Clutter (radar) - Volume Clutter

Volume Clutter

Rain, hail, snow and chaff are examples of volume clutter. An airborne target, at range, is within a rainstorm. What is the effect on the detectability of the target?

First find the magnitude of the clutter return. Assume that the clutter fills the cell containing the target, that scatterers are statistically independent and that the scatterers are uniformly distributed through the volume. The clutter volume illuminated by a pulse can be calculated from the beam widths and the pulse duration, Figure 1. If c is the velocity of light and is the time duration of the transmitted pulse then the pulse returning from a target is equivalent to a physical extent of c, as is the return from any individual element of the clutter. The azimuth and elevation beamwidths, at a range, are and respectively if the illuminated cell is assumed to have an elliptical cross section.

The volume of the illuminated cell is thus:

For small angles this simplifies to:

The clutter is assumed to be a large number of independent scatterers that fill the cell containing the target uniformly. The clutter return from the volume is calculated as for the normal radar equation but the radar cross section is replaced by the product of the volume backscatter coefficient, and the clutter cell volume as derived above. The clutter return is then

Watts

where

• = transmitter power (Watts)
• = gain of the transmitting antenna
• = effective aperture (area) of the receiving antenna
• = distance from the radar to the target

A correction must be made to allow for the fact that the illumination of the clutter is not uniform across the beamwidth. In practice the beam shape will approximate to a sinc function which itself approximates to a Gaussian function. The correction factor is found by integrating across the beam width the Gaussian approximation of the antenna. The corrected back scattered power is

Watts

A number of simpliflying substitutions can be made. The receiving antenna aperture is related to its gain by:

and the antenna gain is related to the two beamwidths by:

The same antenna is generally used both for transmission and reception thus the received clutter power is:

Watts

If the Clutter Return Power is greater than the System Noise Power then the Radar is clutter limited and the Signal to Clutter Ratio must be equal to or greater than the Minimum Signal to Noise Ratio for the target to be detectable.

From the radar equation the return from the target itself will be

Watts

with a resulting expression for the signal to clutter ratio of

The implication is that when the radar is noise limited the variation of signal to noise ratio is an inverse fourth power. Halving the distance will cause the signal to noise ratio to increase (improve) by a factor of 16. When the radar is volume clutter limited, however, the variation is an inverse square law and halving the distance will cause the signal to clutter to improve by only 4 times.

Since

it follows that

Clearly narrow beamwidths and short pulses are required to reduce the effect of clutter by reducing the volume of the clutter cell. If pulse compression is used then the appropriate pulse duration to be used in the calculation is that of the compressed pulse, not the transmitted pulse.