On the Performance of MMSE Channel Estimation in Massive MIMO Systems over Spatially Correlated Rician Fading Channels

Massive multiple-input-multiple-output (M-MIMO) offers remarkable advantages in terms of spectral, energy, and hardware efficiency for future wireless systems. However, its performance relies on the accuracy of channel state information (CSI) available at the transceivers. This makes channel estimation pivotal in the context of M-MIMO systems. Prior research has focused on evaluating channel estimation methods under the assumption of spatially uncorrelated fading channel models. In this study, we evaluate the performance of the minimum-mean-square-error (MMSE) estimator in terms of the normalized mean square error (NMSE) in the uplink of M-MIMO systems over spatially correlated Rician fading. The NMSE allows for easy comparison of different M-MIMO configurations, serving as a relative performance indicator. Besides, it is an advantageous metric due to its normalization, scale invariance, and consistent performance indication across diverse scenarios. In the system model, we assume imperfections in channel estimation and that the random angles in the correlation model follow a Gaussian distribution. For this scenario, we derive an accurate closed-form expression for calculating the NMSE, which is validated via Monte-Carlo simulations. Our numerical results reveal that as the Rician K-factor decreases, approaching Rayleigh fading conditions, the NMSE improves. Additionally, spatial correlation and a reduction in the antenna array interelement spacing lead to a reduction in NMSE, further enhancing the overall system performance.