Robust Hybrid Beamforming in Cooperative Cell-Free mmWave MIMO Networks Relying on Imperfect CSI

A low-complexity robust cooperative hybrid beamformer is designed for both the downlink and uplink of cell-free millimeter wave (mmWave) multiple-input-multiple-output (MIMO) networks, while considering realistic imperfect channel state information (CSI). To begin with, a second-order cone program (SOCP)-based robust fully-digital beamformer (FDBF) is designed for minimizing the worst-case interference for the downlink of multiple-input-single-output (MISO) systems. Subsequently, we develop a Bayesian learning (BL) framework for determining both the analog and digital components of the hybrid transmit precoder (TPC) from the FDBF. The above designs are subsequently extended to employing eigenvector perturbation theory for constructing the robust TPC for the cell-free mmWave MIMO downlink, where the users have multiple receive antennas (RAs). Furthermore, the multi-dimensional covariance fitting (MCF) framework is harnessed for designing the robust TPC of the corresponding uplink. Finally, the efficiency of the proposed TPC designs is evaluated by simulation results both in terms of their ability to mitigate the multi-user interference (MUI), and improving the spectral efficiency achieved. Additionally, the proposed designs are shown to be computationally efficient and equivalent to a minimum variance hybrid beamformer.