In a monostatic RADAR, the same antenna is used to transmit and receive. If the system transmits continuously, the transmitted power (on the order of kW) overwhelms the received signal (on the order of fW). This results in an extremely poor signal-to-noise ratio (SNR), making it impossible for the receiver to distinguish the return signal from the transmitted energy.

There are two primary solutions. First, bistatic RADAR uses separate antennas for transmitting and receiving, physically isolating the signals. Second, pulsed RADAR separates transmission and reception in time by sending short pulses and then listening for returns. Pulsed RADAR is more common because it reduces hardware complexity.

Pulse width, denoted as $\tau$, is the duration of each transmitted RADAR pulse. A longer pulse width increases the energy in each pulse, which improves detection range. However, it also increases $\Delta R$, which reduces the ability to resolve closely spaced targets.

Pulse Repetition Frequency (PRF) is the number of pulses transmitted per second, measured in Hz. A higher PRF means the RADAR updates more frequently, but it can also reduce the maximum unambiguous range.

Pulse Repetition Interval (PRI) is the time between successive pulses. It defines how long the RADAR waits for a return before transmitting again. PRI is related to PRF by $$PRI = \frac{1}{PRF}$$

The maximum unambiguous range is the farthest distance at which a RADAR can correctly determine a target's range without confusion. It is determined by the PRI using $$R_{unamb} = \frac{c \cdot PRI}{2}$$ If a target is beyond this range, its return may be mistaken for a closer target from a later pulse.

Range ambiguity occurs when a return signal from a previous pulse arrives after a new pulse has already been transmitted. The RADAR assumes all returns come from the most recent pulse, so it incorrectly assigns the target a shorter range than its true distance.

Range resolution is the ability of a RADAR to distinguish two targets that are close together in distance. It depends on pulse width and is given by $$\Delta R = \frac{c \cdot \tau}{2}$$ If two targets are closer than $\Delta R$, their returns overlap and appear as a single object.

Pulse width creates a trade-off. Increasing $\tau$ increases pulse energy, improving detection range. However, it also increases $\Delta R$, which reduces the ability to resolve closely spaced targets. Decreasing $\tau$ improves resolution but reduces energy and detection capability.

Doppler shift is the change in frequency of a returned RADAR signal due to relative motion between the RADAR and the target. In RADAR systems, the shift occurs twice (outbound and return), allowing the system to determine target velocity based on the frequency difference. $$f = f_{o}\left(1 \pm \frac{2v\cos\theta}{c}\right)$$ Use + for a closing target and − for a retreating target, where θ is the angle between the target's velocity vector and the line from the target to the RADAR.