论文标题
统一的紧密框架作为最佳信号
Uniform tight frames as optimal signals
论文作者
论文摘要
非正交通信是未来无线网络的一种有前途的技术（例如6G和Wi-Fi 7）。在矢量通道模型中，设计有效的非正交通信方案等于以下极端问题：\ [\ [\ max \ min_k \ frac \ frac {| v_k |^2} {σ^2 + sum_ {l \ sum_ {l \ neq k} $（v_k）_1^n \ subset \ mathbb {r}^d $满足$ c_1 \ leq | v_k | v_k |^2 \ leq c_2 \ leq c_2 $ for every $ k $，而参数$σ> 0 $对应于通道的噪声。我们表明，在$σ= 0 $的情况下，均匀的紧密帧是唯一的最佳配置。我们还对噪声相对较小的向量通道的最佳容量提供了定量界限。
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: \[ \max \min_k \frac{|v_k|^2}{σ^2 + \sum_{l \neq k} \langle v_k, v_l \rangle^2} \] 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 $σ>0$ corresponds to the noise of the channel. We show that in the case $σ= 0$, uniform tight frames are the only optimal configurations. We also give quantitative bounds on the optimal capacity of vector channels with relatively small noise.
