  Non-orthogonal communication is a promising technique for future wireless
networks (e.g., 6G and Wi-Fi 7). In the vector channel model, designing
efficient non-orthogonal communication schemes amounts to the following
extremum problem: \[ \max \min_k \frac{|v_k|^2}{\sigma^2 + \sum_{l \neq k}
\langle v_k, v_l \rangle^2} \] where the maximum is taken among vector systems
$(v_k)_1^N \subset \mathbb{R}^d$ satisfying $c_1 \leq |v_k|^2 \leq c_2$ for
every $k$, and the parameter $\sigma>0$ corresponds to the noise of the
channel. We show that in the case $\sigma = 0$, uniform tight frames are the
only optimal configurations. We also give quantitative bounds on the optimal
capacity of vector channels with relatively small noise.
