In downlink multiuser multiple-input multiple-output (MU-MIMO) systems, the zero-forcing (ZF) transmission is a\r\nsimple and effective technique for separating users and data streams of each user at the transmitter side, but its\r\nperformance depends greatly on the accuracy of the available channel state information (CSI) at the transmitter\r\nside. In time division duplex (TDD) systems, the base station estimates CSI based on uplink pilots and then uses it\r\nthrough channel reciprocity to generate the precoding matrix in the downlink transmission. Because of the\r\nconstraints of the TDD frame structure and the uplink pilot overhead, there inevitably exists CSI delay and channel\r\nestimation error between CSI estimation and downlink transmission channel, which degrades system performance\r\nsignificantly. In this article, by characterizing CSI inaccuracies caused by CSI delay and channel estimation error, we\r\ndevelop a novel bit error rate (BER) expression for M-QAM signal in TDD downlink MU-MIMO systems. We find that\r\nchannel estimation error causes array gain loss while CSI delay causes diversity gain loss. Moreover, CSI delay\r\ncauses more performance degradation than channel estimation error at high signal-to-noise ratio for time varying\r\nchannel. Our research is especially valuable for the design of the adaptive modulation and coding scheme as well\r\nas the optimization of MU-MIMO systems. Numerical simulations show accurate agreement with the proposed\r\nanalytical expressions.
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