Fractional LMS and NLMS Algorithms for Line Echo Cancellation

In long haul communication environments, speech data transmission is severely affected by echoes. This phenomenon results in high bit errors as well as in degraded and annoying performance. Traditionally these problems, including hybrid and acoustic echoes, have been controlled through the use of echo suppressors. These suppressors were subsequently replaced by line echo cancellers using adaptive Finite Impulse Response filters. Fractional calculus has been applied successfully for fixed filtering with constant coefficients and in discrete time adaptive filtering that adjusts the weights according to the environment. This paper presents the Fractional Least Mean Square (FLMS) and Fractional Normalized LMS (FNLMS) algorithms for application in echo cancellation. Moreover, the performances of the FLMS and FNLMS are compared with those provided by the standard LMS, NLMS and Block Discrete Fourier Transform solutions. The mean square error criterion is used as the performance comparison criterion for two types of voice signals namely real and synthetic. The simulation results show a performance improvement of about 50% over the traditional counterparts.