By using a large number of antenna (sensor) elements at the receivers, massive multi-input multi-output (MIMO) offers many benefits for 5G communication systems, such as a huge spectral efficiency gain, significant reduction of latency, and robustness to interference. However, to get these benefits of massive MIMO, accuracy of the channel state information obtained at the transmitter is required. This article proposes a approach for blind joint channel/symbols estimation in 3-D millimeter wave massive MIMO systems based on tensor factorization. More specifically, we suggest a direction-of-arrival (DOA)-based channel estimation method, which provides the best performance in terms of error bound for channel estimation. We show that the massive MIMO signals can be expressed as a third-order (3-D) tensor model, where the matrices of channel (2-D DOA) and symbols can be viewed as two independent factor matrices. Such a hybrid tensorial modeling enables a blind joint estimation of 2-D DOA/symbols. To learn the tensor model, we develop two least squares--based algorithms. The first one is delta bilinear alternating least squares (DBALS) algorithm that exploits the increment values between two iterations of the factor matrices to provide the initializations for such matrices. This avoids the slow convergence caused by random initializations for factor matrices found in the traditional least squares algorithms. The other one is Vandermonde constrained DBALS that takes into account the potential Vandermonde nature structure of the DOA matrix in the DBALS algorithm. This provides the estimation for the DOA matrix and gives a better uniqueness results for the use of tensor model. The performance of the proposed approach is illustrated by means of simulation results, and a comparison is made with the recent approaches. Besides a blind joint 2-D DOA/symbols estimation, our approach offers a better performance due to avoiding the random initializations and taking in the Vandermonde structure of DOA matrix.

中文翻译：

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用于 3-D 毫米波大规模 MIMO 通信系统的盲联合 2-D DOA/符号估计

通过在接收器上使用大量天线（传感器）元件，大规模多输入多输出 (MIMO) 为 5G 通信系统提供了许多好处，例如巨大的频谱效率增益、显着降低延迟和抗干扰能力. 然而，为了获得大规模 MIMO 的这些好处，需要在发射机处获得的信道状态信息的准确性。本文提出了一种基于张量分解的 3-D 毫米波大规模 MIMO 系统中的盲联合信道/符号估计方法。更具体地说，我们提出了一种基于到达方向 (DOA) 的信道估计方法，该方法在信道估计的误差范围方面提供了最佳性能。我们表明，大规模 MIMO 信号可以表示为三阶（3-D）张量模型，其中通道（2-D DOA）和符号矩阵可以看作是两个独立的因子矩阵。这种混合张量建模能够实现二维 DOA/符号的盲联合估计。为了学习张量模型，我们开发了两种基于最小二乘的算法。第一个是增量双线性交替最小二乘 (DBALS) 算法，该算法利用因子矩阵的两次迭代之间的增量值来为此类矩阵提供初始化。这避免了在传统最小二乘算法中发现的因子矩阵的随机初始化导致的缓慢收敛。另一种是 Vandermonde 约束 DBALS，它考虑了 DBALS 算法中 DOA 矩阵的潜在 Vandermonde 性质结构。这提供了对 DOA 矩阵的估计，并为使用张量模型提供了更好的唯一性结果。通过仿真结果说明了所提出方法的性能，并与最近的方法进行了比较。除了盲联合二维 DOA/符号估计外，我们的方法由于避免了随机初始化并采用了 DOA 矩阵的 Vandermonde 结构，因此提供了更好的性能。