# Optimization of Acoustic Communication Links for a Swarm of AUVs: The COMET and NEMOSENS Examples
## 5 Physical Layer
### Modem: Transmitter Side  
A block diagram of the transmitter is shown in Figure 8. The first procedure is the channel encoder. The information bits \(\mathbf{b}_{i}\in\{0,1\}^{N}\) belonging to the each data block \(i\in\mathbb{N}\) are coded:  
\[\mathbf{\bar{b}}_{i}=\mathcal{C}(\mathbf{b}_{i},\rho), \tag{4}\]  
where \(\mathcal{C}(\mathbf{b}_{i},\rho)\) denotes the coding operation performed on \(\mathbf{b}_{i}\), with code rate \(\rho\). The result, \(\mathbf{\bar{b}}_{i}\), is a vector containing \(N/\rho\) coded bits (we consider that \(N\) is an integer multiply of \(\rho\)). The benefit of utilizing a channel encoder is that this mechanism enables the receiver to detect and correct errors that might occur during the transmission. There are two distinct types of encoding available in the modem: the convolutional code, that is followed by an interleaver, and the Low-Density Parity-Check (LDPC) code.  
In the next stage, the coded bits \(\mathbf{\bar{b}}_{i}\) are mapped into symbols \(\mathbf{s}_{i}\) from a differential digital modulation:  
\[\mathbf{s}_{i}=\mathcal{M}(\mathbf{\bar{b}}_{i},\mu), \tag{5}\]  
where \(\mathcal{M}\) represents the differential digital modulation procedure, that maps \(\mu\) bits into one complex modulated symbol. In this case, we employ either D-BPSK or D-QPSK modulation. The employment of differential modulation schemes enables the usage of a receiver with a lower complexity. For this modulation type, no channel equalization is required [21]. As a consequence, no pilot symbols are needed for channel equalization, reducing the overall system overhead [24].  
These modulated symbols are mapped into the subcarriers through the multiplication by an IDFT matrix.  
\[\mathbf{\bar{s}}_{i}=\mathbf{F}^{-1}\mathbf{s}_{i}, \tag{6}\]  
where \(\mathbf{F}^{-1}\in\mathbb{C}^{N_{\text{sub}}\times N_{\text{sub}}}\) is the IDFT matrix with \([\mathbf{F}]_{k,l}=\frac{1}{\sqrt{N_{\text{sub}}}}\mathrm{e}^{-\mathrm{i}\frac{2 \pi}{N_{\text{sub}}}kl}\). We call \(\mathbf{\bar{s}}_{i}\) as the \(i\)-th OFDM symbol.  
Subsequently, a cyclic prefix (CP) with size \(K\) is added to this signal, i.e., the last \(K\) symbols are copied and added at the beginning of the OFDM symbol. The usage of a CP length higher or equal than the channel delay spread warrants that the receiver is able to remove the interblock interference (IBI), that the signal suffers while passing through the channel.  
Following the proposal of [22; 25], each OFDM block (that is the OFDM symbol along with its CP), is multiplied by a squared root raised cosine (SRRC) pulse. In this windowing operation, which is performed over the whole OFDM block, the roll-off period is the same as the CP duration. As a consequence, some energy is saved [25]. In this pulse shaping design, the SRRC pulse is utilized both at transmitter and receiver side.  
Figure 8: OFDM transmitter.  
This signal is modulated by the carrier generating the passband signal. Here, we denote as \(f_{\rm c}\) the carrier frequency. For coping with peak-to-average power ratio (PAPR) issues, this signal is clipped. The real part of it is taken, and the signal is normalized before being transmitted.