  Linear precoding techniques can achieve near- optimal capacity due to the
special channel property in down- link massive MIMO systems, but involve high
complexity since complicated matrix inversion of large size is required. In
this paper, we propose a low-complexity linear precoding scheme based on the
Gauss-Seidel (GS) method. The proposed scheme can achieve the
capacity-approaching performance of the classical linear precoding schemes in
an iterative way without complicated matrix inversion, which can reduce the
overall complexity by one order of magnitude. The performance guarantee of the
proposed GS-based precoding is analyzed from the following three aspects. At
first, we prove that GS-based precoding satisfies the transmit power
constraint. Then, we prove that GS-based precoding enjoys a faster convergence
rate than the recently proposed Neumann-based precoding. At last, the
convergence rate achieved by GS-based precoding is quantified, which reveals
that GS-based precoding converges faster with the increasing number of BS
antennas. To further accelerate the convergence rate and reduce the complexity,
we propose a zone-based initial solution to GS-based precoding, which is much
closer to the final solution than the traditional initial solution. Simulation
results demonstrate that the proposed scheme outperforms Neumann- based
precoding, and achieves the exact capacity-approaching performance of the
classical linear precoding schemes with only a small number of iterations both
in Rayleigh fading channels and spatially correlated channels.
