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Physically constrained unfolded multi-dimensional OMP for large MIMO systems

Nay Klaimi, Clément Elvira, Philippe Mary, Luc Le Magoarou

TL;DR

The paper tackles joint channel estimation and localization in high-dimensional mmWave MIMO under hardware impairments. It proposes MOMPnet, a model-based deep-unfolding framework that leverages three Kronecker-structured dictionaries and a multidimensional OMP to achieve low computational complexity while learning impairment parameters in an unsupervised, online manner. Key contributions include the design of Sparse Channel Representations with nominal and learned dictionaries, the MOMP algorithm for efficient atom search, and a neural-network realization that preserves physical interpretability. Experiments on realistic channel data demonstrate NMSE improvements and accurate recovery of physical parameters, with learned dictionaries closely matching true system properties and outperforming the MOD approach.

Abstract

Sparse recovery methods are essential for channel estimation and localization in modern communication systems, but their reliability relies on accurate physical models, which are rarely perfectly known. Their computational complexity also grows rapidly with the dictionary dimensions in large MIMO systems. In this paper, we propose MOMPnet, a novel unfolded sparse recovery framework that addresses both the reliability and complexity challenges of traditional methods. By integrating deep unfolding with data-driven dictionary learning, MOMPnet mitigates hardware impairments while preserving interpretability. Instead of a single large dictionary, multiple smaller, independent dictionaries are employed, enabling a low-complexity multidimensional Orthogonal Matching Pursuit algorithm. The proposed unfolded network is evaluated on realistic channel data against multiple baselines, demonstrating its strong performance and potential.

Physically constrained unfolded multi-dimensional OMP for large MIMO systems

TL;DR

The paper tackles joint channel estimation and localization in high-dimensional mmWave MIMO under hardware impairments. It proposes MOMPnet, a model-based deep-unfolding framework that leverages three Kronecker-structured dictionaries and a multidimensional OMP to achieve low computational complexity while learning impairment parameters in an unsupervised, online manner. Key contributions include the design of Sparse Channel Representations with nominal and learned dictionaries, the MOMP algorithm for efficient atom search, and a neural-network realization that preserves physical interpretability. Experiments on realistic channel data demonstrate NMSE improvements and accurate recovery of physical parameters, with learned dictionaries closely matching true system properties and outperforming the MOD approach.

Abstract

Sparse recovery methods are essential for channel estimation and localization in modern communication systems, but their reliability relies on accurate physical models, which are rarely perfectly known. Their computational complexity also grows rapidly with the dictionary dimensions in large MIMO systems. In this paper, we propose MOMPnet, a novel unfolded sparse recovery framework that addresses both the reliability and complexity challenges of traditional methods. By integrating deep unfolding with data-driven dictionary learning, MOMPnet mitigates hardware impairments while preserving interpretability. Instead of a single large dictionary, multiple smaller, independent dictionaries are employed, enabling a low-complexity multidimensional Orthogonal Matching Pursuit algorithm. The proposed unfolded network is evaluated on realistic channel data against multiple baselines, demonstrating its strong performance and potential.
Paper Structure (11 sections, 16 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 11 sections, 16 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System model
  3. Physical channel model
  4. Hardware impairments
  5. Problem formulation
  6. Proposed approach
  7. Sparse Channel Representations
  8. Multidimensional Orthogonal Matching Pursuit MOMP
  9. Deep Unfolding
  10. Experiments
  11. Conclusion

Figures (5)

  • Figure 1: Angle–delay maps: impairment-free scenario (left) and scenario with unaccounted hardware impairments (right).
  • Figure 2: Channel estimation performance on synthetic realistic channels for various SNRs
  • Figure 3: Learned parameters comparison at 5 dB SNR
  • Figure 4: Localization error at 5 dB before vs after training
  • Figure :