We describe multi-user MIMO systems with limited feedback precoding. To achieve the capacity of a multi-user MIMO channel, the accurate channel state information must be available at the transmitter. Because the channel state information is fed back from each UE, higher accuracy in feedback information requires larger uplink resource. A receiver in practical system is unable to feed back the perfect channel state information to the transmitter because of uplink resource limitation. Instead, a receiver feeds back the partial channel state information, which improve the efficiency of the uplink resource use. We define such system as the Multi-user MIMO system with limited feedback precoding.