Study On Waveform Design Methods For MIMO Radar Based On Convex Optimization Theory

In recent years,the proposed multiple-input multiple-output(MIMO)radar is a new radar system,which uses multiple antennas to transmit signals and multiple antennas to receive signals.Compared with traditional phased array radar,it has shown enhanced performance in target detection and parameter estimation.The capabilities of MIMO radar systems fundamentally benefit from the waveform diversity.Therefore,how to design a proper transmitted signal has become one of the most interesting problems.The problem of waveform design is essentially a problem of optimization of the cost function under finite energy constraint.It can be solved by the convex optimization theory which has been studied in recent years.The solving process is not only rapid but also ensures that the obtained solution has global optimality.In the previous MIMO radar waveform design study,for the purpose of simplifying the solving process,we just consider ideal Gaussian white noise.In this paper,the noise is extended to colored noise.We seek the optimal transmitted signals when the transmitted power is limited based on mutual information theory and estimation theory.The maximum of relative entropy and the minimum of the mean squared value of the estimated error of the CSLS(Covariance Shaping Least Square)and SLS(Scaled Least Square)estimators are taken as the cost function.The innovation of this paper is as follows:We employ relative entropy associated with detection problem as the figure of merit for MIMO radar waveform design to obtain waveforms which maximize the detection probability for a fixed value of the probability of false alarm.Considering the signal model of the binary hypothesis test,we can formulate this maximization problem.We take the relative entropy between the echoes which the target is not present and the echoes which the target exists as the objective function,and solve the maximization problem when the transmitted energy is limited.In order to solve this non-convex optimization problem,an iterative method based on the minimization-maximization(MM)method is proposed.The original problem is transformed into convex optimization problem and solved by CVX toolbox.The proposed method ensures that the objective function value has monotonicity and convergence.The simulation result shows that compared with the orthogonal waveform and the mutual information waveform the optimal waveform based on the relative entropy criterion can make the radar system obtain better detection performance.The waveform design methods based on CSLS and SLS estimators are proposed for the case where the covariance matrix of the target scattering matrix is unknown.The optimization problem based on the CSLS estimator is transformed into a maximal minimal eigenvalue problem for solving the optimal transmitted waveform.It is expressed as a semi-definite programming(SDP)problem by using the Schur's complement theorem which can be solved by SeDuMi toolbox.The Lagrange multiplier method and KKT(Karush-Kuhn-Tucker)condition are used to obtain the expression of the optimal transmitted waveform based on the SLS estimator.Because the design criteria based on these two estimators do not need to know the specific characteristics of the target,the process of obtaining the target feature through the field test can be omitted,which reduces the cost and difficulty of the waveform design.The simulation results verify the effectiveness of the optimal transmitted waveforms based on CSLS and SLS estimators.