We propose decentralized algorithms and corresponding channel state information (CSI) signaling concepts for weighted sum rate (WSR) maximization via linear downlink transmit-receive processing in multi-cell multi-user MIMO systems operating in the time division duplex (TDD) mode. Decentralized processing relies on a combination of over-the-air pilot signaling and scalar information exchange between the base stations. Each base station (BS) computes the transmit precoders to serve its own user terminals locally. Similarly, the terminals compute their receive filters locally and signal their effective downlink channels to the BSs via precoded uplink sounding. As a result, the transmit strategies of the neighboring cells adapt to each other over time. WSR maximization results in the desirable property that spatial scheduling, or user and beam selection, is carried out implicitly. Thus, only a subset of the potential transmit beams are allocated with non-zero transmit powers.