Conjecture on the clustered multi-antenna relay DMT

Consider the clustered system in which the source, relay, and destination have $m$, $k$, and $n$ antennas, respectively, and let $d(r)$ denote its diversity–multiplexing tradeoff. Let $d_{(m+k)n}(r)$ and $d_{m(n+1)}(r)$ denote the point-to-point MIMO DMTs for the indicated antenna dimensions. Theorem describing the clustered-system DMT for $m=1,2$ gives the claimed formula for those cases.

Clustered-system DMT conjecture. The theorem stating that, for the clustered system, the DMT formula given for $m=1,2$ holds is true for arbitrary $(m,n,k)$.

The conjecture extends the explicitly established clustered-system DMT result from $m=1,2$ to arbitrary numbers of source antennas; the source provides no resolution of this extension.