In this work, we study the asymptotic behavior of the zero-forcing precoder based on the least squares (LS) and the linear minimum mean-square error (LMMSE) channel estimates for the downlink (DL) of a frequency-division-duplex (FDD) massive multiple-input-single-output (MISO) system. We show analytically the rather surprising result that zero-forcing precoding based on the LS estimate leads asymptotically to an interference-free transmission, even if the number of pilots used for DL channel training is less than the number of antennas available at the base station (BS). Although the LMMSE channel estimate exhibits a better quality in terms of the MSE due to the exploitation of the channel statistics, we show that in the case of contaminated channel observations, zero-forcing based on the LMMSE is unable to eliminate the inter-user interference in the asymptotic limit of high DL transmit powers. In order for the results to hold, mild conditions on the channel probing phase are assumed. The validity of our analytical results is demonstrated through numerical simulations for different scenarios.

翻译：本文研究了频分双工（FDD）大规模多输入单输出（MISO）系统下行链路中基于最小二乘（LS）和线性最小均方误差（LMMSE）信道估计的迫零预编码器的渐近特性。我们通过理论分析揭示了一个相当令人惊讶的结果：即使下行信道训练所用导频数少于基站（BS）可用天线数，基于LS估计的迫零预编码也能渐近实现无干扰传输。尽管LMMSE信道估计因利用信道统计信息而具有更优的均方误差（MSE）性能，但研究表明，在信道观测受到污染的情况下，当下行发射功率渐近增加时，基于LMMSE的迫零预编码无法消除用户间干扰。为使结论成立，本文假设了信道探测阶段的温和条件。通过不同场景下的数值仿真验证了理论分析结果的有效性。