Low-complex Bayesian estimator for imperfect channels in massive muti-input multi-output system

Motivated by the fact that the complexity of the computations is one of the main challenges in large multiple input multiple output systems, known as massive multiple-input multiple-output (MIMO) systems, this article proposes a low-complex minimum mean squared error (MMSE) Bayesian channel estimator for uplink channels of such systems. First, we have discussed the necessity of the covariance information for the MMSE estimator and how their imperfection knowledge can affect its accuracy. Then, two reduction phases in dimension and floating-point operations have been suggested to reduce its complexity: in phase 1, eigenstructure reduction for channel covariance matrices is implemented based on some truncation rules, while in phase 2, arithmetic operations reduction for matrix multiplications in the MMSE equation is followed. The proposed procedure has significantly reduced the complexity of the MMSE estimator to the first order O(M), which is less than that required for the conventional MMSE with O(M3) in terms of matrix dimension. It has been shown that the estimated channels using our proposed procedure are asymptotically aligned and serve the same quality as the full-rank estimated channels. Our results are validated by averaging the normalized mean squared error (NMSE) over a length of 500 sample realizations through a Monte Carlo simulation using MATLAB R2020a.