Off-Grid Blind Near-Field Integrated Sensing and Communication: Algorithm Design and Lower Bound
-
摘要: 超大规模天线阵列场景下用户多处于近场区域，现有通信与感知算法面临离格功率泄露、幅度衰减导致模型失配等问题，且大多依赖导频辅助感知。为此，本文提出一种离格盲近场通信感知一体化(Near Field Integrated Sensing and Communication, NF-ISAC)算法，可在无导频条件下实现近场用户的高精度坐标感知、信道估计与符号检测。该算法首先构建NF-ISAC系统的因子图模型，提出幅度-相位分离的混合导向矢量建模方法，通过神经网络实现拟合，并将其作为函数节点嵌入因子图；其次结合矩阵分解与消息传递算法，实现因子图中神经网络的穿透计算，完成离格盲NF-ISAC算法的完整推导；同时推导了基于神经网络的近场感知克拉美罗下界，明确了近场位置感知的理论极限。仿真结果表明，所提算法以与主流算法同阶的计算复杂度，在通信误码率与感知精度上均取得显著性能提升，感知精度较现有近场离格算法提升2～3dB，且性能最接近理论下界。Abstract:
Objective With the widespread deployment of extra-large scale antenna arrays in 6G networks, user terminals are mostly located in the near-field region. Existing near-field integrated sensing and communication (NF-ISAC) algorithms face critical challenges including off-grid power leakage, severe model mismatch, and strong dependence on pilot signals, which cannot meet the requirements of 6G low-overhead and high-performance transmission. This paper aims to design a novel off-grid blind NF-ISAC algorithm, and derive the theoretical performance bound for near-field sensing. Methods To overcome the inherent limitations of analytical geometric steering vectors and accommodate more accurate electromagnetic propagation characteristics without closed-form expressions. First, an amplitude-phase separation method is proposed to decompose the nonlinear near-field steering vector into amplitude and phase terms, which enables high-precision characterization of the steering vector with a single-hidden-layer neural network. Second, the NF-ISAC problem is formulated as a constrained matrix factorization problem, and the corresponding factor graph model is constructed. The trained neural network is embedded into the factor graph as a function node, and the penetration calculation of the neural network is realized via message passing algorithm, to complete joint blind coordinate sensing, channel estimation and signal detection without pilot assistance. Finally, the Cramér-Rao Lower Bound (CRLB) for multi-user near-field joint distance and angle sensing in polar coordinates is derived based on the neural network-fitted steering vector. Results and Discussions Extensive Monte Carlo simulations are conducted to evaluate the performance of the proposed algorithm. Simulation results show that the proposed algorithm achieves millimeter-level high-precision position sensing, and obtains significant performance improvements in both communication bit error rate (BER) and sensing accuracy compared with existing mainstream algorithms. It achieves 2～3dB performance gain in sensing accuracy over the state-of-the-art near-field off-grid method, and its performance is closest to the derived theoretical CRLB, which effectively mitigates off-grid power leakage and model mismatch. Conclusions The proposed off-grid blind NF-ISAC algorithm breaks through the pilot dependency and model mismatch limitations of existing NF-ISAC schemes, and realizes integrated high-precision sensing and reliable communication for near-field users in a pilot-free manner. The derived CRLB provides a theoretical benchmark for performance evaluation of near-field ISAC systems. This work can offer key technical support for the design of 6G near-field ISAC systems. -
表 1 因式分解和函数节点含义
函数 概率 表达式 函数 概率 表达式 函数 概率 表达式 $ {f}_{Y} $ $ P(\boldsymbol{Y}|\boldsymbol{A},\boldsymbol{X,}\beta ) $ $ \mathcal{M}\mathcal{N}\left(\boldsymbol{Y};\boldsymbol{AX},{\boldsymbol{I}}_{R},{\boldsymbol{I}}_{L}\right) $ $ {f}_{\beta } $ $ P(\beta ) $ $ 1/\beta $ $ {f}_{\gamma } $ $ P(\boldsymbol{\gamma }) $ $ \text{Ga}\left(\boldsymbol{\gamma };\epsilon ,\eta \right) $ $ {f}_{{{x}_{l}}} $ $ P({\boldsymbol{x}}_{l}|\boldsymbol{\gamma }) $ $ \text{CN}\left({\boldsymbol{x}}_{l};0,{\boldsymbol{\gamma }}^{-1}\right) $ $ {f}_{{{\alpha }_{j}}} $ $ P({\boldsymbol{\alpha }}_{j}|{d}_{j},{\theta }_{j}) $ $ \mathcal{N}{\mathcal{N}}_{j} $ $ {f}_{{{d}_{j}}},{f}_{{{\theta }_{j}}} $ $ P({d}_{j}),P({\theta }_{j}) $ $ \text{Unif}() $ 
下载: 导出CSV
1 矩阵分解算法
1 初始化：$ {\boldsymbol{U}}_{A}={\boldsymbol{I}}_{R} $, $ {\boldsymbol{V}}_{A}={\boldsymbol{I}}_{J} $, $ \boldsymbol{\hat{A}}={\boldsymbol{A}}_{0} $, $ {\boldsymbol{V}}_{X}={\boldsymbol{I}}_{L} $, $ {\Xi }_{X}={\boldsymbol{1}}_{J\times L} $, $ {\boldsymbol{S}}_{X}={\boldsymbol{0}}_{J\times L} $, $ {\Xi }_{A}={\boldsymbol{1}}_{R\times J} $, $ {\boldsymbol{S}}_{A}={\boldsymbol{0}}_{R\times J} $ 2 For $ t=1\colon T $ 3 $ {\overline{W}}_{X}={\boldsymbol{\hat{A}}}^{\text{H}}\boldsymbol{A+}R{\boldsymbol{V}}_{A} $, $ \left[{\boldsymbol{C}}_{X},{\boldsymbol{D}}_{X}\right]=\text{eig}({\boldsymbol{\overline{W}}}_{X}) $，$ {\boldsymbol{R}}_{X}=\boldsymbol{D}_{X}^{-1/2}\boldsymbol{C}_{X}^{\text{H}}{\boldsymbol{\hat{A}}}^{\text{H}}\boldsymbol{Y},\;\;{\boldsymbol{{\varPhi }}}_{X}=\boldsymbol{D}_{X}^{-1/2}\boldsymbol{C}_{X}^{\text{H}} $， 4 $ {\boldsymbol{V}}_{{{P}_{X}}}={\left| {\boldsymbol{{\varPhi }}}_{X}\right| }^{.2}{\Xi }_{X},\; {\boldsymbol{\hat{P}}}_{X}={\boldsymbol{{\varPhi }}}_{X}\boldsymbol{\hat{X}}-{\boldsymbol{V}}_{{{P}_{X}}}\cdot {\boldsymbol{S}}_{X} $，$ {\boldsymbol{V}}_{{{S}_{X}}}=\boldsymbol{1}./\left({\boldsymbol{V}}_{{{P}_{X}}}+{\beta }^{-1}\right),\; \; {\boldsymbol{S}}_{X}={\boldsymbol{V}}_{{{S}_{X}}}\cdot ({\boldsymbol{R}}_{X}-{\boldsymbol{P}}_{X}) $， 5 $ {\boldsymbol{V}}_{{{Q}_{X}}}=1./\left({\left| \boldsymbol{{\varPhi }}_{X}^{\text{H}}\right| }^{.2}\cdot \; {\boldsymbol{V}}_{{{S}_{X}}}\right),\; {\boldsymbol{Q}}_{X}=\boldsymbol{\hat{X}}+{\boldsymbol{V}}_{{{Q}_{X}}}\cdot \left(\boldsymbol{{\varPhi }}_{X}^{\text{H}}{\boldsymbol{S}}_{X}\right) $，%计算$ \boldsymbol{X} $的外信息均值和方差 6 $ {\mathbf{\Xi }}_{X}={\boldsymbol{V}}_{{{Q}_{X}}}\cdot \boldsymbol{G}_{X}^{\prime}({\boldsymbol{Q}}_{X},{\boldsymbol{V}}_{{{Q}_{X}}}),\; \boldsymbol{\hat{X}}={\boldsymbol{G}}_{X}({\boldsymbol{Q}}_{X},{\boldsymbol{V}}_{{{Q}_{X}}}) $， %外信息和先验合并，计算$ \boldsymbol{X} $后验 7 $ {\boldsymbol{U}}_{X}=\text{diag}(\text{mean}({\mathbf{\Xi }}_{X},2)) $， %计算调制符号矩阵$ \boldsymbol{X} $的逐元素方差 8 $ {\boldsymbol{\overline{W}}}_{A}=\boldsymbol{X}{\boldsymbol{\hat{X}}}^{\text{H}}\boldsymbol{+}L{\boldsymbol{U}}_{X} $, $ \left[{\boldsymbol{C}}_{A},{\boldsymbol{D}}_{A}\right]=eig({\boldsymbol{\overline{W}}}_{A}) $，$ {\boldsymbol{R}}_{A}=\boldsymbol{D}_{A}^{-1/2}\boldsymbol{C}_{A}^{\text{H}}\boldsymbol{\hat{X}}{\boldsymbol{Y}}^{\text{H}},\; \; {\boldsymbol{{\varPhi }}}_{A}=\boldsymbol{D}_{A}^{-1/2}\boldsymbol{C}_{A}^{\text{H}} $， 9 $ {\boldsymbol{V}}_{{{P}_{A}}}={\left| {\boldsymbol{{\varPhi }}}_{A}\right| }^{.2}\Xi _{A}^{\text{H}},\; {\boldsymbol{\hat{P}}}_{A}={\boldsymbol{{\varPhi }}}_{A}{\boldsymbol{\hat{A}}}^{\text{H}}-{\boldsymbol{V}}_{{{P}_{A}}}\cdot {\boldsymbol{S}}_{A} $，$ {\boldsymbol{V}}_{{{S}_{A}}}=\boldsymbol{1}./\left({\boldsymbol{V}}_{{{P}_{A}}}+{\beta }^{-1}\right),\; \; {\boldsymbol{S}}_{A}={\boldsymbol{V}}_{{{S}_{A}}}\cdot ({\boldsymbol{R}}_{A}-{\boldsymbol{P}}_{A}) $， 10 $ {\boldsymbol{V}}_{{{Q}_{A}}}=1./\left({\left| \boldsymbol{{\varPhi }}_{A}^{\text{H}}\right| }^{.2}\cdot \; {\boldsymbol{V}}_{{{S}_{A}}}\right),\; {\boldsymbol{Q}}_{A}={\boldsymbol{\hat{A}}}^{\text{H}}+{\boldsymbol{V}}_{{{Q}_{A}}}\cdot \left(\boldsymbol{{\varPhi }}_{A}^{\text{H}}{\boldsymbol{S}}_{A}\right) $，%导向矢量$ \boldsymbol{A} $的外信息均值和方差 11 $ {\mathbf{\Xi }}_{A}={\boldsymbol{V}}_{{{Q}_{A}}}\cdot \boldsymbol{G}_{A}^{\prime}({\boldsymbol{Q}}_{A},{\boldsymbol{V}}_{{{Q}_{A}}}),\; \boldsymbol{\hat{A}}={\boldsymbol{G}}_{A}({\boldsymbol{Q}}_{A},{\boldsymbol{V}}_{{{Q}_{A}}}) $ %外信息和先验合并，计算$ \boldsymbol{A} $后验均值和方差 12 $ {\boldsymbol{U}}_{A}=\text{diag}(\text{mean}({\mathbf{\Xi }}_{A},1)) $ %计算矢量$ \boldsymbol{A} $的逐元素方差 13 噪声精度$ \beta =ML/C $，其中$ \boldsymbol{C}={\left|\left|\boldsymbol{Y}-\boldsymbol{AX}\right|\right|}^{2}+M\text{Tr}(\boldsymbol{\hat{X}}{\boldsymbol{\hat{X}}}^{\text{H}}{\boldsymbol{V}}_{A})+L\text{Tr}({\boldsymbol{U}}_{X}{\boldsymbol{\hat{A}}}^{\text{H}}\boldsymbol{\hat{A}})+ML\text{Tr}({\boldsymbol{U}}_{X}{\boldsymbol{V}}_{X}) $ 14 EndFor
下载: 导出CSV
2 通信感知一体化算法
1 初始化：网格筛选得到$ (d_{m}^{t-1},\theta _{n}^{t-1})=({d}_{m},{\theta }_{n}),\forall m,n $和表1第1行初始化步骤。 2 For $ t=1\colon T $ 3 由算法1的3-5行得到$ {\boldsymbol{Q}}_{X},{\boldsymbol{V}}_{{{Q}_{X}}} $，分解为向量$ \boldsymbol{q}_{l}^{x},\boldsymbol{v}_{{q}_{l}}^{x},\forall l $； %引用算法1 4 由(15)计算$ {\boldsymbol{\hat{x}}}_{l},{\boldsymbol{v}}_{{{x}_{l}}},\forall l $，并排列为矩阵$ \boldsymbol{\hat{X}},{\boldsymbol{{\varXi }}}_{X} $，由(16)计算稀疏贝叶斯超先验$ \boldsymbol{\gamma } $； 5 由算法1的8-10行计算$ {\boldsymbol{Q}}_{A},{\boldsymbol{V}}_{{{Q}_{A}}} $，分解为向量$ \boldsymbol{q}_{j}^{a},\boldsymbol{v}_{{q}_{j}}^{a},\forall j $； %引用算法1 6 利用$ (d_{m}^{t-1},\theta _{n}^{t-1}) $，由(7)式计算矢量$ {\boldsymbol{\alpha }}_{{{j}_{0}}} $偏导数$ \boldsymbol{e}_{0}^{{\theta }_{j}} $和$ \boldsymbol{e}_{0}^{{d}_{j}},\forall j $； 7 $ {\boldsymbol{\xi }}_{{{j}_{0}}}={\boldsymbol{\alpha }}_{{{j}_{0}}}-{d}^{t-1}\boldsymbol{e}_{{j}_{0}}^{d}-{\theta }^{t-1}\boldsymbol{e}_{{j}_{0}}^{\theta },\forall j $，由(9)计算$ {\boldsymbol{\overrightarrow{d}}}_{j},{\boldsymbol{\overrightarrow{v}}}_{{{d}_{j}}},\forall j $； 8 由(10)计算$ d_{j}^{} $和$ {v}_{{{d}_{j}}},\forall j $，由(11)计算$ {\boldsymbol{\overleftarrow{v}}}_{{{d}_{j}}} $和$ {\boldsymbol{\overleftarrow{d}}}_{j},\forall j $； 9 同理计算$ {\theta }_{j} $,$ {v}_{{{\theta }_{j}}} $,$ {\boldsymbol{\overleftarrow{v}}}_{{{\theta }_{j}}} $和$ {\boldsymbol{\overleftarrow{\theta }}}_{j},\forall j $； 10 由(14)计算$ {\boldsymbol{v}}_{{{\boldsymbol{\alpha }}_{j}}} $和$ {\boldsymbol{\hat{\alpha }}}_{j},\forall j $，并排列为矩阵$ \boldsymbol{\hat{A}},{\boldsymbol{{\varXi }}}_{A} $，由算法1的13行计算$ \beta $； 11 EndFor 12 对$ \boldsymbol{\hat{X}} $解差分解调并判决得到信息比特$ {\boldsymbol{\hat{b}}}_{k} $。
下载: 导出CSV
表 2 近场通信感知一体化系统参数
活跃用户个数K 1～5 基站天线个数R 128 信噪比SNR –3～–10 dB 感知距离范围$ {D}_{{\mathrm{Min}}},{D}_{{\mathrm{Max}}} $ $ d\sim \left[5\;{\mathrm{m}},50\;{\mathrm{m}}\right] $ 数据调制方式 QPSK 每帧数据长度L 100～500 路径衰落$ {a}_{k} $ $ \text{Unif}(0.8,1) $ 感知角度范围$ {\phi }_{{\mathrm{Min}}},{\phi }_{{\mathrm{Max}}} $ $ \theta =\left[30{^{\circ}},150{^{\circ}}\right] $
下载: 导出CSV
-
[1] WANG Xiangrong, ZHAI Weitong, WANG Xianghua, et al. Wideband near-field integrated sensing and communications: A hybrid precoding perspective[J]. IEEE Signal Processing Magazine, 2025, 42(1): 88–105. doi: 10.1109/MSP.2024.3496396. [2] CUI Mingyao, WU Zidong, LU Yu, et al. Near-field MIMO communications for 6G: Fundamentals, challenges, potentials, and future directions[J]. IEEE Communications Magazine, 2023, 61(1): 40–46. doi: 10.1109/MCOM.004.2200136. [3] 邵凯, 花凡玉, 王光宇. 超大规模可重构智能表面混合远-近场信道估计[J]. 电子与信息学报, 2025, 47(11): 4231–4241. doi: 10.11999/JEIT250306.SHAO Kai, HUA Fanyu, and WANG Guangyu. Hybrid far-near field channel estimation for XL-RIS assisted communication systems[J]. Journal of Electronics & Information Technology, 2025, 47(11): 4231–4241. doi: 10.11999/JEIT250306. [4] 杨青青, 蒲雪莱, 彭艺, 等. HRIS辅助的分层稀疏重构混合远近场源定位算法[J]. 电子与信息学报, 2025, 47(11): 4220–4230. doi: 10.11999/JEIT250429.YANG Qingqing, PU Xuelai, PENG Yi, et al. HRIS-aided layered sparse reconstruction hybrid near- and far-field source localization algorithm[J]. Journal of Electronics & Information Technology, 2025, 47(11): 4220–4230. doi: 10.11999/JEIT250429. [5] LIU Fan, CUI Yuanhao, MASOUROS C, et al. Integrated sensing and communications: Toward dual-functional wireless networks for 6G and beyond[J]. IEEE Journal on Selected Areas in Communications, 2022, 40(6): 1728–1767. doi: 10.1109/JSAC.2022.3156632. [6] HUA Haocheng, XU Jie, and ZHANG Rui. Near-field integrated sensing and communication with extremely large-scale antenna array[J]. IEEE Transactions on Wireless Communications, 2025, 24(12): 9962–9977. doi: 10.1109/TWC.2025.3576089. [7] GAO Zhen, HU Chen, DAI Linglong, et al. Channel estimation for millimeter-wave massive MIMO with hybrid precoding over frequency-selective fading channels[J]. IEEE Communications Letters, 2016, 20(6): 1259–1262. doi: 10.1109/LCOMM.2016.2555299. [8] YUAN Zhengdao, LIU Fei, YUAN Weijie, et al. Iterative detection for orthogonal time frequency space modulation with unitary approximate message passing[J]. IEEE Transactions on Wireless Communications, 2022, 21(2): 714–725. doi: 10.1109/TWC.2021.3097173. [9] WANG Zhaolin, MU Xidong, and LIU Yuanwei. Near-field integrated sensing and communications[J]. IEEE Communications Letters, 2023, 27(8): 2048–2052. doi: 10.1109/LCOMM.2023.3280132. [10] HAN Yu, JIN Shi, WEN Chaokai, et al. Channel estimation for extremely large-scale massive MIMO systems[J]. IEEE Wireless Communications Letters, 2020, 9(5): 633–637. doi: 10.1109/LWC.2019.2963877. [11] LU Yu and DAI Linglong. Mixed LoS/NLoS near-field channel estimation for extremely large-scale MIMO systems[C]. ICC 2023 - IEEE International Conference on Communications, Rome, Italy, 2023: 1–6. doi: 10.1109/ICC45041.2023.10278686. [12] 洪伟, 徐俊, 陈继新, 等. 面向6G的最优和次优毫米波大规模波束成形阵列架构[J]. 电子与信息学报, 2025, 47(8): 2405–2415. doi: 10.11999/JEIT250109.HONG Wei, XU Jun, CHEN Jixin, et al. Optimal and suboptimal architectures of millimeter-wave large-scale arrays for 6G[J]. Journal of Electronics & Information Technology, 2025, 47(8): 2405–2415. doi: 10.11999/JEIT250109. [13] YANG Zai, XIE Lihua, and ZHANG Cishen. Off-grid direction of arrival estimation using sparse Bayesian inference[J]. IEEE Transactions on Signal Processing, 2013, 61(1): 38–43. doi: 10.1109/TSP.2012.2222378. [14] CUI Mingyao and DAI Linglong. Channel estimation for extremely large-scale MIMO: Far-field or near-field?[J]. IEEE Transactions on Communications, 2022, 70(4): 2663–2677. doi: 10.1109/TCOMM.2022.3146400. [15] YUAN Zhengdao, GUO Qinghua, ELDAR Y C, et al. Integrated near field sensing and communications using unitary approximate message passing-based matrix factorization[J]. IEEE Transactions on Communications, 2025, 73(10): 9939–9953. doi: 10.1109/TCOMM.2025.3582730. [16] FRIEDLANDER B. Localization of signals in the near-field of an antenna array[J]. IEEE Transactions on Signal Processing, 2019, 67(15): 3885–3893. doi: 10.1109/TSP.2019.2923164. [17] GAO Dawei, GUO Qinghua, LIAO Guisheng, et al. Signal detection in MIMO systems with hardware imperfections: Message passing on neural networks[J]. IEEE Transactions on Wireless Communications, 2024, 23(1): 820–834. doi: 10.1109/TWC.2023.3283275. [18] YUAN Zhengdao, LIU Fei, GUO Qinghua, et al. Blind grant-free random access with message-passing-based matrix factorization in mmWave MIMO mMTC[J]. IEEE Internet of Things Journal, 2024, 11(3): 4815–4825. doi: 10.1109/JIOT.2023.3301018. [19] EL KORSO M N, BOYER R, RENAUX A, et al. Conditional and unconditional cramér–rao bounds for near-field source localization[J]. IEEE Transactions on Signal Processing, 2010, 58(5): 2901–2907. doi: 10.1109/TSP.2010.2043128. [20] 张广驰, 谢志立, 崔苗, 等. 近场感知通信一体化系统的感知与通信性能帕累托优化[J]. 电子与信息学报, 2025, 47(10): 3528–3537. doi: 10.11999/JEIT250231.ZHANG Guangchi, XIE Zhili, CUI Miao, et al. Pareto optimization of sensing and communication performance of near-field integrated sensing and communication system[J]. Journal of Electronics & Information Technology, 2025, 47(10): 3528–3537. doi: 10.11999/JEIT250231. [21] CAO Yue, YANG Shaoshi, SUN Yutong, et al. Graph neural network enhanced parametric belief propagation for distributed cooperative positioning with loopy factor graph[C]. GLOBECOM 2025 - 2025 IEEE Global Communications Conference, Taipei, China, 2025: 4227–4232. doi: 10.1109/GLOBECOM59602.2025.11432483. [22] LUO Man, GUO Qinghua, JIN Ming, et al. Unitary approximate message passing for sparse bayesian learning[J]. IEEE Transactions on Signal Processing, 2021, 69: 6023–6039. doi: 10.1109/TSP.2021.3114985. [23] YUAN Zhengdao, GUO Yabo, GAO Dawei, et al. Neural network-assisted hybrid model based message passing for parametric holographic MIMO near field channel estimation[J]. IEEE Transactions on Wireless Communications, 2025, 24(7): 6211–6224. doi: 10.1109/TWC.2025.3552492. [24] RODRÍGUEZ-FERNÁNDEZ J, GONZÁLEZ-PRELCIC N, VENUGOPAL K, et al. Frequency-domain compressive channel estimation for frequency-selective hybrid millimeter wave MIMO systems[J]. IEEE Transactions on Wireless Communications, 2018, 17(5): 2946–2960. doi: 10.1109/TWC.2018.2804943. -
图(7) / 表(4)
计量
- 文章访问数: 16
- HTML全文浏览量: 5
- PDF下载量: 6
- 被引次数: 0
下载:
