# Enhanced Fully Generalized Spatial Modulation for the Internet of Underwater Things
## 3 Proposed EFGSM  
The block diagram of the proposed EFGSM including the modulator and demodulator is shown in Figure 1. The incoming data bits are partitioned into two groups. The first group contains \(log_{2}(P_{M})+\ log_{2}(S_{M/2})\) bits that are referred to as data bits, where \(P_{M}\) and \(S_{M/2}\) stand for primary and secondary signal constellations, respectively. This group is used for modulating the signal constellation symbol from two signal constellation diagrams as designed in ESM-Type1 in [17]. The second combination of bits represents the spatial bits; it is applied to choose the antenna subset utilized in transmitting information of the constellation symbol. The antenna subset of EFGSM differs from the case of activating just one transmitter antenna to the case of activating \(N_{T}/2\) transmitter antennas for each the primary and secondary signal constellations. This contradicts the approaches of the current FGSM introduced in [15; 16] and ESM-Type1 in [17], in which a varied transmitter antenna number is activated in the case of FGSM, and different signal constellations are used in case of ESM-Type1. The variation of signal constellations and transmitter antennas enhance the underwater acoustic channel utilization, reduces the average energy per transmitted symbol, and obviates the BER deterioration. The proposed EFGSM can be considered as a combination of ESM and FGSM. Therefore, the achievable data rate of the proposed EFGSM can be expressed as follows:  
\[R_{EFGSM}=\ log_{2}(P_{M})+\big{\lfloor}\ log_{2}\sum_{k=2}^{N_{T}}\left( \begin{array}{c}N_{T}\\ k\end{array} \right)\big{\rfloor}+\ log_{2}(S_{M/2}), \tag{6}\]  
where \(k\) represents the number of active antennas for both primary and secondary constellations. Different subspaces based on different number of antennas utilize different combinations of active antennas. In all of these subspaces one/multiple active antennas transmit symbols based on the primary signal constellation, \(P_{M}\), while the other active/multiple antennas transmit symbols based on the secondary signal constellation, \(S_{M/2}\). The group of the spatial bits \(\lfloor\ log_{2}\sum_{k=2}^{N_{T}}\left( \begin{array}{c}N_{T}\\ k\end{array} \right)\big{\rfloor}\), is used to select the combination of active antennas. Generally, we can say that the transmitted information  
Figure 1: Proposed enhanced fully generalized spatial modulation (EFGSM). bits are based on three groups: the primary signal constellation, the secondary signal constellation, and the active antenna indexes. First, the information bits are carried via the primary constellation with an achievable bit rate of \(log_{2}(P_{M})\). Secondly, the information bits are conveyed using the secondary signal constellation with an achievable bit rate of \(log_{2}(S_{M/2})\). Finally, the utilization of the spatial combination of antennas and modulation results in an achievable bit rate of \(\lfloor log_{2}\sum_{k=2}^{N_{T}}\left( \begin{array}{c}N_{T}\\ k\end{array} \right)\rfloor\). Unlike the conventional FGSM, using primary and secondary signal constellations increases the number of antenna/constellation combinations. Therefore, EFGSM increases the achievable data rate and decreases energy consumption without altering system complexity. For example, in case of using 4-QAM as a primary signal constellation and binary phase shift keying (BPSK) as a secondary signal constellation, the gutted achievable data rate is 7 bit per channel used (bpcu), on the other hand, the achievable data rate of the conventional FGSM using the same MIMO configuration is only 5 bpcu. However, when using 8-QAM as a primary signal constellation and QPSK as a secondary signal constellation, with the same number of transmitter antennas, the achievable data rate will increase to 9 bpcu in the proposed EFGSM and only 6 bpcu in case of the conventional FGSM.