# Performance Improvement by FRFT-OFDM for Visible Light Communication and Positioning Systems
###### Abstract  
In indoor visible light communication (VLC) and visible light positioning (VLP) systems, the performance of conventional orthogonal frequency-division multiplexing (OFDM) schemes is often compromised due to the nonlinear characteristics and limited modulation bandwidth of light-emitting diodes, the multipath effect in enclosed indoor environments, and the relative positions of transmitters and receivers. This paper proposes an OFDM scheme based on the fractional Fourier transform (FRFT) to address these issues, demonstrating promising results when applied to indoor VLC and VLP systems. The FRFT, a generalization of the conventional Fourier transform (FT) in the fractional domain, captures information in both the time and frequency domains, offering greater flexibility than the FT. In this paper, we first introduce the computation method of the reality-preserving FRFT for an intensity modulation/direct detection VLC system and integrate it with OFDM to optimize system performance. By adopting FRFT-OFDM under the optimal fractional order, we enhance both the bit error ratio (BER) performance and positioning accuracy. Simulation results reveal that the FRFT-OFDM scheme with an optimized fractional order significantly improves the BER and positioning accuracy compared to the FT-OFDM scheme across most receiver positions within the indoor observation plane. For communication, the FRFT-OFDM scheme achieves over 6 dB \(E_{\text{b}}/N_{0}\) gain compared to the FT-OFDM scheme at a BER of \(3\times 10^{-4}\) when the receiver is positioned at most locations in the room. For positioning, the FRFT-OFDM scheme enhances positioning accuracy by more than 1 cm relative to the FT-OFDM scheme at most locations in the room. Notably, both systems maintain the same computational complexity and spectral efficiency. f [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33  
Providing high-speed wireless communication indoors is a primary focus of VLC applications, primarily leveraging indoor light-emitting diode (LED) lighting systems to simultaneously deliver lighting and communication services. Thanks to the high response rate of LED semiconductor materials, intensity modulation/direct detection (IM/DD) of white light signals can be employed to enable wireless communication. Currently, the modulation bandwidth of most commercial LEDs is limited to around 5 MHz [4]. However, with the increasing transmission rate requirements in the era of big data, researchers are exploring ways to enhance this limited bandwidth. Techniques such as pre- and post-equalization [5; 6], higher-order quadrature amplitude modulation (QAM) [7], discrete multitone (DMT) modulation [8], wavelength-division multiplexing (WDM) [9], and efficient multiple-input multiple-output (MIMO) [10] have all been investigated to extend the modulation bandwidth and increase transmission rates. Among these methods, orthogonal frequency-division multiplexing (OFDM)-based schemes have gained significant attention [11]. Due to the constraints of IM/DD in optical communication, improved OFDM schemes have been introduced into VLC, including widely used variants such as direct-current-biased optical OFDM (DCO-OFDM), asymmetrically clipped optical OFDM (ACO-OFDM), pulse-amplitude-modulated discrete multitone modulation (PAM-DMT), and unipolar OFDM (U-OFDM) [11; 12]. In [13], the authors propose a novel direct time-domain waveform equalization method for indoor VLC using a bidirectional gated recurrent unit (BiGRU) neural network within a DCO-OFDM framework. Experimental results show that the BiGRU-based method offers low complexity and strong nonlinear channel learning capabilities. In [14], a carrierless amplitude-phase (CAP) modulation method is introduced for VLC systems to enhance the performance of MIMO structures, effectively reducing the peak-to-average power ratio (PAPR) of the system.