A Tensor Framework for ISAC: Information Fusion Enhanced Channel Estimation and Target Localization
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摘要: 通信感知一体化(ISAC)能够通过共享频谱与硬件资源实现通信与感知功能的协同，其关键难题之一在于信道与感知目标参数的估计与定位，且二者的信息融合也是提升系统性能的重要环节。为此，该文研究了ISAC系统中基于信息融合的信道/感知目标参数估计与定位问题。首先，利用毫米波多输入多输出ISAC信道与感知目标参数的内在关联，构建统一张量框架，将上行信道与感知目标参数估计分别表述为两个结构化张量分解问题。然后，提出一种迭代与闭式分解相结合的张量算法，实现离开角、到达角、时延、多普勒频移和系数等参数的估计，进而完成移动发射端、散射点及感知目标的定位。通过匹配散射点与感知目标，融合其多普勒频移与位置信息来提高散射点估计精度。此外，该文还推导了克拉美罗界作为性能基准。仿真表明，所提算法在相对低的计算复杂度下实现了高精度的信道估计与目标定位，且信息融合进一步提升了散射点多普勒频移与位置估计性能。Abstract:
Objective Communication and sensing systems are evolving toward higher frequency bands, larger antenna arrays, and greater miniaturization, driving their increasing convergence in terms of hardware architecture, channel characteristics, and signal processing. This synergy gives rise to integrated sensing and communication (ISAC), in which the joint estimation of channel and sensing target parameters has become a primary research hotspot. Although existing studies have realized the co-estimation of these two categories of parameters based on a unified tensor framework, several limitations remain. On the one hand, current research focuses primarily on parameter estimation itself, without further transforming the multidimensional estimation results into precise localization of scatterer points (SPs), mobile terminals, and sensing targets, which makes it difficult to achieve a complete spatial characterization of the wireless propagation environment. On the other hand, limited attention has been paid to the fusion mechanism between channel and sensing target parameter information, thereby hampering the further improvement of parameter estimation and localization accuracy. Methods To address the problems of parameter estimation and localization for channels/sensing targets in millimeter-wave multiple-input multiple-output ISAC systems, a tensor decomposition algorithm based on information fusion is proposed. First, a unified fourth-order parallel factor model is constructed at the base station for the estimation of uplink channel and sensing target parameters. To reduce computational complexity, the fourth-order tensor model is transformed into a third-order form, and the trilinear alternating least squares method is adopted to estimate the three factor matrices. Furthermore, by exploiting the special structure of a factor matrix, the proposed algorithm incorporates a closed-form decomposition to decouple the coupled factor matrix, from which the angle of departure, angle of arrival, time delay, Doppler shift, and coefficients are extracted from the four estimated factor matrices. On this basis, the localization of mobile transmitter (MT), SPs, and sensing targets is realized separately using geometric relationships, while the estimation accuracy of SPs is effectively improved by fusing the Doppler shift and position information of SPs and sensing targets. Besides, the Cramér-Rao bound is derived to establish a theoretical performance benchmark for the five parameters. Results and Discussions The first simulation experiment shows that the proposed algorithm and the Op-QALS algorithm outperform the Co-SVD-BALS algorithm in both channel/sensing target parameter estimation and localization ( Fig. 2 ,Fig. 3 ,Fig. 4 ). With information fusion, the proposed algorithm achieves the best performance in Doppler shift and position estimation for SPs (Fig. 2 (d),Fig. 4 (a)). This is attributed to the fact that both the proposed algorithm and Op-QALS algorithm fully exploit the multi-dimensional structure of the received signal, and the fusion operation further enhances the estimation capability of the proposed algorithm, whereas the Co-SVD-BALS algorithm suffers from severe error accumulation during its stepwise factor matrix estimation. Moreover, the average processing time (APT) required by the proposed algorithm for localization is slightly higher than that of Co-SVD-BALS algorithm, but significantly lower than that of Op-QALS algorithm (Table 1 andTable 2 ). Therefore, the proposed algorithm achieves excellent parameter estimation and localization performance at a reasonable computational cost. The second simulation experiment shows that under two signal-to-noise ratio levels, the localization accuracy of all algorithms improves gradually with the increase of $ K $, while the proposed algorithm maintains comparable SP and MT localization accuracy to Op-QALS algorithm, but with notably lower APT (Fig. 5 ). Furthermore, the incorporation of the fusion operation does not significantly increase the APT of the proposed algorithm (Fig. 5(d) ). The third simulation experiment indicates that increasing $ {M}_{\mathrm{RE}}\left(M_{\mathrm{RE}}^{\mathrm{s}}\right) $and $ N $ helps enhance the ability of the proposed algorithm to resolve multipath signals, thereby obtaining more precise localization performance (Fig. 6 ).Conclusions This paper proposes a unified tensor framework-based information fusion algorithm for channel/sensing target parameter estimation and localization. By exploiting the Vandermonde structure of a factor matrix, the proposed algorithm maintains estimation accuracy while reducing complexity. Besides, fusion operation further improves SP estimation and localization without significantly increasing computational overhead. Future work will extend the algorithm to more general array configurations and explore higher-order tensor processing in multi-base-station cooperation or multi-user access scenarios. -
图 6 在不同$ {M}_{\mathrm{RE}}\left(M_{\mathrm{RE}}^{\mathrm{s}}\right) $和$ N $下，所提算法定位SP、MT和感知目标的RMSE性能随SNR变化图
1 基于信息融合的张量分解算法
输入：上行信道(或感知信道)张量模型$ {{\mathcal{Z}}} $(或$ {{{\mathcal{Z}}}^s} $)，混合预编码矩
阵$ \boldsymbol{F} $(或$ {\boldsymbol{F}}^{\mathrm{s}} $)，组合矩阵$ \boldsymbol{W} $(或$ {\boldsymbol{W}}^{\mathrm{s}} $)输出：$ \left\{{\hat{\theta }}_{l},{\hat{\phi }}_{l},{\hat{\tau }}_{l},{\hat{v}}_{l},{\hat{\alpha }}_{l}\right\} $，$ \left\{\hat{\theta }_{q}^{\mathrm{s}},\hat{\phi }_{q}^{\mathrm{s}},\hat{\tau }_{q}^{\mathrm{s}},\hat{v}_{q}^{\mathrm{s}},\hat{\alpha }_{q}^{\mathrm{s}}\right\} $，$ {\hat{\boldsymbol{p}}}_{\mathrm{M}} $，$ {\hat{\boldsymbol{p}}}_{l} $，
$ \hat{\boldsymbol{p}}_{q}^{\mathrm{s}} $，融合后$ L $个SP的多普勒频移和位置信息(1) 将$ {{\mathcal{Z}}} $进行重排得到$ \overline{\mathcal{Z} } $，利用TALS方法迭代求解出
$ \left\{{\hat{\tilde{\boldsymbol{A}}}}_{\mathrm{T}},{\hat{\tilde{\boldsymbol{A}}}}_{\mathrm{R}},\hat{\boldsymbol{E}}\right\} $(2) for$ l=1,2,\cdots ,L $ (3) 对$ {\boldsymbol{E}}_{\colon ,l} $进行逆矢量化操作得到秩1矩阵$ {\overline{\boldsymbol{E}}}^{\left(l\right)} $，并且计算
$ {\overline{\boldsymbol{E}}}^{\left(l\right)} $的SVD(4) 利用公式(9)得到$ \hat{\boldsymbol{C}} $和$ \hat{\boldsymbol{D}} $ (5) end for (6) 利用公式(10)消除$ \hat{\boldsymbol{C}} $和$ \hat{\boldsymbol{D}} $的尺度模糊 (7) 重复步骤(1)–步骤(6)，得到$ \left\{\hat{\tilde{\boldsymbol{A}}}_{\mathrm{T}}^{\mathrm{s}},\hat{\tilde{\boldsymbol{A}}}_{\mathrm{R}}^{\mathrm{s}},{\hat{\boldsymbol{C}}}^{\mathrm{s}},{\hat{\boldsymbol{D}}}^{\mathrm{s}}\right\} $ (8) 利用公式(11)求解出$ {\hat{\theta }}_{l} $和$ {\hat{\phi }}_{l} $ (9) 利用公式(12)和取相位操作求解出$ {\hat{\tau }}_{l} $和$ {\hat{v}}_{l} $，并结合公式(13)
和(14)求解出$ \hat{\boldsymbol{\alpha }} $(10) 重复步骤(8)-步骤(9)，得到$ \left\{\hat{\theta }_{q}^{\mathrm{s}},\hat{\phi }_{q}^{\mathrm{s}},\hat{\tau }_{q}^{\mathrm{s}},\hat{v}_{q}^{\mathrm{s}},\hat{\alpha }_{q}^{\mathrm{s}}\right\} $ (11) 定义$ {\boldsymbol{p}}_{\mathrm{B}} $，结合公式(16)和(17)求解出$ {\hat{\boldsymbol{p}}}_{\mathrm{M}} $ (12) 利用公式(18)求解出$ {\hat{\boldsymbol{p}}}_{l} $ (13) 在获得感知参数的基础上直接利用几何关系求解出$ \hat{\boldsymbol{p}}_{q}^{\mathrm{s}} $ (14) 构建规范化距离矩阵$ {\boldsymbol{\varPsi }} $，并且初始化全零矩阵$ {\boldsymbol{\varUpsilon}} $ (15) 计算布尔矩阵$ {\boldsymbol{\varTheta }} $，进而得到升序序号矢量$ {\boldsymbol{\mu }}_{\mathrm{seq}} $ (16) for $ e=1,2,\cdots ,Q $ (17) 令$ q=\boldsymbol{\mu }_{\mathrm{s}e\mathrm{q}}^{\mathrm{e}} $，计算$ i=\underset{l}{\arg \min }{{\boldsymbol{\varPsi }}}_{q,l} $，并且更新$ {{\boldsymbol{\varUpsilon}}}_{q,i}=1 $ (18) 将第$ q $个感知目标与第$ i $个SP的位置和多普勒频移信息按
照文献[19]中的匹配融合定理四进行融合，并设置
$ {{\boldsymbol{\varUpsilon}}}_{\colon ,i}=+\mathrm{\infty } $(19) end for 
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表 1 算法1 基于信息融合的张量分解算法表1不同算法定位SP和MT所需要的APT (单位：秒)
算法/SNR(dB) 0 5 10 15 20 25 30 Op-QALS 0.0441 0.0525 0.0638 0.0762 0.0916 0.1090 0.1163 Co-SVD-BALS 0.0088 0.0088 0.0127 0.0233 0.0236 0.0238 0.0249 所提算法 0.0381 0.0370 0.0250 0.0269 0.0271 0.0292 0.0291
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表 2 不同算法定位感知目标所需要的APT (单位：秒)
算法/SNR(dB) 0 5 10 15 20 25 30 Op-QALS 0.0290 0.0318 0.0357 0.0406 0.0438 0.0463 0.0481 Co-SVD-BALS 0.0083 0.0096 0.0096 0.0098 0.0100 0.0103 0.0104 所提算法 0.0184 0.0180 0.0153 0.0149 0.0150 0.0150 0.0154
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