Extremely large-scale multiple-input-multiple-output (XL-MIMO) is a promising technology for the future sixth-generation (6G) networks to achieve higher performance. In practice, various linear precoding schemes, such as zero-forcing (ZF) and regularized zero-forcing (RZF) precoding, are capable of achieving both large spectral efficiency (SE) and low bit error rate (BER) in traditional massive MIMO (mMIMO) systems. However, these methods are not efficient in extremely large-scale regimes due to the inherent spatial non-stationarity and high computational complexity. To address this problem, we investigate a low-complexity precoding algorithm, e.g., randomized Kaczmarz (rKA), taking into account the spatial non-stationary properties in XL-MIMO systems. Furthermore, we propose a novel mode of randomization, i.e., sampling without replacement rKA (SwoR-rKA), which enjoys a faster convergence speed than the rKA algorithm. Besides, the closed-form expression of SE considering the interference between subarrays in downlink XL-MIMO systems is derived. Numerical results show that the complexity given by both rKA and SwoR-rKA algorithms has 51.3% reduction than the traditional RZF algorithm with similar SE performance. More importantly, our algorithms can effectively reduce the BER when the transmitter has imperfect channel estimation.

翻译：极大规模多输入多输出（XL-MIMO）是未来第六代（6G）网络实现更高性能的一项有前景技术。在实践中，各种线性预编码方案，例如迫零（ZF）和正则化迫零（RZF）预编码，能够在传统大规模MIMO（mMIMO）系统中同时实现高频谱效率（SE）和低误码率（BER）。然而，由于固有的空间非平稳性和高计算复杂度，这些方法在极大规模场景下效率不高。针对这一问题，我们考虑XL-MIMO系统中的空间非平稳特性，研究了一种低复杂度预编码算法，例如随机Kaczmarz（rKA）。此外，我们提出了一种新的随机化模式，即无放回采样rKA（SwoR-rKA），其收敛速度比rKA算法更快。同时，推导了考虑下行XL-MIMO系统中子阵列间干扰的频谱效率闭式表达式。数值结果表明，rKA和SwoR-rKA算法的计算复杂度相比传统RZF算法降低了51.3%，且具有相似的频谱效率性能。更重要的是，当发射机存在非理想信道估计时，我们的算法能有效降低误码率。