Blind Joint 2-D DOA/Symbols Estimation for 3-D Millimeter Wave Massive MIMO Communication Systems

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.