Constrained Riemannian Manifold Optimization for the Simultaneous Shaping of Ambiguity Function and Transmit Beampattern

Qiu, Xiangfeng; Jiang, Weidong; Liu, Yongxiang; CHATZINOTAS, Symeon; Gini, Fulvio; Greco, Maria Sabrina

doi:10.1109/TAES.2024.3520951

Article (Scientific journals)

Constrained Riemannian Manifold Optimization for the Simultaneous Shaping of Ambiguity Function and Transmit Beampattern

Qiu, Xiangfeng; Jiang, Weidong; Liu, Yongxiang et al.

2025 • In IEEE Transactions on Aerospace and Electronic Systems, 61 (3), p. 5771 - 5787

Peer Reviewed verified by ORBi

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https://hdl.handle.net/10993/66310

DOI
10.1109/TAES.2024.3520951

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Keywords :

Ambiguity function; beampattern design; manifold optimization; multiple-input multiple-output (MIMO) radar; waveform design; Beam pattern; Beampattern design; Constant modulus constraints; Manifold optimization; Multiple-input multiple-output radars; Optimisations; Range doppler; Waveform designs; Waveforms; Aerospace Engineering; Electrical and Electronic Engineering; Optimization; Vectors; MIMO radar; Manifolds; Aerospace and electronic systems; Shape; Transmitting antennas; Transforms; Signal processing algorithms; Doppler effect

Abstract :

[en] Designing the transmit waveforms with prescribed ambiguity functions (AFs) and beampatterns while adhering to the constant modulus (CM) constraint is pivotal for the forthcoming cognitive multiple-input multiple-output (MIMO) radar systems. This study delves into the AF shaping quandary within the MIMO radar framework, considering the joint constraints of waveform unimodality and desired beampattern. The established model explores higher dimensions to realize the waveform design in range–Doppler and spatial dimensions, to improve the possibility of separating target and interference. Specifically, we first formulate the waveform design problem as a jointly constrained quartic problem, with the aim of minimizing the response values corresponding to the different range–Doppler bins within the defined compound AF. Leveraging the geometric properties of CM constraint, we further transform the jointly constrained problem in the Euclidean space into a single-constraint optimization problem in the Riemannian space. Then, the Riemannian augmented Lagrangian method (RALM) is proposed to iteratively search for the optimal waveform. Subsequently, we conduct numerical experiments to validate the efficacy of the RALM algorithm. In addition, we implemented the designed waveforms in hardware systems to analyze the effects induced by nonlinear instruments.

Disciplines :

Computer science

Author, co-author :

Qiu, Xiangfeng ; National University of Defense Technology, Changsha, China

Jiang, Weidong ; National University of Defense Technology, Changsha, China

Liu, Yongxiang ; National University of Defense Technology, Changsha, China

CHATZINOTAS, Symeon ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SigCom ; National Centre for Scientific Research “Demokritos,”, Athens, Greece

Gini, Fulvio ; University of Pisa, Pisa, Italy

Greco, Maria Sabrina ; University of Pisa, Pisa, Italy

External co-authors :

yes

Language :

English

Title :

Constrained Riemannian Manifold Optimization for the Simultaneous Shaping of Ambiguity Function and Transmit Beampattern

Publication date :

June 2025

Journal title :

IEEE Transactions on Aerospace and Electronic Systems

ISSN :

0018-9251

eISSN :

1557-9603

Publisher :

Institute of Electrical and Electronics Engineers Inc.

Volume :

Issue :

Pages :

5771 - 5787

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://xplorestaging.ieee.org/ielx8/7/11031113/10811862.pdf?arnumber=10811862

Funders :

National Natural Science Foundation of China
Italian Ministry of Education and Research
framework of the FoReLab project

Funding text :

The work of Xiangfeng Qiu was supported in part by the China Scholarship Council and in part by the National Natural Science Foundation of China under Grant 62022091 and Grant 61921001. The work of Fulvio Gini and Maria Sabrina Greco were supported by the Italian Ministry of Education and Research (MUR) in the framework of the FoReLab project (Departments of Excellence).

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