# Modeling of Downlink Interference in Massive MIMO 5G Macro-Cell +
## 3 Interference Evaluation in Downlink
### Fundamentals of 3 GPP Channel Model  
For link-level and detailed system-level simulations, the 3 GPP has provided instructions on how to generate statistical three-dimensional (3D) channel models, as shown in Figure 3[28]. It includes all the necessary radio propagation phenomena that must be considered during a comprehensive simulation to provide an estimation of the radio link budget (including interference) and performance.  
Figure 2: Simplified simulation procedure of the MPM.  
It should be noted that according to [28], dispersion in the angular domain is modeled in steps 4, 6, 7, and 8 of Figure 3. In step 4, when the angular spread (AS) for a given scenario and network layout is generated, i.e., based on the assumed statistical model, the following parameters are generated:  
* [noitemsep,topsep=0 pt]
* azimuth spread of departure (ASD),
* zenith (i.e., elevation) spread of departure (ZSD),
* azimuth spread of arrival (ASA),
* zenith spread of arrival (ZSA).  
In step 6, the power for all rays of all clusters (which arise due to multipath propagation) is generated, whereas in step 7, the angles of departure and arrival are determined for all these rays. Finally, in step 8, random coupling is performed between departure and arrival angles for rays inside a given cluster, in both azimuth and elevation. As can be noticed, according to the 3 GPP channel model [28], the PAS, \(p(\theta,\phi,D)\), obtained at the end of step 8 does not depend on the assumed antenna pattern. It is considered only in step 11, where channel coefficients for each cluster and each Tx and Rx element of antenna arrays are generated. Only at the end of step 11 are results of the spatial filtering of multipath components (clusters and rays) by the Tx and Rx nominal antenna patterns known. Therefore, to correctly calculate the received power of either reference or interfering signal, it is required to determine the effective antenna gains for the Tx and Rx. These effective antenna gains are defined as an integral part of the multiplied nominal antenna pattern (for the Tx or Rx) and PAS, which is equivalent to spatial filtering, as shown below [37]:  
\[G^{Eff}(D)=\iint\limits_{\Omega}g^{Nom}(\theta,\phi)p(\theta,\phi,D)d\theta d\phi, \tag{5}\]  
where \(g^{Nom}(\theta,\phi)\) indicates nominal 3D antenna pattern, either for the Tx or Rx, in either the reference or interfering link. Similarly, \(G^{Eff}(D)\) indicates the effective gain of the Tx or Rx in either the reference or interfering link. Following the notation of Equation (2), the SIR calculated according to the 3 GPP channel model [28] may be presented as follows:  
\[SIR(D)(\text{dB})=10\log_{10}\frac{P_{R0}(D)}{P_{R1}(D)}=10\log_{10}\frac{G_{T0 }^{Eff}(D)\cdot G_{R0}^{Eff}(D)}{G_{T1}^{Eff}(D)\cdot G_{T0}^{Eff}(D)}, \tag{6}\]  
Figure 3: Block diagram of statistical channel model reconstruction according to 3 GPP.  
where \(G_{T0}^{Eff}(D)\), \(G_{R0}^{Eff}(D)\), \(G_{TI}^{Eff}(D)\), and \(G_{RI}^{Eff}(D)\) indicate the effective gains of the Tx and Rx in reference and interfering links, respectively.