We study the Degrees-of-Freedom (DoF) in a wireless setting in which $K$ Transmitters (TXs) aim at jointly serving $K$ users. The performance is studied when the TXs are faced with a distributed Channel State Information (CSI) configuration in which each TX has access to its own multi-user imperfect channel estimate based on which it designs its transmit coefficients. The channel estimates are not only imperfectly acquired but they are also imperfectly shared between the TXs. Our first contribution consists of computing a genie-aided upper bound for the DoF of that setting. Our main contribution is then to develop a new robust transmission scheme that leverages the different qualities of CSI available at the TXs to improve the achieved DoF. We show the surprising result that there is a CSI regime, coined the Weak-CSIT regime, in which the genie-aided upper bound is achieved by the proposed transmission scheme. Interestingly, the optimal DoF in the Weak-CSIT regime only depends on the CSI quality at the best informed TX and not on the CSI quality at all other TXs.

中文翻译：

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论K用户分布式广播频道的自由度

我们在无线环境中研究自由度 (DoF)，其中 $K$ 发射机 (TX) 旨在共同服务 $K$ 用户。当 TX 面临分布式信道状态信息 (CSI) 配置时研究性能，在该配置中，每个 TX 可以访问其自己的多用户不完美信道估计，基于该估计来设计其发射系数。信道估计不仅不能完美地获取，而且它们在 TX 之间也不能完美地共享。我们的第一个贡献包括计算该设置的 DoF 的精灵辅助上限。我们的主要贡献是开发一种新的稳健传输方案，该方案利用 TX 处可用的 CSI 的不同质量来改进实现的 DoF。我们展示了一个令人惊讶的结果，即存在一个 CSI 机制，创造了弱 CSIT 机制，其中精灵辅助上限是通过所提出的传输方案实现的。有趣的是，