Optimization and Evaluation of Physical Complementary Radar Waveforms

The RF spectrum is a precious, finite resource with ever-increasing demand. Consequently, the mandate to be a "good spectral neighbor" is in direct conflict with the requirements for high-performance sensing where correlation error is fundamentally limited. As such, matched-filter radar performance is often sidelobe-limited with estimation error being constrained by the time-bandwidth (TB) of the collective emission. The methods developed here seek to bridge this gap between idealized radar performance and practical utility via waveform design.    

Estimation error becomes more complex when employing pulse-agility. In doing so, range-sidelobe modulation (RSM) spreads energy across Doppler, rendering traditional methods ineffective. To address this, the gradient-based complementary-FM framework was developed to produce complementary sidelobe cancellation (CSC) after coherently combining subsets within a pulse-agile emission. In contrast to the majority of complementary signals, explored via phase-coding, these Comp-FM waveform subsets achieve CSC while preserving hardware-compatibility since they are FM (though design distortion is never completely avoided). Although Comp-FM addressed practicality via hardware amenability, CSC was localized to zero-Doppler. This work expands the Comp-FM notion to a Doppler-generalized (DG) framework, extending the cancellation condition to an arbitrary span. The same framework can likewise be employed to jointly optimize an entire coherent processing interval (CPI) to minimize RSM within the radar point-spread-function (PSF), thereby generalizing the notion of complementarity and introducing the potential for cognitive operation if sufficient scattering knowledge is available a-priori.          

Sensing with a single emitter is limited by self-inflicted error alone (e.g., clutter, sidelobes), while MIMO systems must additionally contend with the cross-responses from emitters operating concurrently (e.g., simultaneously, spatially proximate, in a shared spectrum), further degrading radar sensitivity. Now, total correlation error is dictated by the overlapping TB (i.e., how coincident are the signals) and number of operating emitters, compounding difficulty to estimate if left unaddressed. As such, the determination of "orthogonal waveforms" comprises a large portion of MIMO literature, though remains a phenomenological misnomer for pulsed emissions. Here, the notion of complementary-FM is applied to a multi-emitter context in which transmitter-amenable quasi-orthogonal subsets, occupying the same spectral band, are produced via a similar gradient-based approach. To further practicalize these MIMO-Comp-FM waveform subsets, the same "DG" approach described above, addressing the otherwise-default Doppler-induced degradation of complementary signals, is applied. In doing so, Doppler-independent separability and complementarity greatly improves estimation sensitivity for multi-emitter systems. 

This MIMO-Comp-FM framework is developed for standard matched filter processing. Coupling this framework with a "DG" form of the previously explored MIMO-MiCRFt is also investigated, illustrating the added benefit of pairing optimized subsets with similarly calibrated processing. 

Each of these methods is developed to address unique and increasingly complex sources of estimation error. All approaches are initially developed and evaluated via simulated analysis where ground-truth is known. Then, despite hardware-induced distortion being unavoidable, the MIMO-Comp-FM framework is confirmed via loopback measurements to preserve the majority of CSC that was observed in simulation. Finally, open-air demonstration of each approach validates practical utility on a radar system.