Robust Resource Allocation for Multi-Antenna URLLC-OFDMA Systems in a Smart Factory

In this paper, we investigate the worst-case robust beamforming design and resource block (RB) assignment problem for total transmit power minimization of the central controller while guaranteeing each robot's transmission with target number of data bits and within required ultra-low latency and extremely high reliability. By using the property of the independence of each robot's beamformer design, we can obtain the equivalent power control design form of the original beamforming design. The binary RB mapping indicators are transformed into continuous ones with additional $\ell_0$-norm constraints to promote sparsity on each RB. A novel non-convex penalty (NCP) approach is applied to solve such $\ell_0$-norm constraints. Numerical results demonstrate the superiority of the NCP approach to the well-known reweighted $\ell_1$ method in terms of the optimized power consumption, convergence rate and robustness to channel realizations. Also, the impacts of latency, reliability, number of transmit antennas and channel uncertainty on the system performance are revealed.