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We propose to design a peak-to-average power ratio (PAPR) constrained transmit waveform that achieves the optimal performance (following the Neyman-Pearson lemma) in detecting a target in the presence of signal-dependent interference. The direct time-domain approach allows straightforward characterizations of the correlation and PAPR properties of the designed signals, which are critically important to analyze the system performance in the presence of multiple targets and to assess the transmitter power-utilization, respectively. Therefore, instead of designing a transmit signal only for the optimal detection performance, we solve a biobjective Pareto-optimization problem, subjecting to the PAPR and total energy constraints, in order to simultaneously optimize the detection and cross-correlation performances. With extensive numerical examples, we demonstrate that PAPR-constrained signals produce nearly optimum detection performance even with a strict PAPR requirement, and also highlight the conflicting behavior of the detection and correlation performances. [ABSTRACT FROM PUBLISHER]