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Trainable Least Squares to Reduce PAPR in OFDM-based Hybrid Beamforming Systems

Andrey Ivanov, Alexander Osinsky, Roman Bychkov, Vladimir Kalinin, Dmitry Lakontsev

TL;DR

The paper tackles PAPR reduction for OFDM signals in fully-connected hybrid beamforming systems where both bandwidth and digital subspace are constrained. It introduces a two-step, trainable LS-based framework that first constructs band-limited PAPR-reduction signals per antenna via sparse STR, then fits these signals within a limited subspace using trainable LS (LS1/LS2) with GA training. A CVX-based convex bound benchmarks the approach, showing the proposed method achieves about 0.5 dB higher PAPR than the bound at CCDF = 10^{-4}, with 2 iterations delivering near-optimal performance and low complexity. The work demonstrates feasibility for future generation systems, offering a practical path to PAPR control in HBF with manageable computation and tunable trade-offs between reduction strength and noise in non-peak samples.

Abstract

In this paper, we propose a trainable least squares (LS) approach for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals in a hybrid beamforming (HBF) system. Compared to digital beamforming (DBF), in HBF technology the number of antennas exceeds the number of digital ports. Therefore, PAPR reduction capabilities are restricted by both a limited bandwidth and the reduced size of digital space. The problem is to meet both conditions. Moreover, the major HBF advantage is a reduced system complexity, thus the complexity of the PAPR reduction algorithm is expected to be low. To justify the performance of the proposed trainable LS, we provide a performance bound achieved by convex optimization using the CVX Matlab package. Moreover, the complexity of the proposed algorithm can be comparable to the minimal complexity of the digital ``twin'' calculation in HBF. The abovementioned features prove the feasibility of the trained LS for PAPR reduction in fully-connected HBF.

Trainable Least Squares to Reduce PAPR in OFDM-based Hybrid Beamforming Systems

TL;DR

The paper tackles PAPR reduction for OFDM signals in fully-connected hybrid beamforming systems where both bandwidth and digital subspace are constrained. It introduces a two-step, trainable LS-based framework that first constructs band-limited PAPR-reduction signals per antenna via sparse STR, then fits these signals within a limited subspace using trainable LS (LS1/LS2) with GA training. A CVX-based convex bound benchmarks the approach, showing the proposed method achieves about 0.5 dB higher PAPR than the bound at CCDF = 10^{-4}, with 2 iterations delivering near-optimal performance and low complexity. The work demonstrates feasibility for future generation systems, offering a practical path to PAPR control in HBF with manageable computation and tunable trade-offs between reduction strength and noise in non-peak samples.

Abstract

In this paper, we propose a trainable least squares (LS) approach for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals in a hybrid beamforming (HBF) system. Compared to digital beamforming (DBF), in HBF technology the number of antennas exceeds the number of digital ports. Therefore, PAPR reduction capabilities are restricted by both a limited bandwidth and the reduced size of digital space. The problem is to meet both conditions. Moreover, the major HBF advantage is a reduced system complexity, thus the complexity of the PAPR reduction algorithm is expected to be low. To justify the performance of the proposed trainable LS, we provide a performance bound achieved by convex optimization using the CVX Matlab package. Moreover, the complexity of the proposed algorithm can be comparable to the minimal complexity of the digital ``twin'' calculation in HBF. The abovementioned features prove the feasibility of the trained LS for PAPR reduction in fully-connected HBF.
Paper Structure (16 sections, 23 equations, 4 figures, 1 table, 2 algorithms)

This paper contains 16 sections, 23 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. PAPR reduction methods
  3. Our contribution
  4. Single antenna -- tone reservation
  5. Sparse STR
  6. Divide-and-conquer
  7. Multiple antennas - Hybrid beamforming
  8. Trainable LS
  9. LS1
  10. LS2
  11. Performance bound
  12. Step-by-step algorithm and its parameters
  13. Computational complexity
  14. Simulation results
  15. Conclusion
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Fully-connected HBF.
  • Figure 2: PAPR reduction signal in the antenna domain. Generated using Scaling 1 and Scaling 2 ($\rm{coef}=1$ for both) and compared to the required one.
  • Figure 3: CCDF for algorithms and bounds.
  • Figure 4: Spectrum for the TX signal and PAPR reduction signals (realistic and unlimited band bound).