Information Theoretic Waveform Design with Application to Physically Realizable Adaptive-on-Transmit Radar

The fundamental task of a radar system is to utilize the electromagnetic spectrum to sense a scattering environment and generate some estimate from this measurement. This task can be posed as a Bayesian estimation problem of random parameters (the scattering environment) through an imperfect sensor (the radar system). From this viewpoint, metrics such as error covariance and estimator precision (or information) can be leveraged to evaluate and improve the performance of radar systems. Here, physically realizable radar waveforms are designed to maximize the Fisher information (FI) (specifically, a derivative of FI known as marginal Fisher information (MFI)) extracted from a scattering environment thereby minimizing the expected error covariance about an estimation parameter space. This information theoretic framework, along with the high-degree of design flexibility afforded by fully digital transmitter and receiver architectures, creates a high-dimensionality design space for optimizing radar performance.

First, the problem of joint-domain range-Doppler estimation utilizing a pulse-agile radar is posed from an estimation theoretic framework, and the minimum mean square error (MMSE) estimator is shown to suppress the range-sidelobe modulation (RSM) induced by pulse agility which may improve the signal-to-interference-plus-noise ratio (SINR) in signal-limited scenarios. A computationally efficient implementation of the range-Doppler MMSE estimator is developed as a series of range-profile estimation problems, under specific modeling and statistical assumptions. Next, a transformation of the estimation parameterization is introduced which ameliorates the high noise-gain typically associated with traditional MMSE estimation by sacrificing the super-resolution achieved by the MMSE estimator. Then, coordinate descent and gradient descent optimization methods are developed for designing MFI optimal waveforms with respect to either the original or transformed estimation space. These MFI optimal waveforms are extended to provide pulse-agility, which produces high-dimensionality radar emissions amenable to non-traditional receive processing techniques (such as MMSE estimation). Finally, informationally optimal waveform design and optimal estimation are extended into a cognitive radar concept capable of adaptive and dynamic sensing. The efficacy of the MFI waveform design and MMSE estimation are demonstrated via open-air hardware experimentation where their performance is compared against traditional techniques