# Modeling of Downlink Interference in Massive MIMO 5G Macro-Cell +
## 1 Introduction  
Achieving greater transmission capacity for wireless links is the main goal of the currently developed fifth-generation (5G) mobile communication system [1, 2]. The use of new spectral resources that cover frequency ranges exceeding 3 GHz provides an increase in the performance and capacity of next generation networks. However, propagationphenomena that occur in the centimeter-wave (cmWave) and millimeter-wave (mmWave) ranges cause numerous problems in the practical implementation of radio transmission equipment solutions [3; 4]. The increase in propagation environment attenuation at higher frequencies makes it necessary to reduce the size of cells and sectors served by individual network base stations (BS). Hence, obtaining full coverage forces increased density of BSs in a given deployment area. The dominant amount of mobile users' equipment (UEs) of wireless networks occurs in urban areas, where the phenomenon of multipath propagation significantly limits the transmission capabilities of radio links. In combination with the Doppler effect, resulting from user motions, this phenomenon leads to signal dispersion in time, frequency, and reception angle domains [5]. A multi-antenna system is one of the basic solutions used in the currently implemented 5G systems that minimize adverse propagation phenomena. A massive multiple-input-multiple-output (mMIMO) technique plays a special role [6; 7]. It uses a beamforming technique [8; 9], which allows for the possibility of practical implementation of spatial multiplexing for radio resources. This multiplexing improves spectral efficiency by using the same frequency sub-bands in angularly separated beams (spatially orthogonal beams). In urban areas, multipath propagation is the cause of the angular dispersion of the received signals [10]. It is the reason for receiving signal components from unwanted beams that significantly interfere with the signal from the serving (i.e., useful, reference) beam. A level of this interference is directly connected with spatial orthogonality between reference and interfering beams. If a signal-to-interference ratio (SIR), i.e., the ratio between received powers of reference and interfering signals, is higher, then the spatial orthogonality between these beams is better. Therefore, at the mMIMO 5G network planning and optimization stages, it is important to assess spatial orthogonality in realistic propagation conditions accurately. This allows achievable performance for a given deployment scenario to be estimated. One of the metrics that can help estimate mMIMO cell performance is the relation between the SIR and angular separation between the reference and interfering beams. Since UEs are distributed mostly on a horizontal plane, rather than a vertical one, in the typical cells of a mobile network, in the majority of cases is enough to consider angular separation only on a horizontal plane to make an accurate estimation of the SIR. In other words, accurate modeling of the relation between the angular separation of reference and interfering beams on a horizontal plane and the SIR helps to estimate many parameters of mMIMO cells. For example, we may determine a minimum distance between UEs that can be served by simultaneous mMIMO beams with an assumed interference level or maximum number of uniformly distributed UEs, which can be served by simultaneous mMIMO beams with the assumed level of the SIR. In the literature, an interference subject concerns interfering signals in a wide-sense. The nature of their formation may be diverse. In most cases, when we talk about interferences, we mean so-called non-intentional interferences, i.e., those arising from the operation of radio, electronic, or mechatronic devices, networks, or whole systems during their work.