In order to solve the problem that traditional denoising methods based on the second order statistics were usually degraded in their performance when the received signal was contaminated by both Gaussian and Alpha stable noises.A fractional lower order statistics based ICA method was introduced.It eliminated the pulse noise from the mixed noise first

and then removed the Gaussian noise with the SVD method.The simulations show that the new method is effective on the noise elimination

and the pure signal in the received signal is not deteriorated.