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RCS can be briefly described as the effective echoing area of the target when it is illuminated by a plane wave as illustrated in Figure 2.3. RCS can also be thought of as the measure of an object's ability to scatter EM signals in the direction of the radar receiver. According to the IEEE Standard Definitions of Terms, RCS or the scattering cross section (SCS) or the echoing area is defined as the following: “For a given scatterer, upon which a plane wave is incident, that portion of the SCS corresponding to a specified polarization component of the scattered wave” (IEEE Std 145‐1993 1993).

A more formal definition of the RCS (σ) of an object can be made as the following: “It is the equivalent area intercepting the amount of power that, when scattered isotropically, produces at the radar receiver a power density W^s that is equal to the density scattered by the actual object” (Chu et al. 1991).

The formula of RCS can be derived easily, as follows: As depicted in Figure 2.3, the object (or the target) is located at R distance from the radar. Incident plane wave from the radar transmitter produces a power density of Wⁱ at the target. If the object (or the target) has an RCS area of σ, the power reflected by that object is then equal to

Figure 2.3 The EM energy scatters in all directions when it hits a target.

(2.6)

According to the above definition of RCS, this reflected power will reradiate in all directions (isotropically). Therefore, the power density W^s of the reflected wave at the radar receiver is

(2.7)

Therefore, σ in the above equation can be left alone to give

(2.8)

The formal equation of RCS can be easily obtained as the following:

(2.9)

In an alternative definition of RCS (σ), it is the measure of the ratio of backscatter power per unit solid angle (steradian) along the radar direction to the power density that is intercepted by the object (or target)

(2.10)

If W^s is the scattered power density from the target, the amount {R²W^s} gives the scattered power per steradian at the radar receiver. Assuming that the incident power density is Wⁱ, the RCS of a target can then be rewritten as exactly equal to formula (2.8).

As the target is located at the far field of radar, the distance R is brought to the infinity in the above equation so that we reach the formula in (2.9). The RCS can also be expressed in terms of the complex electric and magnetic fields at the target (Eⁱ and Hⁱ) and at the radar receiver (E^s and H^s). That is,

(2.11)

As the incident EM wave hits the target, the scattered energy radiates in all directions, as illustrated in Figure 2.3. Only the scattered energy in the direction of radar receiver is included in the RCS calculation. If the radar transmitter and the receiver are collocated, the energy collected by the radar is called the backscattered energy. This radar configuration provides monostatic RCS measurement setup. If the radar receiver is placed at a different position than the transmitter, the calculated cross section will provide bistatic RCS.

The RCS area of a target does not necessarily bear a direct link with the physical cross‐sectional area of that target but depends on other parameters as well. Besides the aperture of the target seen by the radar (or projected cross section), the EM reflectivity characteristics of the target's surface and the directivity of the radar reflection caused by the target's geometric shape are the key parameters that affect the RCS value. Therefore, RCS can be approximated as the multiplication of (i) projected cross section, S; (ii) reflectivity, Γ; and (iii) directivity, D as

(2.12)

Here, projected cross section is the cross‐sectional area of the object along the radar look‐angle direction. This gives the projected area of the illuminated region of the object by the incident wave. Reflectivity of the target gives the amount (percentage) of the intercepted and reradiated EM energy by the target. Directivity is the ratio of scattered energy in the radar direction to the scattered energy from an isotropic scatterer (such that this isotropic scattering is uniform in all directions).

The value of RCS can be stated in different polarization of the incoming and outgoing EM wave. If the radar is transmitting in vertical (V) polarization, vertically polarized scattered energy is used for the determination of RCS. Similarly, if the radar is transmitting in horizontal (H) polarization, horizontally polarized scattered energy should be used for the calculation of RCS. The term SCS refers to all types of polarization for transmission and reception. Therefore, SCS presents the all possible polarization types, such as V–V, V–H, H–V, and H–H where the first letter is used for the transmitted and the second term is used for the received polarization of the EM wave and also for RCS.

It is essential to point out that the RCS of an object is both angle dependent and frequency dependent. As the look angle toward a target changes, the projected cross section of that target generally changes. Depending on the structure and the material of the target, the reflectivity of the target might also change. Overall, the RCS of the target alters as the look angle varies. Similarly, if the frequency of the EM wave changes, the effective electrical size (or projected cross section) of the target changes as well. Furthermore, the EM reflectivity is also a frequency‐dependent quantity; therefore, the RCS of the target also varies as the frequency of the radar changes. Consequently, an RCS of an object is characterized together with the look angle and the particular frequency of operation. It is also important to note that RCS is independent of the target's distance from the radar. Therefore, the RCS of an object at different range distances is exactly the same.