On the Sum Rate of Multi-Antenna Broadcast Channels with Channel Estimation Error

For multiple antenna broadcast channels, perfect channel state information (CSI) at the basestation plays a critical role in achieving the sum rate advantage provided by the multiple antennas. For practical system implementation, the CSI is usually estimated from training sequences. In this paper, we study the effect of channel estimation error on the sum rate capacity of multiple antenna broadcast channels. A lower bound is derived based on the sum rate performance of the zero forcing dirty paper coding scheme under CSI estimation error. A cooperative upper bound is established from the capacity upper bound of a single user multiple-input multiple-output (MIMO) channel given the same channel imperfectness. We further analyze the asymptotic sum rate loss caused by channel estimation error. If we assume that the variance of the channel estimation error is fixed, imperfect CSI results in a sum rate ceiling for high SNR. For systems with orthogonal training sequences and minimum mean square error (MMSE) channel estimator, the asymptotic sum rate loss is about N bit per channel use where N is the number of transmit antennas. I. INTRODUCTION Techniques employing multiple antennas are important for wireless communication systems because they provide the possibility of a significant increase in system spectrum effi- ciency. In the last decade, lots of works have been done on point-to-point, i.e., single user, multiple-input multiple-output (MIMO) systems. Larger rate gains, however, are available when MIMO multi-user systems are considered. Recently, the sum rate capacity of the multiple antenna broadcast channel, which models the downlink in a MIMO cellular network, was solved (1), (2), (3), (4). These works show that perfect channel state information (CSI) at the basestation is critical for the system to achieve the sum rate advantage. With perfect CSI,