广义布尔函数恒模 OFDM 通感一体化波形设计

宁一凡; 刘涛; 李玉博; 史洪印

doi:10.11999/JEIT260998

广义布尔函数恒模 OFDM 通感一体化波形设计

doi: 10.11999/JEIT260998 cstr: 32379.14.JEIT260998

宁一凡^{1, 2,},
刘涛^{1, 2, ,},
李玉博^{1, 2},
史洪印³

1.
燕山大学信息科学与工程学院秦皇岛 066004
2.
河北信息传输与信号处理重点实验室秦皇岛 066004
3.
北京建筑大学电气与信息工程学院北京 100044

基金项目: 国家自然科学基金面上项目(No.62471427, No.62501520)；河北省自然科学基金面上项目(No.F2026203006)；北京市自然科学基金项目(No.4262003)

详细信息

作者简介:
宁一凡：男，硕士研究生，研究方向为通感一体化波形设计，邮箱　ningyifan@stumail.ysu.edu.cn

刘涛：女，博士，燕山大学信息科学与工程学院讲师，硕士生导师，主要研究方向为序列设计与编码、无线通信信号设计，邮箱liutaotao@ysu.edu.cn

李玉博：男，博士，燕山大学信息科学与工程学院教授，博士生导师，研究方向为序列设计与编码、大规模多址接入和通感一体化信号设计

史洪印：男，博士，北京建筑大学电气与信息工程学院教授，博士生导师，研究方向为SAR/ISAR成像、目标检测与识别、微博计算成像、建筑无损检测

通讯作者:
刘涛　liutaotao@ysu.edu.cn

中图分类号: TN92
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出版历程
- 收稿日期: 2026-07-21
- 修回日期: 2026-10-01
- 录用日期: 2026-10-16
- 网络出版日期: 2026-10-28

Generalized Boolean function-based constant-modulus OFDM waveform design for integrated sensing and communication

NING Yifan^{1, 2
,},
LIU Tao^{1, 2
, ,},
LI Yubo^{1, 2},
SHI Hongyin³

1.
School of Information Science & Engineering, Yanshan University, Qinhuangdao 066004, China
2.
Hebei Province Key Laboratory of Information Transmission and Signal Processing, Qinhuangdao 066004, China
3.
School of Electrical and Information Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Funds: The National Natural Science Foundation of China (No.62471427, No.62501520), The Natural Science Foundation of Hebei Province (No.F2026203006), Beijing Natural Science Foundation (No.4262003)

摘要

摘要: 针对正交频分复用(OFDM)通感一体化(ISAC)波形因高峰均功率比(PAPR)导致功率放大器效率受限的问题，提出一种基于广义布尔函数(GBF)的恒模OFDM波形设计方法。该方法利用GBF-Golay闭式构造互补序列对，经相位校正与正交叠加生成0 dB PAPR的严格恒模波形；同时，在波形构造中嵌入通信数据，使得接收端可基于GBF结构实现低复杂度解码。仿真结果表明，相较于迭代式CM-OFDM方法，所提方法频谱更平坦、逐元消除后有效信噪比更高，并具有较好的通信可靠性。
- 通感一体化 /
- 恒模 OFDM /
- 广义布尔函数 /
- Golay 互补序列 /
- 频谱平坦性
Abstract: Objective Integrated sensing and communication (ISAC) is an important technology for future wireless networks because it enables communication and sensing functions to share spectrum, hardware, and signal processing resources. Orthogonal frequency division multiplexing (OFDM) is a promising ISAC waveform due to its flexible spectrum allocation and compatibility with existing communication systems. However, conventional OFDM suffers from a high peak-to-average power ratio (PAPR), which reduces power amplifier efficiency under peak-power-limited transmission. Although constant-modulus OFDM (CM-OFDM) can avoid power back-off, existing iterative CM-OFDM methods may produce severe frequency-domain power fluctuations and deep spectral notches. In element-wise-cancellation-based OFDM radar processing, these notches amplify the equivalent noise and degrade the range-velocity map. To address this problem, a generalized Boolean function (GBF)-based CM-OFDM waveform design method is proposed for sensing-prioritized ISAC scenarios with low communication payloads. Methods The proposed method constructs a pair of Golay complementary sequences from a special quadratic GBF. The quadratic term determines the complementary structure, while the affine term embeds communication information. The two complementary sequences are transformed into OFDM time-domain branches by inverse fast Fourier transform. Then, a sample-wise phase correction factor is introduced according to the phase difference between the two branches, and the corrected branches are orthogonally superposed to generate a strict constant-modulus OFDM signal. Two consecutive OFDM time slots with opposite signs in the second branch are transmitted to support receiver-side component separation. For sensing, element-wise cancellation and two-dimensional discrete Fourier transform are used to obtain the range-velocity map. Spectral flatness measure, deep notch rate, harmonic mean, and SNR efficiency are introduced to analyze noise enhancement caused by non-flat transmit spectra. A thresholded element-wise cancellation model is also considered to avoid direct division on low-power subcarriers. For communication, the receiver adds the paired time slots, removes the known quadratic term, and detects the affine information by fast Walsh-Hadamard transform in the BPSK case. Results and Discussions Simulation results show that the proposed GBF-CM-OFDM method achieves 0 dB PAPR, the same as iterative CM-OFDM, but provides a much flatter final transmit spectrum. When the normalized power threshold is 0.1, the deep notch rate of iterative CM-OFDM is mainly around 0.20, while that of the proposed method is about 0.01–0.03. The spectral flatness measure of the proposed method is mainly above 0.80, whereas that of the iterative method is around 0.3–0.4. Under naive element-wise cancellation, the average SNR efficiency is improved from 0.00732 for iterative CM-OFDM to 0.80604 for GBF-BPSK, and the average effective SNR is improved from –11.35 dB to 9.06 dB. With a −20 dB thresholded cancellation model, the iterative method is improved by discarding low-power subcarriers, but GBF-BPSK still achieves higher sensing performance, increasing the average effective SNR from 0.51 dB to 9.06 dB. Multi-target range-velocity maps further demonstrate that the proposed waveform has lower background noise and clearer target peaks. For communication performance, when \(N=256\), GBF-BPSK and GBF-QPSK carry 9 bits and 18 bits per paired waveform, respectively. The bit error rate results show that the proposed method has better recovery stability than iterative CM-OFDM under the considered low-communication-payload setting. Conclusions This paper proposes a GBF-based CM-OFDM waveform design method for ISAC systems. By using GBF-Golay complementary sequence construction, phase correction, and orthogonal branch superposition, the proposed method achieves strict 0 dB PAPR and supports communication data embedding. Compared with iterative CM-OFDM, the proposed method has better spectral flatness, fewer deep notches, and higher SNR efficiency after element-wise cancellation, thereby reducing noise enhancement and improving sensing performance under peak-power-limited conditions. The proposed method is more suitable for sensing-prioritized ISAC scenarios in which the communication function is used to convey a limited amount of auxiliary information, such as control, identification, synchronization, or status information, rather than to support high-throughput data transmission. Future work will investigate additional structural degrees of freedom in the GBF construction, such as variable permutations and complementary-sequence construction rules, to explore additional information embedding while preserving constant modulus and spectral flatness.
- Integrated sensing and communication /
- Constant-modulus OFDM /
- Generalized Boolean function /
- Golay complementary sequence /
- Spectral flatness

HTML全文

图 1 CM-OFDM信号构造系统框图

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图 2 不同SNR下BER随耦合参数r的变化

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图 3 不同子载波数下SFM与DNR随耦合参数r的变化

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图 4 迭代式 CM-OFDM 与所提 GBF-CM-OFDM 方法的时频特性对比

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图 5 深零陷比例DNR的经验累积分布

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图 7 SNR效率的经验累积分布

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图 6 谱平坦度SFM的经验累积分布

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图 8 PAPR 的互补累积分布图(CCDF)

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图 9 不同逐元消除门限下的感知性能统计结果

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图 10 不同OFDM波形下雷达多目标检测距离-速度图

门限阈值为 ρ=−20 dB，目标参数为 (R,v)={(72,24),(92,−20),(140,−22),(152,8)}，其中距离单位为m，速度单位为m/s。

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图 11 不同方案在 AWGN 与多径信道下随SNR和E_b/N₀变化的误码率性能

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表 1 不同逐元消除模型下的SNR相关参数对比

波形	回退量/ dB	输入SNR/dB	无门限平均SNR效率	–20 dB门限平均SNR效率	无门限平均有效SNR/dB	–20 dB门限平均有效SNR/dB	–20 dB门限保留比例
标准OFDM	11.53	–1.53	1	1	–1.525466	–1.53	1
Golay-OFDM	3.01	6.99	1	1	6.98970	6.99	1
CE-OFDM	0	10	0.20865	0.21124	3.10003	3.25	0.99987
迭代式CM-OFDM	0	10	0.00732	0.11248	–11.35085	0.51	0.94757
GBF-QPSK	0	10	0.40760	0.56640	6.10236	7.53123	0.99910
GBF-BPSK	0	10	0.80604	0.80604	9.06356	9.06356	1

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