A new framework to tackle the double-talk (DT) problem in acoustic echo cancellation (AEC). It is based on a frequency-domain adaptive filter (FDAF) implementation of the so-called prediction error method adaptive filtering using row operations (PEM-AFROW) leading to the FDAF-PEM-AFROW algorithm. We show that FDAF-PEM-AFROW is by construction related to the best linear unbiased estimate (BLUE) of the echo path. We depart from this framework to show an improvement in performance with respect to other adaptive filters minimizing the BLUE criterion, namely the PEM-AFROW and the FDAF-NLMS with near-end signal normalization. The choice of FDAF-PEM-AFROW over PEM-AFROW and FDAF-NLMS with near-end signal normalization, based on performance, computational complexity and related IPC measure values. Moreover, we use the FDAF-PEM-AFROW framework to improve several state-of-the-art variable step-size (VSS) and variable regularization (VR) algorithms. The FDAF-PEM-AFROW versions significantly outperform the original versions in every simulation. In terms of computational complexity, the FDAF-PEM-AFROW versions are themselves about two orders of magnitude cheaper than the original versions.