Intelligent manufacturing in future factories requires ultra-reliable and low-latency communications (URLLC) between central controllers and actuators (e.g., robots). This letter studies a superimposed pilot (SP)-aided uplink transmission system in industrial scenarios, where each actuator sends short-packet messages containing a superimposition of pilot and data signals to the central controller. A practical setting is considered where the blocklength is finite and imperfect pilot removal (IPPR) is available. Then, a closed-form lower bound of the achievable rate with a maximum ratio combining receiver is derived, which can be easily extended to the special cases of perfect pilot removal (PPR) and regular pilot (RP). Based on the derived lower bound, the pilot and data power allocation is optimized by exploiting successive convex approximation method to transform the weighted sum rate maximization problem into a series of geometric programs. Simulation results reveal that the SP-aided transmission outperforms the RP-aided transmission in both the PPR and IPPR cases.
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