Radar Information Theory for Joint Communication and Parameter Estimation with Passive Targets

In this paper, we derive the performance bounds for joint communication data rate and estimation error of radar target parameters from first principles, where the targets are assumed to be passive. Specifically, we let the targets to have control over their passive reflectors in order to transmit their own information back to the radar via reflection-based beamforming or backscattering. Such a setup avoids active radio frequency transmission from battery operated devices such as friendly (or reconnaissance) drones. The concept of target ambiguity function arises naturally from these derivations, which not only poses challenge to waveform designers, but also provides an opportunity for a joint design of waveform and array geometries to achieve an optimal performance. We derive the Cram\'er-Rao lower bounds for the mean squared error in the estimation of target parameters, and derive lower bounds on the data rates with both radar-only and joint radar and communications scenarios. The challenge of transmit waveform design for joint radar-data communication is illustrated via numerical examples.