We consider the design of radar systems that are capable of using knowledge of their interference environment to dynamically design transmit waveforms that afford optimum signal-to-interference-plus-noise ratio while satisfying modulus and ambiguity function constraints. We begin by establishing the inextricable nature of modulus constraints in the waveform optimization problem. We then extend the state of the art in waveform optimization to accommodate these constraints. This is done by solving a secondary optimization problem using the method of alternating projections. We demonstrate that this approach can be a computationally efficient alternative to dynamic programming methods. We then consider the multiple-target detection problem, which is the basis for introducing ambiguity function constraints into the waveform design process. We formulate the waveform optimization problem for several receiver architectures, and solve these problems using sequential quadratic programming and interior point methods. Finally, we address the need for a more computationally tractable approach by considering a number of suboptimal formulations. This includes a novel formulation based on a parametrization of nonlinear frequency modulation.
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