  Quadrature sampling has been widely applied in coherent radar systems to
extract in-phase and quadrature (I and Q) components in the received radar
signal. However, the sampling is inefficient because the received signal
contains only a small number of significant target signals. This paper
incorporates the compressive sampling (CS) theory into the design of the
quadrature sampling system, and develops a quadrature compressive sampling
(QuadCS) system to acquire the I and Q components with low sampling rate. The
QuadCS system first randomly projects the received signal into a compressive
bandpass signal and then utilizes the quadrature sampling to output compressive
I and Q components. The compressive outputs are used to reconstruct the I and Q
components. To understand the system performance, we establish the frequency
domain representation of the QuadCS system. With the waveform-matched
dictionary, we prove that the QuadCS system satisfies the restricted isometry
property with overwhelming probability. For K target signals in the observation
interval T, simulations show that the QuadCS requires just O(Klog(BT/K))
samples to stably reconstruct the signal, where B is the signal bandwidth. The
reconstructed signal-to-noise ratio decreases by 3dB for every octave increase
in the target number K and increases by 3dB for every octave increase in the
compressive bandwidth. Theoretical analyses and simulations verify that the
proposed QuadCS is a valid system to acquire the I and Q components in the
received radar signals.
