# Deep Learning-Based Spread-Spectrum FGSM for Underwater Communication
## 1 Introduction
Coded-index modulation (CIM) and generalized coded-index modulation techniques (GCIM) [24, 25] has been introduced as a competitive scheme for SMTs. In CIM and GCIM, a predefined spreading codes index has been used to convey additional information instead of transmitting antennas index which used in conventional SMTs. The main advantage of the CIM and GCIM is avoiding the hardware complexity by using single input single output system (SISO) in state of the MIMO system. Recently, generalized spatial modulation (GSM) and fully generalized spatial modulation (FGSM) [15, 16, 17] have been proposed to increase the SM achievable data rate. In GSM, to increase the combined number of transmitter antennas and modulation, the constellated information bits are transmitted through more than one antenna to increase the achievable data rate. FGSM combines the ideas of SM and GSM for a high data rate, where one or more antennas are activated to transmit the information bits. In other words, FGSM uses a variable number of transmit antennas as an additional index to achieve a high data rate. FGSM has the advantage of activating fewer transmit antennas compared to GSM to achieve the same data rate and save the consumed power. Quadrature spatial modulation (QSM) [18] and fully quadrature spatial modulation (FQSM) [20] have been presented to transmit the real and imaginary part of the constellated signal through the same/different transmit antennas to achieve high data rate. In QSM and FGSM, the real part of the constellated data symbol is transmitted through one or more transmit antennas and at the same time, the imaginary part is also transmitted through one or more transmit antennas. The different number of transmit antennas in FQSM transmit real and imaginary parts to improve the SE. Recently, SMTs such as FGSM [17] and enhanced fully generalized spatial modulation (EFGSM) [3] have been proposed to enhance the limited channel bandwidth and reduce the consumed power transmission in the underwater acoustic communication. In the same line, this paper proposes a spread-spectrum fully generalized spatial modulation (SS-FGSM) scheme to increase the available data rate and avoid the high ICI of the conventional MIMO technologies. To relax the system complexity, SS-FGSM with a deep learning (DL) detector (DLSS-FGSM) is proposed in the state of the maximum likelihood (ML) detector. The main contributions of this paper can be summarized as follows:  
* The SS-FGSM scheme is proposed, which employs additional index representation by using spreading code to transmit more information data bits. The Walsh code is considered as a spreading code in this paper due to its perfect orthogonality. Thus, SS-FGSM can carry additional bits by index leading to improve both the data rate and the energy efficiency. * A new detector with low computation complexity is proposed to relax the receiver-ML based detector computation complexity and save the system consumed power. A deep learning-based detector is proposed to be used in the proposed SS-FGSM underwater communication scheme. In order to adapt the deep learning-based detector for the UWA channel, which is considered to be time-varied, data are first preprocessed to recover the UWA channel effects, and then the deep learning is employed for detecting the index of active antennas, spreading codes, and physical transmitted bits jointly. * The general mathematical framework for the proposed SS-FGSM performances is laid out thoroughly and an extensive simulation is provided to demonstrate the superiority of the proposed scheme over its benchmarks. It is shown that despite the low-complex detector, the proposed scheme is still outperforming the benchmark with the ML. All the abbreviations used through this paper are mentioned in Table 1, and the rest of this paper is organized as follows: related work is presented in Section 2. Then, the proposed SS-FGSM scheme is presented in Section 3. The analytical analysis of the proposed scheme is presented in Section 4.