This paper attempts to characterize the kinds of physical scenarios in which
an online learning-based cognitive radar is expected to reliably outperform a
fixed rule-based waveform selection strategy, as well as the converse. We seek
general insights through an examination of two decision-making scenarios,
namely dynamic spectrum access and multiple-target tracking. The radar scene is
characterized by inducing a state-space model and examining the structure of
its underlying Markov state transition matrix, in terms of entropy rate and
diagonality. It is found that entropy rate is a strong predictor of online
learning-based waveform selection, while diagonality is a better predictor of
fixed rule-based waveform selection. We show that these measures can be used to
predict first and second-order stochastic dominance relationships, which can
allow system designers to make use of simple decision rules instead of more
cumbersome learning approaches under certain conditions. We validate our
findings through numerical results for each application and provide guidelines
for future implementations.Comment: 15 pages, 15 figures. Final version to appear in IEEE Transaction on
Radar Systems. arXiv admin note: substantial text overlap with
arXiv:2212.0059