# GAE and OBE Enhanced Interference Mitigation Techniques in LDACS
## 3 System and Noise Model  
### LDACS System Model  
The system model consists of the LDACS transmitter, channel which adds additive white Gaussian noise (AWGN) and DME noise, and the LDACS receiver. The detailed block diagram of the LDACS ground station transmitter is as shown in Figure 3. The random data of 91 bytes, generated from the data source, are passed through the Reed-Solomon (RS) coder, which adds 10 bytes of redundant data to the original data. The output of the RS coder further undergoes 6 bit zero padding before passing to the convolutional coder. The output of the convolutional coder is further passed through the permutation interleaver to reduce the burst errors. The blocks symbol mapper, quadrature phase shift keying (QPSK) modulation and frame composer arrange the output of the symbol mapper to the standard LDACS data frame format (S). It is to be noted that all the variables displayed in Figures 3 and 4 are generated for the standard LDACS data frame format (S). The same variables with suffix '\(t\)' represent the same signal for an instant '\(t\)' or the \(t^{th}\) OFDM symbol. For example, the output of the frame composer at an instant '\(t\)' is \(S_{t}=[S_{t}[0],S_{t}[1]\ldots S_{t}[N-1]]^{T}\) and represents the \(t^{th}\) symbol of the LDACS forward link frame (S) with N orthogonal subcarriers. \(S_{t}\) holds the random data \(S_{t}[m]_{m=0,1\ldots N-1}\) with zero mean and variance \(\sigma_{s}^{2}\). The OFDM symbol \(X_{t}=[X_{t}(0),X_{t}(1)\ldots X_{t}(N-1)]^{T}\), generated in the time domain by computing the 64-point IFFT of the data \(S_{t}\) is also modeled with a zero mean Gaussian probability density function. Further to avoid inter-carrier interference, \(N_{CP}\) number of zeros are added to the total \(N\) subcarriers, resulting in \(N+N_{CP}\) subcarriers. Thus, the transmitted vector is \(x_{t}^{\prime}=[x_{t}^{\prime}(0),x_{t}^{\prime}(1)\ldots,x_{t}^{\prime}(N+N_ {cp}-1)]\). The symbols \(\mathsf{X}\) and \(\mathsf{x}^{\prime}\) are the OFDM signals without and with cyclic prefix bits generated for the LDACS forward link frame (S). Figure 3: LDACS transmitter block diagram. The transmitted signal \(x^{\prime}\) passes through the AWGN channel in the presence of DME interference and is received as signal \(y^{\prime}\). For each instant \(t\), the transmitted vector \(x^{\prime}_{t}\) is corrupted by a noise of \(i_{t}=[i_{t}(0),i_{t}(1),\ldots,i_{t}(N+N_{cp-1})]^{T}\), which includes the additive white Gaussian noise \(W_{t}=[W_{t}(0),W_{t}(1),\ldots,W_{t}(N+N_{cp-1})]^{T}\) and the impulse noise \(D_{t}=[D_{t}(0),D_{t}(1),\ldots,D_{t}(N+N_{cp-1})]^{T}\). Hence, the received signal for an instant '\(t\)', is \(y^{\prime}_{t}=[y^{\prime}_{t}(0),y^{\prime}_{t}(1),y^{\prime}_{t}(N+N_{cp}-1 )]^{T}\) and can be represented as depicted in (1). \[y^{\prime}_{t}=x^{\prime}_{t}+i_{t} \tag{1}\]  
where  
\[i_{t}=W_{t}+D_{t} \tag{2}\]  
In the deployment of LDACS as an inlay system between adjacent DME channels, the major part of interference toward LDACS is DME signals. A pair of Gaussian-shaped pulses, separated by a duration of \(\Delta t\), are DME signals. The duration \(\Delta t\) (12 \(\upmu\)s or 36 \(\upmu\)s) and the transmission rate (30 pulse pair per second or 50 ppps) of DME signals changes with a different mode of operation of the distance measuring equipment. A pair of DME pulses in the baseband can be depicted as in (3) [35]. \[D_{p}(t)=e^{\frac{-\alpha t^{2}}{2}}-e^{\frac{-\alpha(t-\Delta t)^{2}}{2}} \tag{3}\]  
where \(\alpha=4.5\times 10^{11}\) s\({}^{-2}\). It has a width of 3.5 \(\upmu\)s at half of the maximum amplitude. As DME pulses are Gaussian shaped, it has same shape in the frequency domain. The spectrum is modulated with a cosine, as the pulses are always occurring pairwise. The resulting signal can be denoted as in (4) [12].