Pareto Optimal Hybrid Beamforming for Short-Packet Millimeter-Wave Integrated Sensing and Communication

Pareto optimal solutions are conceived for radar beamforming error (RBE) and sum rate maximization in short-packet (SP) millimeter-wave (mmWave) integrated sensing and communication (ISAC). Our ultimate goal is to realize ultra-reliable low-latency communication (uRLLC) and real-time sensing capabilities for 6G applications. The ISAC base station (BS) transmits short packets in the downlink (DL) to serve multiple communication users (CUs) and detect multiple radar targets (RTs). We investigate the performance trade-off between the sensing and communication capabilities by optimizing both the radio frequency (RF) and the baseband (BB) transmit precoder (TPC), together with the block lengths. The optimization problem considers the minimum rate requirements of the CUs, the maximum tolerable radar beamforming error (RBE) for the RTs, the unit modulus (UM) elements of the RF TPC, and the finite transmit power as the constraints for SP transmission. The resultant problem is highly non-convex due to the intractable rate expression of the SP regime coupled with the non-convex rate and UM constraints. To solve this problem, we propose an innovative two-layer bisection search (TLBS) algorithm, wherein the RF and BB TPCs are optimized in the inner layer, followed by the block length in the outer layer. Furthermore, a pair of novel methods, namely a bisection search-based majorizer and minimizer (BMM) as well as exact penalty-based manifold optimization (EPMO) are harnessed for optimizing the RF TPC in the inner layer. Subsequently, the BB TPC and the block length are derived via second-order cone programming (SOCP) and mixed integer programming methods, respectively. Finally, our exhaustive simulation results reveal the effect of system parameters for various settings on the RBE-rate region of the SP mmWave ISAC system and demonstrate a significantly enhanced performance compared to the benchmarks.