Rate Meta-Distribution in Millimeter Wave URLLC Device-to-Device Networks With Beam Misalignment

Using the stochastic geometry framework, we study a millimeter wave (mmWave) Device-to-Device (D2D) network dedicated to Ultra-Reliable Low Latency Communications (URLLC), where users employ multiple antennas to perform beamforming. We leverage the notion of meta-distribution in order to capture the reliability requirement of URLLC. The packet transmission process is divided into two phases: a beam training phase, during which exhaustive beam sweeping is adopted, and a data transmission phase. The paper investigates the misalignment error distribution resulting from an imperfect training phase, due to the finite codebooks resolution and the fast variation of the channel. For the data transmission phase, closed-form expressions for all the moments of the conditional rate coverage probability are derived, and the meta-distribution is approximated using the beta approximation. The study evaluates the overall network performance through the effective rate meta-distribution, which accounts for the training overhead and beam misalignment errors. The results show the detrimental impact of misalignment errors when URLLC requirements are stringent and highlight the trade-off between the training overhead and the gain brought by multiple antennas. Insights are provided for optimally and jointly choosing the codebook size and tbe number of antennas.