  Conventional radar transmits electromagnetic waves towards the targets of
interest. In between the outgoing pulses, the radar measures the signal
reflected from the targets to determine their presence, range, velocity and
other characteristics. Radar systems face multiple challenges, generating many
trade-offs such as bandwidth versus range resolution and dwell time versus
Doppler resolution. In MIMO radar, high resolution requires a large aperture
and high number of antennas, increasing hardware and processing requirements.
  Recently, novel approaches in sampling theory and radar signal processing
have been proposed to allow target detection and parameter recovery from
samples obtained below the Nyquist rate. These techniques exploit the sparsity
of the target scene in order to reduce the required number of samples, pulses
and antennas, breaking the link between bandwidth, dwell time and number of
antennas on the one hand and range, Doppler and azimuth resolution,
respectively, on the other.
  This review introduces this so-called sub-Nyquist radar paradigm and
describes the corresponding sampling and recovery algorithms, that leverage
compressed sensing techniques to perform time and spatial compression. We focus
on non radar imaging applications and survey many recent compressed radar
systems. Our goal is to review the main impacts of compressed radar on
parameter resolution as well as digital and analog complexity. The survey
includes fast and slow time compression schemes as well as spatial compression
approaches. We show that beyond substantial rate reduction, compression may
also enable communication and radar spectrum sharing. Throughout the paper, we
consider both theoretical and practical aspects of compressed radar, and
present hardware prototype implementations, demonstrating real-time target
parameter recovery from low rate samples in pulse-Doppler and MIMO radars.
