# Robust Burst Detection Algorithm for Distributed Unique Word TDMA Signal
## 5 Simulation Experiments  
In order to verify the proposed algorithm, simulation signal is tested in the MATLAB environment. Assume that signal modulation mode is QPSK, symbol rate \(R_{s}\) is 2 MBaud, sampling rate \(F_{s}\) is 8 MHz, sampling time is 25 ms, there are three TDMA burst signals, each burst time is 0.36 ms.  
Firstly, in order to test the influence of frequency offset on the detection effect of DUWDC, channel environment is assumed to be additive Gaussian white noise, \(E_{b}/N_{0}=\{0\text{ dB},3\text{ dB},6\text{ dB},9\text{ dB}\}\), the total number of UW is 48 symbols and UW distribution structure: \(N=2;\ P=24;\ L_{0}=100\). The signals with normalized frequency offset \(f_{e}T=0\) and \(f_{e}T=0.1\) are detected, respectively. The correlation coefficient curves obtained under different frequency offsets are shown in Figures 9 and 10. In the case of two normalized frequency offsets, detection effect of DUWDC is basically the same, indicating that it has good anti-frequency offset performance and can be used in large frequency offset environments. The analysis of anti-frequency offset performance of the algorithm is verified. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Multiplication** & **Addition** \\ \hline Traditional dual & \((NP-1)NP\) & \(0.5(NP-1)NP\) \\ correlation [21] & \(2(N-1)P\) & \((N-1)P\) \\ Hou\({}_{2}\) & \(2(P-1)N\) & \((P-1)N\) \\ DUWDC & \(2(NP-1)\) & \(NP-1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Complexity comparison of four detection algorithms. Figure 9: The correlation coefficient curves obtained by DUWDC in the case of \(f_{e}T=0\). In order to verify the influence of DUW distribution structure on the algorithm performance, simulation conditions: let \(E_{b}/N_{0}=6\) dB, normalized frequency offset \(f_{e}T=0.1\), the total number of UW is 48 symbols and the number of symbols inserted in each group is 2, 4, 8 and 16, respectively. As shown in Figure 11, under different distribution structures, detection results are basically the same. Qualitatively verify the theoretical analysis that detection performance of DUWDC is not affected by the distributed structure. Based on the above analysis and simulation results, DUWDC has good anti-frequency offset performance, and detection performance increases with the increase in SNR. It is not affected by UW distribution structure and has good robustness to different distribution structures. For influence of different SNR on the false alarm probability of DUWDC, Monte Carlo simulation is performed on the algorithm under the condition of normalized frequency offset \(f_{e}T=0.1\). As shown in Figure 12, let \(E_{b}/N_{0}=\{-3\) dB, \(0\) dB, \(3\) dB, \(6\) dB, \(9\) dB\(\}\), false alarm probability of algorithm under different thresholds \(th\) is counted, respectively. In the oversampling rate \(F_{s}/F_{s}=4\) in the experiment, actual correlation results generally have two to four positions, which can be judged as the start of burst signal, then  
Figure 11: The correlation coefficient curves obtained by DUWDC under different DUW distribution structures. Figure 10: The correlation coefficient curves obtained by DUWDC in the case of \(f_{e}T=0.1\). select one of the largest correlation coefficient positions to judge the accurate position. From Figure 12, it can be seen that the larger correlation threshold and the higher SNR, the smaller false alarm probability, and the false alarm of DUWDC algorithm changes little with SNR. In order to further verify detection performance of DUWDC, based on DUW TDMA signal, DUWDC, Hou\({}_{1}\) and Hou\({}_{2}\) are simulated and compared. Simulation conditions: normalized frequency offset \(f_{e}T=0.1\), \(E_{b}/N_{0}=\{-3\text{ dB},0\text{ dB},3\text{ dB},6\text{ dB}\}\), the total number of UW is 48 symbols and DUW structure: \(N=2;\ P=24;\ L_{0}=100\). Monte Carlo experiments are carried out on this signal.