Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation (1802.05242v2)

Abstract: The recently proposed orthogonal time frequency space (OTFS) modulation technique was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in Doppler channels. In this paper, we derive the explicit input-output relation describing OTFS modulation and demodulation (mod/demod) for delay-Doppler channels. We analyze the interferences and develop a novel low-complexity yet efficient message passing (MP) algorithm for joint interference cancellation (IC) and symbol detection. The proposed MP algorithm can effectively compensate for a wide range of channel Doppler spreads.

• The paper establishes explicit mathematical formulations for OTFS modulation and demodulation within delay-Doppler channels.
• It characterizes inter-Doppler, inter-carrier, and inter-symbol interference, demonstrating effective mitigation even with practical waveforms.
• A low-complexity message passing algorithm is proposed that achieves near-ideal performance in high Doppler environments.

Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation

The paper under consideration presents a detailed paper of Orthogonal Time Frequency Space (OTFS) modulation—a technique that has been shown to provide notable error performance improvements over Orthogonal Frequency Division Multiplexing (OFDM) in channels characterized by Doppler spread. This work rigorously derives the input-output relationships for OTFS within the context of delay-Doppler channels and examines two key pulse-shaping analyses: ideal waveforms satisfying bi-orthogonality conditions and practical rectangular waveforms that do not.

Key Contributions

1. Input-Output Analysis: The authors establish explicit mathematical formulations for OTFS modulation and demodulation, carefully delineating how transmitted information is transformed in time-frequency and delay-Doppler domains. These transformations are essential for comprehending the inner workings of OTFS in these channels.
2. Interference Characterization: The distinction between inter-Doppler interference (IDI), inter-carrier interference (ICI), and inter-symbol interference (ISI) is clarified through the derived expressions. For rectangular waveforms, which deviate from bi-orthogonal conditions, this includes characterizing how these interferences can be mitigated.
3. Message Passing Algorithm: Central to resolving the interference issues and enhancing detection reliability, the authors propose a low-complexity message passing (MP) algorithm. This algorithm adapts efficiently to the channel's sparsity, using Gaussian approximations where necessary, and strategically applies phase shifts to tackle ICI and ISI.

Numerical Validation

Numerical results demonstrate that OTFS, even when implemented with non-ideal rectangular waveforms, achieves close to the performance bounds of ideal waveform implementations. These simulations reveal that OTFS with the proposed interference cancellation techniques substantially outperforms traditional OFDM, particularly in high Doppler environments.

Implications

The findings of this paper hold significant implications both in practice and theory:

• Practical Implications: By offering a feasible path to achieve the performance of non-realizable ideal pulse-shaping waveforms with practical waveforms, this work suggests a means toward more robust communication systems using OTFS. The adaptability of the MP algorithm across a range of Doppler spreads supports its application in diverse and challenging operational contexts.
• Theoretical Developments: The analysis enriches the understanding of modulations subject to time-varying channels. It invites further exploration of waveform design and detection schemes under the framework of OTFS, potentially contributing to advancements in 5G networks and beyond.

Speculations for Future Research

While the presented work solidifies the case for OTFS in delay-Doppler channels, it also raises avenues requiring further exploration. Considerations for future research might involve:

• Development of enhanced channel estimation techniques specific to OTFS, particularly under severe Doppler scenarios.
• Exploration of coding strategies that can further reinforce the uncoded OTFS system described, aiming for enhanced error correction capabilities.
• Investigation into other non-traditional detection algorithms that might synergize with the MP approach for even greater performance enhancements.

In summary, this paper stands as a profound contribution to the domain of modulation techniques, meticulously unpacking the complexities of OTFS and setting the foundation for ongoing advancement in interference mitigation and signal detection strategies.