On Adaptive Robust Beamforming For Phased- Array And MIMO Radars

Adaptive beamforming is widely used to enhance the expected signal and suppress the interference and noise for target detection and location in many fields,such as radar,sonar,navigation and speech signal processing.The classical minimum variance distortionless response(MVDR)beamformer can achieve the optimal performance,in theory.However,in practical application,the performance of the MVDR beamformer may degrade severely due to the presence of the array steering vector mismatch caused by many imperfections,such as array calibration error,wavefront distortion and random phase error.In addition,multiple-input-multiple-output(MIMO)radar and large scale array are usually confronted with overhigh computational complexity and overlarge amount of the training samples required besides array steering vector mismatch,for their large system dimensionality.For this purpose,this dissertation focuses on adaptive robust beamforming applied to phasedarray and MIMO radar,and reduced-dimension robust beamforming applicable to large scale array.What this dissertation mainly shows is followed.1.A novel iterative generalized Rayleigh quotient(IGRQ)algorithm instead of the traditional second order cone programming(SOCP)is proposed to solve the original nonconvex problem in the classical WCPO performance optimization(WCPO)beamformer.First,the original non-convex model is converted to a generalized Rayleigh quotient problem.Second,a novel iterative algorithm is proposed to solve this problem and the main task in per iteration is to obtain the generalized eigenvector corresponding to the maximum generalized eigenvalue.We solve the principle eigenvector of a new problem instead of the principle generalized eigenvector of the original problem by using the eigenvalue decomposition operation to reduce the computational cost.Here,the power iterative method is used to attain the principle eigenvector.Compared to the traditional SOCP technique,the proposed IGRQ algorithm can significantly reduce the computational cost and be more suitable for the real-time application.2.To overcome the issues in the traditional steering vector estimation method by using semi-definite relaxation(SDR)that the complexity is overhigh and there may be the performance loss,a novel robust beamforming algorithm using sequential quadratic programming(SQP)is proposed.The original non-convex problem is linearly approximated to a convex subproblem using the first order Taylor's series,and the optimal solution is found out by solving the convex subproblem iteratively.Additionally,with consideration of the covariance matrix mismatch,we propose an SQP based on WCPO performance optimization(SQP-WC)to improve the performance of the proposed SQP method.Simulation results show that the proposed SQP algorithm can converge fast and its convergence point approximates the optimal solution of the original problem,which indicate that the SQP method can effectively reduce the computational complexity compared with the SDR method,furthermore,the SQP-WC method can effectively improve the performance of the SQP method with a small parameter.On the other hand,aiming at the transmit and receive steering vectors mismatch problem,an iterative reduced-dimension robust adaptive beamformer for MIMO radar is presented.The general linear combined(GLC)method is applied to MIMO radar to obtain the enhanced covariance matrix estimation,and the transmit and receive steering vectors mismatch model is established.The cost function is established based on the desired signal output power maximum principle to estimate the transmit and receive steering vectors.The bi-iteration(BI)method is proposed to solve the cost function and it is merely necessary to solve two low-dimensional convex quadratically constrained quadratic programming(QCQP)problems in per iteration.Simulation results show that the proposed method can obtain the higher output signal-to-interference-plus-noise(SINR)under the condition of severe steering vector mismatch compared with the conventional robust beamformers,and the proposed method has the lower computational complexity for its fast convergence.3.A robust beamformer with phase response fixed and magnitude response constraint(PFMC)is proposed for uniform linear array(ULA).We find that there is only a phase factor difference between the transfer function of the inverse sequence of the weight vector(WV)and the array response function,and the phase response of the array response function is set to be linear by using this property.Hence,we control the beamwidth and ripple of the robust region by constraining the real magnitude response.Compared with the conventional magnitude response constraint(MRC)beamformer,the proposed method can reduce the calculation cost.In addition,due to the guarantee of the phase response,the proposed beamformer has better performance than the traditional magnitude constraint beamformer.Simulation results demonstrate the effectiveness of the proposed beamformer.4.In this chapter,a robust adaptive beamformer for MIMO radar is proposed with linear phase and magnitude constraints(LPMC)to control flexibly the beamwidth of the robust region.First,the full-dimensional WV is expressed as the Kronecker product of the transmit and receive array WVs based on the WV separable principle.Then,the phase responses of the transmit and receive arrays,respectively,are set to be linear based on designing a finite impulse response(FIR)filter.Finally,the robust model is establish by constraining the real magnitude response to exceed unity.The established problem is a bi-quadratic cost function and can be effectively solved by the bi-iterative algorithm(BIA).The proposed beamformer has lower computational complexity and faster sample convergence rate,compared to the traditional MRC beamfomrers with full degrees of freedom(Do Fs).5.A new robust and fast beamformer with MRC by using the conjugate symmetric characteristic is proposed for MIMO radar.The transmit and receive steering vectors are,respectively,expressed as the conjugate symmetric forms and the robust model is established based on MRC and conjugate symmetric constraints.To reduce the computational complexity and the number of samples required,the original problem is converted into a biquadratic cost function and it is solved by combining the bi-iterative algorithm(BIA)and convex quadratic program(QP).Like the traditional MRC beamformers,the proposed beamformer can flexibly control the beamwidth and ripple of the robust region.However,the proposed method has lower computational complexity and faster sample convergence rate.Besides,as long as the steering vector of MIMO radar is conjugate symmetric,the proposal can be applied to it.6.A reduced-dimension MRC beamformer is proposed for large scale array.By analyzing the expected beampattern of the MRC beamformer in large scale array,we project the principle components of the WV of the MRC beamformer to the subspace spanned by the steering vectors in the designed robust region.Additionally,small part of components orthogonal to that subspace are added to make adaptive processing.Thus,the original highdimensional problem is converted to a low-dimensional one,resulting in the reduction of the computational complexity and the amount of the samples required.The proposed reduceddimension method is essentially a beamspace method with multiple mainbeam channels.Theoretical analysis and simulation experiments show that the reduced-dimension MRC beamformer can significantly reduce the complexity and speed up the sample convergence rate.