Radar Cross Section (RCS) - MATLAB Simulations for Radar Systems Design - page 553

radar applications, glint introduces linear errors in the radar measurements, and
thus it is not of a major concern. However, in cases where high precision and
accuracy are required, glint can be detrimental. Examples include precision
instrumentation tracking radar systems, missile seekers, and automated aircraft
landing systems. For more details on glint, the reader is advised to visit cited
references listed in the bibliography.

Radar cross-section scintillation can vary slowly or rapidly depending on the
target size, shape, dynamics, and its relative motion with respect to the radar.
Thus, due to the wide variety of RCS scintillation sources, changes in the radar
cross section are modeled statistically as random processes. The value of an
RCS random process at any given time defines a random variable at that time.
Many of the RCS scintillation models were developed and verified by experi-
mental measurements.

11.8.1. RCS Statistical Models - Scintillation Models

This section presents the most commonly used RCS statistical models. Sta-
tistical models that apply to sea, land, and volume clutter, such as the Weibull
and Log-normal distributions, will be discussed in a later chapter. The choice
of a particular model depends heavily on the nature of the target under exami-
nation.

Chi-Square of Degree 2 m

The Chi-square distribution applies to a wide range of targets; its pdf is given
by

-------   m

– 1

m
Γ ()σ av

m σ
σ av

– m σσ av ⁄

---------------------

f () = e σ 0 ≥

(11.105)

where is the gamma function with argument , and is the average
value. As the degree gets larger the distribution corresponds to constrained
RCS values (narrow range of values). The limit

Γ () m σ av

m → ∞ corresponds to a con-

stant RCS target (steady-target case).
Swerling I and II (Chi-Square of Degree 2)

In Swerling I, the RCS samples measured by the radar are correlated
throughout an entire scan, but are uncorrelated from scan to scan (slow fluctu-
ation). In this case, the pdf is

1
σ av

σ
σ av

 

f () = -------- exp – -------- σ 0 ≥

(11.106)

 

where denotes the average RCS overall target fluctuation. Swerling II tar-
get fluctuation is more rapid than Swerling I, but the measurements are pulse to

σ av