# Enhanced LDM for Next-Generation Digital Broadcasting Transmission
## 4 Compute and Simulation Results  
### Spectral Efficiency Calculation  
Following Equations (12) and (15), the spectral efficiency shortfall from Shannon for the mobile service of the traditional LDM and En-LDM systems are calculated as  
\[\begin{split} S_{M}^{LDM}&=\left(C_{M}^{LDM}-C_{B, \chi_{1}}\right)/B_{t}\\ &=\log_{2}\Big{(}1+\frac{10^{\alpha/10}}{1+N\cdot(1+10^{\alpha/1 0})}\Big{)}\cdot\frac{1}{B_{t}}-\Bigg{(}m-\sum_{i=1}^{m}E_{b,y}\Bigg{[}\log_{ 2}\frac{\sum_{x\in\chi_{1}}p(y|x)}{\sum_{x\in\chi_{\chi_{\chi_{\chi_{\chi_{\chi _{\chi_{\chi_{\chi_{\chi_{\chi_{\chi_ \chi_{\chi_{\chi____ }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}  
Obviously, it can be observed from Equations (18) and (19) that the spectral efficiency shortfall from Shannon for the mobile service of the traditional LDM system is equal to that of the proposed En-LDM system. Since the mobile service of the traditional LDM system occupies a higher bandwidth than the En-LDM system, the transmission capacity of the mobile service of the LDM system will be slightly higher.  
Figure 3 shows the shortfall from Shannon for the mobile service in the proposed En-LDM and the traditional LDM systems under the AWGN and multipath channels. Note that the system bandwidth is normalized (that is, \(B_{t}=1\)). The results show that within the working SNR range of the mobile service, the shortfall from Shannon for the mobile service in the En-LDM system is the same as that of the traditional LDM system under the AWGN or Rayleigh channel. In addition, from Equations (18) and (19), it can be seen that the Shannon limit of the En-LDM system and the traditional LDM system under the same bandwidth is the same. Therefore, the spectral efficiency of the mobile service in the En-LDM system is consistent with that of the traditional LDM system. When the SNR is equal to 5 dB, the shortfall from Shannon for the mobile service of the En-LDM/LDM system is 0.51 bit/s/Hz under the Rayleigh channel, while the shortfall from Shannon for the mobile service of the En-LDM/LDM system is 0.18 bit/s/Hz under the AWGN channel.  
Following Equations (14) and (15), the spectral efficiency shortfall from Shannon for the fixed service of the traditional LDM and En-LDM systems are calculated as  
\[S_{F}^{LDM} =\left(C_{F}^{LDM}-C_{B,\chi 2}\right)/B_{t} \tag{20}\] \[=\log_{2}\Bigl{(}1+\frac{1}{N\cdot(1+10^{\lambda/10})}\Bigr{)} \cdot\frac{1}{B_{t}^{\prime}}-\left(m-\sum_{i=1}^{m}E_{b,y}\left[\log_{2} \frac{\sum_{x\in\chi 2}P(y|x)}{\sum_{x\in\chi_{0}^{2}}P(y|x)}\right]\right)\cdot \frac{1}{B_{t}^{\prime}}\]  
\[S_{F}^{En-LDM} =\left(C_{F}^{En-LDM}-C_{B,\chi 2}\cdot\Bigl{(}1+\frac{B_{m}}{B_{t}} \Bigr{)}\right)/\left(B_{t}+B_{f}\right) \tag{21}\] \[=\log_{2}\Bigl{(}1+\frac{1}{N\cdot(1+10^{\lambda/10})}\Bigr{)} \cdot\frac{1}{B_{t}+B_{f}}+\log_{2}\Bigl{(}1+\frac{10^{\lambda/10}}{1+N\cdot( 1+10^{\lambda/10})}\Bigr{)}\cdot\frac{B_{f}}{B_{t}\left(B_{t}+B_{f}\right)}\] \[-\left(m-\sum_{i=1}^{m}E_{b,y}\left[\log_{2}\frac{\sum_{x\in\chi 2}P(y|x)}{ \sum_{x\in\chi_{0}^{2}}P(y|x)}\right]\right)\cdot\frac{B_{t}+B_{m}}{B_{t}\left( B_{t}+B_{f}\right)}\]  
Figure 3: The shortfall from Shannon for the mobile service of the LDM and En-LDM systems under the AWGN and Rayleigh channels, where the parameters of the LDM and En-LDM systems were set to \(\Delta=10\) dB, \(B_{f}/B_{t}=1/4\), the constellation for the mobile service was set to QPSK. The shortfall from Shannon for the fixed service in the proposed En-LDM and the traditional LDM systems under the AWGN and multipath channels is shown in Figures 4 and 5. It should be noted that the digital modulation constellation used by the fixed service in the En-LDM system is QPSK and NU\(-\)64 QAM. In Figure 4, the modulation constellation used by the bits extracted by LDPC puncturing is QPSK, which occupies 1/4 of the spectrum resources of the CL. The modulation constellation of the remaining bits of LDPC puncturing is NU\(-\)64 QAM, and the modulation constellation that carries fixed services in the traditional LDM system is only NU\(-\)64 QAM.