LFM-PC Hybrid Modulated Radar Signal Optimization Method Based on Alternating Direction Method of Multiplier

The real-time pricing (RTP) scheme is an ideal method to adjust the power balance between supply and demand in smart grid systems. This scheme has a profound impact on users’ behavior, system operation, and overall grid management in the electricity industry. In this research, we conduct an extended discussion of a RTP optimization model and give a theoretical analysis of the existence and uniqueness of the Lagrangian multiplier. A distributed optimization method based on the alternating direction method of multipliers (ADMM) algorithm with Gaussian back substitution (GBS) is proposed in this study. On the one hand, the proposed algorithm takes abundant advantage of the separability among variables in the model. On the other hand, the proposed algorithm can not only speed up the convergence rate to enhance the efficiency of computing, but also overcome the deficiency of the distributed dual subgradient algorithm, the possibility of nonconvergence in the iteration process. In addition, we give the theoretical proof of the convergence of the proposed algorithm. Furthermore, the interdependent relationship between variables has been discussed in depth during numerical simulations in the study. Compared with the dual subgradient method, the simulation results validate that the proposed algorithm has a higher convergence speed and better implementation effect.

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Hybrid FSK-PSK Waveform Optimization for Radar Based on Alternating Direction Method of Multiplier (ADMM)

Sensors ◽

10.3390/s21237915 ◽

2021 ◽

Vol 21 (23) ◽

pp. 7915

Author(s):

Zhiting Fei ◽

Jiachen Zhao ◽

Zhe Geng ◽

Xiaohua Zhu ◽

Jindong Zhang

Keyword(s):

Alternating Direction Method ◽

Radar Signal ◽

Modulation Scheme ◽

Phase Shift Keying ◽

Phase Encoding ◽

Waveform Optimization ◽

Alternating Direction ◽

Low Sidelobe ◽

Shift Keying ◽

Discrete Phase

In this paper, a new radar signal modulated with a hybrid of the frequency shift keying (FSK) and the phase shift keying (PSK) signal—i.e., the FSK-PSK signal—is studied. Different phase encoding sequences are used to modulate the sub-pulses to obtain lower sidelobe levels and ensure signal orthogonality. In addition, to counter intra-pulse slice repeater jamming of specific length generated by the enemy jammer, an orthogonal waveform made of sub-pulses of equal length based on the FSK-PSK modulation scheme is designed. The simulation results show that the optimized discrete phase encoding sequence can significantly enhance the orthogonality of the sub-pulse in the FSK-PSK signal and effectively suppress the slice repeater jamming. Two algorithms are proposed: (1) the low sidelobe waveform optimization algorithm based on ADMM (LSW-ADMM); and (2) the anti-slice-repeater-jamming algorithm based on ADMM (ASRJ-ADMM). Both algorithms exhibit fast convergence speed and low computational complexity.

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Alternating Direction Method of Multipliers as Simple Heuristic for Topology Optimization of a Truss With Uniformed Member Cross Sections

Journal of Mechanical Design ◽

10.1115/1.4041174 ◽

2018 ◽

Vol 141 (1) ◽

Cited By ~ 1

Author(s):

Yoshihiro Kanno

Keyword(s):

Global Optimization ◽

Topology Optimization ◽

Computational Cost ◽

Optimization Method ◽

Alternating Direction Method ◽

Mixed Integer ◽

Computational Time ◽

Method Of Multipliers ◽

Global Optimization Method ◽

Alternating Direction

This paper presents a simple and effective heuristic for topology optimization of a truss under the constraint that all the members of the truss have the common cross-sectional area. The proposed method consists of multiple restarts of the alternating direction method of multipliers (ADMM) with random initial points. It is shown that each iteration of the ADMM can be carried out very easily. In the numerical experiments, the efficiency of the proposed heuristic is compared with the existing global optimization method based on the mixed-integer second-order cone programming (MISOCP). It is shown that even for large-scale problem instances that the global optimization method cannot solve within practically acceptable computational cost, the proposed method can often find a feasible solution having a fairly good objective value within moderate computational time.

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