Constant-envelope waveform design techniques for collocated MIMO radar

MIMO-radars have many advantages over the phased-array radars, such as high spatial resolution, better parametric identifiably and much flexibility to design transmit beampattern. The design of transmit beampatterns using MIMO radar generally requires the waveforms to have arbitrary auto-and cross-correlation. The synthesis of the waveform correlation/covariance matrix, R, to desig desired beampattern is a constrained optimisation problem. In our proposed algorithm constraints and the redundant information in the covariance matrix, R, are exploited to synthesise it in closed-form. The drawback of this algorithm is that it may yields a pseudo covariance matrix (PCM), which is not guaranteed to be positive-semidefinite (PSD). The PCM can be easily converted into PSD covariance matrix using eigenvalue decomposition and scaling methods. Next a novel closed-form algorithm for generating the constant-envelope (CE) waveforms to realise the synthesised covariance matrix R is proposed. Here, Gaussian random-variables (RV's) are mapped onto the CE RV's by a memoryless non-linear transformation, which converts the problem of finding the non-Gaussian RV's to realise a given covariance matrix R into finding the Gaussian RV's to realise covariance matrix R_g. Simulation results are presented to demonstrate the effectiveness of both methodologies.