Waveform Design for Moving Target Detection With FDA-MIMO Radar Exploiting Correlation and Doppler Tolerance Properties

This article investigates the problem of transmit waveform design in a Frequency Diverse Array (FDA)-Multiple-Input Multiple-Output (MIMO) radar for moving target detection against Doppler frequency shift and range ambiguity. In our system design, the FDA-MIMO radar is developed by transmitting designed phase-coded waveforms with a frequency increment between transmit antenna elements, which provides extra Degrees-Of-Freedom (DOFs) in the range-angle domains for target detection. In specific, for high-speed moving targets, an optimization problem is formulated to devise the phase-coded waveforms with low correlation properties under a constant modulus constraint as well as a similarity constraint involving a known radar waveform with good Doppler tolerance. To tackle such a non-convex optimization problem, the Majorization Minimization-Alternating Direction Method of Multipliers projection (MM-ADMM-projection) algorithm is developed in an iterative way, where an MM method is employed by constructing a series of surrogate functions to approximate the optimal solution. Furthermore, by introducing the ADMM method, each surrogate function is separated into linear and quadratic functions, where the constant modulus and similarity constraints are only imposed on the former. Then, a projection method is proposed to remove the non-convex constraints in the feasible region. In particular, the Conjugate Gradient (CG) method is implemented to reduce the computational burden, and the local convergence of the proposed method is proved. Numerical results are provided to demonstrate the effectiveness of the designed waveform in detecting moving target considering the range ambiguity.