## 2 GLIM System Model  
This section presents the GLIM system model in Figure 1, which focuses on the MIMO transmission of \(n_{\rm T}\times n_{\rm R};n_{\rm T}\) are \(n_{\rm R}\) are the numbers of LEDs and PDs, respectively. Without loss of generality, it can be assumed that \(n_{\rm T}=n_{\rm R}=n\), where \(n\) is an even number. In the GLIM, the OFDM modulator directly processes the complex frequency-domain OFDM frame through inverse fast Fourier transform (IFFT) operation. After the parallel-to-serial (P/S) operation, the time-domain OFDM signals \(x_{l}\) (\(l=1,\cdots,N\)) are separated into their real and imaginary parts (\(x_{l}=x_{l,R}+jx_{l,l}\)) and converted into the time-domain signal vector \(\mathbf{t}=[x_{1,R},x_{1,l},x_{2,R},x_{2,l},\ldots,x_{N,R},x_{N,l}]\) of length \(2N\). Therefore, the GLIM technique transmission can help to convey complex and bipolar signal to the real and unipolar signal to be transmitted through the VLC channel. Consequently, the vector \(\mathbf{z}=[z_{1}\cdots z_{n}]^{T}\) is the signal transmitted by the LEDs. In the receiver side, after estimating the active LEDs and recovering the transmitted signal, the serial-to-parallel (S/P) and fast Fourier transform (FFT) operations convert the received signal to the estimated symbol. More specifically, \(N\) is the number of subcarriers and \(4N\) is divisible by \(n\); consequently, the vector \(\mathbf{t}\) is transformed into a matrix \(\mathbf{T}\) of size \(4N/n\times n/2\). At each time instant \(i\), each column of \(\mathbf{T}\) (a signal vector of length \(n/2\))) is transmitted by all \(n\) LEDs as \(\mathbf{z}_{i}\). More specifically, let  
\[sgn(\mathrm{a})=\left\{\begin{aligned} & 1,\quad\text{if}\quad a\geq 0\\ &-1,\quad\text{if}\quad a<0\end{aligned}\right. \tag{1}\]  
the \(j\)-th signal of the \(i\)-th column of \(\mathbf{T}\) can be transmitted with all \(n\) LEDs as  
\[\begin{split} z_{i}(2(j-1)+1)&=\frac{sgn(\mathbf{T }(i,j))+1}{2}\mathbf{T}(i,j),\\ z_{i}(2j)&=\frac{sgn(\mathbf{T}(i,j))-1}{2}\mathbf{ T}(i,j).\end{split} \tag{2}\]  
Consequently, by activating a half number of LEDs while the other half are inactive, the signal \(\mathbf{z}_{i}\) is transmitted over the \(n\times n\) optical MIMO channel as  
\[\mathbf{y}_{i}=\mathbf{H}\mathbf{z}_{i}+\mathbf{n}_{i}, \tag{3}\]  
where \(\mathbf{y}_{i}=[y_{i}(1),\cdots,y_{i}(n)]\) is the received signal, \(\mathbf{H}\in\mathbb{R}^{n\times n}\) is the optical communication channel matrix, and \(\mathbf{n}_{i}\) is real-valued additive white Gaussian noise with elements distributed as \(\mathcal{N}(0,\sigma_{w}^{2})\). In addition, a flat fading channel is considered in this letter [18].  
Among the three detection techniques, e.g., ZF, MMSE, and MAP, MAP is regarded as the preferred receiver as it can achieve the best BER performance [18]. Moreover, the number of transmitted signals (\(4N\)) is generally high owing to a large number of subcarriers (\(N\)) used for transmission. For example, in the OFDM modulation of eight subcarriers, the transmitted signal vector at the LEDs has a size of 32 and this number is 128 with 32 subcarriers. Meanwhile, a small number of LEDs in MIMO-VLC systems, usually four LEDs [18], or eight LEDs [19], are used in transmission, leads to only four or eight signals that are simultaneously transmitted by LEDs and detected by the MAP detectors at the same time. To improve the demodulation performance, all the received signals (e.g., the vector \(\mathbf{y}=[\mathbf{y}_{1}\ldots,\mathbf{y}_{i}\ldots\mathbf{y}_{4N/n}]\)) instead of only the \(n\)-length received signals \(\mathbf{y}_{i}\) should be simultaneously considered in the demodulation process. In the next section, three model-driven DNN architectures as alternatives to conventional receivers (e.g., ZF, MMSE,  
Figure 1: System model with proposed estimator.  
and MAP detectors) are proposed; the methods combine DNN with expert knowledge for wireless communication.