Optimal Power Allocation for Non-Orthogonal Multiple Access Visible Light Communications with Short Packet and Imperfect Channel Information

In this paper, we investigate the short packet communication (SPC) in non-orthogonal multiple access (NOMA) for a downlink visible light communication (VLC) system with the imperfect channel state information (CSI). Furthermore, transmission rates and power allocation coefficients are optimized to obtain the maximum system throughput while the far user can get a specific effective throughput. To this end, the block error rate (BLER) in SPC-NOMA VLC systems with imperfect CSI is derived in closed-form by utilizing Gaussian Chebyshev quadrature method. Then, the effective throughput expression is deduced. We further compare the SPC-NOMA VLC system versus the SPC-orthogonal multiple access (OMA) VLC system in terms of BLER and effective throughput. The analytical and simulation results demonstrate the superiority of the SPC-NOMA VLC system to the SPC-OMA VLC system. To address the optimal system throughput design, the iterative-method-based one-dimensional search method is proposed to derive the optimal transmission rates and optimal power allocation coefficients.