On communication diversity for blind identifiability and the uniqueness of low-rank decomposition of N-way arrays

Blind separation of communication signals invariably relies on some form(s) of diversity to overdetermine the problem and thereby recover the signals of interest. More often than not, linear (e.g., spreading) diversity is employed, i.e., each diversity branch provides a linear combination of the unknown signals, albeit with possibly unknown weights. If multiple forms of linear diversity are simultaneously available, then the resulting data exhibit multilinear structure, and the blind recovery problem can be shown to be tantamount to low-rank decomposition of the multi-dimensional received data array. This paper generalizes Kruskal's fundamental result on the uniqueness of low-rank decomposition of 3-way arrays to the case of multilinear decomposition of 4- and higher-way arrays. The result characterizes diversity combining for blind identifiability when N forms of linear diversity are available; that is the balance between different forms of diversity that guarantees blind recovery of all signals involved.