We consider a Device-to-Device (D2D) aided multicast channel, where a base station (BS) wishes to convey a common message to many receivers and these receivers cooperate with each other. We analyze the performance of a two-phase cooperative multicasting scheme requiring only statistical channel knowledge at the BS. Our analysis reveals that, as the number of receivers K grows, the two-phase scheme guarantees an average multicast rate of $\frac {1 }{ 2} \log _{2}(1 + \beta \ln \text {K})$ with high probability for any $\beta < \beta ^\star $ where $\beta ^\star $ depends on the network topology. This scheme undergoes a phase transition at threshold $\beta ^\star \ln \text {K}$ where transmissions are successful/unsuccessful with high probability when the Signal to Noise Ratio (SNR) is above/below this threshold. We also analyze the multicast outage rate when a target joint decoding probability is fixed. Finally, we propose two enhanced schemes by optimally allocating the time resource between two phases and combining received signals from two phases.¹¹

A part of the results presented in the current manuscript has been presented at the IEEE International Symposium on Information Theory 2018 [1]. The results are published in Chapter 3 of the P.h.D. Thesis of the first author [2].

中文翻译：

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通用网络拓扑中设备到设备辅助组播的性能分析

我们考虑设备到设备 (D2D) 辅助多播信道，其中基站 (BS) 希望向许多接收器传送公共消息，并且这些接收器相互协作。我们分析了只需要 BS 统计信道知识的两阶段协作组播方案的性能。我们的分析表明，随着接收器 K 数量的增加，两阶段方案保证了平均多播速率为 $\frac {1 }{ 2} \log _{2}(1 + \beta \ln \text {K})$ 任何概率都很高 $\beta < \beta ^\star $ 在哪里 $\beta ^\star $ 取决于网络拓扑。该方案在阈值处经历相变 $\beta ^\star \ln \text {K}$ 当信噪比 (SNR) 高于/低于此阈值时，传输成功/失败的概率很高。当目标联合解码概率固定时，我们还分析了多播中断率。最后，我们通过在两个阶段之间优化分配时间资源并组合来自两个阶段的接收信号，提出了两种增强方案。¹¹

当前手稿中呈现的部分结果已在 2018 年 IEEE 信息理论国际研讨会上发表 [1]. 结果发表在第一作者博士论文第3章[2].