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In this paper, we investigate the system performance of a downlink transmission with fixed relay, where the signals at transmit and relay nodes are pre-processed by linear precoders designed based only on partial channel state information (CSI) obtained from the limited feedback channel. Precoders are designed to minimize the mean square error of the transmit signal under the constraint of total transmit power at source and relay nodes. We assume that there is no direct link between source node and users, all the signal are delivered to user ends with the help of the relay node. Signal model for the described system is derived in details and the system performance is investigated. Performance gain brought by precoding is analyzed as well by comparing the uncoded bit error rate (BER) performance of system with precoding and that of system without precoding. Employing precoders based on limited CSI can still improve the BER performance significantly. The system model derived in this paper hereby can be a reference for applications in similar scenarios.