# LDM-Ex-FDM: A Novel Multi-Service Transmission Scheme for the ATSC 3.0 System
## 2 Advanced Television System Committee (ATSC) 3.0 System Overview
### Bit-Interleaved Coded Modulation (BICM) Capacity Analysis  
BICM can be used to evaluate system performance in a binary communication system, which is an effective solution approaching [PERSON]'s limit with affordable complexity. BICM capacity can be calculated by [19]:  
\[C_{B,X}=\sum_{i=1}^{m}I(b_{i};Y) \tag{8}\]  
\[I(b_{i};Y)=1-E_{b,y}\Bigg{[}\text{log}_{2}\frac{\sum_{x\in X_{b}}p(y|x)}{\sum _{x\in X_{b}^{\prime}}p(y|x)}\Bigg{]} \tag{9}\]  
where \(m\) is the order of the constellation, \(I(\cdot|\cdot)\) denote average mutual information (AMI) function, \(b_{i}\) denotes the \(i\)-th bit carried by a constellation symbol, \(Y\) is the channel output. \(\chi\) represents the alphabet of size \(M=2^{m}\), \(x_{b}^{\prime}\) represents a subset of all signals \(x\in\chi\), and its tag has a value \(b\in\{0,1\}\) at the \(i\)-th bit. \(p(y|x)\) is the transition probability density function  
Figure 8: The receiver structure with the direct interference cancellation (DIC) detector of the LDM-Ex-FDM scheme. of the transmitted signal \(x\) and the received signal \(y\). \(E_{b,y}[\cdot]\) is the expectation respect to the distribution \(E\) and \(y\). _LDM_ enables the simultaneous delivery of mobile services and fixed services in the same time-frequency resources, the _CL_ signal power is regarded as the transmission power of the desired signal, and the _EL_ signal power is regarded as the noise power when calculating the _CL_ channel capacity. In the ATSC 3.0 system with LDM-Ex-FDM scheme, the data symbol is divided into the _LDM_ symbol and the non-_LDM_ symbol part, and the AMI of the mobile service of the _LDM_ symbol part can be calculated by [20]:  
\[l^{\prime}(b_{i};\gamma)=1-\frac{1}{2|\chi_{C}||\chi_{E}|}\underset{\chi_{C}}{ \sum}\underset{\chi_{E}}{\sum}\underset{b}{\sum}E_{N}\left[\log_{2}\frac{ \sum_{x^{\prime}\in\chi_{C}}\exp\left(-\left(\left\|\rho\sqrt{\frac{1}{1+\alpha }}x_{C}+\rho\sqrt{\frac{\alpha}{1+\alpha}}x_{E}+N-\rho\sqrt{\frac{1}{1+\alpha} }x^{\prime}c\right\|^{2}\right)/2\sigma^{2}\right)}{\sum_{x^{\prime}\in\chi_{ C}^{\prime}}\exp\left(-\left(\left\|\rho\sqrt{\frac{1}{1+\alpha}}x_{C}+\rho\sqrt{ \frac{\alpha}{1+\alpha}}x_{E}+N-\rho\sqrt{\frac{1}{1+\alpha}}x^{\prime}c\right\| ^{2}\right)/2\sigma^{2}\right)}\right] \tag{11}\]  
where \(\rho\equiv 1\) under the additive white Gaussian noise (AWGN) channel, \(\rho\sim CN(0,1)\) under the Rayleigh channel, and \(N\sim CN\big{(}0,\sigma^{2}\big{)}\). The AMIs of the fixed service of the _LDM_ symbol part and the non-_LDM_ symbol part can be calculated by Equation (10) because the _CL_ signal of the _LDM_ can be eliminated perfectly. According to (9)-(11), the capacities of the mobile service and the fixed service in ATSC 3.0 system with and without LDM-Ex-FDM scheme over the AWGN and Rayleigh channels respectively are calculated and presented in Figures 9 and 10, respectively. The capacity improvement of the fixed service is expected to be 0.410/0.427 bit/symbol under the AWGN and Rayleigh channels respectively with the puncturing rate of the LDM-Ex-FDM scheme is 1/12. Although the capacity of the mobile service has declined slightly, the capacity improvement of the total service (i.e., mobile service and fixed service) is expected to be 0.244/0.285 bit/symbol under the AWGN and Rayleigh channels, respectively. The reason is that the symbols removed by puncturing the fixed service symbols independently occupy a certain number of subcarriers for transmission, which reduces the transmission bandwidth of the mobile service. Obviously, the channel capacity of the fixed service and the overall service can be further improved by increasing the puncturing rate, but there needs to be a compromise between the performance improvement of the fixed service and the transmission rate of the mobile service. It is worth noting that the spectrum efficiency of the mobile service in the LDM-Ex-FDM scheme remains identical compared to the traditional _LDM_ scheme, while the spectrum efficiency of the fixed service is higher.