# Adaptive DCS-SOMP for Localization Parameter Estimation in 5G Networks
## 4 Proposed Method
### Adaptive Search in DCS-SOMP Approach for 3D Parameter Estimation
In the DCS-SOMP case, \(q_{az}\) and \(q_{el}\) are both set to 18, whereas in the adaptive DCS-SOMP case, \(q_{az}\) and \(q_{el}\) are both set to 6. We used the Root Mean Square Error (RMSE) as the Key Performance Indicator (KPI) for our estimates. The RMSE \(\varepsilon\) is calculated as follows:

\[\varepsilon=\sqrt{\frac{1}{Q}\sum_{i=1}^{Q}|p_{i}-\hat{p}_{i}|^{2}}, \tag{27}\]

where \(Q\) is the number of runs, \(p_{i}\) is the actual value of the chosen parameter at the \(i\)-th run, and \(\hat{p}_{i}\) is the estimated value of the chosen parameter at the \(i\)-th run. Table 4 presents the RMSE for each parameter estimated, where \(\varepsilon_{\phi^{\mu}}\), \(\varepsilon_{\phi^{\mu}}\), \(\varepsilon_{\phi^{\mu}}\), \(\varepsilon_{\phi^{\mu}}\), and \(\varepsilon_{\tau}\) represent the RMSE for azimuth AoD, elevation AoD, azimuth AoA, elevation AoA, and ToA, respectively. The RMSE was determined from 100 runs of each method, considering the average across all paths. The adaptive method exhibits higher precision compared to the non-adaptive method for all analyzed parameters. ## 6 Conclusions

In this work, we addressed the problem of low performance presented by traditional DCS-SOMP approaches, which present convergence and precision to estimate parameters only at the cost of low performance. To achieve this, we proposed an adaptive DCS-SOMP method that dynamically calculates the sensing matrix, presenting high performance in precisely estimating localization parameters while keeping the algorithm simple and with fast convergence. This modification transformed the DCS-SOMP method from solely a coarse estimator to a singular tool for precise parameter estimation. Even in a 3D environment with five parameters to be estimated and multiple paths to be detected, the adaptive DCS-SOMP method exhibited substantial improvements in both accuracy and speed compared to the DCS-SOMP approach. Further enhancements to the adaptive DCS-SOMP could be explored, such as refining the way the residue was updated, potentially enabling improved separation of paths. Furthermore, we plan to explore alternative antenna arrays, including 2D configurations, to enhance beam-forming capabilities in mmWave scenarios within 5G and B5G networks. All authors (P.F.d.C. and F.G.C.R.) contributed equally to this article. All authors have read and agreed to the published version of the manuscript. This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data is contained within the article. **Acknowledgments:** We would like to thank the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) for the financial support provided for the publication of this article. Author \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & \(\varepsilon_{\phi^{\mu}}\) **(rad)** & \(\varepsilon_{\phi^{\mu}}\) **(rad)** & \(\varepsilon_{\phi^{\mu}}\) **(rad)** & \(\varepsilon_{\phi^{\mu}}\) **(rad)** & \(\varepsilon_{\tau}\) **(us)** \\ \hline DCS-SOMP & 0.1334 & 0.0454 & 0.1087 & 0.2851 & 0.0109 \\ Adaptive DCS-SOMP & 0.0017 & 0.0005 & 0.0089 & 0.0256 & 0.0001 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of RMSE between DCS-SOMP and adaptive DCS-SOMP. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Time (s)** & **Number of Mathematical Operations** \\ \hline DCS-SOMP & 84.63 & \(4.0393\times 10^{9}\) \\ Adaptive DCS-SOMP & 0.88 & \(1.4697\times 10^{9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison between DCS-SOMP and Adaptive DCS-SOMP. [PERSON] would like to express gratitude to the Instituto Federal de Goias (IFG) for providing support during his doctoral studies, which significantly contributed to the completion of this work. ## References

* [PERSON] (1986) [PERSON] Multiple Emitter Location and Signal Parameter Estimation. _IEEE Trans. Antennas Propag._**1986**, 34, 276-280. [CrossRef]
* [PERSON] (2006) [PERSON] Compressed Sensing. _IEEE Trans. Inf.