Low complexity closed‐form covariance matrix and direct constant‐envelope waveforms design for MIMO radar transmit beampattern

Multiple‐input multiple‐output (MIMO) radar has many advantages over the phased‐array radar due to the waveform diversity, one of which is the greater flexibility to design the transmit beampattern. In this Letter, a low‐complexity transmit beampattern design method, considering constant envelope (CE) waveforms, is proposed for the uniform linear array MIMO radar. First, the authors parameterise the waveform covariance matrix as the integral form of continuous spatial variable, by exploiting the beamforming weight vector in the main lobe region, to derive the closed‐form solution of the waveform covariance matrix that fulfils positive semi‐definiteness and uniform elemental power constraints. The transmit beampattern designed by the proposed method has the spatial characteristics of low main lobe fluctuation and peak‐to‐sidelobe level, and further mathematical explanation is illuminated. Next, they directly use the parameterised expression of waveform covariance matrix, approximately transformed into a discrete form of the spatial variable based on the Riemann integral definition, to efficiently synthesise correlated CE waveforms. The proposed method can provide transmit beampattern performance comparable to existing methods with a lower computational cost and ensure the CE property of the waveforms. The performance of the proposed method is verified and analysed via numerical examples.