An efficient hybrid strategy for uplink channel estimation in massive MIMO systems based on spatially correlated channels

The channel estimation (CE) process is an important phase that has a considerable influence on the performance of massive multiple-input multiple-output systems, in particular, in a more realistic scenario where the channels are spatially correlated (ScD). Thereby, in this work, the uplink (UL) CE process and channel hardening (CH) feature is addressed for ScD Rayleigh fading channels using the statistical Bayesian minimum mean square error estimator. The spatial correlation (SC) of the channels is described using different models, namely, the Gaussian local scattering (GLS) model, the uniform local scattering model, and the proposed hybrid model. Each model (i.e., GLS model and the uniform local scattering model) is studied using two arrangements, that is, for a uniform linear array (ULA) and uniform planar array (UPA). Moreover, the CH feature is investigated under SC of the channels using different models. Furthermore, this study proposes an efficient hybrid strategy based on SC of the channels for UL CE; that is, this work proposes a hybrid covariance matrix (CM) for UPA arrangement by relying on the Kronecker product of the CMs generated through two ULA arrangements, where the first CM is generated through horizontal ULA using GLS model, whereas the second CM is generated through vertical ULA using uniform local scattering model (i.e., one-ring model). Numerical results regarding CE and CH are provided to assert the theoretical expressions, where the CE is evaluated using the normalized mean square error, whereas the CH is assessed using the variance of CH.