Non-orthogonal Prolate Spheroidal Wave Functions Signal Detection Method with Cross-terms

LU Faping; MAO Zhongyang; XU Zhichao; SHU Yihao; KANG Jiafang; WANG Feng; WANG Mengjiao

doi:10.11999/JEIT250052

Volume 47 Issue 8

Aug. 2025

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Article Navigation > Journal of Electronics & Information Technology > 2025 > 47(8): 2714-2723

LU Faping, MAO Zhongyang, XU Zhichao, SHU Yihao, KANG Jiafang, WANG Feng, WANG Mengjiao. Non-orthogonal Prolate Spheroidal Wave Functions Signal Detection Method with Cross-terms[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2714-2723. doi: 10.11999/JEIT250052

Citation:

LU Faping, MAO Zhongyang, XU Zhichao, SHU Yihao, KANG Jiafang, WANG Feng, WANG Mengjiao. Non-orthogonal Prolate Spheroidal Wave Functions Signal Detection Method with Cross-terms[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2714-2723. doi: 10.11999/JEIT250052

Citation:

LU Faping, MAO Zhongyang, XU Zhichao, SHU Yihao, KANG Jiafang, WANG Feng, WANG Mengjiao. Non-orthogonal Prolate Spheroidal Wave Functions Signal Detection Method with Cross-terms[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2714-2723. doi: 10.11999/JEIT250052

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Non-orthogonal Prolate Spheroidal Wave Functions Signal Detection Method with Cross-terms

doi: 10.11999/JEIT250052 cstr: 32379.14.JEIT250052

LU Faping^{1, 2},
MAO Zhongyang^{1, 2},
XU Zhichao^{1, 2, 3},
SHU Yihao⁴,
KANG Jiafang^{1, 2
,
,},
WANG Feng³,
WANG Mengjiao^{1, 2}

1.
Naval Aviation University, Yantai 264001, China
2.
Key Laboratory of Sea-Air Information Perception and Processing Technology of Shandong Province, Yantai 264001, China
3.
School of Electronic Information Engineering, Beihang University, Beijing 100191, China
4.
Unit 91001 of PLA, Beijing 100038, China

Funds: China National Postdoctoral Program for Innovative Talents (BX20200039), The National Natural Science Foundation of Shandong Province (ZR2023MD045)

Received Date: 2025-01-22
Rev Recd Date: 2025-04-22

Available Online: 2025-05-10

Publish Date: 2025-08-27

Abstract

Abstract

Objective Non-orthogonal Shape Modulation based on Prolate Spheroidal Wave Functions (NSM-PSWFs) utilizes PSWFs with high time-frequency energy concentration as basis waveforms. This structure enables high spectral efficiency and time-frequency energy aggregation, making it a promising candidate for B5G/6G waveform design. However, due to the non-orthogonality of the PSWFs used for information transmission in NSM-PSWFs, mutual interference between non-orthogonal signals and poor bit error performance in coherent detection systems significantly limit their practical deployment. This issue is a common challenge in non-orthogonal modulation and access technologies. To address the problem of low detection performance resulting from mutual interference among non-orthogonal PSWFs, this study incorporates time-frequency domain characteristics into signal detection. A novel detection mechanism for non-orthogonal PSWFs in the time-frequency domain is proposed, with the aim of reducing interference between non-orthogonal PSWFs and enhancing detection performance. Methods Given the different time-frequency domain energy distribution characteristics of PSWF signals at various stages, particularly the "local" energy concentration in different regions, this study introduces cross-terms between signals. Based on an analysis of non-orthogonal signal time-frequency characteristics, with a focus on innovating detection mechanisms, a combined approach of theoretical modeling and numerical simulation is employed to explore novel methods for detecting non-orthogonal PSWF signals via cross-terms. Specifically: (1) The impact of interference between PSWF signals and Gaussian white noise on the time-frequency distribution of cross-terms is analyzed, demonstrating the feasibility of detecting PSWF signals in the time-frequency domain. (2) Building on this analysis, time-frequency characteristics are integrated into the detection process. A novel method for detecting non-orthogonal PSWFs based on cross-terms is proposed, accompanied by a strategy for selecting time-frequency feature parameters. The "integral value of cross-terms over symmetric time intervals at the frequency corresponding to the peak energy density of cross-terms" is chosen as the feature parameter. This shifts signal detection from the "one-dimensional energy domain (time or frequency)" to the "two-dimensional time-frequency energy domain," enabling detection by exploiting localized energy regions while simultaneously mitigating interference during statistical acquisition. Results and Discussions This study demonstrates the feasibility of detecting signals in the two-dimensional time-frequency domain and analyzes the impact of different PSWFs and AWGN on the distribution characteristics of cross-terms. Notably, AWGN interference can be regarded as a special form of “interference between PSWFs” exhibiting a linear superposition with PSWF-induced interference. The interference from PSWFs with time-domain parity opposite to that of the template signal can be eliminated through “symmetric time-interval integration” (Fig. 1, Table 1, Table 2). This establishes a theoretical foundation for the novel detection mechanism based on cross-terms and provides a reference for incorporating other two-dimensional distribution characteristics into signal detection. Additionally, a novel detection mechanism for non-orthogonal PSWFs based on cross-terms is proposed, utilizing time-frequency distribution characteristics for signal detection. This method effectively reduces interference between non-orthogonal PSWFs, thereby enhancing detection performance. It also offers valuable insights for exploring detection mechanisms based on other two-dimensional distribution characteristics. For example, compared to conventional coherent detection, the proposed method achieves a superior performance with approximately 1 dB improvement in bit error rate at 4 × 10^–5 (Fig. 4). Conclusions This paper demonstrates the feasibility of detecting PSWFs in the two-dimensional time-frequency domain and proposes a novel detection method for non-orthogonal PSWFs based on cross-terms. The proposed method transforms traditional coherent detection from “global energy in the time/frequency domain” to “local energy in the time-frequency domain” significantly reducing interference between non-orthogonal signals and enhancing detection performance. This approach not only provides a new perspective for developing efficient detection methods for non-orthogonal signals but also serves as a valuable reference for investigating novel signal detection mechanisms in two-dimensional domains.
- Prolate Spheroidal Wave Functions (PSWFs),
- Non-orthogonal,
- Signal detection,
- Time-frequency domain,
- Cross-term

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References(20)

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