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In this paper, we study the iterative weighted sum rate (WSR) maximizing linear precoder algorithm proposed by Christensen et al. in large correlated MISO broadcast channels. We propose a novel approximation of the signal-to-interference plus noise ratio (SINR) at every iteration. Moreover, for identical distributed channels the proposed approximation of the WSR maximizing precoder is of closed form and has the well known regularized zero-forcing (RZF) structure. Simulation results show that under correlated channels, the novel SINR approximation is more accurate than previously proposed estimates based on the RZF precoder.