  Ultra-reliable and low-latency communication (URLLC) is a pivotal technique
for enabling the wireless control over industrial Internet-of-Things (IIoT)
devices. By deploying distributed access points (APs), cell-free massive
multiple-input and multiple-output (CF mMIMO) has great potential to provide
URLLC services for IIoT devices. In this paper, we investigate CF mMIMO-enabled
URLLC in a smart factory. Lower bounds (LBs) of downlink ergodic data rate
under finite channel blocklength (FCBL) with imperfect channel state
information (CSI) are derived for maximum-ratio transmission (MRT), full-pilot
zero-forcing (FZF), and local zero-forcing (LZF) precoding schemes. Meanwhile,
the weighted sum rate is maximized by jointly optimizing the pilot power and
transmission power based on the derived LBs. Specifically, we first provide the
globally optimal solution of the pilot power, and then introduce some
approximations to transform the original problems into a series of subproblems,
which can be expressed in a geometric programming (GP) form that can be readily
solved. Finally, an iterative algorithm is proposed to optimize the power
allocation based on various precoding schemes. Simulation results demonstrate
that the proposed algorithm is superior to the existing algorithms, and that
the quality of URLLC services will benefit by deploying more APs, except for
the FZF precoding scheme.
