Defense Notices

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

Radar systems perform 3 basic tasks: search/detection, tracking, and imaging. Traditionally, varied operational and hardware requirements have compartmentalized these functions to distinct and specialized radars, which may communicate actionable information between them. Expedited by the growth in computational capabilities modeled by Moore’s law, next-generation radars will be sophisticated, multi-function systems comprising generalized and reprogrammable subsystems. The advance of fully Digital Array Radars (DAR) has enabled the implementation of highly directive phased arrays that can scan, detect, and track scatterers through a volume-of-interest. Conversely, DAR technology has also enabled Multiple-Input Multiple-Output (MIMO) radar methodologies that seek to illuminate all space on transmit, while forming separate but simultaneous, directive beams on receive.

Waveform diversity has been repeatedly proven to enhance radar operation through added Degrees-of-Freedom (DoF) that can be leveraged to expand dynamic range, provide ambiguity resolution, and improve parameter estimation.  In particular, diversity among the DAR’s transmitting elements provides flexibility to the emission, allowing simultaneous multi-function capability. By precise design of the emission, the DAR can utilize the operationally-continuous trade-space between a fully coherent phased array and a fully incoherent MIMO system. This flexibility could enable the optimal management of the radar’s resources, where Signal-to-Noise Ratio (SNR) would be traded for robustness in detection, measurement capability, and tracking.

Waveform diversity is herein leveraged as the predominant enabling technology for multi-function radar emission design. Three methods of emission optimization are considered to design distinct beams in space and frequency, according to classical error minimization techniques. First, a gradient-based optimization of the Space-Frequency Template Error (SFTE) is applied to a high-fidelity model for a wideband array’s far-field emission. Second, a more efficient optimization is considered, based on the SFTE for narrowband arrays. Finally, a suboptimal solution, based on alternating projections, is shown to provide rapidly reconfigurable transmit patterns. To improve the dynamic range observed for MIMO radars employing pulse-agile quasi-orthogonal waveforms, a pulse-compression model is derived that manages to suppress both autocorrelation sidelobes and multi-transmitter-induced cross-correlation. The proposed waveforms and filters are implemented in hardware to demonstrate performance, validate robustness, and reflect real-world application to the degree possible with laboratory experimentation.