# Thermal Impact of 5G Antenna Systems in Sandwich Walls
## 1 Introduction  
The 5G standard was established in late 2018, and 5G cellular networks were rolled out globally in 2019 [1]. Additionally, 5G offers numerous benefits, including higher bandwidth, uninterrupted connectivity, low latency services, interconnected devices (e.g., smart homes, medical devices), and advanced IoT systems, such as autonomous vehicles, precision agriculture, industrial machinery, and advanced robotics [2]. With the new radio (NR) frequency range 1 (FR1), where the frequencies are below 6 GHz, the capacity can be increased up to 20 times higher than 4G [3]. Additionally, 5G cellular networks use a broader bandwidth than 4G, which enables the fast transmission of large amounts of data with a small latency that users do not recognize. The need for a broader bandwidth necessitates a move-up in the carrier frequency, leading to a shorter wavelength of radio waves. However, these radio waves with short wavelengths can easily be blocked, especially in energy-efficient buildings that feature multiple layers of insulation, low-emission air-tight windows, and other signal barriers [4; 5]. To ensure strong signal transmission through thick external walls, antennas must be positioned in optimal locations to take advantage of high-speed indoor wireless coverage. Both activeand passive solutions have been extensively researched in recent years, such as indoor base stations [6; 7] and repeaters [8; 9; 10] for active solutions, and low-emissivity windows with frequency-selective surfaces [11] or signal slots [12; 13] for passive solutions. However, both solutions have limitations; for instance, active solutions often require an expensive radio-frequency-over-fiber network and consume additional energy. On the other hand, passive solutions are energy-efficient, but typically have limited radio frequency (RF) passbands. To the best of our knowledge, there is currently no commonly used passive solution that can operate effectively throughout the lifetime of a building [14; 15]. The wide frequency band of the passive system in [15] ensures that the system is forward compatible. While with the active repeaters, the devices will have to be replaced when new radio systems emerge that use a different radio frequency from legacy systems. The authors developed passive antenna systems embedded in a building wall known as the signal-transmissive wall to enhance 5G indoor coverage [14; 15]. In [15], the signal-transmissive wall with a passive antenna system consisting of two spiral antennas connected back-to-back with stainless steel coaxial cable was analyzed for its electromagnetic transmission characteristics using analytical, numerical, and empirical methods. The embedded antenna system improved the electromagnetic transmission through the wall up to 17 dB compared to a bare wall at the wireless communication frequency of 8 GHz [15]. The U value of the signal-transmissive wall was reported to increase slightly, but no detailed thermal analysis was conducted in [15]. Passive antenna systems often include materials with high thermal conductivity, such as steel or copper, which can result in thermal bridging and negatively impact the building's thermal performance. This paper aims to investigate the thermal impact of the passive antenna systems introduced in [15] on the thermal transmittance of the wall. There are several methods to determine the thermal transmittance (U-value) of building components containing inhomogeneous layers, including measurement, numerical modeling, and analytical approaches. Measurement methods, such as the heat flow meter (HFM) [16], guarded hotplate (GHP) [17], and hot box (HB) [18], are often performed under laboratory conditions to achieve well-controlled environmental conditions, geometries, configurations, and materials [19]. However, these methods can be both time-consuming and costly. Numerical modeling provides detailed three-dimensional (3D) heat transfer analysis [20; 21], enabling the comparison of different building components, configurations, and materials.