Stochastic Geometric Coverage Analysis in mmWave Cellular Networks With Realistic Channel and Antenna Radiation Models

Millimeter-wave (mmWave) bands will play an important role in 5G wireless systems. The system performance can be assessed by using models from stochastic geometry that cater for the directivity in the desired signal transmissions as well as the interference, and by calculating the signal-to-interference-plus-noise ratio (<inline-formula> <tex-math notation="LaTeX">$\mathsf {SINR}$ </tex-math></inline-formula>) coverage. Nonetheless, the accuracy of the existing coverage expressions derived through stochastic geometry may be questioned, as it is not clear whether they would capture the impact of the detailed mmWave channel and antenna features. In this paper, we propose an <inline-formula> <tex-math notation="LaTeX">$\mathsf {SINR}$ </tex-math></inline-formula> coverage analysis framework that includes realistic channel model and antenna element radiation patterns. We introduce and estimate two parameters, <italic>aligned gain</italic> and <italic>misaligned gain</italic>, associated with the desired signal beam and the interfering signal beam, respectively. The distributions of these gains are used to determine the distribution of the <inline-formula> <tex-math notation="LaTeX">$\mathsf {SINR}$ </tex-math></inline-formula> which is compared with the corresponding <inline-formula> <tex-math notation="LaTeX">$\mathsf {SINR}$ </tex-math></inline-formula> coverage, calculated through the system-level simulations. The results show that both aligned and misaligned gains can be modeled as <italic>exponential-logarithmically</italic> distributed random variables with the highest accuracy, and can further be approximated as <italic>exponentially</italic> distributed random variables with reasonable accuracy. These approximations can be used as a tool to evaluate the system-level performance of various 5G connectivity scenarios in the mmWave band.