# Adaptive DCS-SOMP for Localization Parameter Estimation in 5G Networks
## 2 Related Works  
Localization algorithms typically consist of two fundamental steps. First, the estimation of localization parameters extracted from the received signal. Second, using the acquired parameters from the first step, a localization method is employed to determine the position of the mobile station (MS) [5; 8; 9]. Regarding the first step, we highlight several aspects of the literature.  
In [10], the authors estimate AoA and AoD using Sparse Bayes Tensor (SBT) from channel modeling using MIMO and mmWave. However, due to the use of a linear array of antennas, the proposed approach can only determine the azimuth of AoA and AoD and does not enable ToA estimation. In [8], the authors conduct indoor localization using channel modeling and ray tracing. They use two Uniform Linear Arrays (ULA), one perpendicular to the other, to extract the elevation angle. However, the method does not estimate AoD, thus preventing the use of algorithms dependent on this parameter.  
In [5], the authors propose a comprehensive localization algorithm using MIMO, mmWave, and ULA. They employ the DCS-SOMP method for parameter estimation. Due to the linear antenna array, the method applies to a 2D environment. Additionally, the DCS-SOMP method provides only a coarse parameter estimate, demanding further fine-tuning using the SAGE method. In [11], the authors propose a 2D-AoA and 2D-AoD estimation using the MUSIC algorithm. The method utilizes a channel model with a rectangular Uniform Rectangular Array (URA). However, their proposal does not estimate ToA and only allows coarse angle estimation. Similarly to [5], the proposal in [11] requires fine-tuning techniques to provide accurate parameter estimations. In [12], the authors propose a technique named spatial spectrum fusion estimation and localization (SSFEAL) for performing 2D-AoA estimation using UCA in a MIMO mmWave channel.  
In this work, we go beyond the related studies by proposing a joint estimation method of ToA, 2D-AoD, and 2D-AoA, enabling the use of these parameters in 3D localization algorithms in multipath environments. Furthermore, our proposed method accurately estimates the parameters without additional fine-tuning techniques. We employ a MIMO mmWave channel model with UCA to determine 2D-AoD and 2D-AoA, consistent with the works in [12; 13]. Table 1 compares our proposal with others discussed in this section.  
Table 1 demonstrates aspects of some related works and our proposal. Column 2 indicates the method used for parameter estimation. Column 3 displays the antenna array, while columns 4 to 6 specify whether the method estimates ToA, 2D-AoD, and 2D-AoA parameters, respectively. Our proposal presents the advantage of estimating all considered localization parameters (ToA, 2D-AoD, and 2D-AoA), while other methods estimate only some of them, or consider only two-dimensional (2D) environments. Additionally, our proposal utilizes the DCS-SOMP itself to achieve high accuracy, while other methods rely on extra algorithms for a refinement step. Although estimating five parameters increases the number of elements in the sensing matrix, our adaptive approach reduces execution time and yields more accurate results.