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Blind Construction of Angular Power Maps in Massive MIMO Networks

Zheng Xing, Junting Chen

TL;DR

This work tackles unsupervised angular power map construction in massive MIMO by linking mobile trajectories to CSI evolution through a hidden Markov model, enabling trajectory recovery without location labels. It develops a joint Bayesian framework with propagation, pattern, and mobility models, and solves the resulting P1–P3 subproblems using separable regression, log-transformations, and a discretized Viterbi-based trajectory optimization. Theoretical results establish CRLB-type limits showing zero localization error is possible in unlimited regions with sufficient coverage, while limited regions impose a nonzero bound, guiding design. Empirical validation on synthetic and real 5G data demonstrates mean localization errors below 18 meters and effective beam-prediction capabilities, highlighting the practical impact for radio-map-assisted beam management and resource allocation.

Abstract

Channel state information (CSI) acquisition is a challenging problem in massive multiple-input multiple-output (MIMO) networks. Radio maps provide a promising solution for radio resource management by reducing online CSI acquisition. However, conventional approaches for radio map construction require location-labeled CSI data, which is challenging in practice. This paper investigates unsupervised angular power map construction based on large timescale CSI data collected in a massive MIMO network without location labels. A hidden Markov model (HMM) is built to connect the hidden trajectory of a mobile with the CSI evolution of a massive MIMO channel. As a result, the mobile location can be estimated, enabling the construction of an angular power map. We show that under uniform rectilinear mobility with Poisson-distributed base stations (BSs), the Cramer-Rao Lower Bound (CRLB) for localization error can vanish at any signal-to-noise ratios (SNRs), whereas when BSs are confined to a limited region, the error remains nonzero even with infinite independent measurements. Based on reference signal received power (RSRP) data collected in a real multi-cell massive MIMO network, an average localization error of 18 meters can be achieved although measurements are mainly obtained from a single serving cell.

Blind Construction of Angular Power Maps in Massive MIMO Networks

TL;DR

This work tackles unsupervised angular power map construction in massive MIMO by linking mobile trajectories to CSI evolution through a hidden Markov model, enabling trajectory recovery without location labels. It develops a joint Bayesian framework with propagation, pattern, and mobility models, and solves the resulting P1–P3 subproblems using separable regression, log-transformations, and a discretized Viterbi-based trajectory optimization. Theoretical results establish CRLB-type limits showing zero localization error is possible in unlimited regions with sufficient coverage, while limited regions impose a nonzero bound, guiding design. Empirical validation on synthetic and real 5G data demonstrates mean localization errors below 18 meters and effective beam-prediction capabilities, highlighting the practical impact for radio-map-assisted beam management and resource allocation.

Abstract

Channel state information (CSI) acquisition is a challenging problem in massive multiple-input multiple-output (MIMO) networks. Radio maps provide a promising solution for radio resource management by reducing online CSI acquisition. However, conventional approaches for radio map construction require location-labeled CSI data, which is challenging in practice. This paper investigates unsupervised angular power map construction based on large timescale CSI data collected in a massive MIMO network without location labels. A hidden Markov model (HMM) is built to connect the hidden trajectory of a mobile with the CSI evolution of a massive MIMO channel. As a result, the mobile location can be estimated, enabling the construction of an angular power map. We show that under uniform rectilinear mobility with Poisson-distributed base stations (BSs), the Cramer-Rao Lower Bound (CRLB) for localization error can vanish at any signal-to-noise ratios (SNRs), whereas when BSs are confined to a limited region, the error remains nonzero even with infinite independent measurements. Based on reference signal received power (RSRP) data collected in a real multi-cell massive MIMO network, an average localization error of 18 meters can be achieved although measurements are mainly obtained from a single serving cell.

Paper Structure

This paper contains 35 sections, 11 theorems, 81 equations, 8 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System model
  3. Propagation and Measurement Models
  4. Path Loss Model
  5. Pattern Model
  6. Measurement Model
  7. Mobility Model
  8. An Formulation
  9. Fundamental Limits
  10. The Fisher Information Matrix
  11. Deployed in a Limited Region
  12. Deployed in an Unlimited Region
  13. Algorithm Design
  14. Solution to (P1) for the Mobility Model
  15. Solution to (P2) via Separable Regression with Log-transformation
  16. ...and 20 more sections

Key Result

Theorem 1

The of $\mathbf{x}$ satisfies $B(\mathbf{x})=\mathrm{tr}\{\mathbf{F}_{T,x}^{-1}\}\geq\bar{\Delta}_{T,x}$, where equality can be achieved when $\sigma_{\mathrm{\min}}^{2}=\sigma_{q}^{2}$ and $\alpha_{\mathrm{max}}^{2}=\alpha_{q}^{2}$ for all $q$. In addition, $\bar{\Delta}_{T,x}$ is strictly decreasi

Figures (8)

  • Figure 1: The mobile user moves along roads in a environment. For each beam, multipath components predominantly arrive from the direction of the mobile user, while paths from other angles exhibit significantly lower probabilities.
  • Figure 2: The data collection environment of (a) synthetic dataset and (b) real dataset. The signal from (gray points) is measured along the trajectory (distinct line styles and colors, begin with triangles).
  • Figure 3: of (a) $\mathbf{x}$ and (b)$\mathbf{v}$ with different sample number $T$, the number of $Q$, radius $R$, and density $\kappa$.
  • Figure 4: (a) The relationship between MSE($\mathbf{x}$) and the number of . (b) MSE($\mathbf{x}$) under different noise $\sigma_{q}$.
  • Figure 5: (a) The seven scaled patterns of the $q$th in synthetic dataset with measurements (black points) belonging to beam 1. (b) The eight scaled patterns of the $q$th in real dataset with measurements (black points) belonging to beam 4.
  • ...and 3 more figures

Theorems & Definitions (21)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Proposition 1: Separability
  • proof
  • ...and 11 more