A Stochastic Geometry Analysis on The Uplink Performance of Cell-Free Massive MIMO Systems with Hardware Impairments

Abstract

Numerous studies have demonstrated that the benefits of Cell-Free Massive Multiple-Input-Multiple-Output (CF-mMIMO), including consistent coverage, increased Spectral Efficiency (SE), and improved security, cannot be overstated. CF-mMIMO employs distributed Access Points (APs) to eliminate inter-cell interference, a major limitation in traditional cell-based systems. CF-mMIMO relies mainly on low-grade and low-cost hardware transceiver elements, User Equipment (UE), and Internet of Things (IoT) devices to reduce costs. This introduces Hardware Imperfections (HWI) that may degrade network performance, and their impact on system performance requires extensive research. Most current research assumes incorrectly that transceiver hardware is perfect in real-world deployments where low-cost or energy-constrained devices are used. However, HWI, due to low-grade and low-cost elements, produces distortion noise and hinders system performance, especially in the uplink. Moreover, most investigations analyzing the impact of HWI consider the correlation-based Rayleigh model, instead of the geometry-based model that factors practical parameters such as path loss, delay profile, and Angle of Arrival. Another challenge is that the spatial randomization of user and AP sites complicates the impact of HWI. The idea of a spatial channel has surprisingly not been integrated into the HWI analysis in previous publications. Our stochastic-geometry uplink analysis of the CF-mMIMO system includes these and many more reasons. We model the location of APs with a Poisson Point Process (PPP) instead of a uniform distribution. We considered the AP as a ULA and integrated its array response into the channel vector to achieve spatial surroundings for evaluation. The proposed CF-mMIMO model was evaluated using different combining schemes, including Minimum Mean Square Error (MMSE), Regularized Zero-Forcing (RZF), and Maximum Ratio (MR). Monte Carlo simulations reveal that hardware-induced distortions significantly degrade CF-mMIMO’s performance. The outcome indicates that in a stochastic channel, the rate of degradation for both RZF and MMSE is the same, although MMSE occasionally outperforms RZF by a small margin. Furthermore, MR has a lower overall efficiency, even though it can be more resilient. Finally, increasing the number of Uniform Linear Array (ULA) elements was expected to improve SE, as reported by prior research. The stochastic channel with ULA marginally outperformed the correlated Rayleigh model due to spatial environment effects. An ideal (non-spatial) scenario confirmed this, showing a 55.62 percentage increment in SE.