Performance study of the leaky least mean square adaptive algorithm with delayed adjustments. - Laichi, Farouk. (University of Ottawa (Canada), 1993)
Adaptive filters constitute an important part of signal processing. They are widely used in many applications where signal statistics are unknown to the users. One of the most popular adaptive methods is known as the least mean-squared (LMS) algorithm. It is well known for its hardware simplicity and its cost effectiveness. However, the LMS adaptive algorithm does not operate well in non-ideal environments. Leakage in the updated equation of the LMS algorithm was proven to overcome many such problems. This algorithm is known as the leaky LMS (LLMS). The LLMS is very robust to drifting phenomena and overflow in registers; problems that occur in the digital implementation of adaptive algorithms. In many applications, an inherent delay in the feedback error path is encountered. This delay has a definite effect on the performance of the LLMS algorithm. In this thesis, we study the performance of LLMS in the presence of delay (LDLMS). This algorithm is basically the LLMS with a delay incorporated in the coefficient updated equation. A new general stability bound is derived for the LDLMS, from which bounds of convergence of LMS, LLMS, and delayed LMS(DLMS) can be obtained. Stability bounds, convergence behavior, and excess mean squared error for this new algorithm are investigated. Theoretical results are first derived and later verified by simulations. It will be shown that introducing leakage in the DLMS algorithm gives a compromise performance. Finally, examples of applications of the LDLMS algorithm are provided.
Keywords: Engineering, Electronics and Electrical.