# BigGRU-Based Adaptive Receiver for Indoor DCO-OFDM Visible Light Communication
## 2 VLC System  
The architecture of the VLC system based on DCO-OFDM is shown in Figure 1. Equalization in existing DL-based OFDM receivers mainly uses channel modeling methods, where the trained model replaces the CE and equalization parts.  
In contrast, the proposed BiGRU NN-based direct receiver in this study can directly process the oscilloscope-sampled signal to recover the outgoing OFDM-modulated signal. The sampling frequency is set to twice the transmitting signal frequency by adjusting the storage depth, and the channel features carried by the signals in the circular prefix and Hermitian symmetric parts are also fully utilized. To focus on the  
Figure 1: System model of OFDM-VLC system. (**a**) Transmitter side of the visible system (**b**) Conventional receiver side of the VLC. (**c**) Typical DL-based receiver DL-NN processing after _FFT_. (**d**) BiGRU-based direct receiver.  
correction coding techniques were not used. It is worth noting that the sampling rate of direct sampling of the oscilloscope is much greater than the data bit rate, so it needs to be sampled again before \(FFT\), that is, model 2 is directly trained from oversampled data.  
The non-negative signal \(x(n)\) with DC bias was added, transmitted in the optical path through the LED, captured directly by the PD at the receiver side, and received \(y(n)\) after the analog-to-digital conversion. The received \(y(n)\) was directly recovered by BiGRU processing to recover \(x(n)\) and get \(x(n)\), and the \(x(n)\) was taken for de-cp processing. Without considering cp, the discrete-time domain OFDM signal \(x(n)\) can be expressed as  
\[x(n)=\frac{1}{N}\sum_{k=0}^{N-1}X(k)e^{j2\pi kn/N}0\leq t\leq T, \tag{1}\]  
where \(X(k)\) represents the complex sign of the constellation diagram generated using the fast Fourier transform operation to achieve multiplexing; \(j=\sqrt{-1}\), \(N\) is the number of points in the \(FFT\); and \(k\) is the number of subcarriers. The received signal \(y(n)\) can be expressed as  
\[\begin{array}{l}Y(k)=X(k)H(k)+W(k),\\ y(n)=x(n)\otimes h(n)+\omega(n),\end{array} \tag{2}\]  
where \(\otimes\) denotes the circular convolution, \(h(n)\) represents the channel impulse response, and \(w(n)\) represents the additive Gaussian white noise (AWGN). The subcarrier division multiplexing achieved with \(FFT\) can be defined as  
\[Y(k)=FFT\{y(n)\}=X(k)H(k)+W(k), \tag{3}\]  
where \(H(k)\) represents the channel frequency response; \(W(k)\) represents the AWGN.  
The unified reception was obtained using a CE method, such as LS or MMSE, which correctly enables the channel equalization technique. The LS method is based on parameter estimation that minimizes the square of the difference between the observed data \(H_{\text{P}}(k)X_{\text{P}}(k)\) and the expected value \(Y_{\text{P}}(k)\) at the pilot position \(p\) and loss value \(J(\widehat{H})_{LS}\), which is expressed as  
\[J(\widehat{H})_{LS}=\left\|Y-X\hat{H}\right\|^{2}, \tag{4}\]  
where \(Y\) denotes the received signal vector, \(X\) is the transmit signal vector, and \(\hat{H}\) is the estimated value of the channel parameters. The final LS estimation is as follows:  
\[\hat{H}=X^{-1}Y, \tag{5}\]  
The MMSE estimation is based on the LS estimation with the addition of the weighting matrix \(W\):  
\[W=R_{H\hat{H}_{LS}}R_{\hat{H}_{LS}\hat{H}_{LS}}^{-1}, \tag{6}\]  
where \(R_{\hat{H}_{LS}\hat{H}_{LS}}\) is the autocorrelation matrix of the \(\hat{H}_{LS}\) matrix and is obtained from the LS estimation. The final MMSE estimation is  
\[\hat{H}=W\hat{H}_{LS}=R_{H\hat{H}_{LS}}(R_{HH}+\frac{\sigma_{Z}^{2}}{\sigma_{ X}^{2}}I)^{-1}\hat{H}_{LS}, \tag{7}\]  
where \(\sigma_{Z}^{2}\) is the noise variance, \(\sigma_{X}^{2}\) is the transmit signal vector variance, and \(I\) denotes the unit matrix.