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We propose decentralized algorithms and corresponding signaling concepts of effective channel state information (CSI) for weighted sum rate (WSR) maximization via linear downlink transmit-receive beamforming in multi-cell multi-user MIMO systems operating in the time-division duplex (TDD) mode. The iterative processing consists of optimization steps that are run locally by base stations (BS), and facilitated by a combination of over-the-air uplink pilot signaling and scalar backhaul information exchange. In the first novel strategy, the coordinating cells update their transmit precoders and receivers by executing a cell-specific optimization loop one cell at a time, which guarantees monotonic convergence of the network-wide problem. The strategy employs separate uplink channel sounding (CS) and busy burst (BB) signaling to reveal the effective channels of the terminals to the neighboring BSs. In the second strategy, we sacrifice the monotonic convergence and devise a faster scheme where the BSs are allowed to optimize their variables in parallel based on just the CS responses and additional backhaul information. We make use of the optimization framework where the WSR maximization is carried out via weighted sum mean-squared-error (MSE) minimization, and generalize the approach by employing antenna-specific transmit power constraints. The numerical results demonstrate that WSR maximization has the desirable property that spatial scheduling, or user and beam selection, is carried out implicitly.