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Optimum Spectrum Extension for PAPR Reduction of DFT-s-OFDM

Renaud-Alexandre Pitaval, Fredrik Berggren, Branislav M. Popovic

TL;DR

This paper considers FDSS-SE with parametrized FDSS windows spanning a range of possible power ripples, as well as arbitrary circular shifts of the subcarrier coefficients, and shows that there exists an optimal SE size for reducing the PAPR and another one for increasing the rate.

Abstract

Uplink coverage in cellular networks is constrained by the maximum UE transmit power, making peak-to-average power ratio (PAPR) reduction essential. While DFT-s-OFDM with frequency-domain spectral shaping (FDSS) achieves significantly lower PAPR than OFDM, especially with pi/2-BPSK, the PAPR remains too high for higher-rate transmission. Spectrum extension (SE) combined with FDSS (FDSS-SE) can further reduce the PAPR for higher-order QAM. This paper considers FDSS-SE with parametrized FDSS windows spanning a range of possible power ripples, as well as arbitrary circular shifts of the subcarrier coefficients. We optimize both the frequency shift and the SE size, and show that there exists an optimal SE size for reducing the PAPR and another one for increasing the rate. Analysis and simulations reveal that both optima largely depend on the window attenuation but are nearly invariant in proportion to the bandwidth. While the PAPR-optimal SE size is nearly invariant to the constellation order of regular QAM, the rate-optimal SE size depends also on the SNR. These insights provide practical guidelines for beyond-5G uplink coverage enhancement, highlighting that SE size should be individually configured according to the user's FDSS window and link quality.

Optimum Spectrum Extension for PAPR Reduction of DFT-s-OFDM

TL;DR

This paper considers FDSS-SE with parametrized FDSS windows spanning a range of possible power ripples, as well as arbitrary circular shifts of the subcarrier coefficients, and shows that there exists an optimal SE size for reducing the PAPR and another one for increasing the rate.

Abstract

Uplink coverage in cellular networks is constrained by the maximum UE transmit power, making peak-to-average power ratio (PAPR) reduction essential. While DFT-s-OFDM with frequency-domain spectral shaping (FDSS) achieves significantly lower PAPR than OFDM, especially with pi/2-BPSK, the PAPR remains too high for higher-rate transmission. Spectrum extension (SE) combined with FDSS (FDSS-SE) can further reduce the PAPR for higher-order QAM. This paper considers FDSS-SE with parametrized FDSS windows spanning a range of possible power ripples, as well as arbitrary circular shifts of the subcarrier coefficients. We optimize both the frequency shift and the SE size, and show that there exists an optimal SE size for reducing the PAPR and another one for increasing the rate. Analysis and simulations reveal that both optima largely depend on the window attenuation but are nearly invariant in proportion to the bandwidth. While the PAPR-optimal SE size is nearly invariant to the constellation order of regular QAM, the rate-optimal SE size depends also on the SNR. These insights provide practical guidelines for beyond-5G uplink coverage enhancement, highlighting that SE size should be individually configured according to the user's FDSS window and link quality.

Paper Structure

This paper contains 37 sections, 2 theorems, 47 equations, 19 figures.

Table of Contents

  1. Introduction
  2. DFT-s-OFDM Transmission
  3. DFT-s-OFDM with FDSS and Spectrum Extension
  4. Pulse Time-Multiplexing Interpretation
  5. FDSS Windows
  6. PAPR: Definition and Relevance
  7. Statistical Mean Power versus Instantaneous Mean Power
  8. Linear Fitting of Power De-rating by PAPR and CM
  9. Non-Monotonic CM Behavior with FDSS
  10. Spectrum Extension Minimizing the PAPR
  11. PAPR Bounds
  12. Best Shifting Value
  13. Optimum SE Size $N_{\rm e}^{({\rm min \, PAPR})}$ for Minimum PAPR
  14. Observations on the Existence of an Optimal SE Size
  15. Intuitive Explanation
  16. ...and 22 more sections

Key Result

Lemma 1

For an SE size $N_{\rm e}$ with shift $L$ and constellation $\mathcal{C}$ with largest amplitude $A_{\mathcal{C}}$, we have with where $p_i[n]$ are the time-domain pulses eq:pm and $\Omega^{\mathcal{C}}$ being the set of phase differences among constellation symbol modulo $\pi$. This is further upper-bounded by the more general bound

Figures (19)

  • Figure 1: Block diagram of DFT-s-OFDM with FDSS-SE.
  • Figure 2: Illustration of spectrum-extended data sequence as a function of the shift parameter $L$ with $N_{\rm data}=10$ symbols and $N_{\rm e}=4$.
  • Figure 3: Two FDSS window types with single shaping parameters characterizing their maximum FDSS power ripple.
  • Figure 4: Inconsistencies among PAPR definitions when considering FDSS and QPSK in narrowband.
  • Figure 5: Inconsistent behavior of CM and PAPR for FDSS-SE with QPSK.
  • ...and 14 more figures

Theorems & Definitions (3)

  • Lemma 1
  • Lemma 2
  • Remark 1