发表机构
Engineering Division, New York University (NYU) Abu Dhabi; NYU WIRELESS, NYU Tandon School of Engineering（纽约大学阿布扎比分校工程学院; 纽约大学坦顿工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对无线通信信道估计任务，量化了使用数字孪生（DT）时所需的导频训练量，推导了导频等价定律、失配阈值等关键结果，明确了可免除导频训练的DT保真度阈值。
AI 中文摘要
本文研究了当无线电信道的数字孪生（Digital Twin, DT）可辅助无线通信系统完成信道估计任务时，所需的导频训练量问题。无线信道的DT被广泛认为可降低信道估计的导频开销，遵循非正式规则：“孪生体越精确，所需导频越少”。然而，这种权衡关系仅被经验性验证，从未被量化。本文将DT视为接收器与物理世界导频观测值融合的信道补充测量值，通过最佳线性无偏估计器融合物理与数字世界，推导得到DT辅助的克拉美-罗下界，并由此得到“导频等价定律”，将DT保真度转换为等价的训练符号数量。对于估计器未知的有偏孪生体，本文得到了精确的失配阈值，超过该阈值时信任DT的效果将差于忽略它。本文量化了使用DT达到信道估计所需均方误差时的训练量，讨论了可完全绕开物理世界训练的特殊情况，最终将结果转化为块衰落可达速率，其最优训练长度为单一方程的唯一根，并确定了可完全免除导频训练的DT保真度阈值。大量数值结果验证了闭式表达式，揭示DT的价值在有限信噪比时最大，在低信噪比和高信噪比极限下消失。
英文摘要
The following paper addresses how much pilot training is needed when a digital twin (DT) of the wireless radio channel is available to aid a wireless communication system with a channel estimation task. The DT of a wireless channel is widely expected to reduce the pilot overhead of channel estimation, following the informal rule that \emph{``the more accurate the twin, the fewer pilots are needed.''} This trade-off, however, has only ever been demonstrated empirically and never quantified. We close this gap by treating the DT as a complementary measurement of the channel that the receiver fuses with its pilot observations in the physical world. Consequently, fusing the physical and digital worlds through the best linear unbiased estimator, we derive a DT-aided Cramér-Rao bound, and from it a \emph{pilot-equivalence law} that converts DT fidelity into an equivalent number of training symbols. For a biased twin unknown to the estimator, we obtain the exact mismatch threshold beyond which trusting the DT is worse than ignoring it. We quantify how much training is needed with the DT to attain a desired mean square error on channel estimation. Particular cases are discussed to tell when training in the physical world can be completely bypassed. We finally translate these results into a block-fading achievable rate whose optimal training length is the unique root of a single equation, and identify the DT fidelity above which pilot training can be dispensed with altogether. Extensive numerical results corroborate closed-form expression and reveal that the value of a DT is largest at finite signal-to-noise ratio and vanishes in both the low- and high-SNR limits.
