We propose a framework to evaluate the random-coding union bound with parameter $s$ on the achievable error probability in the finite-blocklength regime for a pilot-assisted transmission scheme operating over an imperfectly synchronized and memoryless block-fading waveform channel. Unlike previous results, which disregard the effects of imperfect synchronization, our framework utilizes pilots for both synchronization and channel estimation. Specifically, we provide an algorithm to perform joint synchronization and channel estimation and verify its accuracy by observing its tightness in comparison with the Cramer-Rao bound. Then, we develop an RCUs bound on the error probability, which applies for a receiver that treats the estimates provided by the algorithm as accurate. Additionally, we utilize the saddlepoint approximation to provide a numerically efficient method for evaluating the RCUs bound in this scenario. Our numerical experiments verify the accuracy of the proposed approximation. Moreover, when transmission blocks are received synchronously, numerical results indicate that the number of pilot symbols needed to estimate the fading channel gains to the level of accuracy required in ultra-reliable low-latency communication is also sufficient to acquire sufficiently good synchronization. However, when the blocks are received asynchronously, synchronization becomes the bottleneck for the system performance.

翻译：我们提出一个框架，用于评估在有限分组长度条件下，基于参数$s$的随机编码联合界（RCUs）对不可靠同步且无记忆分块衰落波形信道上导频辅助传输方案的可实现差错概率。与以往忽略非完美同步影响的成果不同，我们的框架同时利用导频进行同步与信道估计。具体而言，我们提出一种联合同步与信道估计算法，并通过与克拉默-拉奥界的紧致性比较验证其准确性。随后，我们推导出适用于将算法估计值视为精确值的接收机误差概率RCUs界。同时，利用鞍点近似法为该场景下RCUs界的评估提供数值高效方法。数值实验验证了所提近似法的准确性。此外，当传输块同步接收时，数值结果表明，为达到超可靠低延迟通信所需的衰落信道增益估计精度而使用的导频符号数量，也足以获得足够好的同步性能。然而，当传输块异步接收时，同步性成为系统性能的瓶颈。