New insights on the transient and steady-state behavior of thequantized LMS algorithm
Bershad, N.J.; Bermudez, J.C.M.
Signal Processing, IEEE Transactions on
Volume 44, Issue 10, Oct 1996 Page(s):2623 - 2625
Digital Object Identifier 10.1109/78.539047
Summary:This correspondence investigates the transient and steady-state
behavior of the quantized LMS algorithm for Gaussian inputs. It is shown
here that the so-called “stopping” phenomenon is really a
“slow-down” phenomenon, which, because of an extremely slow
convergence rate, looks as if the algorithm has stopped. The true
steady-state MSE is shown to be nearly independent of the number of bits
in the digital word-length and very nearly the steady-state MSE of the
infinite precision LMS realization. These results assume that the
algorithm “misadjustment” effects due to coefficient
quantization are negligible in comparison with those due to the
“stopping” phenomena. Since the true steady state is rarely
achievable with a finite number of iterations, determination of the step
size μ that minimizes the residual MSE must be based on a stochastic
model for the transient mode of algorithm operation. It is shown that
the finite word length and infinite precision design cases differ only
in degree and not in kind as far as the selection of μ is concerned
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