Complex Neural Networks for Indoor Positioning with Complex-Valued Channel State Information

In this paper, the use of channel state information (CSI) for indoor positioning is investigated. In the considered model, a base station (BS) equipped with several antennas sends pilot signals to a user that transmits the received pilot signals back to the BS. The BS will use the received CSI data to estimate the position of the user. To this end, we formulate this positioning problem as an optimization problem aiming to minimize the mean square error between the estimated position and the actual position of the user. To solve this problem, we design a complex-valued neural network (CVNN) based positioning algorithm. Compared to real-valued neural networks (RVNNs) that need to convert complex-valued CSI data into real-valued data, the proposed method uses original CSI data to train the CVNN model for user positioning. Since the output of our proposed algorithm is complex-valued and it consists of the real and imaginary parts, we can use it to implement two learning tasks. Based on this property, two use cases of the proposed algorithm are proposed: 1) the algorithm directly outputs the estimated position of the user. Here, the real and imaginary parts of an output neuron represent the 2D coordinates of the user, 2) the algorithm outputs two CSI features (i.e., line-of-sight/non-line-of-sight transmission link classification and time of arrival (TOA) prediction) which can be used in traditional positioning algorithms. Simulation results demonstrate that our designed CVNN based algorithm can reduce the mean positioning error between the estimated position and the actual position by up to 11.1%, compared to a RVNN based method which has to transform CSI data into real-valued data.