# Efficient Low-Complexity Turbo-Hadamard Code in UAV Anti-Jamming Communications
## 4 Simulation Results
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline System Clock & 245.76 MHz \\ Symbol Rate & 0.96 MHz \\ Interpolation Rate & 256 \\ Modulation Filter & Root Raised Cosine \\ Roll-Off Factor & 0.35 \\ Frequency Hopping Numbers & 200 \\ Frequency Hopping Rate & 960,000 hop/s \\ Total Bandwidth & 192 MHz \\ Interference Bandwidth & 38.4 MHz, 76.8 MHz \\ Proportion of Jammed Frequency Bins & 20\%, 40\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Core FH system simulation parameters. Figure 6: BER performance of turbo-Hadamard codes with different numbers of component coders. The impact of the order of Hadamard codes on the BER performance of turbo-Hadamard codes is illustrated in Figure 7. We considered 200 information bits with \(r=2\), \(r=4\) and \(r=5\), respectively. All cases were evaluated using the \(M=3\) component encoder. We observe that our proposed tail-biting turbo-Hadamard codes outperformed the terminate state-zero turbo-Hadamard codes [20] in all conditions of \(r=2\), \(r=4\) and \(r=5\). Similarly to Figure 6, this is because the improved code scheme provided more prior information than that of the terminate state-zero turbo-Hadamard codes [20]. Additionally, we observed that a larger order of Hadamard codes leads to better BER performance. Figure 8 compares the BER performance against the different memory depths of convolutional codes when the overall coded length is 200 and the order of Hadamard codes is set at 5. It shows that the BER performance of all algorithms improved with the increase in the number representing the memory depth of the convolutional code. Moreover, as memory depth \(\eta\) increased, the BER performance of tail-biting turbo-Hadamard codes and terminate state-zero turbo-Hadamard codes became closer. This is because when memory depth \(\eta\) increases, the number of terminate states increases. Since it is confirmed that the start state and the terminate state are the same in our proposed algorithm, it is impossible to confirm the concrete cyclic state when the \(\eta\) is sufficiently large. Figures 9 and 10 show the performance of the proposed algorithm considering an FH system influenced by jamming. We compared the anti-jamming ability by evaluating the BER and FER performance of the tail-biting turbo-Hadamard codes, terminate-state-zero turbo-Hadamard codes [20], concatenated zigzag Hadamard codes [31] and turbo codes with repeating. The code length was set to be \(k=200\), the component encoder number was assumed to be \(M=3\) and the memory length was \(\eta=2\). Figure 7: BER performance of turbo-Hadamard codes with different orders of Hadamard codes. Figure 8: BER performance of turbo-Hadamard codes with different memory depths. Figure 9: Error performance of turbo-Hadamard codes with \(r=4\) with no jamming (**a**), 20% (**b**), 40% (**c**) frequency bins to be jammed. Figure 9 illustrates the anti-jamming performance with \(r=4\). To evaluate the anti-jamming ability at the same level, considering the structure of all the mentioned codes, the code rates of tail-biting turbo-Hadamard codes and terminate-state-zero turbo-Hadamard codes were set to be \(1/11.8\), and the code rate of concatenated zigzag Hadamard codes was \(1/11.2\). It should be noted that the total equivalent rate was \(1/12\) when the \(1/3\) turbo codes were transmitted 4 times. We observed that the BER performance of all codes decreased, which was because the receiver detected the jammed symbol through the received power threshold, and then deleted the jammed frequency bins. Those operations result in less information being available for decoding, which thus reduces the coding gain. When the BER performance is \(\text{e}^{-5}\), the anti-jamming performance of our codes was degraded by \(1.1\) dB under 20% jamming and \(2.6\) dB under 40% jamming, compared with the conditions without jamming, respectively. Moreover, we can observe that the performance of the proposed algorithm and that of the turbo-Hadamard codes [20] are very similar.