Objective The visible light communication (VLC) technology based on white light-emitting diode (LED) uses the modulation bandwidth of LED to transmit data. It has the advantages of high security, utmost privacy, and abundant spectrum. It can provide both lighting and communication and can achieve a high data rate. Orthogonal frequency division multiplexing (OFDM) is introduced into VLC systems to meet the requirement of high data rate, which can effectively resist the inter-symbol interference of optical wireless channels and distortion due to the nonlinear frequency response of LED. Using fast Hartley transform (FHT) instead of fast Fourier transform (FFT) to realize optical OFDM can reduce the computational complexity by almost half. However, the input symbols for FHT should be real to obtain real-time-domain signals for VLC. Some researchers have proposed adding complex-to-real transform (C2RT) before FHT to eliminate the limitation but still sacrifice some of the spectral or power efficiency. Meanwhile, some researchers have proposed using LEDs to distinguish the polarity of the time domain signals. This can improve the spectral and power efficiency but result in high computational complexity owing to using FFT. In this study, we propose a novel optical OFDM scheme based on FHT (NCH-OFDM) that combines the advantages of existing optical spatial modulation systems.

Methods In NCH-OFDM, input symbols can be complex constellation-mapping symbols. The system employs FHT instead of FFT to reduce the computational complexity, and the C2RT function is used to convert complex symbols to real ones in the frequency domain. The limitation of real constellation mapping is mitigated, and the system flexibility is significantly increased. For transmitting the bipolar real signals, the system uses two LEDs to distinguish the positive and negative polarity of time-domain signals and transmits them separately to improve spectral and power efficiency. As for the receiver, the traditional detection method is zero-forcing (ZF). Despite its simplicity, ZF can enhance noise power during demodulation, thus causing the bit error rate (BER) performance loss. Therefore, this paper proposes two detection methods: a method based on the received power (RP) of each LED to distinguish signal polarity and a general polarity (GP) discrimination method for asymmetric placement of LEDs and photodiodes (PDs). Both detection methods can effectively improve BER performance compared with ZF detection.

Results and Discussions In this study, the structure and principle of the NCH-OFDM system are illustrated (Fig.1). At the receiver, ZF detection is employed for LED index demodulation as the benchmark. The BER varies with the distance between LEDs or PDs, and the larger the distance, the weaker the channel correlation, and hence, the better BER performance (Fig.2). The proposed RP detection can improve the performance of the system, especially when PDs’ distance is small. At this point, the channel correlation is high, and the advantage of the RP detection method is more obvious (Fig.3). The GP detection can be applied to general situations where LEDs and PDs are placed randomly, without symmetrical placement requirement. The GP detection method can also effectively improve the system’s performance (Fig.4). For 64-bit quadrature amplitude modulation (64QAM) modulation with BER of 10 ^-4, the system performance improves by about 2.9 dB with each detection method. Compared with asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) or direct current optical orthogonal frequency division multiplexing (DCO-OFDM), NCH-OFDM can improve power and spectral efficiency (Fig.5). In addition, this paper compares the properties of the NCH-OFDM system with existing LED-based optical spatial modulation systems (Table 1) and simulates BER performance comparisons (Figs.6 and 7). The results show that NCH-OFDM can increase design flexibility and reduce the computational complexity without sacrificing reliability.

Conclusions This paper proposes a new optical spatial modulation OFDM system (NCH-OFDM) for the high data rate requirement of VLC. The new scheme employs FHT to replace FFT, which drastically reduces the computational complexity, simplifies the hardware design, and saves the system cost. NCH-OFDM uses C2RT to convert complex constellation-mapping symbols into real ones to mitigate the limitation of real constellation mapping in FHT. Synchronously, two LEDs are used to transmit the positive part and the absolute value of the negative part, respectively, to meet the requirements of real and positive polarity for optical communication. The receiver takes advantage of LEDs’ spatial resources to distinguish the positive and negative polarity of signals. Compared with the traditional optical OFDM modulation scheme, NCH-OFDM can improve power and spectral efficiency. Compared with previous LED-based optical spatial modulation OFDM schemes, computational complexity can be significantly reduced, and system design can be more flexible without BER performance loss. In addition, a new detection method based on the received power to distinguish signal polarity and a general polarity discrimination method for the circumstance of asymmetric placement of LEDs and PDs, both of which can effectively improve the BER performance compared with traditional zero-forcing detection, are proposed.