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.
In multiuser visible light communication (VLC) systems, many transmit precoding (TPC) techniques have been investigated to suppress multiuser interference. However, these conventional works restrict their modulation to the special case of zero mean, which inherently limits their application to some popular modulations associated with the non-zero mean in VLC, such as pulse position modulation (PPM). Since the modulation with non-zero mean leads to more intricate optical power constraints and design objective functions than the case of zero mean, the TPC design that can support a general modulation is still an open problem. In the paper, we conceive of a general solution of the TPC scheme combined with dimming control for multiuser VLC systems, which is capable of mitigating multiuser interference, while at the same time, achieving the desired dimming level. The proposed scheme is applicable to a wide range of modulations in VLC, such as pulse amplitude modulation (PAM), PPM, and so on. Simulation results demonstrate that the proposed scheme outperforms the traditional pseudo-inverse-based zero-forcing TPC in terms of bit error rate (BER).
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