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For massive multiple-input multiple-output (MIMO) systems, linear precoding is preferable to nonlinear precoding for better performance-complexity trade-off. However, linear precoding is still difficult to implement in practice for such large systems, because the precoding matrix involves the complicated matrix inversion that must be rapidly computed in real-time. In this paper, we use the large-scale property of massive MIMO systems, the excellent characteristics of the weighted Neumann series (WNS) matrix, and steepest descent (SD) method to devise a new iterative precoding for massive MIMO systems. First, by exploiting the characteristics of WNS iteration, we proposed a weighted Neumann series-steepest descent (WNS-SD) iterative algorithm to perform precoding with low-complexity, and the convergence condition is always met in underloaded scenarios. Second, by devising a novel first iterative step of the aforementioned WNS-SD iterative algorithm, we proposed an accelerated iterative algorithm, named the accelerated weighted Neumann series-steepest descent (AWNS-SD) algorithm. Furthermore, in the first iterative step of the AWNS-SD algorithm, we designed a promising preconditioning matrix for the SD algorithm based on the WNS matrix. Subsequently, via merger with the WNS iterative method, the AWNS-SD iterative precoding not only greatly improves the convergence rate of WNS-SD and other competitive precoding algorithms while maintaining low-complexity, but also guarantees a wide range of convergence. Finally, simulation results verify the validity of the theoretical analysis and show that without additional iteration steps, the proposed AWNS-SD precoding achieves near-optimal performance of the exact zero forcing (ZF) precoding in just one iterative step for typical massive MIMO system configurations. Furthermore, the diagonal matrix concept is applied to the preconditioning technique to further reduce the overall complexity. INDEX TERMS Massive MIMO, matrix inversion, iterative methods, convergence improvement, lowcomplexity.

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Dactylogyrus ctenopharyngodonid and Ichthyophthirius multifiliis are two important ectoparasites of freshwater fish. Co-infection by the two parasites leads to high fish mortality and results in heavy economic losses. This study aimed to evaluate the efficacy of medicated feed and a ginger extract bath against D. ctenopharyngodonid and I. multifiliis on grass carp and investigate the hematological response of grass carp co-infected by the two parasites. These results demonstrated that red blood cell (RBC) and thrombocyte percentage among leucocytes significantly decreased after grass carp were co-infected by D. ctenopharyngodonid and I. multifiliis. The monocyte and neutrophil percentages significantly increased with the increment of parasite mean intensities, while the lymphocyte percentage decreased. The activities of serum acid phosphatase (ACP), alkaline phosphatase (AKP), lysozyme (LZM), and superoxide dismutase (SOD) significantly increased after co-infection. When grass carp treated with medicated feed containing 4% of Astragalus membranaceus, Allium sativum, Morus alba, and Glycyrrhiza uralensis, the activities of ACP, AKP, LZM, and SOD were significantly enhanced, and the mean intensities of D. ctenopharyngodonid and I. multifiliis were significantly decreased. When grass carp was treated with medicated feed and a 4-mg/L ginger extract bath, all parasites were eliminated during 28 days. The bath of ginger extract at a concentration of 4 mg/L kept a low mean intensity of I. multifiliis and D. ctenopharyngodonid, then the two parasites were eliminated by oral administration of the medicated feed with an immunostimulant (Chinese medicine compound).