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Gaussian Mixture Model Based Bayesian Learning for Sparse Channel Estimation in Orthogonal Time Frequency Space Modulated Systems

Surbhi Gehlot, Suraj Srivastava, Sandeep Kumar Yadav, Lajos Hanzo

Abstract

A novel Gaussian mixture model (GMM) aided sparse Bayesian learning (SBL) framework is proposed for channel state information (CSI) estimation in orthogonal time-frequency space (OTFS) modulated systems. The key attribute of the proposed algorithm lies in casting CSI recovery as an SBL inference problem, where posterior distributions are iteratively refined under a hierarchical GMM prior. Using this approach, the sparsity-inducing variances beneficially promote sparsity in the delay Doppler (DD) domain, while additionally augmenting the capability of SBL to exploit channel statistics more effectively. Moreover, to fully exploit the GMMs ability to approximate arbitrary probability density functions and model complex multipath fading scenarios, the channel statistics are represented using a complex Gaussian mixture. Simultaneously, the method leverages time-domain (TD) pilots without requiring wasteful DD domain guard intervals, thereby ensuring low pilot overhead and high spectral efficiency. The CSI recovered is subsequently applied in a linear minimum mean square error (MMSE) detector for reliable data detection. To benchmark performance, the Oracle-MMSE and the Bayesian Cramèr Rao lower bound (BCRLB) are also derived. Our simulation results demonstrate significant performance improvement over the state of the art sparse estimation methods.

Gaussian Mixture Model Based Bayesian Learning for Sparse Channel Estimation in Orthogonal Time Frequency Space Modulated Systems

Abstract

A novel Gaussian mixture model (GMM) aided sparse Bayesian learning (SBL) framework is proposed for channel state information (CSI) estimation in orthogonal time-frequency space (OTFS) modulated systems. The key attribute of the proposed algorithm lies in casting CSI recovery as an SBL inference problem, where posterior distributions are iteratively refined under a hierarchical GMM prior. Using this approach, the sparsity-inducing variances beneficially promote sparsity in the delay Doppler (DD) domain, while additionally augmenting the capability of SBL to exploit channel statistics more effectively. Moreover, to fully exploit the GMMs ability to approximate arbitrary probability density functions and model complex multipath fading scenarios, the channel statistics are represented using a complex Gaussian mixture. Simultaneously, the method leverages time-domain (TD) pilots without requiring wasteful DD domain guard intervals, thereby ensuring low pilot overhead and high spectral efficiency. The CSI recovered is subsequently applied in a linear minimum mean square error (MMSE) detector for reliable data detection. To benchmark performance, the Oracle-MMSE and the Bayesian Cramèr Rao lower bound (BCRLB) are also derived. Our simulation results demonstrate significant performance improvement over the state of the art sparse estimation methods.

Paper Structure

This paper contains 20 sections, 2 theorems, 64 equations, 5 figures, 5 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Literature Review
  3. Contributions of the Paper
  4. OTFS System Description
  5. OTFS Modulation
  6. Clustered DD domain Channel Model
  7. OTFS Demodulation
  8. GMM-SBL Based Sparse CSI Estimation for OTFS Systems
  9. Performance Benchmarks
  10. Results and Discussion
  11. Simulation Parameters
  12. Performance Comparison
  13. Parameter Sensitivity Analysis
  14. Impact of Mixture Order Selection
  15. Effect of Mixture Configurations
  16. ...and 5 more sections

Key Result

Theorem 1

Let the latent variable $z \in \{1, \ldots, K\}$ indicate the mixture component with probability $\Pr(z{=}k) = \rho_k$. Consider the hierarchical prior where $\boldsymbol{\Gamma}_k = \mathrm{diag}(\boldsymbol{\gamma}_k)$ with $\boldsymbol{\gamma}_k > 0$. Then there exists a constant $C > 0$ so that Proof: Given in Appendix appendix a.

Figures (5)

  • Figure 1: Schematic diagram of GMM-SBL scheme for CP-aided OTFS transceiver.
  • Figure 2: Performance comparison of proposed GMM-SBL algorithm with benchmarks and existing state-of-the-art methods.
  • Figure 3: Analysis of proposed GMM-SBL algorithm with different parameters.
  • Figure 4: Impact of DD grid resolution on GMM-SBL channel estimation performance.
  • Figure 5: Analysis of the proposed GMM-SBL algorithm with clustered channel.

Theorems & Definitions (2)

  • Theorem 1: Sparsity of the GMM-SBL Prior
  • Theorem 2: EM updates for GMM--SBL