Research On Optimal Waveform Design For MIMO Radar With Colocated Antennas

The term “Multi-input Multi-output (MIMO) radar”, in general sense, refers to the radar systems that use multiple channels to transmit and receive signals. Unlike conventional phased-array radar, a MIMO radar can transmit different signals via its antennas to achieve waveform diversity, which can be exploited to improve spatial resolution, reduce interception probability and synthesise desired beampattern. Waveform diversity is manily obtained by transmitting elaborately designed waveforms, thus the point of this study is focused on the design of optimal phase coded waveforms for MIMO radar with collocated antennas. The article is organized as follows.In the first part, waveform design for beampattern matching is investigated. First of all, the relationship between the narrowband beampattern and the underlying transmitting waveform covariance matrix is used to establish the objective function by the criterion of beampattern matching. The optimization problem for waveform covariance matrix synthesis is formulated as a typical semidefinite quadratic programming (SQP) problem which can be efficiently solved by convex optimization algorithms. Next, an cyclic algorithm is adopted to design the corresponding waveforms with desired covariance matrix and envelope shape. Finally, the correlation properties of the waveforms are also taken into consideration to make them more suitable for practical usage. The simulations demonstrate the designed waveforms can approximate the desired beampattern well and have good correlation properties.In the second part, unimodular orthogonal waveform design is considered. Firstly, the objective function is established by the criterion of integral sidelobe level (ISL). Next, the correlation properties optimization is transformed into a power spectral density (PSD) optimization according to the relationship between the waveform PSD and the correlation function. Finally, based on the phase retrieval and alternating projection, a method named multi-dimensional iterative spectral approximation algorithm (MDISAA) is proposed. MDISAA can take advantage of fast Fourier transform (FFT) operations to improve computational efficiency and the other advantage is that it’s actually an algorithm framework, which means this algorithm can have multiple concrete implementations for different usages. Numerical simulations demonstrate MDISAA can design waveforms with good correlation properties and it is computationally efficient.In the third part, the design of unimodular orthogonal waveforms with sparse spectrum is studied. First of all, theories of eigenvector subspace and rank deficient Fourier transform are used to form notches on specified frequency bands to avoid colored noise and electronic jammer. Next, also based on the alternating projection framework, the MDISAA presented in the second part is extended to form a multiple sets alternating projection. Finally, MDISAA-sparse frequency waveforms (MDISAA-SFW) is presented, which can design waveforms with good correlation and spectrum properties. Simulation results are presented to show the effectiveness of MDISAA-SFW. In addition, the algorithm is computationally efficient because its main steps are based on FFT operations as well.