In this paper, we develop a decision theoretic approach for radar waveform design to maximize the joint radar communications performance in spectral coexistence. Specifically, we develop an adaptive waveform design approach by posing the design problem as a partially observable Markov decision process (POMDP), which leads to a hard optimization problem. We extend an approximate dynamic programming approach called nominal belief-state optimization to solve the waveform design problem. We perform a numerical study to compare the performance of the proposed POMDP approach with the commonly used myopic approaches.
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