A comparison of two quantized state adaptive algorithms

Quantized state (QS) adaptive algorithms reduce the numerical complexity and dynamic range requirements of least mean squares (LMS) adaptation by replacing multiplications with shifts, bit comparisons, or table lookups. A theoretical foundation with which to distinguish two primary QS algorithm forms and to predict which algorithm is most appropriate in a given context is presented. An extended Lyapunov approach is used to derive a persistence of excitation (PE) condition which guarantees linear stability of the quantized error (QE) form. Averaging theory is then used to derive PE condition which guarantees exponential stability of the quantized regressor (QReg) form. Failure to meet this latter condition (which is not equivalent to the spectral richness PE condition for LMS) can result in exponential instability. The QE and QReg algorithms are then compared in terms of conditions for stability, convergence properties of the prediction and parameter errors, convergence rates, and steady-state errors.<>