# ROAD Statistics-Based Noise Detection for DME Mitigation in LDACS
## 3 System and Noise Model  
_LDACS System Model_  
The system model includes the LDACS transmitter, the channel which imparts additive white Gaussian (AWGN) noise and DME interference and the LDACS receiver. Figure 3 elaborates the detailed block diagram of the LDACS ground station transmitter. Data source creates random data of 91 bytes and passes to Reed-Solomon (RS) coder resulting in an extra 10 bytes of redundant data for error correction and detection. A 6-bit zero padding is performed on the output of the RS coder before passing to the convolutional coder. The coded output of the convolutional coder is made to pass through permutation interleaver for reducing burst errors. The output of permutation interleaver is arranged into a standard LDACS data format (F) after symbol mapping, modulating with Quadrature Phase Shift Keying (QPSK) and frame composing. All the variables shown in Figures 3 and 4 are generated for standard LDACS data frame format (F). The same variables with suffix '\(t\)' signify the same signal for an instant '\(t\)' or the \(t^{th}\) OFDM symbol. In other words, \(F_{t}=[F_{t}[0],F_{t}[1]...F_{t}[N-1]]^{T}\) stands for the \(t^{th}\) symbol of LDACS forward link frame (F) with N orthogonal subcarriers. \(F_{t}\) carries the random data \(F_{t}[m]_{m=0,1...N-1}\) with zero mean and variance \(\sigma_{F}^{2}\). The OFDM symbol \(S_{t}=[S_{t}(0),S_{t}(1)...S_{t}(N-1)]^{T}\) is generated in the time domain by calculating the 64-point IFFT of the data \(F_{t}\). Further, \(N_{CP}\) number of cyclic prefix bits are added to the total \(N\) subcarriers resulting in transmitted vector \(X_{t}^{\prime}=\big{[}X_{t}^{\prime}(0),X_{t}^{\prime}(1)\ldots,X_{t}^{\prime }(N+N_{cp}-1)\big{]}\). The transmitted signal \(X^{\prime}\) changes to \(r^{\prime}\) when it passes through the channel in the presence of DME. For each instant \(t\), the transmitted vector \(X_{t}^{\prime}\) is affected by a noise component \(i_{t}=[i_{t}(0),i_{t}(1),...,i_{t}(N+N_{cp-1})]^{T}\) which is a mixture of the additive white Gaussian noise \(A_{t}=[A_{t}(0),A_{t}(1),...,A_{t}(N+N_{cp-1})]^{T}\) and the impulse noise (DME) \(p_{t}=[p_{t}(0),p_{t}(1),...,p_{t}(N+N_{cp-1})]^{T}\). Thus, the received signal for an instant '\(t\)' is \(r_{t}^{\prime}=\big{[}r_{t}^{\prime}(0),r_{t}^{\prime}(1),r_{t}^{\prime}(N+N_{ cp}-1)\big{]}^{T}\) and can be denoted as in (1). \[r_{t}^{\prime}=X_{t}^{\prime}+i_{t} \tag{1}\]  
where  
\[i_{t}=A_{t}+p_{t} \tag{2}\]  
As discussed in Section 1, the prime contributor of interference to LDACS is DME. These signals are a pair of Gaussian-shaped pulses, separated by a duration of \(\Delta t\). The transmission rate (30 pulse pairs per second or 50 ppps ), as well as the duration \(\Delta t\) (12 or 36 us) of DME signals, varies with the mode of operation of the distance measuring equipment. A pair of DME pulses in the baseband can be expressed as in (3) [33]. \[P_{d}(t)=e^{\frac{-t^{2}t^{2}}{2}}-e^{\frac{-t(t-\Delta t)^{2}}{2}} \tag{3}\]  
where \(\zeta=4.5\times 10^{11}\) s\({}^{-2}\). It has a width of 3.5 us at half of the maximum amplitude. The frequency domain representation of DME signal is as in (4). The spectrum is modulated with a cosine as the pulses are always happening pairwise [34]. \[I_{pd}(f)=\sqrt{\frac{8\pi}{\zeta}}e^{\frac{2\sigma_{F}^{2}\zeta^{2}}{\zeta}} e^{-j\pi f\Delta t}cos(\pi f\Delta t) \tag{4}\]  
Figure 3: LDACS transmitter block diagram. The base band DME pulse pairs are modulated to the relative carrier frequency of the channel to 0.5 MHz left and to 0.5 MHz right of the LDACS system bandwidth. The DME interfering signal that affects the LDACS system is expressed in (5). \(I_{pd}(t)\) is the total interference signal for a time interval '\(t\)' caused by \(N\) number of DME stations that are operating on the 0.5 MHz offset to the center frequency of the LDACS system [35].