Adaptive Equalization Algorithms: An Overview <s> A. Least Mean Squares Algorithm (LMS) <s> In this paper, a preselected discrete cosine transform-least mean squares (PDCT-LMS) algorithm is proposed. In this method, after a DCT operation, a tapped-delay-line (TDL) form and LMS algorithm are implemented for some preselected DCT bins. Each bin corresponds to an assigned carrier frequency of the signal. Several DCT-LMS algorithms are parallelly implemented, so that fast convergence rate and frequency encoded signals is easily obtained. > <s> BIB001 </s> Adaptive Equalization Algorithms: An Overview <s> A. Least Mean Squares Algorithm (LMS) <s> This paper proposes a new computationally-efficient method for blind equalization and presents a comprehensive review of existing computationally-efficient methods. The proposed method selectively updates the equalizer taps based on the equalizer output radius for QAM signal constellations. Signed-error, dithered signed-error, quantized-error, block, and update-decimated methods are discussed for computationally-efficient blind equalization. The proposed and discussed methods are applied to the constant modulus algorithm (CMA) and multi-modulus algorithm (MMA), and comparisons are provided. <s> BIB002
Least mean squares (LMS) algorithms are a class of adaptive filter used to mimic a desired filter by finding the filter coefficients that relate to producing the least mean squares of the error signal (difference between the desired and the actual signal). It is a stochastic gradient descent method in that the filter is only adapted based on the error at the current time. LMS filter is built around a transversal (i.e. tapped delay line) structure. Two practical features, simple to design, yet highly 64 | P a g e http://ijacsa.thesai.org/ effective in performance have made it highly popular in various application. LMS filter employ, small step size statistical theory, which provides a fairly accurate description of the transient behavior. It also includes H∞ theory which provides the mathematical basis for the deterministic robustness of the LMS filters [1] . As mentioned before LMS algorithm is built around a transversal filter, which is responsible for performing the filtering process. A weight control mechanism responsible for performing the adaptive control process on the tape weight of the transversal filter BIB002 as illustrated in Figure 4 . Filtering process, which involve, computing the output of a linear filter in response to the input signal and generating an estimation error by comparing this output with a desired response as follows: () yn is filter output and is the desired response at time n Adaptive process, which involves the automatics adjustment of the parameter of the filter in accordance with the estimation error. Where  is the step size, ( 1) n  = estimate of tape weight vector at time ( 1) n  and If prior knowledge of the tape weight vector () n is not available, set () n 0  The combination of these two processes working together constitutes a feedback loop, as illustrated in the block diagram of Figure 4 . First, we have a transversal filter, around which the LMS algorithm is built; this component is responsible for performing the filtering process. Second, we have a mechanism for performing the adaptive control process on the tap weight of the transversal filter-hence the designated "adaptive weight -control mechanism" in the figure [1] . i. LMS is the most well-known adaptive algorithms by a value that is proportional to the product of input to the equalizer and output error. ii. LMS algorithms execute quickly but converge slowly, and its complexity grows linearly with the no of weights. iii. Computational simplicity iv. In which channel parameter don't vary very rapidly BIB001 .