Waveform Design For MIMO Radar

Multi-input multi-output (MIMO) radar is a new technology of active radar detection, and has become a hot research topic. Transmit antennas and receive antennas can be flexibly configured according to system requirements and each transmit antenna can freely choose signal waveform. Compared with traditional radar, MIMO radar has waveform diversity with more advantages. Distributed MIMO radar makes full use of spatial diversity to overcome the fade of targets and to improve target detection performance. Centralized MIMO radar has higher spatial resolution, better parameter identification capacity and greater flexibility of transmit beam-pattern design.Waveform diversity is an important feature of MIMO radar, and waveform design is a mean to achieve the advantages of waveform diversity. Recently, MIMO radar waveform design consists mainly of orthogonal waveform design, transmit beam-pattern matching design, transmit signal waveform synthesis and so on. This dissertation focuses on these issues. Firstly, we review the existing methods, and then propose new approaches based on optimization methods. Finally, a thorough comparison and discussion are provided.The main content of this dissertation is summarized as follows.The first part introduces the basic theory of optimization methods, and takes examples of waveform design and signal processing. First of all, the first order and second order optimality conditions of unconstrained optimization and constrained optimization as well as the basic structure of optimization methods are introduced. Then, the convex optimization theory is described, and some common methods of judging convexity are summarized. An example of the optimal peak sidelobe mismatch filter design applies the convex optimization to signal processing. Next, the steepest descent method, Newton method, conjugate gradient method and quasi-Newton method for unconstrained optimization are explained. The links and differences of these optimization methods are pointed out. Finally, the sequential quadratic programming and trust region method for constrained optimization are described. After the introduction to a variety of optimization methods, we take the design of pulse compression signal as an example to illustrate their applications, and compare the performance of various optimization methods. Sequential quadratic programming method is ultimately chosen as the solution to the problem with MIMO waveform design method.The second part is contributed to the orthogonal waveform design problem. Firstly, we review the existing orthogonal waveform design methods-simulated annealing, genetic algorithms and improved Flethcher-Reeves algorithm.Orthogonal polyphase codes with broaden main-lobe are designed via gentic algorithms. Simulations show that the peak sidelobe level has been greatly improved. Next, a software-based Lingo of constrained nonlinear programming and sequential quadratic programming method for the continuous phase encoding orthogonal signal are proposed. Experimental results show that, the optimized orthogonal waveforms have flat sidelobes with lower peak sidelobe level, compared with the improved Flethcher-Reeves algorithm. Finally, based on sequential quadratic programming method, we study the relationship among autocorrelation peak sidelobe level, peak cross-correlation level, the code length N, the signal number L, and the weighted coefficientλ. The results show that, a appropriate; adjustment ofλcan contribute a great improvement of autocorrelation peak sidelobe: level with little loss of peak cross-correlation levelThe third part focuses on the optimal peak sidelobe level mismatched filter design problem, namely, how to design mismatched filters to improve the performance of orthogonal waveforms. Firstly, we review the existing iterative weighted least squares method. Then, we propose a mismatched filter design method based on convex optimization. Next, the simulation results show that, increasing the coefficient length of mismatched filter and with a little loss of signal to noise ratio, both methods can further improve the peak sibelobe level. Finally, by comparison, the convex optimization method has superior performance. It can not only control the SNR loss, but also get a lower peak sidelobe level.The fourth part is contributed to transmit beam-pattern matching design issue, namely, how to obtaine signal covariance matrix from a given ideal beampattern. At first, we review the existing method based on semi-definite programming. Next, we replace the uniform array constraint with a fix-weighted and nonuniform one. We propose an idea that an arbitrary beam-pattern can be synthesized from a set of basic beams. The basic beams and their weight coefficients can be fast obtained via linear programming. Finally, simulation results show that, MIMO radar can freely choose its signal waveforms not only to maximize the electromagnetic energy onto the targets of interest, but also to minimize cross-correlation of echo signals; compared with the semidefinite programming method, the linear programming method can not only fastly get the signal covariance matrix, but also make the synthesized pattern and the correlation pattern have a lower spatial peak sidelobe level.The fifth part focuses on the transmit signal waveform synthesis issue, namely, how to get constant modulus signal waveforms from the known covariance matrix. Firstly, we review the existing cyclic algorithm. Then, we propose the sequential quadratic programming method. Finally, the simulation results show that, the constant modulus signal waveforms, which are optimized via the sequential quadratic programming, make their echo signals have better autocorrelation and cross correlation.The sixth part is contributed to the online design issue on transmit beam-pattern and signal waveforms, namely, how to rapidly synthesize signal waveforms, not only to match the given beam-pattern, but also to make the echo signals have good correlation properties. Firstly, we propose an idea that transmitted signal waveforms can be rapidly synthesized with basic beams and basic signals. Then, we use sequential quadratic programming to design basic signals. Finally, the simulation results show that the basic signals obtained via sequential quadratic programming method have good correlation properties; the transmit signal waveforms rapidly synthesized from basic beams and basic signals, make their echo signals have good autocorrelation and cross correlation properties.