nonlinear filters, such as hard limiter, clipper and hold puncher in traditional digital receivers which only focus on larger amplitude in time domain and without any considerations for actual statistical characteristics of noises. α stable distribution is a non-Gaussian model, which can be adopted to describe the “heavy-tailed” noise well. But there is no closed form expression of the probability density function (PDF) of α stable distribution model except for several special values, which is inconvenient to use. Firstly Cauchy Gaussian Model (CGM), which has specific expressions of PDF, is adopted to approximate α distribution model. Then Gaussianization filter is formulated by estimated PDF, which is special for different value of α. At last simulation results indicate that this filter is better than traditional nonlinear filters.