  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.
