  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.
