A fast-convergent pre-conditioned conjugate gradient detection for massive MIMO uplink

The scaling up of antennae and terminals in massive multiple-input multiple-output (MIMO) systems helps increase spectral efficiency at the penalty of prohibitive computational complexity. In linear minimum mean square error (MMSE) detection, this complexity is mainly resulted from solving large-scale linear equations. Admittedly, iterative approaches such as conjugate gradient (CG) method have theoretically demonstrated their capability in balancing both performance and complexity for massive MIMO detection. Their convergence rate turns out to be really slow for common applications where the base station-to-user antenna ratio decreases. To this end, by introducing a pre-conditioner based on incomplete Cholesky (IC) factorization, this paper proposes a pre-conditioned conjugate gradient (PCG) method, which successfully speeds up the convergence even for small station-to-user antenna ratio scenarios. The analytical as well as numerical results have indicated that the proposed PCG method outperforms the conventional CG method due to the 50% reduced spectral condition number κ. Complexity analysis shows that the proposed PCG method achieves over 75% reduction compared to the conventional Cholesky factorization scheme when N = 40.