  The LMS algorithm is one of the most successful adaptive filtering
algorithms. It uses the instantaneous value of the square of the error signal
as 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 the
mean square sense. In Trigonometric LMS (TLMS) and Hyperbolic LMS (HLMS), two
new versions of LMS algorithms, same formulations are performed as in the LMS
algorithm with the exception that filter tap weights are now expressed using
trigonometric and hyperbolic formulations, in cases for TLMS and HLMS
respectively. Hence appears the CORDIC algorithm as it can efficiently perform
trigonometric, hyperbolic, linear and logarithmic functions. While
hardware-efficient algorithms often exist, the dominance of the software
systems has kept those algorithms out of the spotlight. Among these hardware-
efficient algorithms, CORDIC is an iterative solution for trigonometric and
other transcendental functions. Former researches worked on CORDIC algorithm to
observe the convergence behavior of Trigonometric LMS (TLMS) algorithm and
obtained a satisfactory result in the context of convergence performance of
TLMS algorithm. But revious researches directly used the CORDIC block output in
their simulation ignoring the internal step-by-step rotations of the CORDIC
processor. This gives rise to a need for verification of the convergence
performance of the TLMS algorithm to investigate if it actually performs
satisfactorily if implemented with step-by-step CORDIC rotation. This research
work has done this job. It focuses on the internal operations of the CORDIC
hardware, implements the Trigonometric LMS (TLMS) and Hyperbolic LMS (HLMS)
algorithms using actual CORDIC rotations. The obtained simulation results are
highly satisfactory and also it shows that convergence behavior of HLMS is much
better than TLMS.
