  Driven by the explosive growth of Internet of Things (IoT) devices with
stringent requirements on latency and reliability, ultra-reliability and low
latency communication (uRLLC) has become one of the three key communication
scenarios for the fifth generation (5G) and beyond 5G communication systems. In
this paper, we focus on the beamforming design problem for the downlink
multiuser uRLLC systems. Since the strict demand on the reliability and
latency, in general, short packet transmission is a favorable form for uRLLC
systems, which indicates the literature Shannon's capacity formula is no longer
applicable. With the finite blocklength transmission, the achievable delivery
rate is greatly influenced by the reliability and latency. Using the developed
achievable delivery rate formula for finite blocklength transmission, we
respectively formulate the problems of interest as the weighted sum rate
maximization, energy efficiency maximization, and user fairness optimization by
considering the maximum allowable transmission power and minimum rate
requirement. It's worthy pointing out that this is the first work to design the
beamforming vectors for the downlink multiuser uRLLC systems. To address these
non-convex problems, some important insights have been discovered by analyzing
the function of achievable delivery rate. For example, the minimum rate
requirement can be realized by low bounded the
signal-to-interference-plus-noise ratio. Based on the discovered results, we
provide algorithms to optimize the beamforming vectors and power allocation,
which are guaranteed to converge to a local optimum solution of the formulated
problems with low computational complexity. Our simulation results reveal that
our proposed beamforming algorithms outperform the zero-forcing beamforming
algorithm with equal power allocation widely used in the existing literatures.
