  Modern radar systems are expected to operate reliably in congested
environments. A candidate technology for meeting these demands is frequency
agile radar (FAR), which randomly changes its carrier frequencies. FAR is known
to improve the electronic counter-countermeasures (ECCM) performance while
facilitating operation in congested setups. To enhance the target recovery
performance of FAR in complex electromagnetic environments, we propose two
radar schemes extending FAR to multi-carrier waveforms. The first is Wideband
Multi-carrier Agile Radar (WMAR), which transmits/receives wideband waveforms
simultaneously with every antenna. To mitigate the demanding hardware
requirements associated with wideband waveforms used by WMAR, we next propose
multi-Carrier AgilE phaSed Array Radar (CAESAR). CAESAR uses narrowband
monotone waveforms, thus facilitating ease of implementation of the system,
while introducing {\em spatial agility}. We characterize the transmitted and
received signals of the proposed schemes, and develop an algorithm for
recovering the targets, based on concepts from compressed sensing to estimate
the range-Doppler parameters of the targets. We then derive conditions which
guarantee their accurate reconstruction. Our numerical study demonstrates that
both multi-carrier schemes improve performance compared to FAR while
maintaining its practical benefits. We also demonstrate that the performance of
CAESAR, which uses monotone waveforms, is within a small gap from the wideband
radar.
