A split pre-conditioned conjugate gradient method for massive MIMO detection

In massive multiple-input multiple-output (MIMO) mobile system, the computational complexity of signal detection increases exponentially along with the growing number of antennas. For example, the sub-optimal linear detection schemes, such as zero forcing (ZF) detector and minimum mean square error (MMSE) detector, always have to balance the performance and complexity resulted from the large-scale matrix inversion operations. Recently, some iterative linear solvers, such as conjugate gradient (CG), have been proposed to address this issue. These series of detection algorithms offer a better tradeoff between error-rate performance and computational complexity by avoiding the computation-hungry operations like matrix inversion. However, when the the system loading factor ρ goes up, their results are no longer satisfactory. To solve the aforementioned issues, this paper 1) first introduces a novel, low-complexity pre-conditioner by exploring the properties of the equalization matrix and 2) then proposes a split pre-conditioned conjugate gradient (SPCG) method to speed up the convergence rate of detection. Both analytical and numerical results have demonstrated the performance and complexity advantages of the proposed algorithm over the sate-of-the-art ones. The proposed detector outperforms the conventional CG detector with around 2 dB for BER = 10−4. When the number of user antennas is relatively large, its complexity is only 25% of the existing pre-conditioned conjugate gradient detector based on incomplete Cholesky decomposition (ICCG).