# Performance Evaluation of CF-MMIMO Wireless Systems Using Dynamic Mode Decomposition
## 7 Discussion  
This study delves into the potential of DMD to revolutionize Channel Estimation within CF-MMMO systems. Through extensive simulations and analysis, several critical insights have been gleaned.  
Firstly, PiDMD/mpeDMD methods have consistently outperformed traditional techniques across various metrics. The core advantage of DMD lies in its ability to capture and utilize the dynamic modes from received signal snapshots, effectively tracking the evolving characteristics of wireless channels over time and space. This dynamic tracking capability has proven particularly beneficial in highly mobile scenarios, where traditional methods often struggle to maintain accuracy.  
Our experiments illustrate that DMD-enabled Channel Estimation significantly enhances system performance. Notably, DMD methods demonstrate superior Spectral Efficiency and more effective interference mitigation compared to conventional techniques. This improvement is attributed to the robust extraction and application of CSI, which is crucial for optimal beamforming and spatial multiplexing strategies.  
Additionally, the simulations have shown that DMD methods lead to better scalability in processing signals within large-scale CF-MMMO deployments. This scalability is essential for practical implementations, as it ensures that the system can handle increased user densities and higher mobility without a corresponding increase in computational complexity.  
The impact of DMD on system capacity is another highlight of this study. By accurately estimating and adapting to the channel conditions, DMD methods facilitate higher system capacity and improved communication reliability. This is particularly evident in dynamic and dense wireless environments, where the ability to swiftly adapt to changing conditions is paramount.  
Moreover, the research underscores the importance of considering time- and delay-correlated channels in the evaluation of CF-MMMO systems. The inclusion of realistic channel models in our simulations provides a more accurate depiction of system performance, ensuring that the results are applicable to real-world scenarios.  
This study validates the transformative potential of incorporating DMD into CF-MMMO systems. The demonstrated gains in Spectral Efficiency, interference mitigation, and system capacity underscore the significant advantages of DMD-based methods over traditional methods.  
Future work may include topics such as Reconfigurable Intelligent Surface (RIS) [47, 48], which is a very recent subject and will be explored in future works. In [49], massive synchrony in distributed Antenna Systems is explored, an issue that is a topic that could also be addressed using DMD methods, just to mention two topics among several others that could be studied using DMD and its variants. It is also worth noting that DMD-based methods themselves are a field of much recent research.  
\begin{table}
\begin{tabular}{c c c} \hline
**Modulation Scheme** & **Number of Operations** & **Processing Time*** \\ \hline MR-mpeDMD & \(O(n^{3})+(3N-1)\) & \(\approx\)48.2 ms \\  & & \(\approx\)49.1 ms \\  & & \(\approx\)51.3 ms \\ \hline FZF-mpeDMD & \(O(n^{3})+(NK^{2}+K^{3})\) & \(\approx\)46.3 ms \\  & & \(\approx\)48.1 ms \\  & & \(\approx\)45.2 ms \\ \hline PZFZ-mpeDMD & \(O(n^{3})+O(N^{2})\) & \(\approx\)58.1 ms \\  & & \(\approx\)62.8 ms \\  & & \(\approx\)67.1 ms \\ \hline MMSE-mpeDMD & \(O(n^{3})+O(K^{3})+O(NK^{2})\) & \(\approx\)65.1 ms \\  & & \(\approx\)67.3 ms \\  & & \(\approx\)71.2 ms \\ \hline \end{tabular} \({}^{*}\)Time is shown sequentially according to the scenarios.  
\end{table}
Table 3: Computational Intensity 3. Part 3.