# CUDA-Optimized GPU Acceleration of 3 GPP 3D Channel Model Simulations for 5G Network Planning
## 3 The 3 GPP Channel Model for 5G NR  
Currently, 5G mobile networks have a high device and base station density, low latency, and high data rates. MIMO channels and multi-antenna transmission increase radio link reliability and efficiency. Additionally, Two-dimensional spatial channel models models wireless channel behavior and performance with low computational complexity [24]; however, by considering only a two-dimensional plane, they poorly capture transmission channel characteristics and limit MIMO techniques to azimuth (beamforming, spatial multiplexing, and precoding). Three-dimensional channel models include channel azimuth and elevation. GSCM calculates channel parameters using randomly distributed scatterers [25]. The 3 GPP specifications [12] propose an accurate and reliable stochastic channel model for building, optimizing, and evaluating 5G systems. The GSCM consists of two parts: (1) a large-scale fading model that includes path loss, line-of-sight (LOS) probability, and additional losses combined with (2) a small-scale fading model characterized by the CIR (also called \"channel coefficients\" in the following). In the context of multipath propagation, the received signal is composed of various attenuated replicas of the original transmitted signal. To calculate the channel coefficients, a step-by-step procedure is recommended [12] (Figure 7.5-1). A simplified representation of multipath scattering is shown in Figure 1 for the propagation of \(n\) clusters, each resolvable into \(m\) subpaths. The azimuth and elevation angles at the base station (BS) and user side are \(\phi\) and \(\theta\). The small-scale parameters include cluster powers, delays, and arrival and departure angles in elevation and azimuth,respectively. Channel coefficients include the LOS and non-LOS (NLOS) propagation subpaths. The NLOS component is calculated as  
\[ \begin{split} H_{u,s,n,m}(t)=\underbrace{\sqrt{\frac{P_{n}}{M}}}_{ \text{Power}}\underbrace{\begin{bmatrix}F_{\text{rx},u,\theta}(\theta_{n,m, \text{ZOA}},\phi_{n,m,\text{AOA}})\\ \underbrace{F_{\text{rx},u,\theta}(\theta_{n,m,\text{ZOA}},\phi_{n,m,\text{AOA} })}_{\text{RX Antenna Pattern}(F_{\text{Rx}})}\end{bmatrix}^{T}\times\underbrace{ \begin{bmatrix}e^{i\theta_{n,m}^{\text{Rx}}}&\sqrt{\kappa_{n,m}-1}e^{i\phi_{n,m }^{\text{Rx}}}\\ \frac{\sqrt{\kappa_{n,m}-1}e^{i\phi_{n,m}^{\text{Rx}}}}{\lambda_{0}}\end{bmatrix} \begin{bmatrix}e^{i\phi_{n,m}^{\text{Rx}}}\\ \chi\text{PR}\end{bmatrix}}_{\text{TX}}\\ \end{split} \\ \times\underbrace{ \begin{bmatrix}F_{\text{rx},s,\theta}(\theta_{n,m, \text{ZOD}},\phi_{n,m,\text{AOD}})\\ \underbrace{F_{\text{rx},s,\theta}(\theta_{n,m,\text{ZOD}},\phi_{n,m,\text{ AOD}})}_{\text{RX Antenna Pattern}(F_{\text{Rx}})}\end{bmatrix} \cdot\underbrace{ \begin{bmatrix}e^{2\pi\lambda_{0}^{-1}p_{n,m}^{ \text{Tx}}-\tilde{d}_{n,m}}\cdot e^{i\frac{2\pi\lambda_{0}^{-1}p_{n,m}^{ \text{Tx}}}\cdot\tilde{d}_{n,m}}\cdot e^{i\frac{2\pi\lambda_{0}^{-1}p_{n,m}^{ \text{Tx}}}\cdot\tilde{d}_{n,m}}\cdot e^{i\frac{2\pi\lambda_{0}^{-1}p_{n,m}^{ \text{Tx}}}\cdot\tilde{d}_{n,m}}\cdot\underbrace{e^{i\frac{2\pi\lambda_{0}^{-1}p _{n,m}^{\text{Tx}}}\cdot\tilde{d}_{n,m}}\cdot e^{i\frac{2\pi\lambda_{0}^{-1}p_{ n,m}^{\text{Tx}}}\cdot\tilde{d}_{n,m}}\cdot\underbrace{e^{i\frac{2\pi\lambda_{0}^{-1}p_{n,m}^{ \text{Tx}}}\cdot\tilde{d}_{n,m}}\cdot\tilde{d}_{n,m}}\cdot\underbrace{e^{i\frac{ 2\pi\lambda_{0}^{-1}p_{n,m}^{\text{Tx}}}\cdot\tilde{d}_{n,m}}\cdot\tilde{d}_{n,m}}\cdot\underbrace{e^{i\frac{2\pi\lambda_{0}^{-1}p_{n,m}^{\text{Tx}}}\cdot \tilde{d}_{n,m}}\cdot\tilde{d}_{n,m}}_{\text{TxLocation Doppler Component}}\end{bmatrix}