  FAR has improved anti-jamming performance over traditional pulse-Doppler
radars under complex electromagnetic circumstances. To reconstruct the
range-Doppler information in FAR, many compressed sensing (CS) methods
including standard and block sparse recovery have been applied. In this paper,
we study phase transitions of range-Doppler recovery in FAR using CS. In
particular, we derive closed-form phase transition curves associated with block
sparse recovery and complex Gaussian matrices, based on prior results of
standard sparse recovery under real Gaussian matrices. We further approximate
the obtained curves with elementary functions of radar and target parameters,
facilitating practical applications of these curves. Our results indicate that
block sparse recovery outperforms the standard counterpart when targets occupy
more than one range cell, which are often referred to as extended targets.
Simulations validate the availability of these curves and their approximations
in FAR, which benefit the design of the radar parameters.
