Structure-Exploiting ADMM for Low-Complexity Finite-Blocklength Beamforming in Cellular IoT Networks

Abstract

Ultra-reliable and low-latency communication (URLLC) is essential for mission-critical cellular Internet of Things (IoT) applications requiring reliable short-packet transmission and efficient radio-resource allocation. However, finite-blocklength (FBL)-aware beamforming becomes computationally demanding as the numbers of users and antennas increase. Existing successive convex approximation (SCA) methods typically rely on general-purpose convex solvers without exploiting the structure of the resulting beamforming problem. This paper develops a structure-exploiting consensus alternating direction method of multipliers (ADMM) framework for low-complexity FBL-aware beamforming in downlink multi-user multiple-input single-output (MU-MISO) cellular IoT networks. The FBL sum rate is maximized subject to transmit-power and per-user minimum-rate constraints. Each SCA iteration yields a convex quadratically constrained quadratic program (QCQP), reformulated into an equivalent consensus problem. For an M-antenna base station serving N IoT nodes, the global update exploits Kronecker structure to replace an MN-by-MN factorization with a shared M-by-M factorization, while rank-one channel matrices enable low-complexity local projections. CVX-SCA serves as a general-purpose benchmark, whereas standard ADMM-SCA isolates the gains from structural exploitation. Numerical results demonstrate close agreement with CVX-SCA in objective value, feasibility, and convergence. Under user scaling, the proposed method achieves more than 4-fold end-to-end speedup over CVX-SCA and approximately 6-fold per-iteration speedup over standard ADMM-SCA, demonstrating its computational efficiency for cellular IoT resource allocation.