# Blind Turbo Equalization of Short CPM Bursts for UAV-Aided Internet of Things
## 4 EMLVA for Blind Channel Equalization
### The EMVA/EMLVA Blind Equalizer
In general, a CC with a larger number of states has a larger free distance and can further provide more interleaving gain. However, this only occurs when the interleaving length is large enough and the signal-to-noise ratio is above the convergence threshold. When the frame length is short, a CC with a large number of states exhibits poor convergence, leading to performance degradation. Therefore, Figure 5a compares the BER performance of five types of CC, i.e., (5,7), (17,15), (23,35), (53,75), and (171,131) after 0 outer iterations and 10 outer iterations. The result shows that (5,7) CC is the optimal channel code for the SCCPM system, taking into account the burst length, signal-to-noise ratio, and implementation complexity. The interleaver was used to randomize the order of the code bits before transmission. To select the appropriate interleaver to enhance the performance gain, Figure 5b compares the performance of six types of interleavers: matrix interleaver, random interleaver, S-random interleaver, general interleaver, QPP interleaver, and WCDMA interleaver. The analysis of the BER curves for 0 and 10 outer iterations showed that the S-random interleaver can provide the best coding gain and performance. Therefore, the S-random interleaver was used for subsequent simulations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Value** & **Remarks** \\ \hline Frequency pulse & Gaussian pulse & \(L=3\) \\ \hline Modulation order (M) & 2 & - \\ \hline Modulation index (h) & 1/2 & \(h=p/q\) \\ \hline Training bits & 4,6,8 & ML estimation \\ \hline Coded data bits & 66 & - \\ \hline Baud rate & 150 kHz & - \\ \hline Code rate & 1/2 & convolutional code \\ \hline Samples/symbol & 2 & \(\varepsilon\) \\ \hline Multipath channel & two-ray Rician channel & - \\ \hline Rician factor & \(K_{Rician}=29\) dB & hilly/ mountainous scenarios \\ \hline Maximum delay spread & 7 μs & - \\ \hline Inner iteration (S) & 3 & \(S_{max}\) \\ \hline Outer iteration (T) & 10 & \(T_{max}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters. #### 5.2.2 Performance Comparison of EMLVA, EMVA, and the Method Based on the Training Sequence

Figure 5(a) compares the BER performance of the data-aided coherent detection, EMVA, and EMLVA proposed in this paper with different inner and outer iterations, as well as the SOVA with perfect channel state information (CSI). The BER curves with perfect channel knowledge represent the maximum attainable performance, while the curves for the data-aided method (called Tran.Bits.) represent the baseline to beat, which extracts the channel by using maximum likelihood estimation with training sequence lengths of 4, 6, or 8 bits, respectively. The performance of the data-aided method was lower than that of the blind equalization EMLVA proposed in this paper after 10 outer iterations, indicating

Figure 5: The performance of different convolutional codes and interleavers with perfect channel knowledge. The dashed and solid curves refer to the performance of the optimal coherent detector after the first iteration (\(T=1\)) and the tenth iteration (\(T=10\)), respectively. (**a**) BER as a function of \(E_{b}/N_{0}\) for different convolutional codes; (**b**) BER as a function of \(E_{b}/N_{0}\) for different interleavers. that the data-aided approach has difficulty obtaining an accurate channel with few training bits. Compared to the traditional EMVA, the performance loss of the EMLVA was small, which can be ignored and approximates the curve with perfect channel knowledge after 10 outer iterations. Figure 6: The performance of the EMLVA and T-EMLVA. (**a**) BER as a function of \(E_{b}/N_{0}\) for the EMLVA and T-EMLVA with the BCA initializer. The “With perfect CSI” and “Tran. Bits” curves refer to the performance of the optimal coherent detector and training-based channel estimation, respectively; (**b**) BER as a function of \(E_{b}/N_{0}\) for the EMLVA and T-EMLVA with different initializers.