非理想成型脉冲ODDM系统的干扰分析与迭代信号检测算法设计

华惊宇; 邵梦琳; 闻建刚; 邹园萍; 盛斌

doi:10.11999/JEIT260771

非理想成型脉冲ODDM系统的干扰分析与迭代信号检测算法设计

doi: 10.11999/JEIT260771 cstr: 32379.14.JEIT260771

1.
浙江工商大学信息与电子工程学院杭州 310018
2.
东南大学移动通信全国重点实验室南京 210096

基金项目: 国家自然科学基金(62271445)

详细信息

作者简介:
华惊宇：男，教授，博士，研究方向为无线通信、无线定位、信号处理、数字滤波器等，邮箱　eehjy@163.com

邵梦琳：女，硕士生，研究方向为多载波传输中的干扰分析与信号检测

闻建刚：男，讲师，博士，研究方向为多载波传输、信号处理、数字滤波器等

邹园萍：女，副教授，博士，研究方向为宽带通信、移动通信、信号处理等

盛斌：男，教授，博士，研究方向为通信与信息系统、未来移动通信系统、无线传输技术研究等

通讯作者:
华惊宇　eehjy@163.com

中图分类号: TN929.5
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出版历程
- 收稿日期: 2026-06-09
- 修回日期: 2026-10-16
- 录用日期: 2026-10-16
- 网络出版日期: 2026-10-23

Interference Analysis and Iterative Signal Detection for ODDM Systems with Non-Ideal Pulse Shaping

1.
School of Information & Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, China
2.
National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China

Funds: The National Science Foundation of China (62271445)

摘要

摘要: 正交时延多普勒分集复用(ODDM)是一种按照时延–多普勒(DD)平面分辨率进行正交传输的多载波调制技术，其正交性实现通常要求成型脉冲满足理想奈奎斯特条件。然而受工程可实现性限制，有限长成型脉冲难以严格满足此条件。在载波频率偏移作用下，该非理想成型脉冲会产生理想假设下不存在的残余干扰。基于此，本文分析了非理想成型脉冲与载波频率偏移共同作用下的DD域等效干扰特性，并在此基础上设计了一种线性残余干扰抵消检测算法，以补偿上述残余干扰所导致的性能损失。仿真结果表明，本文采用的干扰模型结果与仿真结果更为接近，所提检测算法能够有效补偿因忽略残余干扰导致的性能损失，并在复杂度低于完整最小均方误差(MMSE)检测的前提下获得接近其性能的检测结果。
- 正交时延多普勒分集复用 /
- 干扰分析 /
- 信号检测
Abstract: Objective Orthogonal Delay-Doppler Division Multiplexing (ODDM) is a delay-Doppler (DD) domain multicarrier modulation scheme that transmits information symbols according to the resolution of the DD plane. By exploiting orthogonal pulses in the DD domain, ODDM achieves a structured input-output relationship and a sparse equivalent channel representation in high-mobility wireless communication scenarios. However, the orthogonality of ODDM typically relies on the ideal Nyquist property of the pulse shaping filter. In practical systems, finite-length pulses cannot strictly satisfy this condition, and their non-ideal Nyquist characteristics introduce additional energy leakage. In the presence of carrier frequency offset (CFO), this energy leakage further couples with inter-carrier interference to form residual interference. If such residual interference is neglected in receiver design, the detector operates based on a mismatched equivalent channel model, resulting in degraded symbol detection performance. To address this issue, this paper investigates the interference characteristics of ODDM systems with non-ideal pulse shaping under CFO, and proposes an iterative detection algorithm to compensate for the performance loss caused by neglecting residual interference under the ideal Nyquist assumption. Methods First, a DD-domain equivalent interference model is established for ODDM systems with non-ideal pulse shaping under CFO, characterizing the residual interference that is neglected under the ideal Nyquist pulse assumption. Second, based on the structure of the derived DD-domain interference matrix, the equivalent interference is decomposed into a nominal interference component captured by the ideal pulse model and a residual interference component introduced by non-ideal pulse shaping. Building on this decomposition, a linear residual interference cancellation (LRC) detection algorithm is designed to suppress residual interference through a small number of iterations, thereby compensating for the performance loss incurred by neglecting such interference. Finally, the accuracy of the adopted interference model based on practical pulses and the effectiveness of the proposed detection algorithm are validated through Signal-to-Interference-plus-Noise Ratio (SINR) and Symbol Error Rate (SER) simulations. Results and Discussions A comprehensive evaluation of the non-ideal pulse interference modeling framework and the proposed LRC detection algorithm is conducted in this paper. Simulation results demonstrate that the SINR computed by the non-ideal pulse interference model maintains consistently closer agreement with Monte Carlo simulations, with a deviation of no more than 0.05 dB, whereas the ideal Nyquist pulse model overestimates SINR by up to 0.7 dB across the simulated SNR range (Fig. 3). This discrepancy is particularly pronounced at low residual CFO and high SNR. In terms of detection performance, the Message Passing (MP) detector commonly used under the ideal pulse assumption exhibits an increasing performance gap from the MMSE detector based on the full interference model as the normalized CFO increases. At an SNR of 19 dB, the SER ratio between MP and the full-model MMSE detector rises from approximately 2.2 at zero CFO to approximately 24.5 when the normalized CFO is 0.1, whereas the proposed LRC detector remains close to the full-model MMSE detector, with its SER staying within about 1.5 times that of the full-model MMSE detector under the same conditions (Fig. 5). This confirms that model mismatch incurs non-negligible performance degradation. The proposed LRC detection algorithm effectively compensates for this performance loss and closely approaches the detection performance of the full-model MMSE detector with as few as 2 iterations across all tested CFO values. Consistent conclusions are further corroborated by results obtained under 16QAM, 64QAM, and 256QAM modulations (Fig. 6): as the modulation order increases, the performance gap between the MP detector and the full-model MMSE detector widens, whereas LRC maintains close approximation to the full-model MMSE across different modulation orders. Furthermore, under doubly selective channels, LRC still achieves SER performance close to that of the full-model MMSE detector and outperforms MP detection (Fig. 7). When imperfect channel state information (CSI) is further considered, the SERs of all three detection methods increase as the channel estimation SNR decreases. Among them, the performance degradation of LRC and the full-model MMSE is relatively limited, and their detection results remain close to each other, whereas MP is more significantly affected by channel estimation errors. These results further demonstrate that the proposed method exhibits good robustness and broad applicability in interference-limited systems with non-ideal pulse shaping. Conclusions This paper investigates the interference analysis and signal detection problem in ODDM systems with non-ideal pulse shaping under CFO. Based on the characterization of the equivalent interference structure in the delay-Doppler domain under the joint effect of non-ideal pulse shaping and CFO, a linear residual interference cancellation detection algorithm is proposed. The algorithm compensates for the residual interference neglected under the ideal Nyquist pulse assumption, thereby recovering the associated performance loss. Simulation results demonstrate that the adopted non-ideal pulse interference model more accurately characterizes the system interference behavior. Based on this model, the proposed LRC detection algorithm effectively compensates for the performance loss caused by model mismatch, achieving close approximation to the detection performance of the full-model MMSE detector while maintaining lower computational complexity.
- Orthogonal Delay-Doppler Division Multiplexing /
- Interference Analysis /
- Signal Detection

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图 1 ODDM系统基于IDFT/DFT近似实现框图

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图 2 CFO影响下理想脉冲与实际脉冲系统干扰能量分布对比

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图 3 不同CFO下两种干扰建模与仿真SINR对比

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图 4 迭代次数与脉冲滚降因子影响

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图 5 不同CFO下三种检测算法的SER性能对比

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图 6 ε=0.03时不同调制阶数下三种检测算法的SER性能对比

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图 7 双选择性信道下不同CSI条件的检测算法SER性能对比

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1 基于LRC的迭代检测算法

输入：$ {\boldsymbol{y}}_{\text{DD}} $, $ {\boldsymbol{H}}_{\text{main}} $, $ {\boldsymbol{H}}_{\text{other}} $, $ \sigma _{\text{n}}^{2} $, $ {I}_{\max } $
输出：$ {\boldsymbol{x}}_{\text{LRC}}={{\hat{\boldsymbol{x}}}}^{({{I}_{\max }})} $
(1) 初始化：$ i=1 $，令$ {\boldsymbol{y}}^{(1)}={\boldsymbol{y}}_{\text{DD}} $
(2) 根据式(22)和(23)预计算各时延分组MMSE检测矩阵$ {\boldsymbol{W}}_{l} $
(3) while $ i\leq {I}_{\max } $
(4) 　for $ l=0,1,\cdots ,M-1 $
(5) 　　$ {\tilde{\boldsymbol{x}}}_{l}^{(i)}={\boldsymbol{W}}_{l}\boldsymbol{y}_{l}^{(i)} $对各时延分组进行分块检测
(6) 　end
(7) 　对所有软输出结果进行硬判决$ {{\hat{\boldsymbol{x}}}}^{(i)}=Q\left({{\tilde{\boldsymbol{x}}}}^{(i)}\right) $
(8) 　重构并抵消残余干扰$ {\boldsymbol{y}}^{(i+1)}={\boldsymbol{y}}_{\text{DD}}-{\boldsymbol{H}}_{\text{other}}{{\hat{\boldsymbol{x}}}}^{(i)} $
(9) 　$ i=i+1 $
(10) end

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表 1 仿真参数

仿真参数	参数值
发送符号数$ M $	33
子载波个数$ N $	64
调制方式	64QAM
脉冲滚降因子$ \alpha $	0.1
过采样因子$ K $	4
截断符号数$ 2Q $	16
归一化载波频率偏移	0, 0.03, 0.1

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