XL-MIMO Based Hierarchical Receive Beamforming Subject to Hardware Impairments in the Uplink of Cell-Free Networks

Extremelylarge-scale multiple-input and multiple-output (XL-MIMO) exhibit substantial spatial multiplexing capabilities owing to their high degree of freedom. As the number of antenna elements increases, it becomes more practically suitable to utilize cost-effective antennas equipped with low-resolution RF chains. However, hardware impairments (HWIs) associated with these cost-effective antennas lead to performance saturation in the high signal-to-noise ratio (SNR) region, which cannot be mitigated by merely increasing the transmit power. To address these challenges, we propose a hierarchical receive beamforming method for XL-MIMO based near-field cell-free networks with HWIs. Specifically, the antenna array of each access point (AP) is partitioned into multiple sub-arrays, with each sub-array independently harnessing the minimum mean-square error (MMSE) receive beamforming algorithm. The local data estimates at each AP are then optimized using the results from all sub-arrays, and the central processing unit (CPU) performs its final information recovery by integrating these local estimates. Our theoretical analysis shows that the proposed hierarchical receive beamforming method achieves a higher ergodic sum-rate than the state-of-the-art (SoA) scheme in XL-MIMO systems in the face of HWIs.