Page 170 - Fundamentals of Radar Signal Processing

common signal models used in designing and analyzing radar signal processors.

It has been seen that multiple views of the radar echo are used: its variation in
amplitude, space, time, and frequency, and deterministic and statistical
interpretations of these variations.
Radar signal modeling traditionally focuses most strongly on amplitude
models, that is, on radar cross section. RCS is viewed as a deterministic
quantity, predictable in principle through the use of Maxwell’s equations if the

scattering is modeled accurately enough. The radar range equation in its many
forms (only a very small subset of which has been introduced here) is the radar
engineer’s most fundamental tool for estimating received signal amplitude or,
conversely, determining required system characteristics such as transmitted
power or antenna gain.
The radar system is a measuring instrument, used to observe the variation
of RCS in space. Its pulse function (modulation and carrier term) and antenna

power pattern determine its measurement characteristics, which in turn
determine the achievable resolution and required sampling rates. The effect of
the radar measurement system on the spatial variation of observed RCS is well
modeled by the convolution of the combined pulse-and-antenna pattern
measurement kernel with the three-dimensional reflectivity function. This
important observation means that the tools of linear systems analysis can be

brought to bear to help analyze and understand the performance of radar
systems. The carrier frequency, in combination with any Doppler shifts,
determines what portion of the reflectivity frequency spectrum is sampled by the
pulse. This observation reinforces the need for frequency domain analyses of
radar measurements. Linear systems and frequency domain viewpoints are
relied on heavily throughout the remainder of the book.
Even though RCS is a deterministic quantity, its sensitivity to radar

frequency, aspect angle, and range coupled with the complexity of typical
targets results in very complex behavior of observed amplitude measurements.
Statistical models are used to describe this complexity. A variety of statistical
models, comprising both probability density functions and correlation
properties, have gained acceptance for various scenarios and form the basis for

much analysis, particularly in calculations of probabilities of detection and false
alarm, two of the most important radar performance measures.

References

Baddour, N., “Operational and Convolution Properties of Three-Dimensional
Fourier Transforms in Spherical Polar Coordinates,” J. Optical Society of
America, vol. 27, no. 3, pp. 2144–2155, Oct. 2010.
Balanis, C. A., Antenna Theory, 3d ed. Harper & Row, New York, 2005.
Baxa, E. G., Jr., “Airborne Pulsed Doppler Radar Detection of Low-Altitude