We propose a decentralized algorithm for weighted sum rate (WSR) maximization via large system analysis. The rate maximization problem is done via weighted sum mean-squared error (WSMSE) minimization. Decentralized processing relies on the exchange via a backhaul link of a low amount of information. The inter-cell interference terms couple the maximization problems at the different base stations (BS)s. Large system approximations are used to replace the inter-cell interference terms and to decouple the problems. We demonstrate that the approximates depend only on the slow fading terms or second order statistics of the channels. Then, each BS computes the transmit precoders to serve its own user equipments (UE)s locally. No feedback channels from the UEs to the serving BSs will be required.