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Score-Based Conditional Flow Models for MIMO Receiver Design with Superimposed Pilots

Ruhao Zhang, Yupeng Li, Yitong Liu, Shijian Gao, Jing Jin, Hongwen Yang, Jiangzhou Wang

TL;DR

A conditional flow matching receiver (CFM-Rx), an unsupervised generative framework that learns directly from received signals, eliminating the need for labeled data and improving adaptability across diverse system settings, is proposed.

Abstract

Accurate channel state information (CSI) is vital for multiple-input multiple-output (MIMO) systems. However, superimposed pilots (SIP), which reduce overhead, introduce severe pilot contamination and data interference, complicating joint channel estimation and data detection. This paper proposes a conditional flow matching receiver (CFM-Rx), an unsupervised generative framework that learns directly from received signals, eliminating the need for labeled data and improving adaptability across diverse system settings. By leveraging flow-based generative modeling, CFM-Rx enables deterministic, low-latency inference and exploits model invertibility to capture the bidirectional nature of signal propagation. This framework unifies flow matching with score-based diffusion modeling via a moment-consistent ordinary differential equation (ODE), replacing stochastic differential equation (SDE) sampling with a deterministic and efficient process. Furthermore, it integrates receiver-side priors to ensure stable, data-consistent inference. Extensive simulation results across various MIMO configurations demonstrate that CFM-Rx consistently outperforms conventional estimators and state-of-the-art data-driven receivers, achieving notable gains in channel estimation accuracy and symbol detection robustness, particularly under severe pilot contamination.

Score-Based Conditional Flow Models for MIMO Receiver Design with Superimposed Pilots

TL;DR

A conditional flow matching receiver (CFM-Rx), an unsupervised generative framework that learns directly from received signals, eliminating the need for labeled data and improving adaptability across diverse system settings, is proposed.

Abstract

Accurate channel state information (CSI) is vital for multiple-input multiple-output (MIMO) systems. However, superimposed pilots (SIP), which reduce overhead, introduce severe pilot contamination and data interference, complicating joint channel estimation and data detection. This paper proposes a conditional flow matching receiver (CFM-Rx), an unsupervised generative framework that learns directly from received signals, eliminating the need for labeled data and improving adaptability across diverse system settings. By leveraging flow-based generative modeling, CFM-Rx enables deterministic, low-latency inference and exploits model invertibility to capture the bidirectional nature of signal propagation. This framework unifies flow matching with score-based diffusion modeling via a moment-consistent ordinary differential equation (ODE), replacing stochastic differential equation (SDE) sampling with a deterministic and efficient process. Furthermore, it integrates receiver-side priors to ensure stable, data-consistent inference. Extensive simulation results across various MIMO configurations demonstrate that CFM-Rx consistently outperforms conventional estimators and state-of-the-art data-driven receivers, achieving notable gains in channel estimation accuracy and symbol detection robustness, particularly under severe pilot contamination.
Paper Structure (21 sections, 30 equations, 12 figures, 1 table, 1 algorithm)

This paper contains 21 sections, 30 equations, 12 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Generative Models and OT Path
  4. FM via Interpolation ODE
  5. Optimal Transport for Efficient Flow Sampling
  6. Moment-Based CFM
  7. Moment Dynamics and Flow Derivation
  8. Framework for Conditional Flow Sampling
  9. Sampling via Conditional Flow Matching
  10. Derivation of Velocity Components
  11. Iterative Inference via Predictor–Corrector Sampling
  12. Simulation Results
  13. Simulation Setup
  14. Benchmarks
  15. Channel Estimation and Link-Level Performance
  16. ...and 6 more sections

Figures (12)

  • Figure 1: Conceptual comparison of generative model trajectories.
  • Figure 2: Illustration of the conditional inference procedure with predictor-corrector iterations.
  • Figure 3: The architecture of the conditional U-Net used to approximate the velocity field $v_\theta(H_t, t)$.
  • Figure 4: The performance comparisons of different channel estimation schemes.
  • Figure 5: The BER comparisons among various schemes.
  • ...and 7 more figures