Before delving into the topic of pulse compression, it is necessary to briefly discuss the advantages of pulse RADAR over CW RADAR. The main difference between the two is with duty cycle (time high vs total time). For CW RADARs this is 100% and pulse RADARs are typically much lower. The efficiency of this comes with the fact that the scattered signal can be observed when the signal is low, making it much more clear. With CW RADARs (which are much less common then pulse RADARs), since the transmitter is constantly transmitting, the return signal must be read over the transmitted signal. In all cases, the return signal is weaker than the transmitter signals due to absorption by the target. This leads to difficulties with continuous wave RADAR. Pulse RADARs can also provide high peak power without increasing average power, leading to greater efficiency.
“Pulse Compression” is a signal processing technique that tries to take the advantages of pulse RADAR and mitigate its disadvantages. The major dilemma is that accuracy of RADAR is dependent on pulse width. For instance, if you send out a short pulse you can illuminate the target with a small amount of energy. However the range resolution is increased. The digital processing of pulse compression grants the best of both worlds: having a high range resolution and also illuminate the target with greater energy. This is done using Linear Frequency Modulation or “Chirp modulation”, illustrated below.
As shown above, the frequency gradually increases with time (x axis).
A “matched filter” is a processing technique to optimize the SNR, which outputs a compressed pulse.
Range resolution can be calculated as follows:
Resolution = (C*T)/2
Where T is the pulse time or width.
With greater range resolution, a RADAR can detect two objects that are very close. As shown this is easier to do with a longer pulse, unless pulse compression is achieved.
It can also be demonstrated that range resolution is proportional to bandwidth:
Resolution = c/2B
So this means that RADARs with higher frequencies (which tend to have higher bandwidth), greater resolution can also be achieved.
To derive the RADAR range equation, it is first necessary to define the power density at a distance from an isotropic radiator. An isotropic radiator is a fictional antenna that radiates equally in all directions (azimuthal and elevation angle accounted for). The power density (in watts/sq meter) is given as:
However, of course RADARs are not going to be isotropic, but rather directional. The power density for this can be taken directly from the isotropic radiator with an additional scaling factor (antenna gain). This simply means that the power is concentrated into a smaller surface area of the sphere. To review, gain is directivity scaled by antenna efficiency. This means that gain accounts for attenuation and loss as it travels through the input port of the antenna to where it is radiated into the atmosphere.
To determine the received power to a target, this value can be scaled by another value known as RCS (RADAR Cross section) which has units of square meters. The RCS of a target is dependent on three main parameters: interception, reflection and directivity. The RCS is a function of target viewing angle and therefore is not a constant. So in short, the RCS is a unit that describes how much from the target is reflected from the target, how much is intercepted by the target as well as how much as directed back towards the receiver. An invisible stealth target would have an RCS that is zero. So in order to determined received power, the incident power density is scaled by the RCS:
The power density back at the receiver can then be calculated from the received power, resulting in the range being to the fourth power. This means that if the range of the radar to target is doubled, the received power is reduced by 12 dB (a factor of 16). When this number is scaled by Antenna effective area, the power received at the radar can be found. However it is customary to replace this effective area (which is less than actual area due to losses) with a receive gain term:
The symbol η represents antenna, and is coefficient between 0 and 1. It is important to note that the RCS value (σ) is an average RCS value, since as discussed RCS is not a constant. For a monostatic radar, the two gain terms can be replaced by a G^2 term because the receive and transmitted gain tends to be the same, especially for mechanically scanned array antennas.
The Doppler Effect is an important principle in communications, optics, RADAR systems and other systems that deal with the propagation of signals through space. The Doppler Effect can be summarized as the resultant change to a signal’s propagation due to movement either by the source or receiving end of the signal. As the distance between two objects changes, so does the frequency. If, for instance, a signal is being propagated towards an object that is moving towards the source, the returning signal will be of a higher frequency.
The Doppler Effect is also applied to rotation of an object in optics and RADAR backscatter scenarios. A rotating target of a radar or optical system will return a set of frequencies which reflect the distances of each point on the target. If one side of the target is moving closer while the other side is moving away, there will be both a higher and lower frequency component to the return signal.