Though, in most practical applications, the length of the adaptive filter is less than that of the unknown system impulse response, analysis of adaptive filtering algorithms almost always assumed a sufficient length adaptive filter whose length is equal to that of unknown system. Theoretical results on the sufficient length adaptive algorithm do not necessarily apply to the realistic insufficient length case and, therefore, it becomes extremely desirable for practical purposes that we quantify the statistical behavior of the insufficient length adaptive algorithm. In this paper, we analyze the popular Transform Domain LMS (TDLMS) algorithm with insufficient length adaptive filter for Gaussian input data and using the common independence assumption. Analysis yields exact theoretical expressions that describe the mean and mean-square convergence of the algorithm, which lead to a better understanding to the performance properties of the insufficient length TDLMS adaptive algorithm. Simulation experiments illustrate the accuracy of the theoretical results in predicting the convergence behavior of the algorithm.
A New Post-whitening Transform Domain LMS Algorithm
