# Visible Light Communication: An Investigation of LED Non-Linearity Effects on VLC Utilising C-OFDM
###### Abstract  
The electro-optic output of light-emitting diodes commonly used in visible light communication systems is generally nonlinear in nature. It is particularly problematic when using advanced modulation formats, such as orthogonal frequency-division multiplexing (OFDM), which have a high peak-to-average power ratio due to clipping and distortion. In this work, we introduce the so-called C-transform to the system architecture, which utilises a Walsh-Hadamard matrix in conjunction with a discrete cosine transform to deterministically spread the information and reduce the peak-to-average power ratio (PAPR). Several bias points along the electro-optic transfer function were selected for comparison purposes, and the new transform was compared with more traditional formulations of OFDM. This paper determines that the C-transform-based OFDM demonstrated the highest degree of independence from the non-linearity and yielded superior bit-error rate (BER) results. We note an improvement of \(\sim\)2.5 dB in the power penalty at a BER of \(10^{-4}\) in comparison to OFDM. bias point; non-linearity; orthogonal frequency division multiplexing (OFDM); peak-to-average power ratio (PAPR); visible light communication (VLC) +
Footnote †: _Photonics_  
Footnote †: _Photonics_In general, two methods can be employed to compensate for LED non-linearities. The first choice is to use a PAPR reduction process as proposed in [12], which operates by applying a semidefinite relaxation approach to tone injection. The second approach is to linearise the LED nonlinear transfer characteristics [13]. Clipping, coding, selected mapping (SLM), partial transmit sequences (PTS), tone reservation (TR), tone injection (TI), as well as other techniques are applied to solve the PAPR issue in conventional radio frequency (RF) communication systems, as summarised in [14; 15]. In the RF domain, power amplifiers introduce a nonlinear distortion. Furthermore, DC-biased OFDM requires a high bias to avoid low-end clipping, which significantly degrades the system's power efficiency. Consequently, reducing the PAPR in the VLC OFDM technique is even more important. In asymmetrically clipped OFDM, subcarrier mapping is utilised to guarantee positive OFDM signals. Therefore, traditional PAPR reduction approaches may not be suitable [12]. A pilot-assisted PAPR reduction technique has been proposed in [16], which can achieve a better PAPR efficiency compared to SLM. However, depending on the density of pilot symbols, the pilot-assisted approach causes some data rate loss. A significant PAPR reduction achieved via an exponential nonlinear commanding algorithm was proposed in [17]. This method achieved a good PAPR reduction, but led to a poor bit-error rate (BER). There are other OFDM architectures that have become the focus of attention recently, and the most important of these is fast OFDM. The time-domain signal of fast OFDM is generated utilising an inverse discrete cosine transform (IDCT), rather than the inverse fast Fourier transform (IFFT) that is used in OFDM. It has significant benefits for VLC, in particular due to forsaking complex modulation formats in favour of actual ones such as pulse-amplitude modulation (PAM), allowing subcarrier spacing to be reduced [18; 19]. In this paper, we propose C-transform-based OFDM. This architecture includes combining two transforms. The time-domain signal stream is obtained as an IDCT preceded by the Walsh-Hadamard transform [20]. In this paper, a comparative study is conducted to examine the effect of LED non-linearities. Furthermore, LEDs have a minimum threshold voltage, referred to as the turn-on voltage (TOV), above which current flow and light emission begin. As a result, the LED is in a cut-off area below the TOV and does not conduct a current. Above the TOV, however, current flow and light output rapidly increase with voltage. The LED produces light linearly with the  
Figure 1: Nonlinear LED transfer function. driving current (see Figure 2, the measured L-I-V curves of the LED).