MIMO雷達通信一體化：波束圖增益最大化波束成形設計

張若愚; 任紅; 陳光毅; 林志; 吳文

doi:10.11999/JEIT240631

MIMO雷達通信一體化：波束圖增益最大化波束成形設計

doi: 10.11999/JEIT240631

張若愚¹,
任紅¹,
陳光毅¹,
林志²,
吳文^1, ,

1.
南京理工大學近程射頻感知芯片與微系統(tǒng)教育部重點實驗室南京 210094
2.
國防科技大學電子對抗學院合肥 230037

基金項目: 國家自然科學基金(62201266, 62201592, 62471477)，江蘇省自然科學基金(BK20210335)

詳細信息

作者簡介:
張若愚：男，副研究員，研究方向為MIMO雷達通信一體化

任紅：女，碩士生，研究方向為雷達通信一體化

陳光毅：男，博士生，研究方向為雷達通信一體化混合波束成形

林志：男，副教授，研究方向為陣列信號處理、空天地一體化通信網(wǎng)絡

吳文：男，研究員，研究方向為毫米波近程探測理論與技術(shù)

通訊作者:
吳文　wuwen@njust.edu.cn

中圖分類號: TN929.5
計量
- 文章訪問數(shù): 102
- HTML全文瀏覽量: 25
- PDF下載量: 27
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2024-07-22
- 修回日期: 2025-02-14
- 網(wǎng)絡出版日期: 2025-02-21

MIMO Dual-functional Radar-communication: Beampattern Gain Maximization Beamforming Design

1.
Key Laboratory of Near-Range RF Sensing ICs & Microsystems, Nanjing University of Science and Technology, Nanjing 210094, China
2.
College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China

Funds: The National Nature Science Foundation of China (62201266, 62201592, 62471477), The National Nature Science Foundation of Jiangsu Province (BK20210335)

摘要

摘要: 無線通信設備數(shù)量的驟增造成頻譜資源日益稀缺，通信用頻逐漸向更高頻段擴展，從而導致通信與雷達頻段出現(xiàn)越來越多的重疊，雷達通信一體化被視為解決頻譜擁擠實現(xiàn)高效共生的潛在技術(shù)。該文考慮一個多輸入多輸出(MIMO)雷達通信一體化系統(tǒng)，在實現(xiàn)目標探測的同時進行多用戶通信。首先，在滿足多用戶信干噪比和總功率約束的條件下，最大化目標方向的波束圖增益。然后，針對一體化發(fā)射波束成形設計問題，提出基于半正定松弛(SDR)和優(yōu)化最小化(MM)的兩種波束成形設計方案，求解得到發(fā)射波束成形矢量。最后，仿真結(jié)果表明基于MM的方案復雜度更低，并且能夠?qū)崿F(xiàn)與基于SDR的方案幾乎相同的波束圖增益。此外，隨著發(fā)射天線數(shù)量的增加，基于MM的方案相比于基于SDR的方案復雜度的降低程度變得更為顯著。
- 雷達通信一體化 /
- 多輸入多輸出 /
- 波束成形 /
- 波束圖增益 /
- 優(yōu)化最小化
Abstract: Objective The rapid growth in the number of wireless communication devices has led to the expansion of frequency bands to higher frequencies, resulting in increased overlap between communication and radar systems. Dual-Functional Radar-Communication (DFRC), which shares spectrum resources on the same hardware platform, is an effective solution to address spectrum congestion. The integration of Multiple-Input Multiple-Output (MIMO) technology, which employs multi-antenna techniques, with DFRC is crucial for achieving both high-precision detection and large-capacity communication. Beamforming technology plays a key role in efficiently allocating resources between these two requirements, further enhancing the collaborative gain of DFRC systems. Beampattern gain, a critical performance metric for target detection, makes it essential to investigate beamforming designs that maximize this gain in MIMO DFRC systems. Methods A MIMO DFRC system is considered, which simultaneously achieves target detection and Multi-User (MU) communication. First, a beamforming problem is formulated to maximize the beampattern gain in the target direction, while satisfying MU Signal-to-Interference-plus-Noise Ratio (SINR) and total power constraints. To address this beamforming design problem, two methods based on Semidefinite Relaxation (SDR) and Majorization Minimization (MM) are proposed to solve for the transmit beamforming vectors. Specifically, the SDR-based method transforms the beamforming problem into a semidefinite programming problem by introducing auxiliary variables and relaxing the rank-one constraint. The MM-based method, on the other hand, uses the first-order Taylor expansion to construct a cost function from the objective function, transforms the SINR constraint into a second-order cone constraint, and iteratively solves the simplified problem. Results and Discussions The convergence curves of the SDR-based and MM-based beamforming design schemes are shown (Figure 2). The results indicate that the MM-based method can achieve almost the same beampattern gain as the SDR-based method. Under the same number of transmit antennas, a higher SINR threshold results in a smaller beampattern gain. This phenomenon reflects the performance trade-off between communication and radar in MIMO DFRC systems. Under the same SINR threshold, increasing the number of transmit antennas leads to a greater beampattern gain. This is because an increase in the number of transmit antennas provides additional degrees of freedom for the radar. The comparison of the single CVX running time of the SDR-based and MM-based methods under different numbers of transmit antennas is shown (Figure 3). The results demonstrate that the single CVX running time of the MM-based method is shorter than that of the SDR-based method for the same number of transmit antennas, and as the number of transmit antennas increases, the complexity reduction of the MM-based method becomes more significant than that of the SDR-based method. The variation curves of beampattern gain with SINR threshold for different numbers of transmit antennas in the MM-based and SDR-based methods are shown (Figure 4). The beampattern gain obtained by the MM-based method is slightly lower than that obtained by the SDR-based method. However, as the number of transmit antennas increases, the difference between the two methods gradually decreases. Moreover, the more transmit antennas there are, the greater the SINR achievable by the communication user. When the number of antennas is fixed, the relationship between beampattern gain and transmit SNR obtained by the radar using the MM-based method is presented (Figure 5). When the SINR threshold remains unchanged, the relationship between them is shown (Figure 6). The results illustrate that, compared with the radar-only scenario, the beampattern gain performance of MIMO DFRC systems is lower, and a larger SINR threshold results in a smaller beampattern gain. Additionally, within a certain range, when the transmit SNR is constant, beampattern gain is directly proportional to the number of transmit antennas. Conclusions This paper addresses the beamforming design problem for MIMO DFRC systems with the objective of maximizing beampattern gain. By jointly optimizing the communication and radar transmit beamforming vectors, the beampattern gain in the target direction is maximized while satisfying the SINR constraint for communication users and the total transmit power constraint. To solve this problem, the SDR-based and MM-based beamforming design methods are proposed. Simulation results demonstrate that the MM-based method offers lower complexity and achieves nearly the same beampattern gain as the SDR-based method. Moreover, as the number of transmit antennas increases, the complexity reduction of the MM-based method is more significant compared to the SDR-based method.
- Dual-Functional Radar-Communication (DFRC) /
- Multiple-Input Multiple-Output (MIMO) /
- Beamforming /
- Beampattern gain /
- Majorization minimization

HTML全文

圖 1 MIMO雷達通信一體化系統(tǒng)

下載: 全尺寸圖片幻燈片

圖 2 波束圖增益隨迭代次數(shù)的收斂曲線圖

下載: 全尺寸圖片幻燈片

圖 3 不同發(fā)射天線數(shù)下單次CVX的運行時間對比圖

下載: 全尺寸圖片幻燈片

圖 4 不同發(fā)射天線數(shù)下的波束圖增益隨SINR閾值變化曲線

下載: 全尺寸圖片幻燈片

圖 5 ${N_t} = 8$的波束圖增益隨發(fā)射SNR的變化曲線

下載: 全尺寸圖片幻燈片

圖 6 $\varGamma = 18\;{\text{dB}}$的波束圖增益隨發(fā)射SNR的變化曲線

下載: 全尺寸圖片幻燈片

1 基于SDR的波形設計方案

輸入：初始化${P_t}$, ${{{\boldsymbol{h}}}_k}$, ${{\boldsymbol{f}}}({\theta _0})$, ${\sigma ^2}$, $\varGamma $。
輸出：總發(fā)射波束成形矢量$ {\bar w} $。
步驟：
1：使用MATLAB的CVX工具箱求解問題式(12)得到　${\tilde {\boldsymbol{R}}},{{\tilde {\boldsymbol{R}}}_1},{{\tilde {\boldsymbol{R}}}_2}, \cdots ,{{\tilde {\boldsymbol{R}}}_K}$；
2：根據(jù)式(13)求解通信發(fā)射波束成形矢量$ {{\bar {\boldsymbol{w}}}_k} $；
3：根據(jù)式(14)和式(15)求解雷達發(fā)射波束成形矩陣$ {{\bar {\boldsymbol{W}}}_r} $；
4：將$ K $個$ {{\bar {\boldsymbol{w}}}_k} $與$ {{\bar {\boldsymbol{W}}}_r} $的各列按列堆疊得到總發(fā)射波束成形矢量$ {\bar {\boldsymbol{w}}} $。

下載: 導出CSV

2 基于MM的波形設計方案

輸入：初始化${{{\boldsymbol{w}}}_0}$, ${P_t}$, ${{{\boldsymbol{h}}}_k}$, ${{\boldsymbol{f}}}({\theta _0})$, ${\sigma ^2}$, $\varGamma $, $\varepsilon $。
輸出：總發(fā)射波束成形矩陣的向量化形式$ {\bar {\boldsymbol{w}}} $。
步驟：
1：$t = 0$，隨機初始化${{{\boldsymbol{w}}}_t}$；
2：$t = t + 1$；
3：使用MATLAB的CVX工具箱求解問題式(20)得到${{\boldsymbol{w}}}$；
4：計算${\text{res}} = {{\left\| {\mathcal{P}({\theta _0},{{\boldsymbol{w}}}) - \mathcal{P}({\theta _0},{{{\boldsymbol{w}}}_t})} \right\|} \mathord{\left/ {\vphantom {{\left\| {\mathcal{P}({\theta _0},{w}) - \mathcal{P}({\theta _0},{{w}_t})} \right\|} {\mathcal{P}({\theta _0},{{w}_t})}}} \right. } {\mathcal{P}({\theta _0},{{{\boldsymbol{w}}}_t})}}$；
5：若${\text{res}} \gt \varepsilon $，則${{{\boldsymbol{w}}}_t} = {{\boldsymbol{w}}}$并返回第2步；否則$ {\bar {\boldsymbol{w}}} = {{\boldsymbol{w}}} $。

下載: 導出CSV

參考文獻(28)

[1]	IMT-2030(6G)推進組. 6G總體愿景與潛在關(guān)鍵技術(shù)白皮書[R]. 2020. IMT-2030(6G) Promotion Group. 6G vision and candidate technologies[R]. 2020.
[2]	劉凡, 袁偉杰, 原進宏, 等. 雷達通信頻譜共享及一體化: 綜述與展望[J]. 雷達學報, 2021, 10(3): 467–484. doi: 10.12000/JR20113. LIU Fan, YUAN Weijie, YUAN Jinhong, et al. Radar-communication spectrum sharing and integration: Overview and prospect[J]. Journal of Radars, 2021, 10(3): 467–484. doi: 10.12000/JR20113.
[3]	LIU Fan, ZHOU Longfei, MASOUROS C, et al. Toward dual-functional radar-communication systems: Optimal waveform design[J]. IEEE Transactions on Signal Processing, 2018, 66(16): 4264–4279. doi: 10.1109/TSP.2018.2847648.
[4]	CHEN Guangyi, ZHANG Ruoyu, REN Hong, et al. Hybrid beamforming design with overlapped subarrays for massive MIMO-ISAC systems[C]. Proceedings of GLOBECOM 2023 - 2023 IEEE Global Communications Conference, Kuala Lumpur, Malaysia, 2023: 528–533. doi: 10.1109/GLOBECOM54140.2023.10437590.
[5]	ZHOU Wenxing, ZHANG Ruoyu, CHEN Guangyi, et al. Integrated sensing and communication waveform design: A survey[J]. IEEE Open Journal of the Communications Society, 2022, 3: 1930–1949. doi: 10.1109/OJCOMS.2022.3215683.
[6]	肖博, 霍凱, 劉永祥. 雷達通信一體化研究現(xiàn)狀與發(fā)展趨勢[J]. 電子與信息學報, 2019, 41(3): 739–750. doi: 10.11999/JEIT180515. XIAO Bo, HUO Kai, and LIU Yongxiang. Development and prospect of radar and communication integration[J]. Journal of Electronics & Information Technology, 2019, 41(3): 739–750. doi: 10.11999/JEIT180515.
[7]	張若愚, 袁偉杰, 崔原豪, 等. 面向6G的大規(guī)模MIMO通信感知一體化: 現(xiàn)狀與展望[J]. 移動通信, 2022, 46(6): 17–23. doi: 10.3969/j.issn.1006-1010.2022.06.003. ZHANG Ruoyu, YUAN Weijie, CUI Yuanhao, et al. Integrated sensing and communications with massive MIMO for 6G: Status and prospect[J]. Mobile Communications, 2022, 46(6): 17–23. doi: 10.3969/j.issn.1006-1010.2022.06.003.
[8]	ZHANG J A, RAHMAN M L, WU Kai, et al. Enabling joint communication and radar sensing in mobile networks—a survey[J]. IEEE Communications Surveys & Tutorials, 2022, 24(1): 306–345. doi: 10.1109/COMST.2021.3122519.
[9]	HASSANIEN A, AMIN M G, ZHANG Y D, et al. Dual-function radar-communications: Information embedding using sidelobe control and waveform diversity[J]. IEEE Transactions on Signal Processing, 2016, 64(8): 2168–2181. doi: 10.1109/TSP.2015.2505667.
[10]	WANG Xiangrong, HASSANIEN A, and AMIN M G. Dual-function MIMO radar communications system design via sparse array optimization[J]. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(3): 1213–1226. doi: 10.1109/TAES.2018.2866038.
[11]	LIU Yongjun, LIAO Guisheng, XU Jingwei, et al. Adaptive OFDM integrated radar and communications waveform design based on information theory[J]. IEEE Communications Letters, 2017, 21(10): 2174–2177. doi: 10.1109/LCOMM.2017.2723890.
[12]	KUMARI P, CHOI J, GONZáLEZ-PRELCIC N, et al. IEEE 802.11ad-based radar: An approach to joint vehicular communication-radar system[J]. IEEE Transactions on Vehicular Technology, 2018, 67(4): 3012–3027. doi: 10.1109/TVT.2017.2774762.
[13]	CUI Yuanhao, LIU Fan, JING Xiaojun, et al. Integrating sensing and communications for ubiquitous IoT: Applications, trends, and challenges[J]. IEEE Network, 2021, 35(5): 158–167. doi: 10.1109/MNET.010.2100152.
[14]	LIU Fan, MASOUROS C, LI Ang, et al. MU-MIMO communications with MIMO radar: From co-existence to joint transmission[J]. IEEE Transactions on Wireless Communications, 2018, 17(4): 2755–2770. doi: 10.1109/TWC.2018.2803045.
[15]	LIU Xiang, HUANG Tianyao, SHLEZINGER N, et al. Joint transmit beamforming for multiuser MIMO communications and MIMO radar[J]. IEEE Transactions on Signal Processing, 2020, 68: 3929–3944. doi: 10.1109/TSP.2020.3004739.
[16]	LIU Fan, LIU Yafeng, LI Ang, et al. Cramér-Rao bound optimization for joint radar-communication beamforming[J]. IEEE Transactions on Signal Processing, 2022, 70: 240–253. doi: 10.1109/TSP.2021.3135692.
[17]	HUA Haocheng, SONG Xianxin, FANG Yuan, et al. MIMO integrated sensing and communication with extended target: CRB-Rate tradeoff[C]. Proceedings of GLOBECOM 2022 - 2022 IEEE Global Communications Conference, Rio de Janeiro, Brazil, 2022: 4075–4080. doi: 10.1109/GLOBECOM48099.2022.10000676.
[18]	CHEN Li, WANG Zhiqin, DU Ying, et al. Generalized transceiver beamforming for DFRC with MIMO radar and MU-MIMO communication[J]. IEEE Journal on Selected Areas in Communications, 2022, 40(6): 1795–1808. doi: 10.1109/JSAC.2022.3155515.
[19]	DU Ying, LIU Yao, HAN Kaifeng, et al. Multi-user and multi-target dual-function radar-communication waveform design: Multi-fold performance tradeoffs[J]. IEEE Transactions on Green Communications and Networking, 2023, 7(1): 483–496. doi: 10.1109/TGCN.2023.3234275.
[20]	HUA Haocheng, XU Jie, and HAN T X. Optimal transmit beamforming for integrated sensing and communication[J]. IEEE Transactions on Vehicular Technology, 2023, 72(8): 10588–10603. doi: 10.1109/TVT.2023.3262513.
[21]	ZHANG Ruoyu, CHENG Lei, WANG Shuai, et al. Tensor decomposition-based channel estimation for hybrid mmWave massive MIMO in high-mobility scenarios[J]. IEEE Transactions on Communications, 2022, 70(9): 6325–6340. doi: 10.1109/TCOMM.2022.3187780.
[22]	ZHANG Ruoyu, CHENG Lei, WANG Shuai, et al. Integrated sensing and communication with massive MIMO: A unified tensor approach for channel and target parameter estimation[J]. IEEE Transactions on Wireless Communications, 2024, 23(8): 8571–8587. doi: 10.1109/TWC.2024.3351856.
[23]	LUO Zhiquan and YU Wei. An introduction to convex optimization for communications and signal processing[J]. IEEE Journal on Selected Areas in Communications, 2006, 24(8): 1426–1438. doi: 10.1109/JSAC.2006.879347.
[24]	TRAN L N, HANIF M F, TOLLI A, et al. Fast converging algorithm for weighted sum rate maximization in multicell MISO downlink[J]. IEEE Signal Processing Letters, 2012, 19(12): 872–875. doi: 10.1109/LSP.2012.2223211.
[25]	SUN Ying, BABU P, and PALOMAR D P. Majorization-minimization algorithms in signal processing, communications, and machine learning[J]. IEEE Transactions on Signal Processing, 2017, 65(3): 794–816. doi: 10.1109/TSP.2016.2601299.
[26]	MOSEK ApS. Mosek optimization toolbox for matlab[R]. 2025.
[27]	WANG Kunyu, SO A M C, CHANG T H, et al. Outage constrained robust transmit optimization for multiuser MISO downlinks: Tractable approximations by conic optimization[J]. IEEE Transactions on Signal Processing, 2014, 62(21): 5690–5705. doi: 10.1109/TSP.2014.2354312.
[28]	BEN-TAL A and NEMIROVSKI A. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2001. doi: 10.1137/1.9780898718829.