Performance Analysis of Reconfigurable Holographic Surfaces in the Near-Field Scenario of Cell-Free Networks Under Hardware Impairments

We propose a hybrid beamforming architecture for near-field reconfigurable holographic surfaces (RHS) harnessed in cell-free networks. Specifically, the holographic beamformer of each base station (BS) is designed for maximizing the channel gain based on the local channel state information (CSI). By contrast, the digital beamformer at the central processing unit is designed based on the minimum mean squared error criterion. Furthermore, the near-field spectral efficiency of the RHS in cell-free networks is derived theoretically by harnessing the popular stochastic geometry approach. We consider both the phase shift error (PSE) at the RHS elements and the hardware impairment (HWI) at the radio frequency (RF) chains of the transceivers. Furthermore, we theoretically derive the asymptotic capacity bound, when considering an infinite physical size for the RHS in the near-field channel model. The theoretical analysis and simulation results show that the PSE at the RHS elements and the HWI at the RF chains of transceivers limit the spectral efficiency in the high signal-to-noise ratio region. Moreover, we show that the PSE at the RHS elements and the HWI at the RF chains of BSs can be compensated by increasing the number of BSs. Finally, we also demonstrate that the ergodic spectral efficiency based on the near-field channel model is higher than that based on the far-field channel model assumption.