In this paper, the precoders capable of maximizing the weighted sum rate (WSR) for multicell scenarios under power budget constraint conditions per cell were considered based on the MIMO system performance. This rate is strongly affected by intracellular interference, so we recommend using coordinated beam forming (CBF). If the number of user equipment provided per cell is small enough to the number of transmit antennas, simple linear beamformers, such as matched filter (MF), achieve higher performance rates. In general cases, two algorithms meet the best performance in terms of the total achievable rate; these are KG (Kim Giannakis) and WSMSE (Weighted Sum Minimum Squared Error) algorithms. In the KG method, the objective function of the sum rate is suggested to be divided into two functions, one function for the desired user rate and the other for the sum rate of the remaining users. In the WSMSE algorithm, maximizing the sum rate is solved by redefining it as the problem of minimizing the MSE (Mean Square Error) function. These functions are convex and nonconvex functions, respectively. In the proposed method, the WSMSEs were modified to reduce the complexity and calculations to provide optimal performance in beamforming.
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