This work identifies the optimal Degrees-of-Freedom (DoF) of the $K$ -User MISO Broadcast Channel (BC) with delayed Channel-State Information at the Transmitter (CSIT) and with additional current noisy CSIT where the current channel estimation error scales in $P^{-\alpha }$ for $\alpha \in [{0,1}]$ . These two settings had in the past been studied separately; the setting of imperfect current CSIT has attracted considerable interest over the last decade, while the setting of delayed CSIT was studied in the seminal work of Maddah-Ali and Tse in 2010 where an optimal DoF of $K/\sum _{k=1}^{K} \frac {1}{k}$ was established. Since then there have been several efforts to combine the two settings of delayed and imperfect-current CSIT. Our work establishes for the first time the optimal DoF in this joint setting, capitalizing on a novel transmission scheme that is presented here, which combines a structurally new approach of handling past and current interference, to achieve the optimal performance. We establish the once elusive optimal DoF to be of the form $\alpha K + (1-\alpha)K /\left({\sum _{k=1}^{K} \frac {1}{k}}\right)$ . This further shows that the two types of DoF gains, from current and delayed CSIT, can be combined additively.

中文翻译：

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具有延迟和不完美电流 CSIT 的 K 用户广播信道的最佳自由度

这项工作确定了最佳自由度 (DoF) $K$ - 用户 MISO 广播信道 (BC)，在发射机 (CSIT) 处具有延迟的信道状态信息，并且具有额外的当前噪声 CSIT，其中当前信道估计误差按比例缩小 $P^{-\alpha }$ 为了 $\alpha \in [{0,1}]$ . 过去曾分别研究过这两种设置；在过去的十年中，不完美当前 CSIT 的设置引起了相当大的兴趣，而延迟 CSIT 的设置在 Maddah-Ali 和 Tse 于 2010 年的开创性工作中得到了研究，其中最佳 DoF 为 $K/\sum _{k=1}^{K} \frac {1}{k}$ 建立了。从那时起，已经有一些努力将延迟和不完美电流 CSIT 的两种设置结合起来。我们的工作首次在这种联合设置中建立了最佳 DoF，利用这里介绍的一种新颖的传输方案，该方案结合了处理过去和当前干扰的结构新方法，以实现最佳性能。我们将曾经难以捉摸的最佳 DoF 建立为以下形式 $\alpha K + (1-\alpha)K /\left({\sum _{k=1}^{K} \frac {1}{k}}\right)$ . 这进一步表明，来自当前和延迟 CSIT 的两种类型的 DoF 增益可以相加组合。