Research On The Design Of Constant Modulus Waveforms Based On Consensus-ADMM Algorithm

Alternating Direction Method of Multipliers(ADMM)is a combination of augmented lagrangian function and dual rise method.It is a method used to solve decomposable convex optimization problem,which can be widely applied in the machine and statistical learning,signal processing,data mining,compression sensing of mass data processing field.The ADMM algorithm for convex optimization problems and its improved version have some general achievements in convergence and convergence speed.When the optimization problem is non-convex,the relevant theoretical results are not general.However,the optimization problems in practical applications,such as signal and image processing,data mining,machine learning and other fields are mostly non-convex.How to design ADMM solution algorithm with theoretically-guaranteed performance and high execution efficiency combining with the internal structure of practical application problems has very clear practical significance.In this thesis,an efficient distributed ADMM algorithm is designed for the constant modulus waveform design problem(non-convex optimization problem)in different demand scenarios,and the convergence and computational complexity of the algorithm are studied.The main contents and work of this thesis are as follows:1.Constant modulus sequences with good correlation characteristics are widely used in wireless communication systems.This thesis aims to design such constant modulus sequences for problem modeling.The objective function of the formulated model is a quartic non-convex polynomial,and the constant modulus constraint is also non-convex,so the non-convex model is difficult to solve directly.In this thesis,a phase variable is introduced to drop the non-convex constant modulus constraints,and then auxiliary variables are introduced to make it equivalent to a consensus optimization problem.This thesis proposes consensus ADMM and consensus PDMM algorithm to approximately solve this consensus problem.It should be emphasized that the reformulated problemsplit into multiple subproblems about local variables and can be solved distributed among each subproblem.Therefore,the designed ADMM algorithm can be suitable for the design optimization of large scale constant modulus sequences.Finally,the performance of the proposed distributed algorithm including convergence,local optimality and computational complexity is analyzed theoretically.The analysis results show that the proposed algorithms converge to the stationary point of the original non-convex problem under certain preset conditions.The corresponding simulation results show that compared with existing algorithms,constant modulus sequences generated by the proposed algorithms have better correlation performance.2.By designing the MIMO radar probing waveform reasonably,the signal energy can be concentrated in the specific spatial direction,so as to improve the detection performance of the radar system.Based on above requirements,the probing waveform design problem of MIMO radar is modeled as a nonconvex quadric polynomial optimization problem with with constant modulus constraints.For this non-convex problem,an ADMM approximate solution algorithm with distributed execution structure is proposed by introducing auxiliary variables to transform it into a consensus optimization problem.On this basis,the performance analysis of the proposed algorithm proves that the proposed algorithm converges to the stationary point of the original problem.The simulation results show that the beampattern of the generated waveform in a specific direction fits well with the desired beampattern,and has good correlation characteristics in the concerned spatial direction.3.An optimal design model for MIMO radar probing waveform is proposed to minimize the peak correlation sidelobe,and the corresponding ADMM algorithm is proposed.In the problem formulation,the objective function is first modeled as an infinite norm function and then approximated as a p-norm model which is easy to be solved.Because the proposed p-norm optimization model has a similar consensus optimization problem architecture to the 2-norm optimization model in research content 2,the paper further proposes the distributed ADMM solution algorithm,and proves that the algorithm can converge to the stationary point of the original non-convex problem.Simulation results show that compared with the existing probing waveform algorithm,the generated constant modulus probing waveform can obtain lower sidelobe correlation characteristics,which verifies the effectiveness of the proposed algorithm.