Low-Complexity Channel Estimation Scheme for Cell-Free Massive MIMO with Hardware Impairment

Cell-free (CF) massive multi-input multi-output (mMIMO) is a potential key technology in future 6G wireless networks, which is in a position to service many users uniformly. In this paper, we aim to investigate the impact of multi-antenna access points (APs) and users on the channel estimation of CF mMIMO with two different linear minimum mean-squared error (LMMSE) estimators when low-quality hardware is applied. We firstly give the LMMSE estimator on multi-antenna users via vectorization operation with all radio frequency (RF) chains and the low-complexity LMMSE estimator with a single-RF chain, where the impact of transmit and receive spatial correlation, hardware impairment (HI) and different pilot assignment are considered. Then, we provide the comparison of the normalized MSE (NMSE) performance and computational complexity between the two schemes. Simulation results show that the single-RF scheme can significantly reduce the complexity as the number of antennas increases. Meanwhile, the loss of NMSE performance is relatively trivial, and the single-RF scheme may outperform the full-RF scheme with random pilot assignment and other schemes like element-wise MMSE and least-square estimators.