In many application of noise cancellation, the changes in signal characteristics could be quite fast. This requires the utilization of adaptive algorithms, which converge rapidly. Least Mean Squares (LMS), Normalized Least Mean Squares (NLMS) and Unbiased and Normalized Adaptive Noise Reduction UNANR adaptive filters have been used in a wide range of signal processing application because of its simplicity in computation and implementation. The UNANR algorithm has established itself as the "ultimate" adaptive filtering algorithm in the sense that it is the adaptive filter exhibiting the best convergence behavior. Various Adaptive filter algorithms have been derived such as LMS, NLMS and UNANR to solve the dilemma of fast convergence rate or low excess root mean-square (RMS) error in the past two decades. This paper presented a new, easy to implement, LMS, NLMS and UNANR algorithm with various channels such as AWGN and Rician channel using the MATLAB R2013a that employs the RMS and the PSNR estimated system noise power to control the quality of online speech signal. Simulation experiments show that the NLMS and UNANR algorithm performs very well than LMS.