基于一阶优化算法的无线通信资源分配问题研究

第五代及未来的无线通信预计将支持各种新兴技术，如移动边缘计算、联邦 学习、痛感一体化以及空中计算。为了探索这些技术的潜力，本文设计了一个协作 的边缘云计算框架和一个集通感算一体化的框架。在这两个框架下，分别研究了 资源分配和波束形成设计问题。为了解决这些问题，本文基于梯度信息提出了一 些高效的一阶优化算法。在非线性优化方面，本文首先提出了松弛的近端点算法 和预测校正方法来处理具有非线性约束的凸问题。通过利用变分框架的收敛条件， 可以直接获得它们的收敛性。在理论上，证明了这两种方法在随机意义上可以达 到 𝑂(1/𝑡) 的收敛率。接着，针对复数域中的凸优化问题，研究了一些复变量的迭 代方法。对于无约束情况，理论分析显示梯度下降法在复域中是收敛的。并且，证 明了投影梯度下降法可以有效地解决易于投影约束的凸问题。进一步，本文提出 了一种广义的对偶校正方法来解决一般非线性约束的凸问题，并且证明它在复数 域可以实现 𝑂(1/𝑡) 的序列收敛速率。 然而，由于复杂的系统框架，无线通信中的优化问题通常是非凸的。具体来 说，在边缘云计算网络中，本文构建了一个混合整数非线性规划问题来最小化能 量消耗和延迟。利用交替优化技术，这个非凸 NP 困难的问题被分解为一个非凸的 连续变量问题和一个整数线性规划问题。然后它们分别被所提出的极值下降法和 分支定界法求解。理论分析表明，所提出的极值下降法具有 𝑂(1/𝑠) 的速率收敛， 而交替优化可以收敛到次优解甚至是最优解。接下来，在资源受限的边缘云计算 网络中构建了另一个混合整数非线性规划问题来加速联邦学习。同样，使用交替 优化技术将这个问题分解为连续和整数变量优化问题。为了解决这两个问题，从 理论上推导出最佳的卸载顺序。基于松弛的近端点算法，优化了数据分配和迭代 次数选择。最后，在集通感算一体化的框架中，本文研究了全向和定向波束成形的 设计问题来提高频谱效率和服务质量。基于推导的定向波束图，考虑了多个波束 成形设计问题来平衡感知和空中计算的性能。由于这些非凸的波束设计问题属于 复数域非线性优化，本文采用交替优化方法和投影梯度下降法去求解它们。此外， 本文提出了一种低复杂度的两步投影梯度下降法来解决具有两个范数球约束的凸 问题。仿真结果表明所提出的一阶优化算法能够高效地处理所提出的问题。

[1] MARTINET B. R'egularisation d"in'equations variationnelles par approximations successives [C]//Rech. Oper. 1970.
[2] BONNANS J F, GILBERT J C, LEMARéCHAL C, et al. A family of variable metric proximal methods[J]. Appl Manag Sci, 1995, 68: 15–47.
[3] BURKE J, QIAN M. On the superlinear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating[J]. Appl Manag Sci, 2000, 88: 157–181.
[4] GU G, HE B, YUAN X. Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: A unified approach[J]. Comput Optim Appl, 2014, 59: 135–161.
[5] ROCKAFELLAR R T. Monotone operators and the proximal point algorithm[J]. SIAM J. Control Optim., 1976, 14(5): 877-898.
[6] ARROW K, HURWICZ L, UZAWA H. Studies in linear and non-linear programming[J]. Stan- ford University Press, 1958.
[7] ZHU M, CHAN T F. An efficient primal-dual hybrid gradient algorithm for total variation image restoration[C]//UCLA CAM technical report. 2008: 08-34.
[8] HE B, XU S, YUAN X. On convergence of the Arrow-Hurwicz method for saddle point prob- lems[J]. J Math Imaging Vis, 2022, 64(6): 662-671.
[9] HE B. PPA-like contraction methods for convex optimization: A framework using variational inequality approach[J]. J. Oper. Res. Soc. China, 2015, 3: 391-420.
[10] CHAMBOLLE A, POCK T. A first-order primal-dual algorithm for convex problems with applications to imaging[J]. J Math Imaging Vis, 2011, 40: 120-145.
[11] HE B, YUAN X, ZHANG W. A customized proximal point algorithm for convex minimization with linear constraints[J]. Comput Optim Appl, 2013, 56: 559–572.
[12] CAI X, GU G, HE B, et al. A relaxed customized proximal point algorithm for separable convex programming[C]//Optimization online. 2011.
[13] ZHU Y, WU J, YU G. A fast proximal point algorithm for 𝓁1-minimization problem in com- pressed sensing[J]. Appl Math Comput, 2015, 270: 777-784.
[14] CHEN H M, CAI X J, XU L L. Approximate customized proximal point algorithms for sepa- rable convex optimization[J]. J. Oper. Res. Soc. China, 2022, 11: 383–408.
[15] JIANG B, PENG Z, DENG K. Two new customized proximal point algorithms without re- laxation for linearly constrained convex optimization[J]. Bull. Iranian Math. Soc., 2020, 46: 865–892.
[16] HE B, MA F, YUAN X. An algorithmic framework of generalized primal-dual hybrid gradient methods for saddle point problems[J]. J Math Imaging Vis, 2017, 58: 279-293.
[17] HE B, MA F, XU S, et al. A generalized primal-dual algorithm with improved convergence condition for saddle point problems[J]. SIAM J. Imaging Sci., 2022, 15(3): 1157-1183.
[18] BEN-TAL A, NEMIROVSKI A, ROOS C. Extended matrix cube theorems with applications to 𝜇-theory in control[J]. Math. Oper. Res., Aug. 2003, 28(3): 497-523.
[19] LUSTIG M, DONOHO D, PAULY J M. Sparse MRI: The application of compressed sensing for rapid MR imaging[J]. Magn. Reson. Med., Dec. 2007, 58(6): 1182-1195.
[20] HUANG Y, PALOMAR D P. Randomized algorithms for optimal solutions of double-sided QCQP with applications in signal processing[J]. IEEE Trans. Signal Process., Mar. 2014, 62 (5): 1093-1108.
[21] WANG S, LI X, LIU F, et al. Integrated sensing, communication, and computation over-the- air: Beampattern design[C]//2023 IEEE International Conference on Communications (ICC). in prep, 2023.
[22] SORBER L, BAREL M V, LATHAUWER L D. Unconstrained optimization of real functions in complex variables[J]. SIAM J. Optim., 2012, 22(3): 879-898.
[23] ZHANG S, XIA Y. Solving nonlinear optimization problems of real functions in complex variables by complex-valued iterative methods[J]. IEEE Trans. Syst., Man, Cybern., Jan. 2018, 48(1): 27-287.
[24] ZHANG S, XIA Y. Two fast complex-valued algorithms for solving complex quadratic pro- gramming problems[J]. IEEE Trans. Cybern., Dec. 2016, 46(12): 2837-2847.
[25] QIN S, FENG J, SONG J, et al. A one-layer recurrent neural network for constrained complex- variable convex optimization[J]. IEEE Trans. Neural Netw., Mar. 2018.
[26] ZHANG S, XIA Y, XIA Y, et al. Matrix-form neural networks for complex-variable basis pursuit problem with application to sparse signal reconstruction[J]. IEEE Trans. Cybern., July 2022, 52(7): 7049-7059.
[27] ZHANG H, MANDIC D P. Is a complex-valued stepsize advantageous in complex-valued gradient learning algorithms?[J]. IEEE Trans. Neural Netw. Learn. Syst., Dec. 2016, 27(12): 2730-2735.
[28] WANG S, GONG Y. Nonlinear convex optimization: From relaxed proximal point algorithm to prediction correction method[A]. 2023. arXiv: 2307.14615.
[29] SALEEM U, LIU Y, JANGSHER S, et al. Mobility-aware joint task scheduling and resource allocation for cooperative mobile edge computing[J]. IEEE Trans. Wireless Commun., Jan. 2021, 20(1): 360-374.
[30] HE S, REN J, WANG J, et al. Cloud-edge coordinated processing: Low-latency multicasting transmission[J]. IEEE J. Sel. Areas Commun., May 2019, 37(5): 1144-1158.
[31] SONG Z, LIU Y, SUN X. Joint task offloading and resource allocation for NOMA-enabled multi-access mobile edge computing[J]. IEEE Trans. Commun., Mar. 2021, 69(3): 1548-1564.
[32] PORAMBAGE P, OKWUIBE J, LIYANAGE M, et al. Survey on multi-access edge computing for internet of things realization[J]. IEEE Commun. Surv. Tutorials, Fourthquarter 2018, 20(4): 2961-2991.
[33] MAO Y, YOU C, ZHANG J, et al. A survey on mobile edge computing: The communication perspective[J]. IEEE Commun. Surv. Tutorials, Fourthquarter 2017, 19(4): 2322-2358.
[34] PARK C, LEE J. Mobile edge computing-enabled heterogeneous networks[J]. IEEE Trans. Wireless Commun., Feb. 2021, 20(2): 1038-1051.
[35] ABBAS N, ZHANG Y, TAHERKORDI A, et al. Mobile edge computing: A survey[J]. IEEE Internet Things J., Feb. 2018, 5(1): 450-465.
[36] LIU B, LIU C, PENG M. Resource allocation for energy-efficient MEC in NOMA-enabled massive IoT networks[J]. IEEE J. Sel. Areas Commun., April 2021, 39(4): 1015-1027.
[37] LABRIJI I, MENEGHELLO F, CECCHINATO D, et al. Mobility aware and dynamic migration of MEC services for the internet of vehicles[J]. IEEE Trans. Netw. Service Manag., Mar. 2021, 18(1): 570-584.
[38] LI L, CHENG Q, TANG X, et al. Resource allocation for NOMA-MEC systems in ultra-dense networks: A learning aided mean-field game approach[J]. IEEE Trans. Wireless Commun., Mar. 2021, 20(3): 1487-1500.
[39] LIU C, ZHANG H, JI H, et al. MEC-assisted flexible transcoding strategy for adaptive bitrate video streaming in small cell networks[J]. China Commun., Feb. 2021, 18(2): 200-214.
[40] REN J, YU G, HE Y, et al. Collaborative cloud and edge computing for latency minimization [J]. IEEE Trans. Veh. Technol., May 2019, 68(5): 5031-5044.
[41] ZHANG Y, DI B, ZHENG Z, et al. Distributed multi-cloud multi-access edge computing by multi-agent reinforcement learning[J]. IEEE Trans. Wireless Commun., April 2021, 20(4): 2565-2578.
[42] LIU J, MAO Y, ZHANG J, et al. Delay-optimal computation task scheduling for mobile-edge computing systems[C]//2016 IEEE International Symposium on Information Theory (ISIT). Barcelona, Spain, Aug. 2016: 1451-1455.
[43] LIU C F, BENNIS M, DEBBAH M, et al. Dynamic task offloading and resource allocation for ultra-reliable low-latency edge computing[J]. IEEE Trans. Commun., June 2019, 67(6): 4132-4150.
[44] WU Y, NI K, ZHANG C, et al. NOMA-assisted multi-access mobile edge computing: A joint optimization of computation offloading and time allocation[J]. IEEE Trans. Veh. Technol., Dec. 2018, 67(12): 12244-12258.
[45] XU J, CHEN L, ZHOU P. Joint service caching and task offloading for mobile edge computing in dense networks[C]//IEEE INFOCOM 2018 - IEEE Conference on Computer Communica- tions. Honolulu, HI, USA, Oct. 2018: 207-215.
[46] GUO K, GAO R, XIA W, et al. Online learning based computation offloading in MEC systems with communication and computation dynamics[J]. IEEE Trans. Commun., Feb. 2021, 69(2): 1147-1162.
[47] GUO C, HE W, LI G Y. Optimal fairness-aware resource supply and demand management for mobile edge computing[J]. IEEE Trans. Wireless Commun., Mar. 2021, 10(3): 678-682.
[48] GUO H, LIU J. Collaborative computation offloading for multiaccess edge computing over fiber–wireless networks[J]. IEEE Trans. Veh. Technol., May 2018, 67(5): 4514-4526.
[49] XU C, ZHENG G, ZHAO X. Energy-minimization task offloading and resource allocation for mobile edge computing in NOMA heterogeneous networks[J]. IEEE Trans. Veh. Technol., Dec. 2020, 69(12): 16001-16016.
[50] YANG B, WU D, WANG H, et al. Two-layer Stackelberg game-based offloading strategy for mobile edge computing enhanced fiwi access networks[J]. IEEE trans. green commun. netw., Mar. 2021, 5(1): 457-470.
[51] LI S, SUN W, SUN Y, et al. Energy-efficient task offloading using dynamic voltage scaling in mobile edge computing[J]. IEEE Trans. Netw. Sci. Eng., Jan. 2021, 8(1): 588-598.
[52] KIANI A, ANSARI N. Edge computing aware NOMA for 5G networks[J]. IEEE Internet Things J., April 2018, 5(2): 1299-1306.
[53] CAO X, WANG F, XU J, et al. Joint computation and communication cooperation for energy- efficient mobile edge computing[J]. IEEE Internet Things J., June 2019, 6(3): 4188-4200.
[54] DAI Y, XU D, MAHARJAN S, et al. Joint computation offloading and user association in multi- task mobile edge computing[J]. IEEE Trans. Veh. Technol., Dec. 2018, 67(12): 12313-12325.
[55] YANG L, ZHANG H, LI M, et al. Mobile edge computing empowered energy efficient task offloading in 5G[J]. IEEE Trans. Veh. Technol., July 2018, 67(7): 6398-6409.
[56] WANG F, XU J, DING Z. Multi-antenna NOMA for computation offloading in multiuser mobile edge computing systems[J]. IEEE Trans. Commun., Mar. 2019, 67(3): 2450-2463.
[57] MAO Y, ZHANG J, SONG S H, et al. Stochastic joint radio and computational resource man- agement for multi-user mobile-edge computing systems[J]. IEEE Trans. Wireless Commun., Sept. 2017, 16(9): 5994-6009.
[58] DING C, WANG J B, ZHANG H, et al. Joint MU-MIMO precoding and resource allocation for mobile-edge computing[J]. IEEE Trans. Wireless Commun., Mar. 2021, 20(3): 1639-1654.
[59] LIAO Z, PENG J, HUANG J, et al. Distributed probabilistic offloading in edge computing for 6G-enabled massive internet of things[J]. IEEE Internet Things J., April 2021, 8(7): 5298-5308.
[60] ZHANG J, HU X, NING Z, et al. Energy-latency tradeoff for energy-aware offloading in mobile edge computing networks[J]. IEEE Internet Things J., Aug. 2018, 5(4): 2633-2645.
[61] TRAN T X, POMPILI D. Joint task offloading and resource allocation for multi-server mobile- edge computing networks[J]. IEEE Trans. Veh. Technol., Jan. 2019, 68(1): 856-868.
[62] MAO Y, ZHANG J, LETAIEF K B. Joint task offloading scheduling and transmit power allo- cation for mobile-edge computing systems[C]//2017 IEEE Wireless Communications and Net- working Conference (WCNC). San Francisco, CA, USA, May 2017: 1-6.
[63] JIA Z, WU Q, DONG C, et al. Hierarchical aerial computing for internet of things via cooper- ation of HAPs and UAVs[J]. IEEE Internet Things J., April 2023, 10(7): 5676-5688.
[64] CHEN J, WU Q, XU Y, et al. A multi-leader multi-follower Stackelberg game for coalition- basedUAV MEC networks[J]. IEEE Wireless Commun. Lett., Nov. 2021, 10(11): 2350-2354.
[65] YOU W, DONG C, CHENG X, et al. Joint optimization of area coverage and mobile-edge computing with clustering for FANETs[J]. IEEE Internet Things J., Jan. 2021, 8(2): 695-707.
[66] YANG B, CAO X, YUEN C, et al. Offloading optimization in edge computing for deep- learning-enabled target tracking by internet of UAVs[J]. IEEE Internet Things J., June 2021, 8 (12): 9878-9893.
[67] LIN Z, NIU H, AN K, et al. Refracting RIS aided hybrid satellite-terrestrial relay networks: Joint beamforming design and optimization[J]. IEEE Trans. Aerosp. Electron. Syst., Aug. 2022, 58(4): 3717-3724.
[68] AN K, LIN M, OUYANG J, et al. Secure transmission in cognitive satellite terrestrial networks [J]. IEEE J. Sel. Areas Commun., Nov. 2016, 34(11): 3025-3037.
[69] LIN Z, AN K, NIU H, et al. SLNR-based secure energy efficient beamforming in multibeam satellite systems[J/OL]. IEEE Trans. Aerosp. Electron. Syst., early access, 2022: 1-4. DOI: 10.1109/TAES.2022.3190238.
[70] LIN Z, LIN M, WANG J B, et al. Joint beamforming and power allocation for satellite-terrestrial integrated networks with non-orthogonal multiple access[J]. IEEE J. Sel. Topics Signal Process., June 2019, 13(3): 657-670.
[71] WANG S, GONG Y. Joint power control and task offloading in collaborative edge-cloud com- puting networks[J]. IEEE Internet Things J., Sept. 2023, 10(17): 15197-15208.
[72] ZHANG Y, LAN X, REN J, et al. Efficient computing resource sharing for mobile edge-cloud computing networks[J]. IEEE/ACM Trans. Netw., June 2020, 28(3): 1227-1240.
[73] PHAM C, NGUYEN D T, NJAH Y, et al. Share-to-run IoT services in edge cloud computing [J]. IEEE Internet Things J., Jan. 2022, 9(1): 497-509.
[74] LIU T, FANG L, ZHU Y, et al. A near-optimal approach for online task offloading and resource allocation in edge-cloud orchestrated computing[J]. IEEE Trans. Mobile Comput., Aug. 2022, 21(8): 2687-2700.
[75] WANG S, GONG Y. Convergence analysis of cloud-aided federated edge learning on non-IID data[C]//2022 IEEE 23rd International Workshop on Signal Processing Advances in Wireless Communication (SPAWC). July 2022: 1-5.
[76] WU Q, HE K, CHEN X. Personalized federated learning for intelligent IoT applications: A cloud-edge based framework[J]. IEEE Open J. Comput. Soc., Aug. 2020, 1: 35-44.
[77] BATTILORO C, DI LORENZO P, MERLUZZI M, et al. Lyapunov-based optimization of edge resources for energy-efficient adaptive federated learning[J]. IEEE Trans. Green Commun. Netw., Mar. 2023, 7(1): 265-280.
[78] SUN W, LI Z, WANG Q, et al. FedTAR: Task and resource-aware federated learning for wireless computing power networks[J]. IEEE Internet Things J., Mar. 2023, 10(5): 4257-4270.
[79] LI Y, CUI Y, LAU V. An optimization framework for federated edge learning[J]. IEEE Trans. Wireless Commun., Feb. 2023, 22(2): 934-949.
[80] NIE Y, ZHAO J, GAO F, et al. Semi-distributed resource management in UAV-aided MEC sys- tems: A multi-agent federated reinforcement learning approach[J]. IEEE Trans. Veh. Technol., Dec. 2021, 70(12): 13162-13173.
[81] LIU J, XU H, WANG L, et al. Adaptive asynchronous federated learning in resource-constrained edge computing[J]. IEEE Trans. Mobile Comput., Feb 2023, 22(2): 674-690.
[82] JI Z, CHEN L, ZHAO N, et al. Computation offloading for edge-assisted federated learning[J]. IEEE Trans. Veh. Technol., Sept. 2021, 70(9): 9330-9344.
[83] PRATHIBA S B, RAJA G, ANBALAGAN S, et al. Cybertwin-driven federated learning based personalized service provision for 6G-V2X[J]. IEEE Trans. Veh. Technol., May 2022, 71(5): 4632-4641.
[84] PANDEY S R, NGUYEN M N H, DANG T N, et al. Edge-assisted democratized learning toward federated analytics[J]. IEEE Internet Things J., Jan. 2022, 9(1): 572-588.
[85] MA Q, XU Y, XU H, et al. FedSA: A semi-asynchronous federated learning mechanism in heterogeneous edge computing[J]. IEEE J. Sel. Areas Commun., Dec. 2021, 39(12): 3654- 3672.
[86] GUO H, HUANG W, LIU J, et al. Inter-server collaborative federated learning for ultra-dense edge computing[J]. IEEE Trans. Wireless Commun., July 2022, 21(7): 5191-5203.
[87] NGUYEN D C, HOSSEINALIPOUR S, LOVE D J, et al. Latency optimization for blockchain- empowered federated learning in multi-server edge computing[J]. IEEE J. Sel. Areas Commun., Dec. 2022, 40(12): 3373-3390.
[88] KIM J, KIM D, LEE J, et al. A novel joint dataset and computation management scheme for energy-efficient federated learning in mobile edge computing[J]. IEEE Wireless Commun. Lett., May 2022, 11(5): 898-902.
[89] HUANG S, ZHANG Z, WANG S, et al. Accelerating federated edge learning via topology optimization[J]. IEEE Internet Things J., Feb. 2023, 10(3): 2056-2070.
[90] LUO S, CHEN X, WU Q, et al. HFEL: Joint edge association and resource allocation for cost- efficient hierarchical federated edge learning[J]. IEEE Trans. Wireless Commun., Oct. 2020, 19(10): 6535-6548.
[91] ZHOU T, LI X, PAN C, et al. Multi-server federated edge learning for low power consumption wireless resource allocation based on user QoE[J]. J Commun Netw, Dec. 2021, 23(6): 463-472.
[92] SHINDE S S, BOZORGCHENANI A, TARCHI D, et al. On the design of federated learning in latency and energy constrained computation offloading operations in vehicular edge computing systems[J]. IEEE Trans. Veh. Technol., Feb. 2022, 71(2): 2041-2057.
[93] TAM P, MATH S, KIM S. Optimized multi-service tasks offloading for federated learning in edge virtualization[J]. IEEE Trans. Netw. Sci. Eng., Nov.-Dec. 2022, 9(6): 4363-4378.
[94] ALBASEER A, ABDALLAH M, AL-FUQAHA A, et al. Semi-supervised federated learning over heterogeneous wireless IoT edge networks: Framework and algorithms[J]. IEEE Internet Things J., Dec. 2022, 9(24): 25626-25642.
[95] NGUYEN M N H, TRAN N H, TUN Y K, et al. Toward multiple federated learning services resource sharing in mobile edge networks[J]. IEEE Trans. Mobile Comput., Jan. 2023, 22(1): 541-555.
[96] QIAO D, GUO S, LIU D, et al. Adaptive federated deep reinforcement learning for proactive content caching in edge computing[J]. IEEE Trans. Parallel Distrib. Syst., Dec. 2022, 33(12): 4767-4782.
[97] WANG X, LI R, WANG C, et al. Attention-weighted federated deep reinforcement learning for device-to-device assisted heterogeneous collaborative edge caching[J]. IEEE J. Sel. Areas Commun., Jan. 2021, 39(1): 154-169.
[98] ZHOU Z, YANG S, PU L, et al. CEFL: Online admission control, data scheduling, and accuracy tuning for cost-efficient federated learning across edge nodes[J]. IEEE Internet Things J., Oct. 2020, 7(10): 9341-9356.
[99] SUN C, LI X, WEN J, et al. Federated deep reinforcement learning for recommendation-enabled edge caching in mobile edge-cloud computing networks[J]. IEEE J. Sel. Areas Commun., Mar. 2023, 41(3): 690-705.
[100] ZHU Z, WAN S, FAN P, et al. Federated multiagent actor–critic learning for age sensitive mobile-edge computing[J]. IEEE Internet Things J., Jan. 2022, 9(2): 1053-1067.
[101] MHAISEN N, ABDELLATIF A A, MOHAMED A, et al. Optimal user-edge assignment in hierarchical federated learning based on statistical properties and network topology constraints [J]. IEEE Trans. Netw. Sci. Eng., Jan.-Feb. 2022, 9(1): 55-66.
[102] ZHENG C, LIU S, HUANG Y, et al. Unsupervised recurrent federated learning for edge pop- ularity prediction in privacy-preserving mobile-edge computing networks[J]. IEEE Internet Things J., Dec. 2022, 9(23): 24328-24345.
[103] FENG T, XIE L, YAO J, et al. UAV-enabled data collection for wireless sensor networks with distributed beamforming[J]. IEEE Trans. Wireless Commun., Feb. 2022, 21(2): 1347-1361.
[104] DU R, ÖZçELIKKALE A, FISCHIONE C, et al. Towards immortal wireless sensor networks by optimal energy beamforming and data routing[J]. IEEE Trans. Wireless Commun., Aug. 2018, 17(8): 5338-5352.
[105] LIU Y, LI J, WANG H. Robust linear beamforming in wireless sensor networks[J]. IEEE Trans. Commun., June 2019, 67(6): 4450-4463.
[106] LIU F, MASOUROS C. A tutorial on joint radar and communication transmission for vehicular networks—part I: Background and fundamentals[J]. IEEE Commun. Lett., Feb. 2021, 25(2): 322-326.
[107] KUMARI P, MYERS N J, HEATH R W. Adaptive and fast combined waveform-beamforming design for MMWave automotive joint communication-radar[J]. IEEE J. Sel. Topics Signal Pro- cess., June 2021, 15(4): 996-1012.
[108] LIU F, ZHOU L, MASOUROS C, et al. Toward dual-functional radar-communication systems: Optimal waveform design[J]. IEEE Trans. Signal Process., Aug. 2018, 66(16): 4264-4279.
[109] LIU R, LI M, LIU Q, et al. Dual-functional radar-communication waveform design: A symbol- level precoding approach[J]. IEEE J. Sel. Topics Signal Process., Nov. 2021, 15(6): 1316-1331.
[110] SU N, LIU F, MASOUROS C. Secure radar-communication systems with malicious targets: Integrating radar, communications and jamming functionalities[J]. IEEE Trans. Wireless Com- mun., Jan. 2021, 20(1): 83-95.
[111] ZHANG J A, HUANG X, GUO Y J, et al. Multibeam for joint communication and radar sensing using steerable analog antenna arrays[J]. IEEE Trans. Veh. Technol., Jan. 2019, 68(1): 671-685.
[112] YANG J, ZENG Y, JIN S, et al. Communication and localization with extremely large lens antenna array[J]. IEEE Trans. Wireless Commun., May 2021, 20(5): 3031-3048.
[113] TONG X, ZHANG Z, WANG J, et al. Joint multi-user communication and sensing exploiting both signal and environment sparsity[J]. IEEE J. Sel. Topics Signal Process., Nov. 2021, 15(6): 1409-1422.
[114] WANG Z, HAN K, SHEN X, et al. Achieving the performance bounds for sensing and commu- nications in perceptive networks: Optimal bandwidth allocation[J]. IEEE Wireless Commun. Lett., Sept. 2022, 11(9): 1835-1839.
[115] YOU L, QIANG X, TSINOS C G, et al. Beam squint-aware integrated sensing and communi- cations for hybrid massive MIMO LEO satellite systems[J/OL]. IEEE J. Sel. Areas Commun., Oct. 2022, 40(10): 2994-3009. DOI: 10.1109/JSAC.2022.3196114.
[116] CHEN X, FENG Z, WEI Z, et al. Performance of joint sensing-communication cooperative sensing UAV network[J]. IEEE Trans. Veh. Technol., Dec. 2020, 69(12): 15545-15556.
[117] CAI X, GIALLORENZO M, SARABANDI K. Machine learning-based target classification for MMW radar in autonomous driving[J]. IEEE Trans. Intell. Veh., Dec. 2021, 6(4): 678-689.
[118] LUO F, BODANESE E, KHAN S, et al. Spectro-temporal modeling for human activity recog- nition using a radar sensor network[J]. IEEE Trans. Geosci. Remote Sens., 2023, 61: 1-13.
[119] STEINER M, GREBNER T, WALDSCHMIDT C. Millimeter-wave SAR-imaging with radar networks based on radar self-localization[J]. IEEE Trans. Microw. Theory Techn., Nov. 2020, 68(11): 4652-4661.
[120] SUN H, LI M, ZUO L, et al. Resource allocation for multitarget tracking and data reduction in radar network with sensor location uncertainty[J]. IEEE Trans. Signal Process., 2021, 69: 4843-4858.
[121] BAI L, LIU J, HAN R, et al. Wireless radar sensor networks: Epidemiological modeling and optimization[J]. IEEE J. Sel. Areas Commun., Jun. 2022, 40(6): 1993-2005.
[122] ZHAI X, CHEN X, XU J, et al. Hybrid beamforming for massive MIMO over-the-air compu- tation[J]. IEEE Trans. Commun., April 2021, 69(4): 2737-2751.
[123] LIU W, ZANG X, LI Y, et al. Over-the-air computation systems: Optimization, analysis and scaling laws[J]. IEEE Trans. Wireless Commun., Aug. 2020, 19(8): 5488-5502.
[124] CAO X, ZHU G, XU J, et al. Transmission power control for over-the-air federated averaging at network edge[J]. IEEE J. Sel. Areas Commun., May 2022, 40(5): 1571-1586.
[125] LI X, ZHU G, GONG Y, et al. Wirelessly powered data aggregation for IoT via over-the-air function computation: Beamforming and power control[J]. IEEE Trans. Wireless Commun., July 2019, 18(7): 3437-3452.
[126] ZHU G, HUANG K. MIMO over-the-air computation for high-mobility multimodal sensing [J]. IEEE Internet Things J., Aug. 2019, 6(4): 6089-6103.
[127] WANG S, HONG Y, WANG R, et al. Edge federated learning via unit-modulus over-the-air computation[J]. IEEE Trans. Commun., May 2022, 70(5): 3141-3156.
[128] HAN F, LAU V K N, GONG Y. Over-the-air computation of large-scale nomographic functions in mapreduce over the edge cloud network[J]. IEEE Internet Things J., July 2022, 9(14): 11843- 11857.
[129] FANG W, JIANG Y, SHI Y, et al. Over-the-air computation via reconfigurable intelligent surface [J]. IEEE Trans. Commun., Dec. 2021, 69(12): 8612-8626.
[130] QI Q, CHEN X, KHALILI A, et al. Integrating sensing, computing, and communication in 6G wireless networks: design and optimization[J]. IEEE Trans. Commun., Sept. 2022, 70(9): 6212-6227.
[131] DING C, WANG J B, ZHANG H, et al. Joint MIMO precoding and computation resource allocation for dual-function radar and communication systems with mobile edge computing[J]. IEEE J. Sel. Areas Commun., July 2022, 40(7): 2085-2102.
[132] LI X, LIU F, ZHOU Z, et al. Integrated sensing, communication, and computation over-the-air: MIMO beamforming design[J]. IEEE Trans. Wireless Commun., Aug. 2023, 22(8): 5383-5398.
[133] LI X, GONG Y, HUANG K, et al. Over-the-air integrated sensing, communication, and com- putation in IoT networks[J]. IEEE Wireless Commun., Feb. 2023, 30(1): 32-38.
[134] WANG S, GONG Y. A generalized primal-dual correction method for saddle-point problems with the nonlinear coupling operator[A]. 2023. arXiv: 2308.05388.
[135] BECK A. First-order methods in optimization[M]. Philadelphia: SIAM, 2017.
[136] HE B, YUAN X. On the 𝑂(1/𝑛) convergence rate of the Douglas–Rachford alternating direc- tion method[J]. SIAM J. Numer. Anal., 2012, 50(2): 700-709.
[137] HE B, YUAN X. Convergence analysis of primal-dual algorithms for a saddle-point problem: From contraction perspective[J]. SIAM J. Imaging Sci, 2012, 5(1): 119-149.
[138] CAI X, GU G, HE B. On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators[J]. Comput. Optim. Appl., 2014, 57: 339-363.
[139] HE B, HE X Z, LIU H X, et al. Self-adaptive projection method for co-coercive variational inequalities[J]. Eur. J. Oper. Res, July 2009, 196(1): 43-48.
[140] HE B, LIAO L. Improvements of some projection methods for monotone nonlinear variational inequalities[J]. J. Optim. Theory Appl., Jan. 2002, 112(1): 111–128.
[141] KRONQVIST J, BERNAL D E, LUNDELL A, et al. A review and comparison of solvers for convex MINLP[J]. Optim Eng, June 2019, 20(2): 397-455.
[142] WANG S, WU Y C, XIA M, et al. Machine intelligence at the edge with learning centric power allocation[J]. IEEE Trans. Wireless Commun., Nov. 2020, 19(11): 7293-7308.
[143] LI X, WANG S, ZHU G, et al. Data partition and rate control for learning and energy efficient edge intelligence[J]. IEEE Trans. Wireless Commun., Nov. 2022, 21(11): 9127-9142.
[144] LI J, STOICA P. MIMO Radar Signal Processing[M]. Hoboken, NJ, USA: Wiley, Oct. 2008.
[145] WANG S, GONG Y. Low-complexity iterative methods for complex-variable matrix optimiza- tion problems in Frobenius norm[A]. 2023. arXiv: 2303.07614.
[146] PETERS B, HERRMANN F J. Algorithms and software for projections onto intersections of convex and non-convex sets with applications to inverse problems[A]. 2019. arXiv: 1902.09699.
[147] TIBSHIRANI R J. Dykstra’s algorithm, ADMM, and coordinate descent: connections, insights, and extensions[J]. Adv. Neural Inf. Process Syst., Dec. 2017, 30.
[148] LóPEZ W, RAYDAN M. An acceleration scheme for Dykstra’s algorithm[J]. Comput. Optim. Appl, 2016, 63(1): 29–44.