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Non-Orthogonal Time-Frequency Space Modulation

Mahdi Shamsi, Farokh Marvasti

TL;DR

The paper addresses the challenge of maintaining high spectral efficiency and low latency in high-mobility channels by introducing a Time-Frequency Space Transformation (TFST) to derive non-orthogonal bases over the delay-Doppler plane. It develops Non-Orthogonal Time Frequency Space (NOTFS) modulations, including Overloaded Delay-Doppler Modulation (ODDM), which blend OTFS and OFDM benefits without orthogonality constraints. A two-dimensional sphere decoding (2D-SD) algorithm and an inverse-system-based soft decoding approach are proposed to reduce detection complexity and mitigate distortions, with simulations showing strong performance under AWGN and high overloading. The work aims to advance non-orthogonal modulation for next-generation high-mobility systems (e.g., 6G) by achieving superior spectral efficiency and low latency, backed by a practical decoding strategy.

Abstract

This paper proposes a Time-Frequency Space Transformation (TFST) to derive non-orthogonal bases for modulation techniques over the delay-doppler plane. A family of Overloaded Delay-Doppler Modulation (ODDM) techniques is proposed based on the TFST, which enhances flexibility and efficiency by expressing modulated signals as a linear combination of basis signals. A Non-Orthogonal Time-Frequency Space (NOTFS) digital modulation is derived for the proposed ODDM techniques, and simulations show that they offer high-mobility communication systems with improved spectral efficiency and low latency, particularly in challenging scenarios such as high overloading factors and Additive White Gaussian Noise (AWGN) channels. A modified sphere decoding algorithm is also presented to efficiently decode the received signal. The proposed modulation and decoding techniques contribute to the advancement of non-orthogonal approaches in the next-generation of mobile communication systems, delivering superior spectral efficiency and low latency, and offering a promising solution towards the development of efficient high-mobility communication systems.

Non-Orthogonal Time-Frequency Space Modulation

TL;DR

The paper addresses the challenge of maintaining high spectral efficiency and low latency in high-mobility channels by introducing a Time-Frequency Space Transformation (TFST) to derive non-orthogonal bases over the delay-Doppler plane. It develops Non-Orthogonal Time Frequency Space (NOTFS) modulations, including Overloaded Delay-Doppler Modulation (ODDM), which blend OTFS and OFDM benefits without orthogonality constraints. A two-dimensional sphere decoding (2D-SD) algorithm and an inverse-system-based soft decoding approach are proposed to reduce detection complexity and mitigate distortions, with simulations showing strong performance under AWGN and high overloading. The work aims to advance non-orthogonal modulation for next-generation high-mobility systems (e.g., 6G) by achieving superior spectral efficiency and low latency, backed by a practical decoding strategy.

Abstract

This paper proposes a Time-Frequency Space Transformation (TFST) to derive non-orthogonal bases for modulation techniques over the delay-doppler plane. A family of Overloaded Delay-Doppler Modulation (ODDM) techniques is proposed based on the TFST, which enhances flexibility and efficiency by expressing modulated signals as a linear combination of basis signals. A Non-Orthogonal Time-Frequency Space (NOTFS) digital modulation is derived for the proposed ODDM techniques, and simulations show that they offer high-mobility communication systems with improved spectral efficiency and low latency, particularly in challenging scenarios such as high overloading factors and Additive White Gaussian Noise (AWGN) channels. A modified sphere decoding algorithm is also presented to efficiently decode the received signal. The proposed modulation and decoding techniques contribute to the advancement of non-orthogonal approaches in the next-generation of mobile communication systems, delivering superior spectral efficiency and low latency, and offering a promising solution towards the development of efficient high-mobility communication systems.
Paper Structure (9 sections, 19 equations, 4 figures, 1 table, 2 algorithms)

This paper contains 9 sections, 19 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Overloading Delay-Doppler Modulation Techniques
  3. Derivation of the Modulation Technique
  4. Non-Orthogonal Time Frequency Space
  5. Sphere Decoding and Inverse Systems
  6. 2-D Sphere Decoding
  7. Inverse System
  8. Simulation Results
  9. Conclusion

Figures (4)

  • Figure 1: Typical block-diagram of Delay-Doppler (DD) modulation techniques.
  • Figure 2: BER vs EB/N0: NOTFS, AWGN channel, IM and soft decoding (different $\lambda$s).
  • Figure 3: BER vs EB/N0: NOTFS, AWGN channel, IM and soft decoding ($\lambda$): $(M, N)=(4,4)$, $(\alpha, \beta)= (0.675, 0.675)$ equivalent to $\eta=119.5\%$.
  • Figure 4: BER vs EB/N0: NOTFS, AWGN channel, 2D-SD, initial estimation: IM and soft decoding (different $\lambda$'s): $(M, N)=(4,4)$.