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

TL;DR

This work addresses the performance of reconfigurable holographic surfaces (RHS) in near-field cell-free networks under hardware impairments and phase shift errors. It introduces a hybrid beamforming framework where RHS-based holographic beamformers at distributed BSs are designed from local CSI and the CPU applies a MMSE digital beamformer using global CSI, explicitly incorporating $PSE$ and $HWI$ in the analysis. Using stochastic geometry, it derives an ergodic spectral efficiency upper bound and shows that high-SNR performance is limited by $PSE$ and $HWI$, though increasing BS density $\eta$ can compensate RHS and BS-HWI effects (but not UE-HWI). The results also reveal that near-field channel models yield higher ergodic rates than far-field models and provide asymptotic capacity bounds for infinitely large RHS sizes, highlighting the benefits and limitations of densification and near-field modeling for RHS-based cell-free networks.

Abstract

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.

Figures (7)

• Figure 1: System model of reconfigurable holographic surfaces-based cell-free network.
• Figure 2: Theoretical analysis (\ref{['Theoretical_Analysis_4']}), (\ref{['Theoretical_Analysis_14']}) and simulation results of the ergodic achievable rate $R$ versus the transmit power $\rho$ for different number of RHS elements, with perfect RHS phase shift design and ideal hardware quality of the RF chains at the BSs and UEs.
• Figure 3: Theoretical analysis (\ref{['Theoretical_Analysis_11_1']}), (\ref{['Theoretical_Analysis_11_2']}), (\ref{['Theoretical_Analysis_14']}) and simulation results of the ergodic achievable rate $R$ versus the transmit power $\rho$ for different number of RHS elements.
• Figure 4: Theoretical analysis (\ref{['Theoretical_Analysis_11_3']}), (\ref{['Theoretical_Analysis_14']}) and simulation results of the ergodic achievable rate $R$ versus the transmit power $\rho$ for different number of RHS elements, with imperfect RHS phase shift design, i.e. $\sigma_\mathrm{p}^2>0$.
• Figure 5: Theoretical analysis (\ref{['Theoretical_Analysis_11_1']}), (\ref{['Theoretical_Analysis_11_2']}) and simulation results of the achievable sum-rate $R$ versus the deployed BS density $\eta$ for different number of UEs $K$, with $\rho=20\mathrm{dB}$.