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In this paper, several combination algorithms between Partial Update LMS (PU LMS) methods and previously proposed algorithm (New Variable Length LMS (NVLLMS)) have been developed. Then, the new sets of proposed algorithms were applied to an Acoustic Echo Cancellation system (AEC) in order to decrease the filter coefficients, decrease the convergence time, and enhance its performance in terms of Mean Square Error (MSE) and Echo Return Loss Enhancement (ERLE). These proposed algorithms will use the Echo Return Loss Enhancement (ERLE) to control the operation of filter's coefficient length variation. In addition, the time-varying step size is used.The total number of coefficients required was reduced by about 18% , 10% , 6%, and 16% using Periodic, Sequential, Stochastic, and M-max PU NVLLMS algorithms respectively, compared to that used by a full update method which  is very important, especially in the application of mobile communication since the power consumption must be considered. In addition, the average ERLE and average Mean Square Error (MSE) for M-max PU NVLLMS are better than other proposed algorithms.

The problem with some methods of Partial Update (PU) is that when using a special kind of input (Cyclostationary Signal), the system fails to converge or becomes unstable. These problems have been solved in this paper by using a newly proposed algorithm with two concepts of dynamic length Least Mean Square (LMS). The first is the length variation of the total filter coefficients N , while the second variation applies to the number of coefficients to be updated at each iteration M. This algorithm is called New Variable Length LMS algorithm NVLLMS. In the NVLLMS algorithm, the value of the Mean Error Square (MSE) is used to control N and M. Moreover, the step size is time varying. The proposed algorithm shows better performance compared with PU LMS algorithms through simulation results of system identification .

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