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In this article, we develop a new waveform codesign approach for radar-communications spectral coexistence using a decisiontheoretic framework called partially observable Markov decision process (POMDP). The POMDP framework's natural look-ahead feature allows us to trade off short-term for long-term performance, which is necessary in waveform codesign problems with competing objectives and dynamic user needs. As POMDPs are computationally intractable, we extend two approximation methods called nominal belief-state optimization and random-sampling multipath hypothesis propagation to make the codesign approaches tractable.

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