Model-Based Learning Network for 3-D Localization in mmWave Communications

Millimeter-wave (mmWave) cloud radio access networks (CRANs) provide new opportunities for accurate cooperative localization, in which large bandwidths and antenna arrays and increased densities of base stations enhance the delay and angular resolution. This study considers the joint location and velocity estimation of user equipment (UE) and scatterers in a three-dimensional mmWave CRAN architecture. Several existing works have achieved satisfactory results by using neural networks (NNs) for localization. However, the black box NN localization method has limited robustness and accuracy and relies on a prohibitive amount of training data to increase localization accuracy. Thus, we propose a model-based learning network for localization to address these problems. In comparison with the black box NN, we combine NNs with geometric models. Specifically, we first develop an unbiased weighted least squares (WLS) estimator by utilizing hybrid delay and angular measurements, which determine the location and velocity of the UE in only one estimator, and can obtain the location and velocity of scatterers further. The proposed estimator can achieve the Cramer-Rao lower bound under small measurement noise and outperforms other state-of-the-art methods. Second, we establish a NN-assisted localization method called NN-WLS by replacing the linear approximations in the proposed WLS localization model with NNs to learn the higher-order error components, thereby enhancing the performance of the estimator, especially in a large noise environment. The solution possesses the powerful learning ability of the NN and the robustness of the proposed geometric model. Moreover, the ensemble learning is applied to improve the localization accuracy further. Comprehensive simulations show that the proposed NN-WLS is superior to the benchmark methods in terms of localization accuracy, robustness, and required time resources.