Research On Waveform Design For MIMO Radar And Array Calibration

Multiple-input multiple-output radar utilizes multiple transmitting antennas to emit a variety of waveforms and multiple receiving antennas to obtain multi-channel echo data,which owns the most flexible working mode and the highest system degree of freedom in all the existing radar systems.With the development of electronic science and technology and the growth of military requirements(warning,surveillance,identification,communication,etc.),modern radars usually need to integrate multiple functions to ensure their survival and effective operation in complex electromagnetic environments.Compared with conventional phased array radars,the emergence of MIMO radar provides the possibility to further improve the radar performance in the battlefield environment.The core advantage of MIMO radar is waveform diversity.According to whether the transmitting waveform is orthogonal,MIMO radar can be divided into two modes: orthogonal and partially correlated.There is much discussion on the orthogonal mode of MIMO radar,but less research on the more general partial correlation mode.For waveform optimization design,most of the existing methods are based on the ideal array manifold,which is often inconsistent with the actual situation.To that end,this dissertation mainly focuses on the partially correlated waveform optimization design,array error calibration and robust transmitting and receiving beamforming.The main work and contribution of this dissertation can be summarized as follows: 1.Aiming at the problem of MIMO radar transmitting waveform optimization,two algorithms with low computational complexity are proposed based on the gradient projection method and the alternating direction method of multipliers,respectively.In the actual battlefield environment,the electromagnetic interference and clutter background may change rapidly.Real-time transmitting waveform design based on time-varying scenarios is the key to make full use of the advantages of MIMO radar with waveform diversity and high optimization freedom.According to the signal processing flow for partially correlated MIMO radar,the cost function for waveform optimization is constructed based on the minimum matching mean square error(MSE)criterion.An auxiliary variable is introduced,and then the matching MSE can be regarded as a function of the waveform vector and the desired transmitting gain level.Since the MSE itself is non-negative,if the cost function can be monotonically decreased by alternatingly updating the above variables,the convergent solution can be obtained after a finite number of iterations.Motivated by this idea,the complex original problem is decomposed into several simple sub-problems.The gradient projection method and the alternating direction method of multipliers are introduced to obtain the closed-form solutions,respectively.The convergence conditions of the two algorithms and the KKT conditions of the convergent solutions are theoretically analyzed.With the proper parameter selection,the two proposed algorithms can guarantee to converge.Since only linear matrix operations are included,the computational complexity of the proposed algorithms is significantly reduced compared to the existing methods.2.Aiming at the problem of gain and phase error calibration for the transmitter and receiver of MIMO radar,a clutter-based orthogonal subspace projection algorithm is proposed.In actual radar systems,various non-ideal factors will lead to inevitable array errors and the array manifold mismatch will decrease the MIMO radar performance.In order to make full use of the advantages of MIMO radar waveform diversity and high system freedom,it is necessary to obtain accurate transmitter and receiver array manifold.Utilizing the orthogonality between the transmitting waveforms,a virtual array with aperture expansion can be formed after pulse compression,which provides the possibility to estimate the gain and phase errors of transmitter and receiver simultaneously.Based on the non-full rank characteristic of the virtual array manifold for monostatic MIMO radar,a non-zero orthogonal projection matrix can be formed.The clutter projection output is zero if array is perfectly calibrated.Motivated by this idea,an auxiliary calibrated receive subarray is introduced and the cost function is established by minimizing the clutter projection output power.Utilizing the Lagrange multiplier method,the closed-form solutions of gain and phase error estimation for transmitter and receiver can be obtained,respectively.The necessary conditions and computational complexity of the proposed algorithm are analyzed.Compared with the existing methods utilizing the point target echo,the proposed algorithm has a small amount of computation burden and is applicable to more flexible scenarios.3.Aiming at the problem of calibration residual errors for transmitter and receiver array,a robust receiving beamforming weight optimization design algorithm based on the alternating direction method of multipliers is proposed for orthogonal MIMO radar.In actual radar systems,most of array errors are usually time-varying.After updating the array manifold with self-calibration methods,some residual errors may still exist.In order to weaken their adverse effects as much as possible,robust beamforming weight optimization design is necessary.According to the priori information,the actual steering vectors for transmitter and receiver are limited to an uncertain set and the cost function is established based on the idea of the best performance in the worst case.Considering the constraint conditions as the definition domain of the optimization variable,the original optimization problem can be decomposed into several simple sub-problems,whose closed-form solutions can be obtained by the alternating direction method of multipliers.In addition,according to the structure information of the virtual array manifold,the full-dimensional beamforming weight can be decomposed into the Kronecker product of two low-dimensional transmitting and receiving weight vectors.Motivated by this idea,a bi-iterative algorithm is discussed.Compared with the full-dimensional robust optimization method,it further reduces the computational complexity and the requirement of the number of training samples.4.Aiming at the problem of calibration residual errors for transmitter array,a robust transmit waveform optimization design method based on minimizing the transmit gain in the sidelobe region is proposed for partial correlation MIMO radar.Unlike the orthogonal mode,the transmit beampattern for partial correlation MIMO radar is no longer omnidirectionally covered.The residual errors of transmitter array have a great influence on the transmitting beamforming gain for the sidelobe,especially for the nulling region.To solve this problem,the transmitter steering vector errors are limited to an uncertain set based on priori information,and the cost function for waveform covariance matrix optimization is established based on the idea of best performance in the worst case.Utilizing the S-Procedure,the non-convex original problem is transformed into a semi-definite programming problem to obtain the solution of the optimal waveform covariance matrix.The robust transmitting waveforms can be obtained by the existing waveform synthesis method.The influence of the residual error norm on the depth of nulling is discussed.Numerical simulation experiments verify the effectiveness of the proposed method.