Analysis of an anti-Hebbian adaptive FIR filtering algorithm

In this brief, a recently proposed adaptive FIR filtering algorithm based upon an anti-Hebbian learning scheme is analyzed. Approximate evolution equations for the mean coefficient vector and coefficient correlation matrix are derived assuming noise-corrupted input and desired response signals. From our analysis, it is shown that the proposed algorithm can achieve an unbiased estimate of the unknown system in a system identification task if the input noise is uncorrelated with the same variance as the output noise. In more general situations, the solution obtained by the algorithm is biased. Moreover, the adaptive filter coefficients can diverge if the signal-to-noise ratio of the desired response signal is sufficiently small. Simulations verify the theoretical predictions and indicate the range of behaviors of the anti-Hebbian learning scheme for FIR system identification tasks.