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Extremely large-scale multiple-input-multiple-output (XL-MIMO) is a promisingtechnology for the future sixth-generation (6G) networks to achieve higherperformance. In practice, various linear precoding schemes, such aszero-forcing (ZF) and regularized zero-forcing (RZF) precoding, are capable ofachieving both large spectral efficiency (SE) and low bit error rate (BER) intraditional massive MIMO (mMIMO) systems. However, these methods are notefficient in extremely large-scale regimes due to the inherent spatialnon-stationarity and high computational complexity. To address this problem, weinvestigate a low-complexity precoding algorithm, e.g., randomized Kaczmarz(rKA), taking into account the spatial non-stationary properties in XL-MIMOsystems. Furthermore, we propose a novel mode of randomization, i.e., samplingwithout replacement rKA (SwoR-rKA), which enjoys a faster convergence speedthan the rKA algorithm. Besides, the closed-form expression of SE consideringthe interference between subarrays in downlink XL-MIMO systems is derived.Numerical results show that the complexity given by both rKA and SwoR-rKAalgorithms has 51.3% reduction than the traditional RZF algorithm with similarSE performance. More importantly, our algorithms can effectively reduce the BERwhen the transmitter has imperfect channel estimation.

Low-Complexity Precoding for Extremely Large-Scale MIMO Over Non-Stationary Channels