# Deep Learning-Based Spread-Spectrum FGSM for Underwater Communication
## 2 Related Work
The EFGSM is capable of achieving data rate as fellows [3]:  
\[R_{EFGSM}=\ log_{2}(M)+\ \left\lfloor log_{2}\sum_{k=2}^{N_{t}}\left( \begin{array}{ c}N_{t}\\ N_{u}\end{array} \right)\right\rfloor+\ log_{2}\left(\frac{M}{2}\right). \tag{4}\]  
Based on expanding the constellated data into two orthogonal dimensions; real and imaginary, QSM has been proposed in [18; 32; 33]. Unlike the SM, GSM, and FGSM, the QSM does not transmit the constellated data including real and imaginary parts via the same transmit antennas, but they are transmitted independently according to the incoming data bits. This way, the achievable data rate increases without increasing the system complexity. The expression of QSM \(R_{\text{QSM}}\) data rate can be written as [15]:  
\[R_{QSM}=\ log_{2}(M)+\ log_{2}(N_{t})^{2}. \tag{5}\]  
All the above addressing schemes, and others, have been tried to increase the number of combinations between the transmitting antennas and modulations to increase the data sent via the antenna index. Other schemes try to improve the achievable data rate by adding other indices such as signal constellations indices [12; 21]. The signal constellation combination with the transmit antennas indices is used to carry additional information by increasing the number of modulations and transmit antenna combinations using primary and secondary constellations. Despite the advantage of improving the SE using SMTs, competitive studies were presented in [27; 28] in order to avoid the requirement of MIMO hardware. In CIM and GCIM [24; 25], a predefined spreading code is used to spread the constellated data symbol before transmission, and then use the code index as an information-bearing unit instead of transmitting antenna index in SMTs. In GCIM [28], the real and also imaginary parts of the signal are spread using a predefined code based on the Hadamard-Walsh matrix. Then, at the receiving side, the received signal is multiplied with all possible codes to choose the index of that code whose result is the maximum. Additional data bits are carried by the spreading code index. The achievable data rate by using GCIM \(R_{GCIM}\) can be expressed as:  
\[R_{GCIM}=\ log_{2}(M)+\ 2\cdot log_{2}(\mathcal{N}), \tag{6}\]  
where \((\mathcal{N})\) is the number of available spreading orthogonal Walsh codes. To improve the performance of SM, spreading codes are used as an additional index into SM with binary phase-shift keying (BPSK) modulation in SM-CIM. In the transmission side, the modulated data was spread using a predefined spread code among the available codes of Hadamard-Walsh matrix and then transmitted through one single antenna out of transmitting antennas. The indices of the spread code and the active antennas are used to carry additional information bits. Consequently, the data rate achieved in spatial modulation coded index modulation (SM-CIM) \(R_{SM-CIM}\) is expressed as follows [34]:  
\[R_{SM-CIM}=\ 2\cdot(log_{2}(M)+\ log_{2}(\mathcal{N})). \tag{7}\]  
The achievable data rate in (7) is applicable when only binary digital modulation is used, but for higher modulation orders, it becomes impractical. Generally, the higher transmission data rate in SMTs can be achieved by increasing the bits transmitted via the antenna index to reduce the physical transmitted bits and avoid the ICI with low receiver complexity compared with the conventional MIMO schemes. However, in current SMTs, increasing the transmitted bits requires a high receiver complexity because the ML decoder complexity is increasing exponentially with the transmitted data rate. Therefore, various schemes are aimed to reduce the complexity of the ML decoder [35; 36]. Unfortunately, complexity reduction decreases SMTs performance. Based on those studies mentioned above, a new SS-FGSM scheme is presented to address the significant drawback in the UWA channel bandwidth limitation and the restriction of availability for a sustainable energy sources to feed the battery of the underwater nodes and overcome ICI restriction existed in the conventional MIMO systems.