  This paper proposes an energy efficient resource allocation design algorithm
for an intelligent reflecting surface (IRS)-assisted downlink ultra-reliable
low-latency communication (URLLC) network. This setup features a multi-antenna
base station (BS) transmitting data traffic to a group of URLLC users with
short packet lengths. We maximize the total network's energy efficiency (EE)
through the optimization of active beamformers at the BS and passive
beamformers (a.k.a. phase shifts) at the IRS. The main non-convex problem is
divided into two sub-problems. An alternating optimization (AO) approach is
then used to solve the problem. Through the use of the successive convex
approximation (SCA) with a novel iterative rank relaxation method, we construct
a concave-convex objective function for each sub-problem. The first sub-problem
is a fractional program that is solved using the Dinkelbach method and a
penalty-based approach. The second sub-problem is then solved based on
semi-definite programming (SDP) and the penalty-based approach. The iterative
solution gradually approaches the rank-one for both the active beamforming and
unit modulus IRS phase-shift sub-problems. Our results demonstrate the efficacy
of the proposed solution compared to existing benchmarks.
