###### Abstract  
Future generations of wireless communications systems are expected to evolve toward allowing massive ubiquitous connectivity and achieving ultra-reliable and low-latency communications (URLLC) with extremely high data rates. Massive multiple-input multiple-output (m-MIMO) is a crucial transmission technique to fulfill the demands of high data rates in the upcoming wireless systems. However, obtaining a downlink (DL) training sequence (TS) that is feasible for fast channel estimation, i.e., meeting the low-latency communications required by future generations of wireless systems, in m-MIMO with frequency-division-duplex (FDD) when users have different channel correlations is very challenging. Therefore, a low-complexity solution for designing the DL training sequences to maximize the achievable sum rate of FDD systems with limited channel coherence time (CCT) is proposed using a waterfilling power allocation method. This achievable sum rate maximization is achieved using sequences produced from a summation of the user's covariance matrices and then applying a waterfilling power allocation method to the obtained low-complexity training sequence. The results show that the proposed TS outperforms the existing methods in the medium and high SNR regimes while reducing computational complexity. The obtained results signify the proposed TS's feasibility for practical consideration compared with the existing DL training sequence designs. massive MIMO systems; uniform planar array; training sequence; sum rate maximization; spatial correlation; FDD; channel estimation 2023122494103390/electronics211  
reducing the impact of fading and interference that can increase the reliability of wireless communication, and allowing a uniform quality of service [8; 9]. Finally, an m-MIMO system improves energy efficiency, because it enables the use of low-power radio-frequency (RF) components and reduces the need for complex signal processing [8]. The aforementioned advantages introduce m-MIMO systems as a key technology for future wireless communications systems [10]. However, channel state information (CSI) must be estimated accurately in order for an m-MIMO system to achieve its full potential gain. When using time-division-duplex (TDD) transmission, the necessary CSI for precoding is obtained by combining orthogonal training sequence (TS) broadcasting by the users in the uplink (UL) transmission during every channel coherence time (CCT) period [3]. With channel reciprocity, no downlink (DL) TS is needed, and hence, the TS overhead is proportional to the number of users (\(K\)) rather than the number of antennas \(N\)[4; 8; 11; 12; 13; 14; 15; 16]. Hence, \(N\) can be made very large without affecting the system overhead [17]. This is why previous work on m-MIMO systems has focused on TDD transmission mode. However, the limitations of TDD-based systems with partial CSI typically originate from the transceiver hardware limitations and calibration error in the UL/DL RF chains, notwithstanding the encouraging findings of TDD transmission mode with m-MIMO systems [18; 19; 20; 21; 14]. In addition, because the power amplifier is only activated part of the time, TDD systems often have poorer signal-to-noise ratios (SNR) than FDD-based systems. If the UL and DL channels use the same frequency band, which is the case for TDD operation protocol, there can be a significant amount of interference between the UL and DL signals. Separating the frequencies used for UL and DL, which is the case in FDD operation protocol, makes it easier for the system to distinguish between the signals transmitted by different users and helps in reducing the interference and hence improving system performance. Furthermore, the FDD system is a well-established duplexing technique that is widely used in many existing wireless communication systems. For example, FDD operation mode is used by approximately 85% of the present-day mobile communication networks that use long-term evolution (LTE) technology for mobile communication [22].