# The Role of Correlation in the Performance of Massive MIMO Systems
## 1 Introduction  
The essential goal of the next generation of wireless communication systems (sixth generation (6G)) is to accommodate the significant growth in mobile data traffic [1, 2]. In particular, 6G networks aim to substantially increase the spectral efficiency (SE), maintain the quality of service (QoS), and achieve a reliable communication system [3, 4]. To meet these enormous demands, advanced disruptive technologies are needed [5]. One of the key enabling technologies for wireless communications systems is massive multiple-input multiple-output (m-MIMO) [6, 7, 8, 9]. Specifically, m-MIMO systems, which utilize large-scale antenna arrays at the base station, can be used to support the tremendous growing demands in terms of data traffic [6, 10, 11]. The concept of m-MIMO was initially introduced by [PERSON] in [10], since then, it has gained considerable attention. The advantages of m-MIMO systems are in combating the effects of the fast fading and enabling the use of linear precoding and combining techniques with a reduced signal processing complexity [12]. m-MIMO systems can also be useful for radar applications [13]. Furthermore, the array gain in m-MIMO systems can be increased significantly and the link budget can be increased proportional to the number of base station antennas. In addition, m-MIMO systems have the capability of reducing the required energy and hardware power consumption significantly [14]. From an information-theoretic point of view, the SE performance depends strongly not only on the signal-to-noise ratio (SNR) but also on the level of correlation. Although considerable attention has been given to studying the received SNR, a little attention has been dedicated to investigating the effect of correlation. In particular, the vast majority of m-MIMO research has assumed that the channels are uncorrelated, which can be modeled using the Rayleigh fading channels [12; 14; 15; 16; 17]. These investigations rely on the assumption of the law of large numbers, which implies that when the number of antenna elements at the base station grows asymptotically large without limit, the channel coefficients become uncorrelated. Therefore, the interference can be completely eliminated. This observation is extremely strict and seems unrealistic. This is because such an interference-free scenario cannot be achieved in practice with a finite number of base station antennas. Hence, the assumption of uncorrelated channels considered conventionally by the previous research works seems highly idealistic. Furthermore, from a practical point of view, field measurements have shown that MIMO channels are correlated considering various trials and testbeds [18; 19; 20; 21; 22; 23]. Therefore, investigating m-MIMO systems in a more general fading scenario, which takes into account the correlation conditions, is an interesting research topic that should be considered. This motivates us to investigate the m-MIMO system performance in terms of mean square error (MSE) and SE in a more realistic scenario where the channels are correlated. Paper contributions and findings: The vast majority of massive MIMO research has assumed that the channels are modeled with uncorrelated Rayleigh fading channels, which seems highly idealistic. Therefore, the following contributions are offered in the present paper. * This study addresses the challenge of investigating the performance of m-MIMO systems in a practical setting in the presence of spatial correlation and using limited coherence time. * This study explores the impact of having arbitrary array geometries on the performance of m-MIMO systems by using different array topologies, namely uniform linear array (ULA) and uniform rectangular array (URA). * This study seeks to answer the following question: Which array configuration maximizes the SE of m-MIMO systems. For this reason, this study considers a Laplacian physical channel model to design the channel covariance matrices with distinct array geometries.