Uplink-downlink duality in normalized MSE or SINR under imperfect channel knowledge

Duality between the multi-antenna multi-user uplink and the downlink has been discovered in terms of sum rate, capacity region, signal-to-interference-plus-noise-ratio (SINR) region or normalized mean-squared error (MSE) region. Previous work on duality has assumed perfect channel knowledge. However, channel estimation is never perfect in practice. In this paper, channel estimation error as well as antenna correlation at the base station (BS) is taken into account. A multi-user system with multiple antennas at the BS and with single-antenna users is studied. Joint detection and transmission are used in the uplink and the downlink, respectively. It is analytically shown that with imperfect channel state information (CSI), under the same sum power constraint, the achievable SINR regions or the normalized MSE regions in both links are the same, as in the case with perfect CSI. Monte Carlo simulation results and discussions are also provided to complement the analysis.