# Performance Evaluation of CF-MMIMO Wireless Systems Using Dynamic Mode Decomposition
###### Abstract  
Cell-Free Massive Multiple-Input-Multiple-Output (CF-MIMO) systems have transformed the landscape of wireless communication, offering unparalleled enhancements in Spectral Efficiency and interference mitigation. Nevertheless, the large-scale deployment of CF-MIMO presents significant challenges in processing signals in a scalable manner. This study introduces an innovative methodology that leverages the capabilities of Dynamic Mode Decomposition (DMD) to tackle the complexities of Channel Estimation in CF-MIMO wireless systems. By extracting dynamic modes from a vast array of received signal snapshots, DMD reveals the evolving characteristics of the wireless channel across both time and space, thereby promising substantial improvements in the accuracy and adaptability of channel state information (CSI). The efficacy of the proposed methodology is demonstrated through comprehensive simulations, which emphasize its superior performance in highly mobile environments. For performance evaluation, the most common techniques have been employed, comparing the proposed algorithms with traditional methods such as MMSE (Minimum Mean Squared Error), MRC (Maximum Ration Combining), and ZF (Zero Forcing). The evaluation metrics used are standard in the field, namely the Cumulative Distribution Function (CDF) and the average UL/DL Spectral Efficiency. Furthermore, the study investigates the impact of DMD-enabled Channel Estimation on system performance, including beamforming strategies, spatial multiplexing within realistic time- and delay-correlated channels, and overall system capacity. This work underscores the transformative potential of incorporating DMD into massive MIMO wireless systems, advancing communication reliability and capacity in increasingly dynamic and dense wireless environments. c 2024 14 June 2024 19  
of antennas at the base station, thereby enabling simultaneous communication with multiple users [4]. The synergy of CF-MMIMO and its dynamic communication environments hold the potential to revolutionize wireless systems, yet the complexity of accurate Channel Estimation in these scenarios remains a significant challenge. In CF-MMIMO systems, the fundamental principle of exploiting spatial diversity and multiplexing gain is augmented by the presence of a large number of antennas at the base station [2, 5]. This affords substantial improvements in the signal-to-interference-plus-noise ratio (SINR), enhancing both capacity and reliability. However, the practical implementation of CF-MMIMO introduces novel challenges, particularly in Channel Estimation, due to the sheer number of antennas and the dynamic nature of wireless channels [6]. The implementation of CF-Mmassive MIMO is not a trivial problem; it has significant challenges. Coordinating and synchronizing a large number of geographically distributed antennas without a clear cell structure requires high precision in time and frequency synchronization to avoid interference and improve signal coherence. Implementing efficient and effective signal processing algorithms in a distributed manner across multiple antennas necessitates the development of robust algorithms capable of processing large volumes of data in real time. Managing the interference between users and antennas in a cell-free environment requires advanced beamforming techniques and interference cancellation methods. Accurately estimating communication channels in a dynamic and dispersed environment demands advanced Channel Estimation methods that can adapt to rapid variations in the channels. Providing a backhaul infrastructure capable of supporting the high volume of data exchanged between distributed antennas and the central processing unit needs high-capacity, low-latency backhaul links to ensure smooth and fast communication. Managing the energy consumption of a large number of distributed antennas requires energy-saving techniques and the optimization of resource usage.