This paper proposes novel pilot optimization and channel estimation algorithm for the downlink multiuser massive multiple input multiple output (MIMO) system with $K$ decentralized single antenna mobile stations (MSs), and time division duplex (TDD) channel estimation which is performed by utilizing $N$ pilot symbols. The proposed algorithm is explained as follows. First, we formulate the channel estimation problem as a weighted sum mean square error (WSMSE) minimization problem containing pilot symbols and introduced variables. Second, for fixed pilot symbols, the introduced variables are optimized using minimum mean square error (MMSE) and generalized Rayleigh quotient methods. Finally, for $N=1$ and $N=K$ settings, the pilot symbols of all MSs are optimized using semi definite programming (SDP) convex optimization approach, and for the other settings of $N$ and $K$, the pilot symbols of all MSs are optimized by applying simple iterative algorithm. When $N=K$, it is shown that the latter iterative algorithm gives the optimal pilot symbols achieved by the SDP method. Simulation results confirm that the proposed algorithm achieves less WSMSE compared to that of the conventional semi-orthogonal pilot symbol and MMSE channel estimation algorithm which creates pilot contamination.

翻译：本文建议对下行的多用户大规模多输入多输出产出(MIMO)系统进行新的试点优化和频道估算算法,该系统使用美元分散的单一天线移动站(MSs)和用美元试点符号进行的时分双曲(TDD)频道估算。拟议算法解释如下。首先,我们将频道估算问题作为加权和加权平均平方差(WSMSE)最大限度地减少包含试点符号和引入变量的问题。第二,对于固定的试点符号,引入的变量使用最低平均平方差(MMSE)和通用的RayLayLeorgy商基方法进行优化。最后,对于美元=1美元和美元=K$的设置,所有MS的试点符号都使用半确定程序(SDP)矩形优化方法进行优化,对于其他设定的美元和美元,所有MS的试点符号通过应用简单的迭代算法优化。当美元=K$K美元时,可以证明后一种迭代算法提供了SDP方法所实现的最佳试点符号。模拟结果证实,与常规的MOVA的试点模型相比,拟议的SMS和M-E实验室的模型的模型的模型的模型的模型的模型没有那么。