  Target localization based on frequency diverse array (FDA) radar has lately
garnered significant research interest. A linear frequency offset (FO) across
FDA antennas yields a range-angle dependent beampattern that allows for joint
estimation of range and direction-of-arrival (DoA). Prior works on FDA largely
focus on the one-dimensional linear array to estimate only azimuth angle and
range while ignoring the elevation and Doppler velocity. However, in many
applications, the latter two parameters are also essential for target
localization. Further, there is also an interest in radar systems that employ
fewer measurements in temporal, Doppler, or spatial signal domains. We address
these multiple challenges by proposing a co-prime L-shaped FDA, wherein
co-prime FOs are applied across the elements of L-shaped co-prime array and
each element transmits at a non-uniform co-prime pulse repetition interval
(C$^3$ or C-Cube). This co-pulsing FDA yields significantly large
degrees-of-freedom (DoFs) for target localization in the
range-azimuth-elevation-Doppler domain while also reducing the time-on-target
and transmit spectral usage. By exploiting these DoFs, we develop C-Cube
auto-pairing (CCing) algorithm, in which all the parameters are ipso facto
paired during a joint estimation. We show that C-Cube FDA requires at least
$2\sqrt{Q+1}-1$ antenna elements and $2\sqrt{Q+1}-1$ pulses to guarantee
perfect recovery of $Q$ targets as against $Q+1$ elements and $Q+1$ pulses
required by both L-shaped uniform linear array and L-shaped linear FO FDA with
uniform pulsing. We derive Cram\'er-Rao bounds (CRBs) for joint
angle-range-Doppler estimation errors for C-Cube FDA and provide the conditions
under which the CRBs exist. Numerical experiments with our CCing algorithm show
great performance improvements in parameter recovery.
