# Interference Mitigation for Metro Train Location Based on Karhunen-Loeve Decomposition
## 5 Conclusions  
This paper proposes a method for suppressing the interference of metro train positioning based on Karhunen-Loeve decomposition. The method uses KL decomposition to project the signal into the orthogonal subspace, uses the size of the eigenvalue to distinguish the interference signal and the positioning signal, uses the inverse KL decomposition to reconstruct the interference signal, and subtracts the interference signal from the received signal to achieve interference suppression. We built an interference test platform, and compared this with the traditional method to analyze the interference suppression capability and computational complexity. From the experimental results, the suppression performance of the KL-based suppression algorithm is better than that of the STFT and WPCT algorithms under single-tone interference and chirp interference. Furthermore, the KL algorithm is less affected by the interference jamming-signal-and-noise-ratio. We also compared the complexity of the three algorithms, and the complexity of the KL algorithm is significantly higher than that of the STFT and WPCT algorithms. Deploying interference suppression algorithms in practical receivers requires a trade-off between suppression performance and computational complexity.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **MSE (dB)** & **Complexity** \\ \hline STFT & 1.67 & \(O(N)\) \\ \hline WPCT & 1.19 & \(O(kNL_{w})\) \\ \hline KL & 0.24 & \(O\big{(}N^{2}\big{)}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mitigation performance and implementation complexity comparison. JSNR = 30 dB.  
Figure 14: Comparison of positioning accuracy of different algorithms in three jamming scenarios.  
In the future work, how to quickly and accurately identify the jamming signal will be studied when the type of jamming signal is unknown. Furthermore, we will consider further reducing the computational complexity of KL decomposition and improve the feasibility of algorithm hardware deployment. Generally speaking, interference signals are highly correlated (or even deterministic), while the positioning signal samples at the receiver can approximately be considered to be Gaussian-independent and identically distributed (i.i.d) random variables. Random matrix theory provides efficient tools to separate correlated terms from the sum of correlated and i.i.d. signals. In the future, we will consider analyzing the eigenvalues of the sample covariance matrix to obtain very useful information about interference and interference subspaces.  
Conceptualization, X.D.; Data curation, X.D.; Formal analysis, X.D., J.L. and Z.Z.; Investigation, X.D., J.L. and Z.Z.; Project administration, Z.D. (Zhongliang Deng), X.D., J.L., Z.D. ([PERSON]) and Z.Z.; Resources, Z.D. ([PERSON]) and X.D.; Software, X.D., J.L., Z.D. ([PERSON]) and Z.Z.; Supervision, J.L., Z.D. ([PERSON]) and Z.Z.; Validation, X.D. and Z.Z.; Visualization, X.D.; Writing--original draft, X.D.; Writing--review and editing, X.D., J.L., Z.D. ([PERSON]) and Z.Z. All authors have read and agreed to the published version of the manuscript. This work was financially supported by the Beijing Municipal Natural Science Foundation under Grant No. L191003. The authors would like to express their thanks to [PERSON] for help in the simulation. The authors declare no conflict of interest. The authors declare no conflict of interest.