## 4 Machine-Learning-Aided Positioning in 5G Networks
### Advances in Positioning Aided by Machine Learning
In the single BFF positioning, the average error ranges from 4.57 m to 6.17 m in the case of the CNN and from 3.31 m to 5.13 m in the case of the hierarchical CNN with \(K=64\) partitions, subject to the noise level. The average errors in the BFF tracking are reduced thanks to the increased number of datapoints. At lower sequence numbers, the TCN outperformed the LSTM (2.3 m vs. 3 m), but in the case of longer sequences, the gap shrank while the TCN remained reasonable. In low-noise scenarios, the TCN achieved an average error of 1.78 m.  
[PERSON] et al. [58] proposed a fingerprint-based single-site localization method for massive Multiple-Input Multiple-Output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems using both the AOA and PDP parameters as fingerprint. In massive MIMO-OFDM systems, fingerprint extraction and matching has high computational complexity due to the high multipath resolution in the angle and delay domains; therefore, they proposed an efficient fingerprint extraction method with a corresponding similarity function and a fingerprint clustering algorithm with a new location estimation method. The fingerprints are extracted from the channel estimation results through Fast Fourier Transform (FFT) and named as the Angle Delay Channel Power Matrix (ADCPM). The authors argue that the ADCPM contains rich multipath information with clear physical interpretation, such as the channel power associated with the specific AOA and TOA. To exploit the information in fingerprints, they proposed a new similarity criterion for fingerprints, the Joint Angle Delay Similarity Coefficient (JADSC), which is used to calculate the distance between two fingerprints. For fingerprint compression, they developed a two-step fingerprint clustering algorithm for database preprocessing, which uses the spatial characteristics of fingerprints to significantly reduce matching operations. Finally, they used the Weighted K-Nearest Neighbor (WKNN) method for accurate location estimation. Their simulation results show that their fingerprint-based method is able to outperform DiSouL and TF-MUSIC in an outdoor scenario. With multiple BSs, their method achieves 90% reliability at 2 m accuracy and with one BS it provides 95% reliability at 3 m accuracy. [PERSON] et al. [59] proposed a Deep Convolutional Gaussian Process (DCGP) based regression for fingerprinting-based mmWave positioning in an outdoor environment. For the simulations, the authors used an open-source mmWave dataset, which contains beamforming images from 160,801 bidimensional positions [50]. According to their results, the 95 th percentile error for a CNN model is 14.289 m and for the DCGP model it is 7.018 m; however, on their hardware, the training time for the DCGP took longer (533 min) than for the CNN model (376 min). They also evaluated the impact of the number of epochs on the mean distance error. In their experiments, the highest number of epochs was 550, and in this case the mean distance error is 4.46 m for the CNN and 2.79 m for the DCGP. [PERSON] et al. [27] evaluated the performance of thirteen ML algorithms employed in conjunction with fingerprint-based MT localization for distributed massive MIMO wireless systems configurations. The fingerprints used RSRP measurements of one BS solely with an \(8\times 8\) antenna array from a simulated outdoor environment. The authors investigated the effect of the number of antennas, the inter-element separation distance, the frequency, and the weather. In each case, the kNN achieved the lowest MAE (Mean Absolute Error), followed by the random forest and gradient boosting. In most cases, the SVM and NN achieved the highest MAE. The lowest MAE of the kNN was 3.3 m in the best-case scenario. The frequency and the weather had no significant effect on the error, while the increased number of antennas and the increased inter-element separation distance decreased the average error. [PERSON] et al.