Study of LMS Algorithm Using Adaptive Filtering Technique

Many filter design techniques in Digital Signal Processing applications were based on second order statistics which include channel equalization, echo cancellation and system modeling. In these applications filters with adjustable coefficients, called Adaptive Filters were employed. Such Filters incorporate algorithms that allow the filter coefficients to adapt to signal statistics. Adaptive filtering techniques are used in a wide range of applications including echo cancellation, linear prediction, adaptive equalization, adaptive noise cancellation and adaptive beam forming. The design of adaptive filter includes i) Determination of Cost functions like Minimum Square Error (MSE) criterion and exponentially weighted Least Square Error criterion. ii) The performance of adaptive filtering algorithm which depends on the factors like Rate of convergence, misadjustment, tracking capability, computational requirement, and numerical robustness. iii) Structure determination which is inter related with the algorithm. Four common structures namely direct, parallel, cascade and lattice form structures were used. Here in this present paper the basic Least Mean Square Algorithm which is based on gradient optimization for determining the coefficients was observed. We considered the basic Widrow?s Least Mean Square Algorithm in which we study optimization criterion, Adaption procedure and Performance Analysis. The two important Performance measures in LMS algorithms are Rate of Convergence and Misadjustment.