An Analysis of Noise Aggregation from Multiple Distributed RF Emitters

The purpose of this technical note is to explore the aggregate noise generated by a large number of distributed radio emitters. There have been concerns that the widespread and ubiquitous use of ultra-wide-ba nd (UWB) devices might increase the ambient noise levels beyond today's conditions. There are particular concerns regarding aircraft safety due to substantial line-of-sight propagation through the air. Both the theoretical analysis (1) and past experiences with actual, spatially reused, radio systems are related to this theoretical model and strongly indicate that substantial noise build-up does not and will not occur. From our derivations, it becomes clear that possible problems cannot come from an aggregation of emitters within a 45 degree cone below the victim receiver. Rather, any possible problem must come from an aggregation on the horizon. However, the smallest amount of attenuation eliminates any possibility of serious aggregation from this source. The developed model applies equally to all radio emitters, addressing spatial reuse of AM and FM radio, spread spectrum, and UWB sources alike. The density of the emitters is not an issue, only the spatial reuse. The longstanding observation of non-aggregati on of noise of such emitters as AM and FM radio and cellular systems speaks to the effectiveness of damping on the possible horizontal aggregation. 1. Aggregation Model We consider the aggregate power at the apex of a solid cone resulting from the aggregate power emitted by the disk forming the base of the cone (Fig. 1). We will eventually apply this model with the base of the cone on the surface of the Earth and the apex at some height above the surface. We take the radius of the disk to be r and the height of the apex above the ground plane to be h. The areal power density in the base disk is P. Using the inverse square law we can integrate in cylindrical coordinates over the base disk and arrive at Papex, the apex receiver power density per unit area of apex receiver antenna ( x is the radius from the base of the cone):