# Advanced Technology in ATSC3.0: Boosting Data Signal Rates Using Polarization Properties and FSS +
## 3 Proposed System  
In this section, we present an OFDM-based transmission scheme that utilizes cross-polarization discrimination (XPD). Figure 4 provides an overview of the proposed system architecture. In particular, Figure 4a shows the architecture of the proposed transmitter. In this design, data streams are first converted from serial to parallel (S/P) and then modulated using QPSK. The broadcasting data are transmitted using the vertical antenna, while additional data are transmitted via the horizontal antenna. To generate the OFDM signal for the additional data, frequency symbol spreading (FSS) is applied before IFFT, as illustrated in Figure 5. This technique uses Hadamard codes to spread symbols across subcarriers, providing frequency diversity and improving robustness in multipath fading environments. \(u_{dd}(m,i)\) represent the \(i\)-th symbol at the \(m\)-th subcarrier following FSS, and it is given by,  
\[u_{dd}(m,i)=\sum_{k=0}^{N_{SF}-1}c_{k}(m\mod N_{SF})\] \[\cdot d_{dd}(\lfloor m/N_{SF}\rfloor N_{SF}+k,i), \tag{21}\]  
where \(N_{SF}\) represents the length of the spreading code. The term \(d_{dd}(m,i)\) refers to the additional data associated with the \(i\)-th symbol on the \(m\)-th subcarrier, and is normalized, such that \(E[|d_{dd}(m,i)|]=1\). The notation \(\lfloor a\rfloor\) indicates the greatest integer less than or equal to \(a\). The function \(c_{k}(n)\) denotes the Hadamard code used for FSS, which satisfies the orthogonality condition:  
\[\sum_{k=0}^{N_{SF}-1}c_{k}(n)c_{\Omega}^{*}(n)=\left\{ \begin{array}{ll}N_{ SF}&(k=\Omega)\\ 0&(k\
eq\Omega),\end{array} \right. \tag{22}\]  
where \(|c_{k}(n)|=1\) and \({}^{*}\) denotes the complex conjugate. Figure 3: The XPD of polarization for \(\xi=45^{\circ}\). After that, the OFDM time signal is generated by IFFT and the guard interval (GI) is inserted. The transmit antennas consist of two antennas (one vertical and one horizontal), \(s_{o}\) and \(s_{h}\) indicate the signals transmitted from the base station vertically and horizontally, respectively. They are expressed as follows. Figure 4: Proposed system. Figure 5: Concept of FSS method. \[s_{v}(t) = \sum_{i=0}^{N_{p}+N_{d}-1}g(t-iT)\sqrt{\frac{2S}{N_{c}}} \tag{23}\] \[-[\sum_{i=0}^{N_{v}-1}d_{bc}(m,i)\exp j2\pi(t-iT)m/T_{s}],\]  
\[s_{h}(t) = \sum_{i=0}^{N_{p}+N_{d}-1}g(t-iT)\sqrt{\frac{2S}{N_{c}}} \tag{24}\] \[\cdot[\sum_{i=0}^{N_{v}-1}u_{dd}(m,i)\exp j2\pi(t-iT)m/T_{s}],\]  
where \(N_{p}\), \(N_{d}\), and \(N_{c}\) denote the number of pilot symbols, data symbols, and subcarriers, respectively. The term \(d_{bc}(m,i)\) represents the broadcast signal of the \(i\)-th symbol on the \(m\)-th subcarrier. \(T\) denotes the total duration of an OFDM symbol, including the GI of duration \(T_{g}\), while \(T_{s}\) refers to the effective symbol duration (excluding the GI) systems, the GI is inserted to mitigate inter-symbol interference (ISI) caused by multipath fading. \(S\) represents the average transmit power, and \(g(t)\) is the transmission pulse, which is defined as follows:  
\[g(t)=\left\{ \begin{array}{ll}1,&-T_{g}\leq t\leq T_{s}\\ 0,&\text{otherwise}.\end{array} \right. \tag{25}\]  
Figure 6 illustrates the configuration of cross-polarized antenna pairs used at both the transmitter and receiver. In this setup, vertical and horizontal polarization components are transmitted and received independently, enabling the system to exploit the benefits of cross-polarization discrimination (XPD). The receiver employs two antennas: one aligned for vertical polarization and the other for horizontal polarization. The received signals at these antennas, denoted as \(r_{v}\) and \(r_{h}\), are mathematically expressed, as follows:  
\[r_{v} = h_{vv}s_{v}+h_{tv}s_{h}+n_{1} \tag{26}\] \[= h_{vv}s_{v}+\hat{n_{1}},\]  
\[r_{h} = h_{vh}s_{v}+h_{hh}s_{h}+n_{2} \tag{27}\] \[= h_{hh}s_{h}+\hat{n_{2}},\]  
where \(n_{1},n_{2}\) is the Additive White Gaussian Noise (AWGN), and \(h_{vh}\), \(h_{tv}\) are the channel response between the different polarization antennas.