Research On MIMO Radar Waveform Design Technology Based On Manifold Optimization

The multiple-input multiple-output(MIMO)waveform design technique is a key technology for improving the detection performance of MIMO radar,and has received widespread attention in recent years.Among them,constant modulus waveform design technology has become one of the research hotspots.This thesis focuses on the research hotspot of constant modulus waveform design,and systematically studies the narrowband beamforming,wideband beamforming,and constant modulus waveform design for airborne MIMO interference suppression.The thesis introduces optimization theory and Riemannian manifold geometry into waveform design,and achieves the following innovative results:1.A Riemannian limited-memory Broyden-Fletcher-Goldfarb-Shanno(RLBFGS)method is proposed for direction-of-arrival(DOA)estimation of narrowband MIMO radar,which does not suffer from the relaxation error problem of existing methods.The proposed method first transforms the NP-hard high-dimensional non-convex original problem into an unconstrained quartic problem on the Riemannian complex unit circle manifold,and then efficiently solves the problem by deriving the manifold descent direction and an adaptive step size.Compared with existing methods,the proposed method achieves lower DOA estimation error and lower computational cost.2.An adaptive momentum optimization(AMO)algorithm is proposed for DOA estimation of wideband MIMO radar,which also does not suffer from the relaxation error problem of existing methods.The proposed method first transforms the original problem into an unconstrained optimization problem on the Riemannian complex unit circle manifold.Then,based on the momentum property of moving particles,a composite descent direction combining steepest descent and momentum is constructed,and an efficient AMO algorithm based on momentum descent direction is designed.Compared with existing methods,the proposed method achieves a 10 d B reduction in the zero point gain.3.A highly efficient decoupling method based on Riemannian conjugate gradient descent is proposed for joint design of transmit waveforms and receive filters in airborne MIMO radar.The proposed method utilizes the constant modulus property of the feasible set on the Riemannian complex unit circle manifold,and transforms the original coupled problem into an unconstrained coupled problem on the manifold.Then,a highly efficient Riemannian conjugate gradient method is proposed to solve for the waveform,while a closed-form minimum variance distortionless response(MVDR)algorithm is used to solve for the filter with the waveform fixed.Compared with existing methods,the proposed method requires less computational cost and has better signal-to-interferenceplus-noise ratio(SINR).