Information Theoretic Radar Waveform Design for Multiple Targets

In this paper we use information theoretic approach to design radar waveforms suitable for simultaneously estimating and tracking parameters of multiple targets. Our approach generalizes the information theoretic water-filling approach of Bell. The paper has three main contributions: a new information theoretic design criteria for single transmit waveform with a receiving array using a weighted linear sum of the mutual informations between targets´ radar signatures and the corresponding received beams (given the transmitted waveforms), we provide a family of design criteria that weight the various targets according to priorities. Then we generalize the information theoretic design criteria for designing multiple waveforms under joint power constraint when beamforming is used both at transmitter and receiver. Finally we provide a highly efficient optimization algorithm for optimizing the transmitted waveforms both for single target and multiple targets. We show that the optimization problem in both cases can be decoupled into a parallel set of low dimensional search problems at each frequency, with dimension defined by the number of targets, instead of the number of frequency bands used. The power constraint is forced through the optimization of a single Lagrange multiplier for the dual problem. We end with comments on the generalization of the proposed technique for other design criteria, e.g., for the linearly weighted MMSE design criterion.