Energy-Efficient Precoder Design for Downlink Multi-User MISO Networks with Finite Blocklength Codes

One of the key applications in the fifth generation (5G) cellular networks is to support ultra-reliable and low-latency communication (URLLC) which requires extremely high reliability ( 99.999%) and low latency (< 1 ms). In this article, the energy efficiency (EE) is maximized for downlink multi-user multiple-input single-output (MISO) networks under short packet transmission. We jointly optimize the precoders at the base station (BS) for serving multiple downlink users and the decoding error probability (DEP) with finite blocklength (FBL) codes, subject to the constraints on the BS transmit power and DEP per URLLC user. This non-convex optimization problem is then accurately approximated by applying the Dinkelbach method and approximating the channel dispersion in the high signal-to-interference-plus-noise ratio (SINR) regime and the entire (practical) SINR regime, respectively. The resulting problems are convex in the design variables of the precoders and DEPs when the remaining variables are held fixed, and using this fact we provide iterative algorithms to efficiently find locally optimal solutions. Furthermore, the convergence of the proposed algorithms and the closed-form expressions of the precoders are also derived. Simulation results validate the effectiveness of the proposed algorithms that support energy-efficient URLLC as well as the impact of various network parameters such as the blocklength, number of users, distance between the BS and URLLC users and the threshold of the DEP on the EE and spectral efficiency (SE) performance.