# Optical OFDM for SiPM-Based Underwater Optical Wireless Communication Links
## 5 Description of the Considered Signaling Schemes
### Laco-Ofdm  
The general block diagram of LACO-OFDM is shown in Figure 2. The transmitted signal is obtained as the superposition of \(L\) frames of symbols, each one corresponding to a \"layer.\" Within each layer, the signaling principle is similar to ACO-OFDM, as explained in the following [25; 41]. * For the first layer, ACO-OFDM signaling is used where \(N/4\) symbols and their complex conjugates (according to the Hermitian symmetry requirement) are sent on the odd sub-carriers \(2q+1\) with \(q=0,1,..,N/2-1\). These are then transformed into time domain after \(N\) point IFFT. * For the subsequent layers, the corresponding frames are mapped onto the remaining even sub-carriers. * For the second layer, \(N/8\) symbols and their complex conjugates are sent on sub-carriers \(2(2q+1)\) with \(q=0,1,...,N/4-1\); they are transformed into time domain after \(N\)-point IFFT, while the amplitudes of the remaining sub-carriers are set to zero. * In general, for the \(\ell^{\text{th}}\) layer, \(\ell>1\), \((N/2^{\ell+1})\) symbols and their complex conjugates are sent on sub-carriers \(2^{\ell-1}(2q+1)\) with \(q=0,1,...,N/2^{\ell+1}-1\). Then, setting the amplitudes of the remaining sub-carriers to zero, they are transformed into time domain after \(N\)-point IFFT. Note that the constellation size in each layer can be adjusted to result in a desired overall data-rate \(R_{b}\) (in bps). Afterwards, the time-domain signals of the \(L\) layers are superimposed before adding the CP, applying scaling, adding a bias, and clipping, as shown in Figure 2. Here, lower clipping of the time-domain signal will generate distortion in the frequency domain, which concerns those sub-carriers unused for a given layer [41]. Nevertheless, since this affects the even sub-carriers, only signals of the layers \(\ell\geq 2\) are distorted. For a given sub-carrier used in the \(\ell^{\text{th}}\) layer, the resulting distortion from all lower layers will be added to the transmitted signal in the frequency domain. For example, the third layer uses sub-carriers \(4,12,...,(N/16)\), which will be affected by distortion from layers \(1\) and \(2\). Figure 2: Block diagram of LACO-OFDM signaling with \(L\) layers. To recover the transmitted data, successive detection is done at the Rx, as proposed in [25], where symbols are recovered layer by layer from \(r_{n}\), as shown in Figure 3. Note that the first layer is not affected by distortion; hence, the corresponding symbols, \(\hat{X}_{k}^{(1)}\), can be detected directly, as in ACO-OFDM, see Section 5.2. These symbols are then used in the second layer to remove the corresponding distortion prior to signal detection. For signal detection in the \(\ell^{\text{th}}\) layer, we proceed as follows (see Figure 3):  
* Use detected symbols in the previous layers to obtain the corresponding time-domain signals \(\hat{x}_{d,n^{\prime}}^{(1)},\cdots,\hat{x}_{d,n}^{(\ell-1)}\), as it is done at the Tx,
* Calculate their contribution \(\hat{r}_{n}^{(1)},\cdots,\hat{r}_{n}^{(\ell-1)}\) in the received signal;
* Subtract the resulting signals from \(r_{n}\);
* Use the same steps as for the first layer on the (partially) distortion-removed signal to obtain \(\hat{X}_{k}^{(\ell)}\). The obtained \(\hat{X}_{k}^{(1)},\cdots,\hat{X}_{k}^{(L)}\) are then passed to a QAM demapper to retrieve the transmitted bits. As explained, compared to ACO, LACO transmits \(L\) frames in parallel, which for a given rate allows for using lower-order signal constellations within layers. Hence, it potentially needs a lower signal-to-noise ratio (SNR) for signal detection to achieve a target BER. In other words, LACO would have a better power efficiency, in addition to the advantage of having a lower PAPR [25; 42].