# Deep Learning-Based Spread-Spectrum FGSM for Underwater Communication
## 3 Proposed SS-FGSM Scheme
### SS-FGSM Scheme  
Despite the high data rate offered by MIMO communication technologies, MIMO systems suffer from ICI challenges and high receiver computational complexity. MIMO-CDMA has been proposed to overcome the ICI and increase the transmission data rate [11; 40]. However, MIMO-CDMA bandwidth is restricted by ICI interference. Unlike conventional MIMO, SMTs represents an alternative solution for data transmission. In SMTs, a part of data bits is encapsulated in the index of transmit antenna. In other words, one or more transmission antennas will be transmitting the same constellated symbol, and their index out of available transmit antennas will be carrying additional information bits avoiding the conventional MIMO ICI by reducing the MIMO order. This paper proposes a new SMTs, Figure 1 shows the proposed system model of the SS-FGSM with low-complexity deep learning receiver (DLSS-FGSM). In the proposed SS-FGSM, the upcoming bit blocks of transmitted data are split into three groups of bits, the first one is the data bits and embeds to \(log_{2}(M)\) bits, the second group is the code index bits and embeds to \(2 log_{2}(\mathcal{N})\) bits, and the third group of bits is the antenna index bits and embeds to \((N_{t}-1)\) bits. The first group is embedded by any digital modulation (e.g., quadrature amplitude modulation (QAM) is used in this paper). Hence, the resulted constellated bits include the real and imaginary parts, \(s)=a_{\gamma}+jb_{\gamma}\), where \(a_{\gamma}\) and \(b_{\gamma}\) represent the real and imaginary parts of the constellated symbols in data block \(\gamma\)-th, respectively. Then, \(a_{\gamma}\) and \(b_{\gamma}\) are spread using the same/different spreading codes according to the incoming bits in the second group of bits. The codes index chosen is used for spreading \(a_{\gamma}\) and \(b_{\gamma}\) embeds data bits of length \(2 log_{2}(\mathcal{N})\). At the end, the spreading signal is transmitted via one or more antennas whose indices carry data bits of length \((N_{t}-1)\) bits. Therefore, the available data rate in the proposed DLSS-FGSM can be represented as follows:  
\[R_{SS-FGSM}=\underbrace{log_{2}(M)}_{Data\ Bits}+\underbrace{2 log_{2}(\mathcal{N })}_{Code\ Bits}+\underbrace{(N_{t}-1)}_{Antenna\ Bits}. \tag{13}\]  
As shown in Figure 1, the \(M\)-ary modulated symbols and \(\mathcal{N}\) orthogonal Walsh codes, \(\mathcal{W}=\{\exists_{1},\ \cdots\cdots,\exists_{\mathcal{N}}\}\) are employed at the transmitter side. Each spreading orthogonal code consists of \(\mathcal{L}\) chips with the \(T_{c}\) chip period, where \(\backslash\)-th code can be represented in vector form as \(\exists_{\backslash}=\left[\exists_{\backslash,1},\cdots\cdots,\exists_{ \backslash,\mathcal{L}}\right]^{T}\). The transmitted \(\backslash\)-th block of bits in the proposed SS-FGSM can be presented in the vector form as:  
\[\mathbf{d}_{\backslash}=\Big{[}d_{1_{\backslash}},\cdots,d_{(2\log_{2}(\mathcal{N })+\log_{2}(M)+N_{t}-1),\rangle}\Big{]}^{T}=\ \Big{[}\mathbf{d}_{M-ary_{t}}^{T} \mathbf{d}_{I_{\backslash}}^{T}\ \mathbf{d}_{Q_{\backslash}}^{T}\ \mathbf{d}_{(N_{t}-1), \rangle}^{T}\ \Big{]}^{T}, \tag{14}\]  
where \(\mathbf{d}_{M-ary_{t}}^{T}\) is the modulated \(M\)-bits subblock. Vectors \(\mathbf{d}_{I_{\backslash}}^{T}\) and \(\mathbf{d}_{Q_{\backslash}}^{T}\) have \(log_{2}(\mathcal{N})\) bits and it represents the bits transmitted encapsulated in the index of spreading codes for real and imaginary constellation symbols. The signal transmitted of the SS-FGSM scheme can be expressed as:  
\[ \begin{array}{ll}x_{q}(t)=\sum\limits_{\backslash=1}^{B}\sum\limits_{k=1}^{ \mathcal{L}}&\Big{\{}a_{\backslash}\exists_{d_{I_{\backslash}}\backslash,k}p( t-(\mathcal{L}+k)T_{c})\ \cos(2\pi f_{o}t)\\ &+b_{\backslash}\exists_{d_{Q_{\backslash}}\backslash,k}p(t-(\mathcal{L}+k)T_ {c})\ \sin(2\pi f_{o}t)\Big{\}}\end{array}