Cell-free massive multiple-input multiple-output (MIMO) consists of a large set of distributed access points (APs) serving a number of users. The APs can be far from each other, and they can also have a big number of antennas. Thus, decentralized architectures have to be considered so as to reduce the interconnection bandwidth to a central processing unit (CPU) and make the system scalable. On the other hand, the APs in a heterogeneous network might have limited processing capabilities and fully-decentralized processing may not be available. In a recent paper, a trade-off between level of decentralization and decentralized processing complexity has been identified. Furthermore, a novel matrix decomposition -- the WAX decomposition -- which, if applicable to the channel matrix, allows for exploitation of said trade-off without loss of information. The results on WAX decomposition are only available for random channel matrices without specific structures, while in a cell-free massive MIMO scenario the channel can have sparse structures. In this work, we study the applicability of WAX decomposition to cell-free massive MIMO with its implications to the above-mentioned trade-off.