Optimum MIMO Radar Signal Design:Ambiguity Function And Duration-bandwidth

After the introduction of Multi-Input Multi-Output(MIMO)radar,because the radar transmitted signal is an important factor that determines the performance of the radar system,people have invested a lot of energy in the design of the transmitted signal and the synthesis of the waveform.The transmitted signal mainly depends on the orthogonal basis and weights.Existing methods usually use more commonly used functions as orthogonal basis functions,such as cosine function and sine function.However,the energy of these basis functions is not concentrated in the time domain and frequency domain,so the performance of the radar signal synthesized by it is poor.When optimizing the radar signal,the radar signal's covariance matrix is required to be as close to the ideal matrix as possible to ensure that the design waveform has good auto-correlation and cross-correlation characteristics,while existing methods often use the Euclidean distance algorithm to calculate the distance between the covariance matrices,the accuracy is very low.At the same time,in the optimization process,because the objective function of the design variable is non-convex,the solution obtained is not necessarily the optimal solution.In response to the above problems,the main contents of this thesis are as follows:1.We consider the signal design problem for a Multi-Input Multi-Output(MIMO)radar,because the radar signal mainly depends on the orthogonal basis and the coefficient matrix,and we take into consideration of the energy concentration of the designed signal in its essential duration and essential bandwidth,that means the duration-bandwidth of the design signal is the largest,because the small bandwidth can reduce the signal distortion caused by the transmission on the scattered channel,and the short pulse can improve the resolution.What's more,the WLJ function is the function with the largest duration-bandwidth,so we using WLJ functions as the orthogonal basis of the synthesized signal.The simulation results show that the signal performance of the WLJ functions as orthogonal basis is better than that of the cosine functions.2.After selecting the appropriate orthogonal basis function,the coefficient matrix needs to be optimized to optimize the radar signal.In the process of optimization,the goal is todesign a signal vector having a desired covariance(Co V)matrix while ensuring that the side-lobes of the designed signal's ambiguity function are small.Since Co V matrices are not free structures,but semi-positive definite and symmetrical,they form a manifold in the signal space.Hence,we argue that the difference between these matrices should not be measured in terms of the conventional Euclidean distance(ED)algorithm,while the distance should be measured along the surface of the manifold,i.e.,in terms of the Riemannian distance(RD)algorithm.3.In the process of optimizing the radar signal,whether the objective function is measured with ED or RD,the signal optimization problems are non-convex of the design variable,involving respectively a quartic and a square-root of the variable.An iteration algorithm based on convex quadratic optimization is developed in which the original non-convex problems are transformed so that they can be approximated by a convex quadratically-constrained quadratic problem at each stage.And the optimal solution can be obtained through the iterative process.The simulation results show that the convergence of the objective function can be significantly faster when optimizing signal over the manifold(signal space of RD)than when optimizing signal over the Euclidean distance space(signal space of ED).More importantly,for tight constraints,when the signal is optimized over the Euclidean distance space,the ambiguity function of the signal cannot meet the constraint;when the signal is optimized on the manifold,the ambiguity function of the signal can still satisfy the constraint well.4.In order to verify the performance of different designed signals,we uses the different transmitted signals to estimate the target parameters and perform error analysis at the end.The results show that no matter in estimating the target speed or target position,the transmitted signal obtained when the WLJ function set is used as the orthogonal basis and the signal is optimized on the manifold is used to estimate the target parameter,the error is minimum,and the system performance is correspondingly the best.