Pareto-Optimal Hybrid Beamforming for Finite-Blocklength Millimeter Wave Systems

Short-packet communication (SPC) is essentially synonymous with ultra-reliable low-latency communication (uRLLC), which must meet stringent latency and reliability requirements. However, achieving efficient hybrid beamforming (HBF) in SPC-based millimeter wave (mmWave) systems is challenging due to the constraints of finite block lengths, limited number of radio frequency chains (RFCs), and owing to the complex optimization of transmit precoders (TPCs). In this work, we investigate the achievable rate region of an SPC-based mmWave downlink system. We harness the HBF for finite block lengths low-latency communication, relying on a low number of RFCs. We formulate a Pareto optimization problem for characterizing the achievable rate region, while considering the transmit power, mmWave hardware, and block length constraints. To solve this highly non-convex problem, we propose a bisection search-based block coordinate descent (Bi-BCD) algorithm, in which we optimize the RF TPC, the baseband (BB) TPC, and the block length. Specifically, we jointly optimize the RF and BB TPCs for a fixed block length, which involves both Remanian conjugate gradient (RCG) and second-order cone programming (SOCP) techniques, and then we optimize the block length by the mixed integer programming method. Subsequently, we update the achievable rate via the bisection search method. Finally, we present simulation results and quantify the efficiency of the proposed scheme.