The Waveform Design For Detecting And Parameter Estimation Of Target In Cognitive Radar With PAR Constraint

Cognitive radar is a new intelligent radar system with the ability of environmental awareness,self-learning,and adjusting the transmitted waveform adaptively.Compared with traditional radars that can only transmit the fixed waveform,cognitive radar can dynamically adjust the transmitted waveform according to the actual target and environmental information to improve the performance of radar reliably,effectively and robustly.Adaptive waveform design is one of the key technologies of cognitive radar.In order to improve the freedom of waveform design while taking into account the performance of the transmitter,the radar waveform is usually required to have a low peak-to-average ratio(PAR).Therefore,in this thesis we mainly discuss the reasonable design of the transmitted waveform under the PAR constraint to improve the performance of target detection and parameter estimation of radar.The main contributions are as follows:(1)The basic concepts of cognitive radar are introduced,and the key points involved in adaptive waveform design are summarized.Meanwhile,we make a detailed discussion about present research status of waveform design in terms of target detection,parameter estimation,and taking both the detection and estimation into consideration under the PAR constraint.(2)The waveform design problem about the target detection under the PAR constraint is studied.The signal model of adaptive waveform design is given and the relationship between detection performance and transmitted waveform is analyzed.Then the optimization criterion is also selected.All of above works are the groundwork of the next research works.Aiming at the waveform design problem under the PAR constraint with the known prior knowledge,a joint design method of waveform and filter based on convex optimization is proposed.Firstly,the problem model of waveform and filter joint design about radar output signal-to-interference-and-noise ratio(SINR)under the PAR constraint is constructed.Then the problem models of two types of target impulse response(TIR)(deterministic and statistical)are unified.Based on this,the filter and waveform are alternately optimized by using the alternating projection method.The analytical expression of the filter is given according to the Rayleigh quotient model.Moreover,the non-convex problem is transformed into the convex problem by the semi-positive definite relaxation(SDR)method to obtain the waveform matrix solution.Finally,the waveform vector solution is obtained from the waveform matrix solution by combining the rank one approximation method and the nearest neighbor method.The proposed method can achieve optimal waveform under the specified PAR constraint,and the designed waveform can maximize the output SINR within the PAR constraint.Aiming at the waveform design problem under the PAR constraint with the imprecise prior knowledge of TIR and clutter impulse response(CIR),a robust waveform and filter joint design method based on uncertain set is proposed.Two types of TIR(deterministic and statistical)are discussed.The joint design idea is as follows: firstly,the uncertainty set of TIR and CIR is constructed,and the joint design problem model about output SINR is constructed based on the maximum minimization criterion under the PAR constraint.Secondly,within the uncertain set range,the values of TIR and CIR in the worst SINR case(the SINR is the minimum value)are given.Finally,the robust waveform and the filter are jointly optimized by the alternating projection method.The optimal waveforms both have good robust performance in the case of two TIR types.Compared with the traditional method,the amount of computation of the proposed method is significantly reduced with the same performance.Meanwhile,the proposed method has better robust performance with the same amount of computation.(3)The waveform design problem about the target parameter estimation under the PAR constraint is studied.The relationship between estimation performance and transmitted waveform is analyzed,and the optimization criterion is selected.When the prior knowledge is known,the waveform design problem under the PAR constraint cannot be solved in the time domain by the traditional method.To solve this problem,two different methods which both can tackle the problem in time domain are proposed: the waveform design method based on sequential linear programming(SLPW)which focus on reducing the algorithm complexity,and the waveform design method based on Minorization-Maximization(AMMW)which focus on improving the estimation performance of the algorithm.The problem model of the waveform design is constructed by maximizing mutual information(MI).The SLPW uses the linear form to meet the objective function and constraints of the optimization problem,and the conversion of the non-convex problem to the convex problem is realized.Considering that the waveform vector cannot be directly optimized,the waveform vector solution can be obtained by extracting from the waveform matrix which can be got by solving the convex problem.The AMMW constructs the lower bound function of the original objective function by utilizing the Minorization-Maximization method,so that the problem which has been transformed is closer to the original optimization problem.Then the matrix-to-vector transformation is performed by using the characteristics of the Toeplitz matrix,so that the waveform vector can be directly solved.Because the convergence speed of Minorization-Maximization is always slow,the acceleration scheme is further used to improve the convergence speed of the proposed method.Both of these methods can optimize the waveform with the specified PAR constraint,and the estimated performance is better than the traditional algorithm.Both methods have their own advantages,SLPW has lower algorithm complexity,and AMMW has better estimation performance.In addition,the problem is extended to the case where the prior knowledge of TIR and CIR is imprecise.Their uncertainty set can be constructed by the eigenvalues of their covariance matrix.Combined with SLPW,the robust waveform can be got based on the maximum minimization criterion.The robust waveform under the PAR constraint has good robust performance.(4)The waveform design problem to optimize the detection and estimation performance simultaneously under the PAR constraint is studied.Aiming at the problem that the traditional method has a high computational complexity when TIR is known,an efficient waveform design method based on the alternating direction multiplier method(ADMM)is proposed.Firstly,the problem model of waveform design based on the maximal SINR criterion and MI criterion is constructed.Then,through the introduction of auxiliary variable,the model transformation is carried out based on the ADMM,and the original non-convex problem is transformed into three sub-problems which can be solved easily.Finally,the solutions of the sub-problems can be solved efficiently and the global optimization solution of the original problem can be obtained by coordinating the solutions of the sub-problems.Compared with the traditional method,the proposed method has significantly reduced complexity under the same performance.In addition,the proposed method can optimize the waveform under the specified PAR constraint and adjust the weight coefficient to realize balance between the performance of detection and estimation.Aiming at the problem that the traditional method tends to deviate from the original solution and has high computational complexity when TIR fluctuates,an efficient time-domain-based waveform design method under PAR constraint is proposed.Firstly,the minimal estimation error of TIR is taken as the optimization criterion and the waveform design problem is modeled under the detection performance,PAR and energy constraint.Secondly,an auxiliary variable is introduced and the structural characteristic of Toeplitz matrix is utilized to realize the conversion of the non-convex problem to the convex problem.Finally,to further reduce the computational complexity,the convex problem is decomposed into two problems: inner iteration and outer iteration,which can be solved efficiently.Compared with the traditional method,the proposed method not only reduces the complexity of the algorithm,but also has better estimation accuracy on the basis of satisfying the detection performance.