Analysis of Coverage Probability in 6G Millimeter-Wave Cellular Networks: Impact of Alignment Information Availability

Beam alignment remains a fundamental challenge in millimeter wave (mmWave) communication systems due to their high directionality and sensitivity to angular misalignment. Prior works commonly model alignment errors using a truncated Gaussian distribution with fixed angular boundaries and either an arbitrarily chosen standard deviation or one derived from the Cramér-Rao lower bound (CRLB). Although CRLB-based models provide valuable analysis of specific misalignment scenarios, their reliance on estimator-specific variance assumptions limits the representation of the full range of alignment uncertainty. To address this, we propose a unified probabilistic beam alignment error model based on a novel alignment information parameter, an abstract parameter quantifying directional knowledge availability in the system. This parameter governs both the variance and truncation boundaries of the alignment error distribution, enabling a continuous representation that transitions between a uniform distribution (no directional knowledge), truncated Gaussian (partial knowledge), and a distribution approaching a Dirac delta function (near-perfect knowledge). The model also incorporates a hardware inefficiency factor that, together with the information parameter, controls the error variance. We derive an analytical expression for downlink coverage probability using stochastic geometry and validate it via Monte Carlo simulations. Our alignment-aware model reveals trade-offs between beamwidth configurations and alignment information availability: wide beams are preferable under scarce information, medium beams perform best with moderate information, and narrow beams excel only when alignment information is near-perfect. These findings provide guidance for beamwidth selection in scenarios where acquiring alignment information is challenging or resource-intensive, supporting robust mmWave system design.