# Building Penetration Losses at 3.5 GHz: Dependence on Polarization and Incidence Angle
## 1 Introduction  
Since they emerged in the 1990s, the development of digital cellular communications has been in an endless race in which user numbers, services, data rates and industry revenue continue to grow from year to year, at times exponentially. This expansion requires new resources and developments in order to manage a scarce and limited electromagnetic spectrum. Despite modulation efficiencies having substantially improved, bandwidth requirements for these systems have grown in parallel to data rate demands. From the initial 200 KHz required for a GSM (2G) channel, we have reached 20 MHz with LTE (4G) and up to 100 MHz and 400 MHz in 5G systems, for the sub-6 GHz (FR1) and the millimetre wave (FR2) bands, respectively [1; 2]. Primary spectrum bands chosen for 5G network deployments are C-bands n77 and n78 (3300-4200 MHz) [3]. These deployments require a deep knowledge on the radio channel behaviour at this frequency band, so that mobile network operators improve the planning tools needed for network rollout. As a large number of user terminals are expected to be located indorors, but served by outdoor base stations, there is a need to assess the propagation path losses for outdoor to indoor links. This is necessary to analyze the base station coverage indoors, but also to calculate the attenuation of interfering signals due to building facades and to determine the possibility of frequency reuse in the radio network. A common outdoor to indoor propagation model [4; 5; 6] divides the path losses (PL) in three components:  
\[\mathrm{PL}=\mathrm{PL}_{\mathrm{b}}+\mathrm{PL}_{\mathrm{tw}}+\mathrm{PL}_{ \mathrm{in}}\left[\mathrm{dB}\right] \tag{1}\]  
where \(\mathrm{PL}_{\mathrm{b}}\) is the basic outdoor propagation loss, \(\mathrm{PL}_{\mathrm{w}}\) are the building penetration losses and \(\mathrm{PL}_{\mathrm{in}}\) are the indoor propagation losses. Modeling building penetration losses is not an easy task. Although Maxwell equations may be useful to solve the problem of a plane wave impinging on an infinite flat surface separating two linear, isotropic and homogeneous media (see e.g., [7]), or on a series of successive dielectric slabs (also separated by infinite flat surfaces, with each slab being homogeneous), actual building facades are far more complex structures. Real facades maynot have electrically flat surfaces (at least at 3.5 GHz); they may not be homogeneous; and they may even have an internally oriented structure. This makes it difficult to find an exact solution for the electromagnetic problem; thus, empirical modeling becomes necessary. Different empirical studies of building penetration losses have been published, showing that the losses depend on the facade material and structure, frequency, angle of incidence and even, as we will see in this paper, on the polarization of the incident field. A compendium of some studies on penetration losses can be found, for instance, in [1; 8; 9; 10]. Regarding the 3.3-4.2 GHz frequency band, attenuation values vary from below 5 dB for old office buildings to 20-30 dB for modern office buildings [11]. Recent studies in new building materials based on concrete reinforcement and admixtures show attenuations constants of 0.8 to 4 dB/cm [12; 13]. According to [1], citing [10], residential buildings with standard glass windows induce penetration losses up to 10 dB. All these values correspond to normal incidence, which represents a situation where the base station is placed in front of the building facade.