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We consider the design of radar transmit waveforms that are optimal for the purposes of detecting multiple unknown targets in a known interference environment. Specifically, we introduce constraints on the waveform's autocorrelation function, which is of fundamental importance in practice. The incorporation of autocorrelation constraints leaves the problem analytically intractable, and numeric techniques must be employed. We introduce the concept of "waveform optimized performance" in order to provide a framework for suggesting and analyzing various approaches. We show that unlike the solutions to the more relaxed formulations found in the literature, eigenfunction solutions are no longer optimal, and the Neyman-Pearson receiver is no longer the most appropriate choice for many scenarios. Furthermore, for some scenarios, numeric solutions to the autocorrelation-constrained problems can provide signal-to-interference-plus-noise ratio improvements comparable to the solutions of the more relaxed formulations found in the literature. RDManuscript received March 7, 2009; revised September 7, 2010; released for publication February 21, 2011.