# Performance Evaluation of CF-MMIMO Wireless Systems Using Dynamic Mode Decomposition
## 6 Results
### Performance Evaluation of DMD in a System Considering Delay-Doppler Correlated Channel
Increasing the normalized Doppler shift \(f_{d}T_{s}\) from 0 to 0.004 results in a 34% median SE loss for DMD, a 44% median SE loss for MRC, and a 60% median SE loss for PZFZ. This is because DMD leverages network-wide fading statistics to calculate coefficients, effectively minimizing interference and mitigating the effects of channel aging. It is noteworthy that the ZF systems, despite employing a stricter capacity bound through channel estimates in data detection, still perform poorly under channel aging. Another point to highlight with respect to the Doppler effect is that this effect is directly related to the speed of the UEs. Therefore, it is a direct indicator of the behavior of DMD in a static or dynamic system. As can be seen, the higher the speed, the better the performance of DMD compared to non-DMD schemes. Figure 24 illustrates the CDF of the per-user downlink Spectral Efficiency (SE) for both coherent and non-coherent transmissions at full power, with normalized Doppler shifts of \(f_{d}T_{s}=0\), \(f_{d}T_{s}=0.0005\), \(f_{d}T_{s}=0.001\), \(f_{d}T_{s}=0.0015\), and 0.002. The results demonstrate that coherent transmission achieves significantly higher SE compared to non-coherent transmission, irrespective of whether the UEs are stationary or in motion. An increase in the normalized Doppler shift \(f_{d}T_{s}\) from 0 to 0.002 leads to a 37% decrease in median SE for coherent transmission and a 42% decrease for non-coherent transmission. This disparity arises because, in non-coherent transmission, UEs detect signals from the APs sequentially, making them more susceptible to the impacts of channel aging. Evaluation of the Performance in Overall System Capacity Achieved through DMD-Based Channel Estimation  
In this section, we aim to determine the overall behavior of the network with the use of DMD. To achieve this, we compare the performance of DMD models with non-DMD models and appropriately adjust the most important parameters that affect network behavior. These parameters include the number of base stations (BSs) and the number of users. Additionally, in a highly concentrated scenario, we analyze the effect of the number of samples taken on the performance of the two major system groups we are using: DMD and non-DMD. Figure 23: CDF of median SE and 95% likely per-user uplink transmission with full power and \(f_{d}T_{s}=[0,0.002]\) (X-scale in Graphs are scaled by \(10^{-3}\)). (**A**) Uplink CDF of different Channel Estimation techniques (\(L=100\), \(K=20\), \(N=2\), ASD = \(30^{\circ}\), \(50<v<150\)). (**B**) 95%-likely per-user uplink SE vs. \(f_{D}T_{s}\) (\(L=100\), \(K=20\), \(N=2\), ASD = \(30^{\circ}\), \(50<v<150\)). (X-axis scale multiplied by \(10^{-3}\)). Figure 25 displays the Average Spectral Efficiency (SE) per User Equipment (UE) as a function of the number of base stations (BSs), denoted by \(L\). The parameters used in the simulation include \(\tau_{p}=7\), \(K=10\), \(N=8\), and \(p_{k}=100\) mW for each UE. As the network becomes denser, local network traffic can increase, leading to an overall increase in global traffic. However, the rise in interference can cause a decrease in global traffic. Experimental results demonstrate that DMD optimizes global network traffic exceptionally well, achieving an almost linear increase with the density of both BSs and UEs, as shown in Figures 25 and 26. This is attributed to the efficient handling and implicit power control in the DMD model, which optimally manages the separation of strong signals with appropriate handling and weak signals. Figure 26 illustrates the CDF of the uplink (UL) sum Spectral Efficiency (SE) for a system with \(K=50\) users, plotted as a function of the number of base station (BS) antennas. Figure 24: CDF of the per-user downlink SE for coherent and non-coherent transmission with full power with \(f_{d}T_{s}=0\), \(f_{d}T_{s}=0.0005\), \(f_{d}T_{s}=0.001\)\(f_{d}T_{s}=0.0015\) and \(0.002\) (X-scale in the graphs are multiplied by \(10^{-3}\)).