## 4 Simulation Results  
The ABER performance between the received bits of index antennas and the constellated symbols and the ABER performance of index/data SM received bits have been evaluated numerically using Monte Carlo simulations as shown in Figure 6. The ABER performance has been evaluated by using Equations (19), (22), and (23) to get the upper bound of the antennas index, the constellation symbol, and total SM ABER. Then, these asymptotic ABER analytical formulations are confirmed by using Monte Carlo simulations. The simulation results are gotten for \(10^{6}\) symbols conveyed at each SNR for \(10^{6}\) iterations over the simulated channel and the measured underwater acoustic channel collected from sea experiment, ASCOT01 conducted off the coast of New England in June 2001 as reported in [25] and used in [26]. The ABER performance for SM (index/data) and the unseparated SM are shown in Figure 6, using SM technique with 9-bit per channel use (9-bpcu) using SM with \(Nt=4\) and 128-QAM modulation. As shown in Figure 6, the analytical outcomes display a high constancy with the simulation results gotten for SM scheme for the realistic SNR values. However, at the low SNR values, the analytical results disclose a small discrepancy to the simulation results gotten for the ABER of the constellation and index antennas mathematically. In other words, the upper bound is slack to the simulation results at low SNR values, but it stiffens to the simulation results at the realistic SNR values. This agrees with other obtained results with similar bound as in [5; 27; 28; 29; 30]. As shown in Figure 6, the difference between the ABER of transmitted symbols and antennas index in the SM is about 8.5 times. Although the unseparated SM ABER has similar performance using SM (data). Therefore, the separation of transmission of critical and noncritical image bitstream over antennas index and data symbols are highly motivated for a different level of data protection in SM, respectively. To evaluate the proposed UEP-SM, the SPIHT coder is applied for (\(256\times 256\)) \"Lena\" and dolphin swimming underwater image [6], using wavelet coefficients to generate the source bitstream with a 0.5 bpp and  
Figure 5: M- SPIHT progressive source decoder. the SPIHT encoder provide \(N=32,754\) bits. In conventional SM, these bits are transmitted directly via SM based on the SM lock-up table; however, in the proposed UEP-SM, the SPIHT encoded bits are divided based on their significance into two groups: \(G_{1}=[1:7278]\) bits and \(G_{2}=[7279:32,754]\) bits. The incoming M-SPIHT \(G_{1}\) bits are transferred via index antenna selector, and \(G_{2}\) is transferred via the modulation constellation sector. Using the progressive transmission image ability of the SPIHT coder, the sets of distortion in the received image are obtained from the same received bit stream. The M-SPIHT decoder reads the first bytes of the received bit stream \(\widetilde{G}=[G_{1},G_{2}]\) and calculates the inverse sub-band. By calculating the inverse sub-band transformation and then comparing the recovered image with the original, the distortion can be measured by using PSNR as follows,  
\[PSNR=10\ \text{log}_{10}\Bigg{(}\frac{255^{2}}{MSE}\Bigg{)}\ \text{dB} \tag{30}\]  
where MSE is the square of mean error between the original and reconstructed image and calculated in Equation (25). The SM-UEP has been compared in terms of the PSNR for the received image with the conventional SM under assumption of using the same \(Nt\) and M-QAM at same SNR of underwater channel. Reconstructed \"Lena\" and dolphin swimming underwater image transmitted via UEP-SM over underwater acoustic channel are shown in Tables 1 and 2, respectively. Figure 6: ABER performance comparison between the constellation transmitted symbol, antennas index, and total ABER of SM at 9 bpcu spectral efficiency. As shown in Table 1, the SM-UEP is improving the PSNR of received \"Lena\" image by 4.92 dB and 7.1 dB at channel SNR = 10 dB and SNR = 20 dB, respectively. For dolphin swimming underwater