### Related Work  
Several studies have explored the enhancement of DL TS design by using a well-known filter known as a minimum-mean-square-error (MMSE) that takes into account both the statistics of the channel and the noise [27; 28; 29; 30]. To this end, considering different system models, the authors in [27; 28; 29; 30] investigate the m-MIMO performance when there is the same spatial correlation among the users at the BS. Specifically, the work in [27; 28; 29; 30] considers the time and spatial domains correlations and designs TS based on the spatial domain and then use the time domain for CSI prediction. The authors in [31; 32; 33] consider compressed sensing (CS) techniques and design the TS assuming the users have a common correlation pattern. In these studies, the TS duration needed for the DL channel estimate of the FDDtransmission mode benefits from the sparsity structure. However, the users might exhibit distinct spatial correlation patterns in practice. Therefore, the TS design proposed in [27; 28; 29; 30; 31; 32; 33] cannot apply to the multiuser m-MIMO when the users have different correlations.  
To overcome the issue of having different channel correlations with FDD transmission mode, numerous studies have looked into the TS design using various methods. For example, the authors in [34; 35] proposed a method with two-stage precoding. In this two-stage approach, the users are partitioned into different groups with common correlation users, and then each group has a different channel correlation to simplify the TS design and reduce the TS length to estimate CSI. To make the two-stage approach effective, it is important to use a sophisticated scheduling algorithm and clustering method for both user groups and individual users within those groups. Additionally, although a two-stage method might help reduce the length of the DL TS, it is still necessary to employ these scheduling and clustering algorithms. Otherwise, assuming a finite number of users to be chosen at the scheduling stage and realistic propagation conditions with heterogeneous user channels, the system performance could be significantly reduced due to the residual interference between the users in the same group and the users in different groups. Moreover, the study in [34; 35] does not deal with the single-stage approach with \(K\) independent user CCMs, making it impossible to predict the FDD m-MIMO system performance in a single-stage precoding scenario. The work in [36; 37; 38; 39; 40] considers a single-stage precoding process assuming the users have different transmit correlations in FDD transmission mode. The DL TS has been optimized using extensive iterative algorithms. The optimization algorithms used have a slow rate of convergence, leading to high latency and computational complexity. In practical systems with a URLLC, the channel could exhibit a short CCT. As a result, it is necessary to obtain CSI estimation more frequently while maintaining low latency between the CSI estimation and precoding. Therefore, there is an essential need for developing a feasible TS design in FDD m-MIMO systems that can maximize the sum rate while not increasing the computational complexity. Recently, the work in [41] proposed a training design without the need for using iterative algorithms. However, the sum rate of FDD systems with short CCT is not yet discovered. Specifically, the effect of TS overhead has not yet been taken into consideration in [41], and thus, the sum rate of FDD m-MIMO systems with the practical consideration of limited CCT is not yet discovered. Furthermore, the rate can be maximized through the use of efficient and low-complexity DL TS design.