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Linear precoding for multiuser multiple input multiple output (MIMO) cellular systems has generally focused on a single isolated cell. A crucial tool in algorithm development has been a downlink/uplink duality. Here we investigate downlink multiuser communications across multiple cells. Previous work identified the resulting asynchronous interference as a key issue. We prove the existence of a downlink/uplink duality requiring time reversal. This duality is used to develop an effective linear precoding algorithm for multiuser, multi-cell, MIMO systems. Simulation results illustrate the importance of accounting for, and to quantify the loss due to, asynchronous interference.