# A Novel 4 \(\times\) 1 MISO-VLC System with FBMC-OQAM Downlink Signals
## 2 Material and Methods  
Figure 1 shows the block diagrams of OFDM and FBMC transceivers, respectively. In the OFDM system, the high-speed data stream is divided into multiple low-speed subcarriers, which are modulated using QAM modulation. The subcarriers are then converted into time-domain signals through inverse fast Fourier transform (IFFT). A CP is added to the time-domain signals to address the ISI issue in data transmission [17; 18; 19]. The time-domain signals are then converted back into frequency-domain signals through a fast Fourier transform (FFT) for demodulation and recovery of the original data. In the FBMC system, the transmitter modulates the signal through a synthesis filter that utilizes the polyphase network (PPN) for filtering after the IFFT stage, while the receiver processes the signal through an analysis filter (PPN+FFT) [20; 21]. The specific implementation steps are shown in Figure 1b. Figure 1: (**a**) OFDM transmitter and receiver and (**b**) FBMC-OQAM transmitter and receiver. Compared to OFDM modulation, the advantage of FBMC-OQAM is using prototype filters instead of conventional rectangular filters. The design of the prototype filter is based on the Nyquist sampling theorem [22]. With the increase in the overlap factor, the quality of signal transmission and reception can be improved, but the trade-off is that the complexity of digital signal processing (DSP) also increases. As \(K\) (overlap factor) is 2, 3, or 4, the frequency tap coefficients of the filter are shown in Table 1.  
The frequency-domain expression of the filter is as follows:  
\[H(f)=\sum_{k=-(K-1)}^{K-1}H_{k}\frac{\sin(\pi(f-\frac{k}{MK})MK)}{MK\sin(\pi(f- \frac{k}{MK}))} \tag{1}\]  
When different values of the overlap factor \(K\) are used, the filter exhibits varying performance characteristics. We compared the frequency-response performance of \(K=2,3\), and 4, as shown in Figure 2.  
We can observe that the sidelobe attenuation of the signal increases as the overlap factor \(K\) increases. This implies that the out-of-band leakage decreases. When \(K=4\), the sidelobe attenuation is approximately 40 dB, which meets the system requirements. Therefore, in our study, we choose \(K=4\). As illustrated in Figure 3, it is evident that the FBMC signal exhibits significantly less out-of-band leakage in comparison to the OFDM signal. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(K\) & \(H_{0}\) & \(H_{1}\) & \(H_{2}\) & \(H_{3}\) & \(\sigma^{2}\)**(dB)** \\ \hline
2 & 1 & \(\sqrt{2}/2\) & / & / & \(-35\) \\
3 & 1 & 0.911438 & 0.411438 & / & \(-44\) \\
4 & 1 & 0.971960 & \(\sqrt{2}/2\) & 0.235147 & \(-64\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The tap coefficient of filter with different overlap factor. Figure 3: Power spectral density plot of OFDM signal and FBMC signal. Figure 2: Frequency response of filters with different overlap factors. The interference between subcarriers undergoes an orderly transformation between the real and imaginary parts [23,24]. Therefore, we can transmit real part information when there is interference in the imaginary part and transmit imaginary part information when there is interference in the real part. This way, the interference between adjacent subcarriers can be effectively eliminated. Separating the real and imaginary parts can reduce interference but also cut the data transmission rate in half. The OQAM algorithm achieves an increase in symbol rate to twice the original rate by reducing the symbol period T to T/2, thus it does not decrease the bandwidth utilization [25,26]. The time-frequency characteristics of the QAM modulation signals and the OQAM modulation signals are shown in Figure 4.  
Algorithm complexity has always been a crucial factor in filter bank design. High computation complexity will result in the occupation of hardware resources and signal transmission time delay. The main problem faced by FBMC is its extensive computational workload. We analyze the implementation complexity below.