Analysis of Unconstrained Partitioned-Block Frequency-Domain Adaptive Filters

Previously, we have presented a performance analysis of the unconstrained partitioned-block frequency-domain adaptive filter (PBFDAF) with 50% overlap. It was found that the unconstrained PBFDAF always converges to a biased solution, and hence the mean-square deviation (MSD) learning curve does not match the mean-square error (MSE) learning curve. To deal with this problem, we present an alternative theoretical model of the unconstrained PBFDAF by introducing a modified time-domain weight vector. We show that the new weight vector can converge to the true system impulse response in the mean sense. We also derive the analytical expressions for the MSD and the MSE. The analysis here is equivalent to that in our previous work, but the former is much simpler and easier to handle. Also, the MSD learning curve calculated from the new weight vector is in good agreement with the MSE learning curve. Computer simulations support the analytical results well.