# Deep Learning-Based Spread-Spectrum FGSM for Underwater Communication
## 5 Simulation Results
### Achievable Data Rate  
The available data rate of the spatial modulation techniques (SMTs) can be dependent on one of two axes, the number of antenna transmitter \(N_{t}\) and spreading code length \(\mathcal{N}\). Based on these two axes, the SMTs can be classified into three categories; first, SMTs schemes which are dependent only on the number of antenna transmitter \(N_{t}\) and convey the transmitted index bits in the spatial domain of the transmitted active antenna as in case of the SM, GSM, QSM, FGSM, and EFGSM. Second, the SMTs dependent only on the spreading code length \(\mathcal{N}\) and convey the transmitted index bits in the code index as the GCIM which considered as a SISO system. Third, the SMTs dependent on two axes the number of antenna transmitter \(N_{t}\) and spreading code length \(\mathcal{N}\) as in the case of the proposed scheme, and according to our knowledge, it is the first work in this category. Under infinite SNR values, this paper compares the proposed SS-FGSM achievable data rate (13) with the maximum achievable data rate of SM, GSM, FGSM, EFGSM, QSM, and GCIM provided by (1)-(6), respectively. The achievable data rate comparison is considered in three cases. First, only the axis of the number of antenna transmitter \(N_{t}\) is varied and the axis of spreading code length \(\mathcal{N}\) is constant. Second, only the axis of the number of antenna transmitter \(N_{t}\) is constant, and the axis of spreading code length \(\mathcal{N}\) is varied. Third, the axis of the number of antenna transmitter \(N_{t}\) and the axis of spreading code length \(\mathcal{N}\) are varied simultaneously. All these cases have been addressed for the achievable data rate under the same modulation order, 4-QAM. Furthermore, only two activated antennas out of available transmit antennas used for transmitting the constellated data symbols \(N_{u}\) are chosen to avoid the possibility of having the same antenna index in the different antenna subset of GSM. For EFGSM, the primary signal constellation and secondary signal constellation are chosen to be QAM and BPSK, respectively. (1) Achievable Data Rate at Different Number of \(N_{t}\) and Fixed Spreading Codes \(\mathcal{N}\). The different number of transmitter antenna \(N_{t}\) and weighted against the SMTs which are only dependent on the value of \(N_{t}\). For the proposed SS-FGSM scheme, the length of the orthogonal code \(\mathcal{N}\) is fixed to be 16. The results of the comparison are depicted in Figure 2. The proposed SS-FGSM outperforms all conventional schemes in the achievable data rate in this case. For example, at \(N_{t}=8\), the achievable SE of SS-FGSM is 17 bpcu compared to 5 bpcu, 6 bpcu, 5 bpcu, 9 bpcu, and 11 bpcu of SM, GSM, FGSM, QSM, and EFGSM, respectively. (2) Achievable Data Rate at Different Number of \(\mathcal{N}\) and Fixed Number of Transmitted Antennas \(N_{t}\). As in Equation (5), the achievable data rate of the GCIM is independent on the number of the antenna transmitter \(N_{t}\) and it is a function only on the length of the spreading code \(\mathcal{N}\) to compare the proposed scheme with GCIM. In this case, we fixed the number of transmit antenna to be \(N_{t}=4\). The results of this comparison are shown in Figure 3. The proposed DLSS-FGSM outperforms the GCIM scheme in terms of the achievable data rate (\(N_{t}-1\)). For example, when \(\mathcal{N}=8\), the achievable SE of FGSM-SS is \(11\) bpcu compared to \(8\) bpcu for GCIM. (3) Achievable Data Rate at Different Number of Spreading Codes \(\mathcal{N}\) and Different Value of Transmitted Antennas \(N_{t}\). This case has a full utilization of the feature of our proposed scheme. Where the proposed scheme uses the two axes of index modulation code and transmitted antenna for simplicity. In this experiment,  
Figure 3: The maximum achievable data rates of GCIM and proposed DLSS-FGSM under different code length \(\mathcal{N}\). Figure 2: The maximum achievable data rates of different SMTs under different number of \(N_{t}\).