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The existence of multipath brings extra "looks" of targets. This paperconsiders the extended target detection problem with a narrow bandMultiple-Input Multiple-Output(MIMO) radar in the presence of multipath fromthe view of waveform-filter design. The goal is to maximize the worst-caseSignal-to-Interference-pulse-Noise Ratio(SINR) at the receiver against theuncertainties of the target and multipath reflection coefficients. Moreover, aConstant Modulus Constraint(CMC) is imposed on the transmit waveform to meetthe actual demands of radar. Two types of uncertainty sets are taken intoconsideration. One is the spherical uncertainty set. In this case, the max-minwaveform-filter design problem belongs to the non-convex concave minimaxproblems, and the inner minimization problem is converted to a maximizationproblem based on Lagrange duality with the strong duality property. Then theoptimal waveform is optimized with Semi-Definite Relaxation(SDR) andrandomization schemes. Therefore, we call the optimization algorithm DualityMaximization Semi-Definite Relaxation(DMSDR). Additionally, we further studythe case of annular uncertainty set which belongs to non-convex non-concaveminimax problems. In order to address it, the SDR is utilized to approximatethe inner minimization problem with a convex problem, then the innerminimization problem is reformulated as a maximization problem based onLagrange duality. We resort to a sequential optimization procedure alternatingbetween two SDR problems to optimize the covariance matrix of transmit waveformand receive filter, so we call the algorithm Duality Maximization DoubleSemi-Definite Relaxation(DMDSDR). The convergences of DMDSDR are provedtheoretically. Finally, numerical results highlight the effectiveness andcompetitiveness of the proposed algorithms as well as the optimizedwaveform-filter pair.

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