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Optimal detection of a target return contaminated by signal-dependent interference, as well as additive channel noise, requires the design of a transmit pulse f(t) and a receiver impulse response h(t) jointly maximizing the output signal to interference plus noise ratio, SINR. Despite the highly nonlinear nature of this problem, it has been possible to show that f(t) may always be chosen minimum-phase. A full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs (f,h) that appears to converge satisfactorily for most values of input SINR. Extensive simulation reveals that the shape of f(t) can be a critical factor. In particular the performance of a chirp-like pulse is often unacceptable, especially when the clutter and channel noise are low-pass dominant and comparable.