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We propose a novel robust design method to jointly optimize the radar transmit code and receive filter, exploiting the Signal-to-Interference plus Noise Ratio (SINR) at the receiver end as design figure of merit. We confer robustness to our method against uncertainties on the target impulse response (TIR) using a worst-case optimization approach based on two different uncertainty sets. The former is composed of a finite collection of TIRs, obtained by sampling the actual TIR at some aspect angles; the latter is a spherical uncertainty set. We further enforce a peak-to-average power ratio (PAR) constraint to the transmit code, which is very important for radar applications where the transmitter operates close to saturation. The design problem is tackled using a sequential optimization procedure alternating between two semi-definite programming (SDP) problems, followed by randomization steps. Our numerical results highlight the robustness and applicability of the proposed method in different scenarios. [ABSTRACT FROM PUBLISHER]