Nonlinear quantization effects in the LMS and block LMS adaptive algorithms-a comparison

Digital implementations of the least-mean-square (LMS) and block LMS (BLMS) algorithms are compared with respect to finite word effects. The algorithm stalling phenomenon is studied using Gaussian data models and conditional expectation arguments. It is shown that the BLMS algorithm requires (1/2 log/sub 2/ L-K) fewer bits for the same stalling behavior (L=block length and K lies between 0.2 and 1.0, depending on the precise definition of algorithm stalling). On the other hand, the LMS algorithm requires log/sub 2/ L fewer bits than BLMS for the same level of saturation behavior (transient response) at algorithm initialization. Hence, the LMS algorithm requires (1/2 log/sub 2/ L+K) fewer bits than the BLMS algorithm for the same saturation and stalling effects.<
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