Implementation of the Trigonometric LMS Algorithm using original CORDIC ROTATION

Abstract

The LMS algorithm is one of the most successful adaptive filtering\nalgorithms. It uses the instantaneous value of the square of the error signal\nas an estimate of the mean-square error (MSE). The LMS algorithm changes\n(adapts) the filter tap weights so that the error signal is minimized in the\nmean square sense. In Trigonometric LMS (TLMS) and Hyperbolic LMS (HLMS), two\nnew versions of LMS algorithms, same formulations are performed as in the LMS\nalgorithm with the exception that filter tap weights are now expressed using\ntrigonometric and hyperbolic formulations, in cases for TLMS and HLMS\nrespectively. Hence appears the CORDIC algorithm as it can efficiently perform\ntrigonometric, hyperbolic, linear and logarithmic functions. While\nhardware-efficient algorithms often exist, the dominance of the software\nsystems has kept those algorithms out of the spotlight. Among these hardware-\nefficient algorithms, CORDIC is an iterative solution for trigonometric and\nother transcendental functions. Former researches worked on CORDIC algorithm to\nobserve the convergence behavior of Trigonometric LMS (TLMS) algorithm and\nobtained a satisfactory result in the context of convergence performance of\nTLMS algorithm. But revious researches directly used the CORDIC block output in\ntheir simulation ignoring the internal step-by-step rotations of the CORDIC\nprocessor. This gives rise to a need for verification of the convergence\nperformance of the TLMS algorithm to investigate if it actually performs\nsatisfactorily if implemented with step-by-step CORDIC rotation. This research\nwork has done this job. It focuses on the internal operations of the CORDIC\nhardware, implements the Trigonometric LMS (TLMS) and Hyperbolic LMS (HLMS)\nalgorithms using actual CORDIC rotations. The obtained simulation results are\nhighly satisfactory and also it shows that convergence behavior of HLMS is much\nbetter than TLMS.\n