Development Studies For The Adaptive Filtering Algorithms Based On The Correlation Function

With the developing information age, the issue of communication quality has become one of the most popular and important topic in the field of signal processing. Since long ago, the echo problem has been a major trouble which is negative to the communication quality. Today, the high delay application in communication such as satellite communication makes the echo problem as a more prominent problem. To this end, the echo cancellation device was introduced to the communication equipments in order to reduce the negative impact which comes from the echo to the communication quality. At present, the echo cancellation devices which in the main use the traditional adaptive filtering algorithm represented by the Least Mean Square (LMS) algorithm have been widely used. The biggest disadvantage of traditional adaptive filtering algorithm is that it is can only applicable to the single-talk environment but the double-talk environment that now prevails. Normally, a double-talk detector is added for suspending the adaptive filtering to track of each path when the double-talk environment exists. This negative approach will reduce the convergence speed of the adaptive filtering, and may lead the algorithm failure when the echo path changed. In recent years, a class of new type adaptive filtering algorithm based on the correlation function which designed for double-talk environment has been proposed. These new algorithms do not use double-talk detector, and can maintain the adaptive filtering on echo path tracking in double-talk environment, which effectively solved the algorithm failure problem when echo path changes under the double-talk environment.However, the existing adaptive filtering algorithms based on correlation function are also problematic. On the one hand, compares to the traditional adaptive filtering algorithms, the computational complexity of adaptive filtering algorithms based on correlation function algorithm are inevitable increased because the introduction of the correlation functions. On the other hand, the convergence speed of the existing adaptive filtering algorithms based on correlation function is not fast enough. In this paper, the above two issues have been raised, and two new adaptive filtering algorithms under Hartley transform based on the correlation function has been proposed? the Hartley transform extended correlation least mean square (HECLMS) algorithm and the direct proportion Hartley transform extended correlation least mean square (PHECLMS) algorithm. The HECLMS algorithm reduced the computational complexity, but the convergence speed does not improve. PHECLMS is more clearly improved the convergence speed, its computational complexity is slightly higher than HECLMS algorithm, but still lower than the existing adaptive filtering algorithms based on correlation function. The two new algorithms inherit the advantage of the existing adaptive filtering algorithms based on correlation function, and can be applied under double-talk environment more efficiently.