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Complex-Valued Neural Network based Federated Learning for Multi-user Indoor Positioning Performance Optimization

Hanzhi Yu, Yuchen Liu, Mingzhe Chen

TL;DR

This work addresses indoor positioning from complex-valued CSI by introducing a CVNN-based federated learning framework that jointly enables accurate position estimation and CSI feature extraction without sharing raw data. The CVNN processes complex CSI directly, uses a two-task output (position or LOS/TOA features), and employs a novel real/imaginary-part selective aggregation to reduce communication. Theoretical convergence is established under standard FL assumptions, and extensive simulations on 5G and ultra-dense CSI datasets show up to 36% improvement in mean positioning error over real-valued baselines, along with notable gains in TOA and LOS/NLOS tasks. The approach demonstrates improved privacy, reduced data transformation loss, and practical viability for multi-user indoor positioning in dense deployments.

Abstract

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.

Complex-Valued Neural Network based Federated Learning for Multi-user Indoor Positioning Performance Optimization

TL;DR

This work addresses indoor positioning from complex-valued CSI by introducing a CVNN-based federated learning framework that jointly enables accurate position estimation and CSI feature extraction without sharing raw data. The CVNN processes complex CSI directly, uses a two-task output (position or LOS/TOA features), and employs a novel real/imaginary-part selective aggregation to reduce communication. Theoretical convergence is established under standard FL assumptions, and extensive simulations on 5G and ultra-dense CSI datasets show up to 36% improvement in mean positioning error over real-valued baselines, along with notable gains in TOA and LOS/NLOS tasks. The approach demonstrates improved privacy, reduced data transformation loss, and practical viability for multi-user indoor positioning in dense deployments.

Abstract

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.
Paper Structure (22 sections, 31 equations, 10 figures, 2 tables, 1 algorithm)

This paper contains 22 sections, 31 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. CSI Data Collection
  4. Problem Formulation
  5. Proposed Complex-valued Neural Network Based FL
  6. Components of the Local FL Model
  7. Training Procedure of Federated Learning Algorithm
  8. Loss Function for Use Case I
  9. Loss Function for Use Case II
  10. Training Process
  11. Convergence Analysis
  12. Convergence Analysis of the Designed CVNN based FL
  13. Implementation and Complexity
  14. Simulation Results
  15. Dataset Introduction
  16. ...and 7 more sections

Figures (10)

  • Figure 1: The considered indoor positioning system.
  • Figure 2: The CVNN model structure of use case I and use case II.
  • Figure 3: The training loss changes as the number of training iterations varies for use case I of the 5G CSI dataset.
  • Figure 4: CDF of positioning MSE for use case I of the 5G CSI dataset.
  • Figure 5: The training loss changes as the number of training iterations varies for use case I of the 5G CSI dataset.
  • ...and 5 more figures

Theorems & Definitions (2)

  • proof
  • proof