# Deep Learning-Based Spread-Spectrum FGSM for Underwater Communication
## 2 Related Work  
In recent years, many SMTs have been proposed to improve the SE. On one hand, the SMTs can be classified in terms of information carried over the spatial antenna domain to four categories. First, SMTs which activate a few numbers of transmit antennas without transmitting any information bits over these active antennas as in space shift keying modulation (SSK) [26; 27; 28], generalized space shift keying (GSSK) [29; 30] and quadrature space shift keying (QSSK) [18]. Second, transmitting additional information bits over the index of the active antenna in addition to the constellated data symbol over active antennas, such as SM and GSM [13; 14], increasing the combination between and FGSM [15; 16]. Third, constellated symbols have been split into real and imaginary parts; those real and imaginary parts of constellated symbols are used to increase the combination between transmitting antennas and modulation by mapping them into same/different antennas independently, such as QSM, differential quadrature spatial modulation (DQSM), and generalized quadrature spatial modulation (GQSM) [18; 19; 20; 31; 32; 33]. Finally, adding a new index into the transmit antennas, such as another constellation signal or predefined spreading codes [12; 24; 25; 34]. On the other hand, the CIM and GCIM have been introduced as a competitive scheme for SMTs to avoid the hardware complexity of the MIMO system using a predefined spreading code index combined with the SISO system. The SM has been proposed based on the constellation habitual data symbols to be sent through the active antennas out of all transmitting antennas [13; 14]. The index of the activated transmit antennas is utilized to carry additional information bits. The achievable data rate of the SM \(R_{SM}\) can be expressed as [13; 14]:  
\[R_{SM}=\ log_{2}(M)+\ log_{2}(N_{t}), \tag{1}\]  
where \(M\) and \(N_{t}\) represent the modulation order and the number of transmit antennas, respectively. To improve the SM data rate, the researchers have proposed the GSM [15; 16], where the same constellation data is transmitted through more than one transmits antennas to increase the number combination between the active antennas and modulations. Hence, the achieved data rate is improved while the receiver's complexity is increased compared to SM. The expression of the achievable data rate of GSM \(R_{GSM}\) can be represented as [15; 16]:  
\[R_{GSM}=\ log_{2}(M)+\ \left\lfloor log_{2}\left( \begin{array}{c}N_{t}\\ N_{u}\end{array} \right)\right\rfloor, \tag{2}\]  
where \(N_{u}\), \(\left\lfloor.\right\rfloor\), and, \(\left( \begin{array}{c}\cdot\\ \cdot\end{array} \right)\), represent the number of active antennas out of the transmitting antennas, the floor operator, and the binomial coefficient, respectively. Recently, FGSM [20] has been proposed as a combination of SM and GSM; such combination increases the achievable data rate with different numbers of active antennas during time instant to transmit data constellated symbol. In other words, either one transmits antennas is activated as SM scheme, or multiple transmit antennas are activated as GSM during time instant to transmit the constellated data symbols while the transmit antennas indices are also used as an information-bearing unit. The achievable data rate in FGSM \(R_{FGSM}\) can be expressed as follows [14; 17]:  
\[R_{FGSM}=\ log_{2}(M)+\ \left\lfloor log_{2}\sum_{k=1}^{N_{t}}\left( \begin{array} []{c}N_{t}\\ N_{u}\end{array} \right)\right\rfloor=\ log_{2}(M)+\ N_{t}-1, \tag{3}\]  
where \(k\) is an indicator for the number of the active antennas at each time slot out of the transmit available antennas. The EFGSM has been proposed as a combination of enhanced SM (ESM) and FGSM. Conveying data bits in the type of signal constellation increase the data bit transmitted over the limited underwater acoustic channel and saves the power consumed in underwater wireless sensornodes of the internet of underwater things (IoUTs).