  In this article, the use of channel state information (CSI) for indoor
positioning is studied. In the considered model, a server equipped with several
antennas sends pilot signals to users, while each user uses the received pilot
signals to estimate channel states for user positioning. To this end, we
formulate the positioning problem as an optimization problem aiming to minimize
the gap between the estimated positions and the ground truth positions of
users. To solve this problem, we design a complex-valued neural network (CVNN)
model based federated learning (FL) algorithm. Compared to standard real-valued
centralized machine learning (ML) methods, our proposed algorithm has two main
advantages. First, our proposed algorithm can directly process complex-valued
CSI data without data transformation. Second, our proposed algorithm is a
distributed ML method that does not require users to send their CSI data to the
server. Since the output of our proposed algorithm is complex-valued which
consists of the real and imaginary parts, we study the use of the CVNN to
implement two learning tasks. First, the proposed algorithm directly outputs
the estimated positions of a user. Here, the real and imaginary parts of an
output neuron represent the 2D coordinates of the user. Second, the proposed
method can output 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 FL can reduce the mean positioning
error between the estimated position and the actual position by up to 36%,
compared to a RVNN based FL which requires to transform CSI data into
real-valued data.
