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:$\max \underset{k}{\min }\frac{|v_k{|}^2}{{\sigma }^2+{\sum }_{l\ne k}{〈v_k,v_l〉}^2}$ where the maximum is taken among vector systems ${(v_k)}_1^N\subset {\mathbb{R}}^d$ satisfying $c_1⩽|v_k{|}^2⩽c_2$ 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.

中文翻译：

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均匀紧凑的帧作为最佳信号

对于未来的无线网络（例如6G和Wi-Fi 7），非正交通信是一种有前途的技术。在矢量信道模型中，设计有效的非正交通信方案将导致以下极端问题：$\mathrm{最大限度}\underset{ķ}{\mathrm{分}}\frac{|v_{ķ}{|}^{\mathrm{2个}}}{{\sigma }^{\mathrm{2个}}+{\sum }_{升\ne ķ}{〈v_{ķ}，v_{升}〉}^{\mathrm{2个}}}$ 向量系统中取最大值的地方 ${（v_{ķ}）}_{\mathrm{1个}}^{ñ}\subset {\mathbb{[R}}^d$ 满意的 $C_{\mathrm{1个}}⩽|v_{ķ}{|}^{\mathrm{2个}}⩽C_{\mathrm{2个}}$对于每个k，以及参数$\sigma >0$对应于通道的噪声。我们证明在这种情况下$\sigma =0$，统一的紧密框架是唯一的最佳配置。我们还给出了噪声相对较小的矢量通道的最佳容量的定量界限。