Adaptive transmission for radar arrays using Weiss-Weinstein bounds

The authors present an algorithm for adaptive selection of pulse repetition frequency or antenna activations for Doppler and direction of arrival estimation. The adaptation is performed sequentially using a Bayesian filter, responsible for updating the belief on parameters, and a controller, responsible for selecting transmission variables for the next measurement by optimising a prediction of the estimation error. This selection optimises the Weiss-Weinstein bound (WWB) for a multi-dimensional frequency estimation model based on array measurements of a narrow-band far-field source. A particle filter implements the update of the posterior distribution after each new measurement is taken, and this posterior is further approximated by a Gaussian or a uniform distribution for which computationally fast expressions of the WWB are analytically derived. They characterise the controller's optimal choices in terms of signal-to-noise ratio and variance of the current belief, discussing their properties in terms of the ambiguity function and comparing them with optimal choices of other WWB constructions in the literature. The resulting algorithms are analysed in simulations where they showcase a practically feasible real-time evaluation based on look-up tables or small neural networks trained off-line.