Robust MIMO Radar Waveform-Filter Design for Extended Target Detection in the Presence of Multipath [article]

Zhou Xu, Chongyi Fan, Jian Wang, Xiaotao Huang
2020 arXiv   pre-print
The existence of multipath brings extra "looks" of targets. This paper considers the extended target detection problem with a narrow band Multiple-Input Multiple-Output(MIMO) radar in the presence of multipath from the view of waveform-filter design. The goal is to maximize the worst-case Signal-to-Interference-pulse-Noise Ratio(SINR) at the receiver against the uncertainties of the target and multipath reflection coefficients. Moreover, a Constant Modulus Constraint(CMC) is imposed on the
more » ... mit waveform to meet the actual demands of radar. Two types of uncertainty sets are taken into consideration. One is the spherical uncertainty set. In this case, the max-min waveform-filter design problem belongs to the non-convex concave minimax problems, and the inner minimization problem is converted to a maximization problem based on Lagrange duality with the strong duality property. Then the optimal waveform is optimized with Semi-Definite Relaxation(SDR) and randomization schemes. Therefore, we call the optimization algorithm Duality Maximization Semi-Definite Relaxation(DMSDR). Additionally, we further study the case of annular uncertainty set which belongs to non-convex non-concave minimax problems. In order to address it, the SDR is utilized to approximate the inner minimization problem with a convex problem, then the inner minimization problem is reformulated as a maximization problem based on Lagrange duality. We resort to a sequential optimization procedure alternating between two SDR problems to optimize the covariance matrix of transmit waveform and receive filter, so we call the algorithm Duality Maximization Double Semi-Definite Relaxation(DMDSDR). The convergences of DMDSDR are proved theoretically. Finally, numerical results highlight the effectiveness and competitiveness of the proposed algorithms as well as the optimized waveform-filter pair.
arXiv:2009.13261v1 fatcat:w66reu4n7vgurjo7kwjkjwirr4