On the Impact of Dynamic Beamforming on EMF Exposure and Network Coverage: A Stochastic Geometry Perspective

This paper introduces a new mathematical framework for dynamic beamforming-based cellular networks, grounded in stochastic geometry. The framework is used to study the electromagnetic field exposure (EMFE) of active and idle users as a function of the distance between them. A novel multi-cosine antenna pattern is introduced, offering more accurate modeling by incorporating both main and side lobes. Results show that the cumulative distribution functions of EMFE and coverage obtained with the multi-cosine pattern align closely with theoretical models, reducing error to less than 2\%, compared to a minimum of 8\% for other models. The marginal distribution of EMFE for each user type is mathematically derived. A unique contribution is the introduction of the SCAIU (\underline{S}patial \underline{C}DF for \underline{A}ctive and \underline{I}dle \underline{U}sers), a metric that ensures coverage for active users while limiting EMFE for idle users. Network performance is analyzed using these metrics across varying distances and antenna elements. The analysis reveals that, for the chosen network parameters, with 64 antenna elements, the impact on idle user EMFE becomes negligible beyond 60~m. However, to maintain active user SINR above 10 dB and idle user EMFE below -50~dBm at 2~m, more than 256 elements are required.