# ROAD Statistics-Based Noise Detection for DME Mitigation in LDACS
## 4 Nonlinear Estimators
### Proposed ROAD PB  
When the LDACS signal is affected by DME interference, the amplitude of the received data exhibits a large variation in amplitude from neighboring data. The variation in amplitude due to bit change or additive white Gaussian noise is less due to DME interference. Therefore, the most affected data are those whose amplitude is much different from neighbors. The proposed ROAD PB uses ROAD statistics to quantify the variation in amplitude of particular LDACS (OFDM) data from the neighboring data for each time epoch. Further, the most basic threshold-based detection approach is utilized to identify the data signal affected by DME interference. The goal of fixing a suitable threshold is to recognize the OFDM data that are significant outliers.  
The calculation of ROAD value [32] for a one-dimensional LDACS OFDM symbol involves the following steps:  
1. The received OFDM symbol for each time epoch is considered as a one-dimensional vector. For a one-dimensional vector of size \((1\times 2t+1)\), the absolute difference between a center sample and a receiving sample for each time epoch \(f_{d}(k)\) are calculated as in (6) \[f_{d}(k)=|r_{k}-[r_{k-f},...,r_{k+f}]|\] (6)
2. The difference vector \((\,f_{d}(k))\) is sorted in increasing order. \[Q(k)=sort(f_{d}(k)).\] (7)
3. The ROAD value is calculated as the sum of first \(f\) values of \(Q(k)\) \[ROAD=\Sigma_{k=1}^{f}Q(k).\] (8)  
The simple way to recognize the effectiveness of ROAD statistics is to incorporate the method into any existing DME mitigation method. Hence, the proposed ROAD PB incorporates ROAD statistics into pulse blanking. The mathematical depiction of ROAD pulse blanking is as in (9). Here, \(R_{p}\) is the lower threshold value used to discriminate LDACS signals affected with DME interference.  
\[x_{|R_{p}|}(r)=\begin{cases}|r|e^{jarg(r)}&\text{if }ROAD(r)\leq R_{p}\\ 0&\text{Otherwise}\end{cases} \tag{9}\]  
The reduction in bit error rate at the receiver is compared with normal pulse blanking in Section 5.  
The extra computational complexity put forward by ROAD PB compared to conventional pulse blanking is the sum of the computational complexity put forward by the steps involved to calculate ROAD value, as in (6)-(8). As these three steps have no complex multiplication in calculating the ROAD value, it is evident that the extra complex multiplication contributed by ROAD PB is zero. Hence, there is no change in number of complex multiplication compared to LDACS OFDM receiver (without any mitigation) or to pulse blanking. As we have used fast Fourier transform in LDACS OFDM receiver, the total number of complex multiplications involved is \((N/2)\cdot log_{2}(N)\), where \(N\) is the number of subcarriers in OFDM signal [36].  
The steps in (6) introduce the extra complex additions \(N\cdot(N-1)\) or real number addition \(2N\cdot(2N-1)\). Hence, the total number of complex additions of LDACS OFDM receiver with ROAD PB is \(N\cdot log_{2}N+N\cdot(N-1)\). The number of real-time additions put forward by sorting depends on the type of sorting that is used. For instance, if selective sorting is used, it introduces \(\frac{N^{-}(N-1)}{2}\) number of real-time additions. Finally, the number of real value additions introduced by step (8) is \(\frac{N\cdot(N-1)}{2}\). The proof is included in Appendix A.