Further insights on the equivalence of AVF and MSWF

The auxiliary vector filter (AVF) and the multistage Weiner filter (MSWF) are two important categories of reduced-rank filters and have been widely applied to the adaptive signal processing domain. The relationship between AVF and MSWF has also drawn a lot of attention. It has been indicated that AVF is equivalent to MSWF due to the identical reduced-rank subspace in the literature. However, except for the same subspace, the structures and the corresponding parameters of AVF are considerably different to that of MSWF. In order to gain further insights on the equivalence between AVF and MSWF, a computation scheme of parameters and a nested structure are presented for AVF in this paper. According to the identical nested structure, it can be proven that AVF has the same parameters as MSWF, which are calculated in different ways. As a consequence, it can be claimed that AVF and MSWF are two alternative computation schemes for the same reduced-rank filter.