Successive interference alignment for grouped 3K-user channels

Consider a $3K$-user interference channel with $K otin\mathbb{Z}^+$? No: let $K\in\mathbb{Z}^+$, and partition the transmitter–receiver pairs into groups $G_1,G_2,\ldots,G_K$, each containing three users. Every node in the $i$th group has $3i-1$ antennas. For $2\leq k\leq K$, construct effective channels among the nodes of $G_k$ using the interference subspaces and precoders of the preceding groups $G_1,\ldots,G_{k-1}$, and perform successive IA on $G_k$. Grouped successive IA conjecture. This procedure achieves the same degrees of freedom as interference alignment performed jointly by all $3K$ users. The statement gives a concrete family supporting the broader successive IA proposal, but no resolution is supplied in the source.