antenna. The loss, 1/(1 − |Γrx|2) ≜ Lrx, associated by the impedance mismatch at the transmitter, is known as the receiver loss. Of course, if the antenna is matched, the received power will be equal to the power captured by the antenna as
(2.25)
Rewriting Eq. 2.23 in terms of the received power, one can easily obtain
(2.26)
This power is then transmitted to radar receiver by using a transmission line. If there are some electric and/or dielectric losses, L2, within the line, the power output to the radar receiver will be equal to
(2.27)
If we insert the input power to the above equation with the help of Eqs. 2.13 and 2.14, we can get the famous radar range equation as below:
In this equation, Ltot is the total loss accounted for all the losses and is given by
(2.29)
If both the transmitter and the receiver antenna are perfectly matched and there are no losses inside the transmission lines, then Ltot = 1; therefore, Eq. 2.28 can be simplified to give
2.4.2 Monostatic Case
In the case of monostatic operation of radar, the same antenna is used for transmitting the radar signal and receiving the backscattered wave from the target (see Figure 2.7). Therefore, the antenna gains, G1 and G2 in Eq. 2.30, become identical, say G(= G1 = G2). Similarly, the target distance from the transmitter and the receiver distance from the target becomes equal, say R (= R1 = R2). Then the radar range equation can be obtained in its simplified form as shown below:
Figure 2.7 Geometry for obtaining monostatic radar range equation.
2.5 Range of Radar Detection
While working with radars, another important parameter that should be carefully considered is the detection range of radar, that is, the farthest distance of the target that can be detected over the noise floor of the radar. This distance can be easily calculated starting from the radar range equation. Let us rewrite Eq. 2.31 in terms of antenna effective aperture, Aeff = 4π ⋅ G2/λ2, as
The minimum power at the receiver output can only be detected if the received signal is greater than the noise floor, as demonstrated in Figure 2.8. If the power level at the receiver output is lower than the noise floor, this signal cannot be distinguished from the noise mostly produced by the environment and the electronic equipment and therefore can either be considered as noise or clutter.
Figure 2.8 Minimum receiver power corresponding to maximum range of radar.
Considering that the input power to the radar remains unchanged, the output power at the receiver in Eq. 2.32 is selected as the minimum detectable signal, Pmin, for the maximum range distance of Rmax as
(2.33)
Therefore, it is easy to find the maximum range of radar by rearranging the above equation to leave Rmax alone as
(2.34)
The above equation gives the maximum range of an object that can be detectable by the radar. The meaning of “maximum range” is clarified with the following example: For a radar antenna with 26 dB gain at 10 GHz, the corresponding antenna effective area becomes 28 472 m2. If the input power of this monostatic radar is 75 W with a receiver sensitivity of −55 dBmW (3.16 nW) and used to detect a target with an RCS of 0.5 m2 at 10 GHz, then the maximum range can be readily calculated by plugging the appropriate numbers into above equation to give
(2.35)
If this target is located at the range closer than 170.78 km (~171 km), then it will be detected by this radar. However, any object that has a maximum RCS of 0.5 m2 and located beyond 171 km will not be perceived as a target since the received signal level will be lower than the sensitivity level (or the noise floor) of the radar as illustrated in Figure 2.8.
2.5.1 Signal‐to‐Noise Ratio
Similar to all electronic devices and systems, radars must function in the presence of internal noise and external noise. The main source of internal noise is the agitation of electrons caused by heat. The heat inside the electronic equipment can also be caused by environmental sources such as the sun, the earth, and buildings. This type of noise is also known as thermal noise (Johnson 1928) in the electrical engineering community.
Let us investigate the signal‐to‐noise ratio (SNR) of a radar system: Similar to all electronic
