In order to reduce the computational complexity of the inverse matrix in the regularized zero-forcing (RZF) precoding algorithm, this paper expands and approximates the inverse matrix based on the truncated Kapteyn series expansion and the corresponding low-complexity RZF precoding algorithm is obtained. In addition, the expansion coefficients of the truncated Kapteyn series in our proposed algorithm are optimized, leading to further improvement of the convergence speed of the precoding algorithm under the premise of the same computational complexity as the traditional RZF precoding. Moreover, the computational complexity and the downlink channel performance in terms of the average achievable rate of the proposed RZF precoding algorithm and other RZF precoding algorithms with typical truncated series expansion approaches are analyzed, and further evaluated by numerical simulations in a large-scale single-cell multiple-input-multiple-output (MIMO) system. Simulation results show that the proposed improved RZF precoding algorithm based on the truncated Kapteyn series expansion performs better than other compared algorithms while keeping low computational complexity.
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