Fairness-Maximizing Precoder Design for Multi-User Visible-Light Communication Systems
Objective Visible light communication(VLC)leverages the visible light spectrum to offer significantly greater bandwidth than radio frequency(RF)communication,addressing RF spectrum congestion and meeting the demands of the Internet of Things(IoT)and future 6G technologies.Typically,multiple light-emitting diodes(LEDs)are installed to meet lighting requirements.By employing multiple input multiple output(MIMO)technology,high data rates and reliability are achieved without additional time and spectrum resources.However,the use of MIMO technology causes overlapping optical signals,resulting in severe multi-user interference(MUI).Transmitter precoding techniques,such as block diagonal(BD)precoding,have been extensively studied as key methods to mitigate MUI.However,due to the high correlation in optical channels,BD precoding suffers from significant disparities in subchannel gains,leading to poor overall bit error rate(BER)performance.Addressing this subchannel gain disparity and mitigating MUI is essential for achieving high-speed,reliable communication.Methods To address these challenges,we propose an improved multi-user precoding scheme based on fairness maximization in BD precoding.Building upon the BD precoding's ability to eliminate MUI and considering VLC's unique characteristics,we formulate an optimization problem aimed at maximizing the minimum subchannel gain under the constraints of non-negative transmitted optical signals and total transmission power.Due to the non-convex nature of the problem,solving it directly is difficult.To overcome this,we decompose the problem into two independent subproblems:intra-user channel equalization and inter-user power allocation.In the first subproblem,we parameterize the precoding matrix and derive its optimal structure.Then,we use a branch-and-bound algorithm to manage the non-convex constraints,transforming the problem into a mixed-integer constrained convex programming problem.This approach effectively solves the optimal precoding matrix parameters,ensuring that each user's subchannel gain is maximized.In the second subproblem,we derive a closed-form solution for optimal user power allocation,achieving the goal of maximizing the minimum subchannel gain.This method mitigates the significant subchannel gain disparities in BD precoding and enhances the system's overall resistance to noise.Results and Discussions We validate the proposed precoding scheme for multi-user MIMO-VLC systems using Monte Carlo simulations.The key parameters of the VLC system are summarized in Table 1.Two scenarios are considered:one with densely clustered users experiencing significant MUI,and another with dispersed users,where MUI effects are less pronounced.We first analyze the effect of the receiver's field of view(FOV)on BER performance in both scenarios(Figs.2 and 3).The objective is to identify the optimal FOV that ensures adequate communication coverage while maximizing system performance.These investigations provide reference values for the receiver's FOV and partially validate the efficacy of the proposed precoding scheme.Across various communication scenarios,the proposed precoding scheme consistently outperforms alternative methods,demonstrating significantly lower BER irrespective of FOV variations.With the optimal FOV determined,we further evaluate the BER performance of the three precoding schemes under different signal-to-noise ratios(SNR)and modulation schemes(Figs.4 and 5).Under moderate to high SNR conditions,the proposed scheme shows superior BER performance compared with baseline BD precoding.Furthermore,compared to recent nonlinear precoding methods based on geometric mean decomposition(GMD),our scheme delivers comparable BER performance,gradually surpassing GMD-based precoding as SNR increases.It is important to note that GMD-based precoding does not fully address MUI,requiring complex successive interference cancellation at the receiver,which can lead to error propagation.Thus,considering both system performance and receiver complexity,the proposed scheme proves to be a more practical option compared to GMD-based precoding.Conclusions In this paper,we propose a fairness-maximized precoding scheme for multi-user MIMO-VLC systems,considering the constraints of non-negative optical signals and total power.This scheme formulates an optimization problem aimed at maximizing the minimum subchannel gain and decomposes this challenging non-convex problem into two independent subproblems:intra-user channel equalization and inter-user power allocation.In the first subproblem,we parameterize the precoding matrix and derive its optimal structure.Using a branch-and-bound method to handle the non-convex constraints,we transform the subproblem into a mixed-integer constrained convex programming problem.This enables the effective determination of the global optimal solution,identifying the unknown parameters of the precoding matrix.The second subproblem derives the closed-form solution for optimal user power allocation,optimizing the system's overall BER performance.Experimental results demonstrate that the proposed scheme outperforms both baseline BD precoding and GMD-based precoding(from Reference[18])in terms of BER performance under medium to high SNR conditions.In addition,the complexity at the user receiver is reduced compared to the GMD precoding,making our proposed scheme more suitable for practical engineering applications.
visible light communicationmulti-userprecodingmixed-integer convex programmingsystem bit error rate
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