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This paper proposes a novel non-Hermitian symmetry <inline-formula><tex-math notation="LaTeX">${2 \times 2}$</tex-math></inline-formula> MIMO-OFDM (Multiple Input Multiple Output-Orthogonal Frequency Division Multiplexing) system based on fast Hartley transform (FHT) with unipolar encoding (referred to as HU-OFDM) for visible light communications. The new scheme uses FHT instead of FFT (fast Fourier transform) to process the complex-valued signals reducing the computational complexity and hardware cost and employs two LEDs (light-emitting diodes) to transmit the real and imaginary parts of a complex-valued OFDM signal respectively. Unipolar encoding is applied to the transmitted signal from each LED to ensure non-negative. The restrictions of Hermitian symmetry in traditional optical OFDM systems and real constellation mapping in FHT based optical OFDM systems can be removed simultaneously in the proposed system. Compared with MIMO-ACO/DCO-OFDM system, HU-OFDM has significant performance improvement along with a tremendous decrease in hardware cost and computational complexity. Compared with other non-Hermitian symmetry MIMO-OFDM systems, HU-OFDM has significant advantages in terms of power efficiency, system design flexibility, computational complexity, or hardware cost without losing reliability.

A Novel Non-Hermitian Symmetry Orthogonal Frequency Division Multiplexing System for Visible Light Communications