Orthogonal Chirp Division Multiplexing (1601.06576v1)

Abstract: Chirp waveform plays a significant role in radar and communication systems for its ability of pulse compression and spread spectrum. This paper presents a principle of orthogonally multiplexing a bank of linear chirp waveforms within the same bandwidth. The amplitude and phase of the chirps are modulated for information communication. As Fourier trans-form is the basis for orthogonal frequency division multiplexing (OFDM), Fresnel transform underlies the proposed orthogonal chirp division multiplexing (OCDM). Digital implementa-tion of the OCDM system using discrete Fresnel transform is proposed. Based on the con-volution theorem of the Fresnel transform, the transmission of the OCDM signal is analyzed under the linear time-invariant or quasi-static channel with additive noise, which can gener-alize typical linear transmission channels. Based on the eigen-decomposition of Fresnel transform, efficient digital signal processing algorithm is proposed for compensating chan-nel dispersion by linear single- tap equalizers. The implementation details of the OCDM system is discussed with emphasis on its compatibility to the OFDM system. Finally, simula-tion are provided to validate the feasibility of the proposed OCDM under wireless channels. It is shown that the OCDM system is able to utilize the multipath diversity and outperforms the OFDM system under the multipath fading channels.

• The paper introduces Orthogonal Chirp Division Multiplexing (OCDM) as a new multiplexing framework utilizing the Fresnel transform, analogous to OFDM's use of the Fourier transform.
• The authors detail a digital implementation method using discrete Fresnel transforms and propose efficient signal processing techniques enabling linear single-tap equalization for LTI channels.
• Numerical simulations demonstrate OCDM's feasibility and show superior bit-error rate performance compared to OFDM in multipath fading environments, suggesting potential for enhanced communication systems.

Orthogonal Chirp Division Multiplexing: Insights and Implications

Orthogonal Chirp Division Multiplexing (OCDM), as proposed by Xing Ouyang and Jian Zhao, introduces an innovative framework for the multiplexing of chirp waveforms via the Fresnel transform, supplementing the foundation provided by the Fourier transform used in Orthogonal Frequency Division Multiplexing (OFDM). In this paper, the authors provide a comprehensive methodology for the implementation of OCDM using discrete Fresnel transforms (DFnT) and propose efficient signal processing techniques for communication through linear time-invariant (LTI) channels.

Key Contributions

The paper’s central contribution is the definition and elaboration of OCDM as a means to maximize communication rates by orthogonally overlaying chirp waveforms within a given bandwidth. Utilizing the Fresnel transform, analogous to the role of the Fourier transform in OFDM, represents a significant conceptual shift, providing a new domain for waveform manipulation that retains orthogonality among chirps.

The authors also present a method for digital implementation employing the discrete Fresnel transform. Through simulations, they demonstrate that OCDM brings advantages in multipath fading environments, with performance surpassing that of OFDM systems. The key components of the OCDM framework include:

• Chirp Modulation: Chirp signals are modulated using formats such as Phase Shift Keying (PSK) or Quadrature Amplitude Modulation (QAM). These modulated chirps are transmitted orthogonally, exploiting both amplitude and phase for information embedding.
• Channel Analysis and Equalization: The transmission of OCDM signals is investigated under LTI channel conditions. A notable advantage of OCDM is the ability to compensate for channel effects using linear single-tap equalizers, thanks to a novel computationally efficient algorithm proposed by the authors.

Numerical Results

Simulation results substantiate the feasibility and performance benefits of OCDM systems, especially in multipath channels. The system exhibits notable immunity to multipath fading, demonstrating improved bit-error rate (BER) performance over OFDM when using minimum mean square error (MMSE) equalization. Even under zero-forcing (ZF) equalization, the system efficiently manages noise enhancement, emphasizing its robustness and potential for practical communication systems.

Theoretical and Practical Implications

Theoretically, OCDM offers a new framework for communications and invites further exploration into the spatial-temporal characteristics of Fresnel domain implementations. This approach potentially leads to more efficient data transmission methods by leveraging unique properties of chirp diversity. Practically, the compatibility of OCDM with existing OFDM systems allows for a straightforward integration into current digital communication systems, thus ensuring its utility and adaptability in real-world applications.

Future Directions

Given the strong performance of OCDM in simulations, future research could explore:

• Integration with Advanced Modulation Techniques: Further exploration of higher-order modulation schemes could enhance the spectral efficiency and robustness of OCDM systems.
• Hardware Implementation: Developing practical implementations and real-world validations using configurable hardware platforms such as FPGA or ASIC could catalyze OCDM's adoption.
• Complex Channel Environments: Extending performance analysis to more challenging and dynamic channel conditions, such as those found in mobile environments, could provide a deeper understanding of OCDM's potential advantages over traditional methods.

In summary, the research presented in this paper forms a rigorous and methodical foundation for the emerging field of OCDM, highlighting its advantages over traditional multiplexing techniques, particularly in scenarios where exploiting multipath channel diversity is crucial. The theoretical groundwork and practical simulations position OCDM as a compelling alternative for enhancing the performance and efficiency of modern communication systems.