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：在这项工作中,我们根据最小正方(LS)和线性最低平均平方差(LMMSE)频道对频率分散(DL)系统大规模多投入-单一输出(MIOSO)系统的下行链接(DL)的估计,对零强制前编码的无症状行为进行了研究。我们从分析上看,基于LS估计的零强制前编码导致无干扰传输,即使用于DL频道培训的飞行员数量少于基地台(BS)现有天线的数量。虽然LMMSE频道对频率分散(DLL)系统下行连接(DLL)的估计显示,由于对频道统计数据的利用,MSE的质量有所提高,但我们表明,在受污染的频道观测中,基于LMMSE的零推进无法消除用户间对高DL传输功能无症状限制的干扰。为了保持结果,对频道模拟阶段的温和条件是假设的。我们通过不同分析阶段的模拟结果是真实的。