# Performance Improvement by FRFT-OFDM for Visible Light Communication and Positioning Systems
###### Abstract
The authors of [15] present an adaptive least squares (LS) channel estimation algorithm for VLC systems using a DCO-OFDM scheme, achieving improved performance in terms of the received constellation diagram, mean square error (MSE), and bit error ratio (BER). In parallel, traditional Global Positioning System (GPS) technologies suffer from low positioning accuracy in complex indoor environments due to multipath effects. This has spurred interest in LED-based indoor visible light positioning (VLP) systems, especially in spaces equipped with numerous LED lighting devices [16; 17]. In [18], the authors introduce a machine learning approach for accurately predicting the two-dimensional indoor position of a mobile receiver using measured received signal strength (RSS) values from four photodiodes (PDs) arranged in a star architecture. In [19], the authors propose a lightweight artificial neural network architecture designed to predict human blockages in hybrid indoor visible light/radio frequency (RF) communication systems. This approach optimizes beamforming matrices and time allocation parameters, achieving a near-optimal uplink sum rate. Consequently, VLP will play a significant role in future wireless networks [20]. And, the integration of OFDM-based schemes into LEDs enables them to provide illumination while supporting both wireless communication and indoor positioning, further demonstrating the potential and importance of VLC and VLP technology. However, OFDM has several significant drawbacks, such as its sensitivity to the carrier frequency offset (CFO), Doppler shift, phase noise, nonlinear effects, and chromatic dispersion (CD). These factors can introduce inter-carrier interference (ICI), reducing the reliability of system transmission. This leads to an error floor, where increasing the transmitter's power fails to significantly reduce the BER at the receiver, ultimately degrading system performance. To enhance the interference immunity of OFDM schemes, researchers have extended the concept of the Fourier transform (FT) and proposed the FRFT-OFDM scheme, which combines the fractional Fourier transform (FRFT) with OFDM. Unlike exponential signals, chirp signals offer more flexible and variable modulation frequencies. As a result, the FRFT-OFDM scheme can adapt to different channel conditions by adjusting the tuning frequency specifically by changing the order \(p\) of the FRFT. This adaptability enables improved BER performance and positioning accuracy compared to FT-OFDM schemes. It is worth noting that the computational complexity of the FRFT is comparable to that of the conventional fast Fourier transform (FFT) [21]. As a result, FRFT-OFDM has seen rapid development since FRFT was first introduced into OFDM schemes [22]. In [23], the author analyzed the ICI issue in MIMO-OFDM systems in high-mobility, fast-fading, double-dispersion, and non-stationary environments. By replacing the FFT with the FRFT, the correlation coefficient was increased, the effects of ICI were mitigated, and BER performance was improved. In [24], a novel orthogonal time-frequency space (OTFS) modulation technique based on FRFT-OFDM was proposed, demonstrating superior resilience to the severe Doppler effect in double-dispersion channels compared to conventional OTFS systems. Furthermore, a multi-block sparse Bayesian learning channel estimation method for hydroacoustic communication based on FRFT-OFDM was introduced in [25]. In this case, the FRFT effectively compensated for the Doppler shift, resulting in enhanced channel estimation performance and an improved signal-to-noise ratio (SNR). In conclusion, FRFT-OFDM schemes have been widely applied in various fields, including RF communication [26], fiber optics [21; 27], and hydroacoustic communication systems [5].