Convergence analysis and design of an adaptive filter with finite-bit power-of-two quantized error

The analysis and design of an adaptive filter governed by an LMS algorithm with finite-bit power-of-two quantization of the error signal are discussed. Both the input data and the optimal filter weights are assumed stationary. An expression of the steady-state error power is derived. According to this expression, the error power is linearly increasing in the step size μ and exponentially decreasing in the number of quantizer bits B. A practically interesting result is derivation of a threshold value of B above which the error power is constant versus B. The threshold is a decreasing function of the noise power. Expressions of B and μ that achieve a given tolerable value of the error power with the fastest convergence and the minimum hardware complexity are provided