6 problems

Outage Probability Conjecture for MISO.

MISO broadcast-channel sum-gain conjecture. The optimal sum beamforming gain is

Linear-scheme optimality conjecture. The lower bound is tight, and linear schemes are optimal in terms of the beamforming gain.

Achievable beamforming-gain optimality conjecture. The achievable beamforming gain is optimal for the setting with the second-moment input constraint.

Second-moment beamforming-gain conjecture. The beamforming gain under the second-moment input constraint is the same as under the fourth-moment input constraint:

Let $t$ be a positive integer, let … and let $(H_i)_{1\leq i\leq t}$ be independent and identically distributed as $\mathcal{N}_{\mathbb{C}}(1)$. Write $H=(H_1,\ldots,H_t)$ and let…