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Oversampled Low Ambiguity Zone Sequences for Channel Estimation over Doubly Selective Channels

Zhi Gu, Zhengchun Zhou, Pingzhi Fan, Avik Ranjan Adhikary, Zilong Liu

TL;DR

This work tackles OFDM pilot design for doubly selective channels by introducing oversampled ambiguity concepts to account for fractional Doppler shifts. It defines O-LAZ sequences as pilots with low sidelobes in the region spanning delays and fractional Doppler, and develops the OA-ITROX algorithm to construct unimodular O-LAZ sequences by minimizing the ISL of the oversampled ambiguity function. The proposed approach yields performance gains in channel estimation and BER compared to traditional ZC, m-sequences, and LAZ designs, approaching CLRB limits in DSC scenarios. The results demonstrate practical benefits for high-mobility communications without modifying OFDM frame structure, with implications for LTE/NR-style systems in DSC settings.

Abstract

Pilot sequence design over doubly selective channels (DSC) is challenging due to the variations in both the time- and frequency-domains. Against this background, the contribution of this paper is twofold: Firstly, we investigate the optimal sequence design criteria for efficient channel estimation in orthogonal frequency division multiplexing systems under DSC. Secondly, to design pilot sequences that can satisfy the derived criteria, we propose a new metric called oversampled ambiguity function (O-AF), which considers both fractional and integer Doppler frequency shifts. Optimizing the sidelobes of O-AF through a modified iterative twisted approximation (ITROX) algorithm, we develop a new class of pilot sequences called ``oversampled low ambiguity zone (O-LAZ) sequences". Through numerical experiments, we evaluate the efficiency of the proposed O-LAZ sequences over the traditional low ambiguity zone (LAZ) sequences, Zadoff-Chu (ZC) sequences and m-sequences, by comparing their channel estimation performances over DSC.

Oversampled Low Ambiguity Zone Sequences for Channel Estimation over Doubly Selective Channels

TL;DR

This work tackles OFDM pilot design for doubly selective channels by introducing oversampled ambiguity concepts to account for fractional Doppler shifts. It defines O-LAZ sequences as pilots with low sidelobes in the region spanning delays and fractional Doppler, and develops the OA-ITROX algorithm to construct unimodular O-LAZ sequences by minimizing the ISL of the oversampled ambiguity function. The proposed approach yields performance gains in channel estimation and BER compared to traditional ZC, m-sequences, and LAZ designs, approaching CLRB limits in DSC scenarios. The results demonstrate practical benefits for high-mobility communications without modifying OFDM frame structure, with implications for LTE/NR-style systems in DSC settings.

Abstract

Pilot sequence design over doubly selective channels (DSC) is challenging due to the variations in both the time- and frequency-domains. Against this background, the contribution of this paper is twofold: Firstly, we investigate the optimal sequence design criteria for efficient channel estimation in orthogonal frequency division multiplexing systems under DSC. Secondly, to design pilot sequences that can satisfy the derived criteria, we propose a new metric called oversampled ambiguity function (O-AF), which considers both fractional and integer Doppler frequency shifts. Optimizing the sidelobes of O-AF through a modified iterative twisted approximation (ITROX) algorithm, we develop a new class of pilot sequences called ``oversampled low ambiguity zone (O-LAZ) sequences". Through numerical experiments, we evaluate the efficiency of the proposed O-LAZ sequences over the traditional low ambiguity zone (LAZ) sequences, Zadoff-Chu (ZC) sequences and m-sequences, by comparing their channel estimation performances over DSC.
Paper Structure (14 sections, 4 theorems, 81 equations, 8 figures, 2 tables)

This paper contains 14 sections, 4 theorems, 81 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Zero/Low Correlation/Ambiguity Zone Sequence
  4. System Model of OFDM and Channel Estimation
  5. Optimal Pilot Design Criterion for DSC
  6. Optimal Pilot Design Criterion
  7. O-LAZ Sequence: Properties and Construction
  8. Oversampled Ambiguity Function (O-AF)
  9. O-LAZ Sequence Design Based on ITROX
  10. Numerical Experiments
  11. Performance Analysis of OA-ITROX Algorithm
  12. Performance Comparison with Traditional AF
  13. Simulation Results
  14. Conclusion

Key Result

Lemma 1

Let $h[l,n]$ be the true channel response at the $n$-th instant and the $l$-th path corresponding to an OFDM symbol, and $\mathbf{h}_n$ contains the channel response of all the $L$ multipaths at $n$-th instant, i.e., $\mathbf{h}_n=[h[0,n],h[1,n],\ldots,h[L-1,n]]^\mathrm{T}$. The average channel resp where $\mathbf{h}_\mathrm{avg}=1/N\sum_{n=0}^{N-1}\mathbf{h}_n$. Furthermore, the channel estimatio

Figures (8)

  • Figure 1: The transmission frame structure.
  • Figure 2: The planform figure of the O-AF of the o-LAZ sequence generated by OA-ITROX algorithm.
  • Figure 3: Semi-log plot of the ISL with respect to the iteration index.
  • Figure 4: The planform figure of the traditional AF of the sequences.
  • Figure 5: Semi-log plot of the ISL with respect to the iteration index.
  • ...and 3 more figures

Theorems & Definitions (17)

  • Remark 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 1: mostofi2005ici
  • Definition 4
  • Remark 2
  • Remark 3
  • Definition 5
  • Definition 6
  • ...and 7 more