Extremely large-scale multiple-input-multipleoutput (XL-MIMO) has been reviewed as a promising technology for future sixth-generation (6G) networks to achieve higher performance. In practice, various linear precoding schemes, such as zero-forcing (ZF) and regularized ZF (RZF) precoding, are sufficient to achieve near-optimal performance in traditional massive MIMO (mMIMO) systems. It is critical to note that in large-scale antenna arrays the operation of channel matrix inversion poses a significant computational challenge for these precoders. Therefore, we explore several iterative methods for determining the precoding matrix for XL-MIMO systems instead of direct matrix inversion. Taking into account small- and large-scale fading as well as spatial correlation between antennas, we study their computational complexity and convergence rate. Furthermore, we propose the Jacobi-Preconditioning Conjugate Gradient (Jac-PCG) iterative inversion method, which enjoys a faster convergence speed than the CG method. Besides, the closed-form expression of spectral efficiency (SE) considering the interference between subarrays in downlink XL-MIMO systems is derived. In the numerical results, it is shown that the complexity given by the Jac-PCG algorithm has about 54% reduction than the traditional RZF algorithm at basically the same SE performance.

翻译：超大规模多输入多输出（XL-MIMO）被视为未来第六代（6G）网络实现更高性能的潜在关键技术。在实际应用中，各类线性预编码方案（如迫零（ZF）和正则化迫零（RZF）预编码）在传统大规模MIMO（mMIMO）系统中足以实现接近最优的性能。需要特别指出的是，在大规模天线阵列中，信道矩阵求逆运算给这些预编码器带来了显著的计算挑战。因此，我们探索了几种迭代方法用于确定XL-MIMO系统的预编码矩阵，以替代直接矩阵求逆。综合考虑小尺度衰落、大尺度衰落以及天线间的空间相关性，我们研究了这些方法的计算复杂度和收敛速率。此外，我们提出了Jacobi预条件共轭梯度（Jac-PCG）迭代求逆方法，其收敛速度优于共轭梯度（CG）方法。同时，推导了下行XL-MIMO系统中考虑子阵列间干扰的频谱效率（SE）闭式表达式。数值结果表明，在基本相同的SE性能下，Jac-PCG算法的复杂度比传统RZF算法降低约54%。