10 problems

DDF multi-antenna conjecture. DDF will not be able to sustain its optimality even in the low-multiplexing-gain regime when the terminals have multiple antennas.

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 $(m,n,k)$.

Let $m=\min(M,N)$ and $n=\max(M,N)$ denote the smaller and larger numbers of transmit and receive antennas, respectively, and let $r$ be the multiplexing gain. The diversity order…

Let $d_1(r)$ be the piecewise linear function connecting the points $(r,[(m-r)(n-2r)]^+)$ where $2r\in\mathbb{Z}$, and let $d_2(r)$ be the piecewise linear function connecting the…

Operational-significance conjecture. As in the corresponding point-to-point MIMO results, link adaptation and HARQ will reduce or eliminate the need to use degrees of freedom for d…

Asymmetric-code suboptimality conjecture. Almost all asymmetric codes with minimum delay are suboptimal from the DMT point of view.

Consider a symmetric $(n,k,n)$ half-duplex MIMO relay channel, meaning that the source and destination each have $n$ antennas and the relay has $k$ antennas. Let $d^*(r)$ denote it…

Let an $(m,k,n)$ half-duplex MIMO relay channel (HD-RC) have $m$, $k$, and $n$ antennas at its three nodes, and let its diversity–multiplexing tradeoff (DMT) be compared with that…

Modified compress-and-forward DM-tradeoff conjecture. The modified compress-and-forward strategy can achieve the optimal DM-tradeoff in general.

Consider a two-hop cooperative network with a direct link, using a Slotted-Amplify-and-Forward (SAF) protocol. The relays are not isolated when their channels may exhibit dependenc…