A

**range profile** describes the

waveform shape returned by a

radar target that has been illuminated by a

wideband radar pulse. As

electromagnetic energy travels radially away from the radar, the returned pulse will have a one-dimensional characteristic, typically

intensity versus

time.

Using the relationship that the down-range distance *d* can be derived from time *t* using the relationship *d* = *ct*, where *c* is the speed of light, the various intensities in the returned pulse can be interpreted as the various scattering centers of the target in the down-range direction.

The range profile may also be constructed by post-processing a frequency-stepped or chirped waveform. The radar transmits a signal that steps through a range of *N* frequencies, *f*_{0} … *f*_{N-1}. The radar then recieves a scattered signal from the target that is then sampled, resulting in sampled frequency-intensity values *w*_{k} where k = 0, N-1. These values can be converted to a time-domain range profile *s*_{n} by taking the inverse FFT:

The resulting time (or range) domain samples (called

range bins) can be shown to have sample width Δ R =

*c*/(2

*B*), where

*B*) is the

bandwidth of the data,

*f*_{N-1} -

*f*_{0}. Via the above relationship, the range bins have

emporal width Δ t = Δ R /

*c*, or Δ t = 1 / (2

*B*).

Range profiles are becoming very important in the area of automatic target recognition (ATR) and remote sensing, as these range profiles can be used to derive information about the length of the target object, its scattering centers, and its relative motion (spinning, tumbling, etc). This information can be used to perform object classification and is also useful in areas of ballistic missile defense.