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The LMS algorithm is one of the most successful adaptive filteringalgorithms. It uses the instantaneous value of the square of the error signalas an estimate of the mean-square error (MSE). The LMS algorithm changes(adapts) the filter tap weights so that the error signal is minimized in themean square sense. In Trigonometric LMS (TLMS) and Hyperbolic LMS (HLMS), twonew versions of LMS algorithms, same formulations are performed as in the LMSalgorithm with the exception that filter tap weights are now expressed usingtrigonometric and hyperbolic formulations, in cases for TLMS and HLMSrespectively. Hence appears the CORDIC algorithm as it can efficiently performtrigonometric, hyperbolic, linear and logarithmic functions. Whilehardware-efficient algorithms often exist, the dominance of the softwaresystems has kept those algorithms out of the spotlight. Among these hardware-efficient algorithms, CORDIC is an iterative solution for trigonometric andother transcendental functions. Former researches worked on CORDIC algorithm toobserve the convergence behavior of Trigonometric LMS (TLMS) algorithm andobtained a satisfactory result in the context of convergence performance ofTLMS algorithm. But revious researches directly used the CORDIC block output intheir simulation ignoring the internal step-by-step rotations of the CORDICprocessor. This gives rise to a need for verification of the convergenceperformance of the TLMS algorithm to investigate if it actually performssatisfactorily if implemented with step-by-step CORDIC rotation. This researchwork has done this job. It focuses on the internal operations of the CORDIChardware, implements the Trigonometric LMS (TLMS) and Hyperbolic LMS (HLMS)algorithms using actual CORDIC rotations. The obtained simulation results arehighly satisfactory and also it shows that convergence behavior of HLMS is muchbetter than TLMS.

Implementation of the Trigonometric LMS Algorithm using Original Cordic Rotation