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# SNR Gain Due to Range Processing (pulse compression)

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Equation / Last modified by KurtHeckman on 2018/10/02 00:20
`G_r = `

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TylerJones.SNR Gain Due to Range Processing (pulse compression)

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The **Signal to Noise Ratio Gain due to Range Processing** calculator computes the gain based on the effective pulse width, noise bandwidth and reduction in signal noise.

**INSTRUCTIONS**: Choose units and enter the following:

- (
**T**) Effective pulse width of the radar_{eff} - (
**B**) Noise bandwidth at the antennae_{N} - (
**L**) Reduction in signal to noise ratio gain due to non-ideal range filtering._{r}

**Signal to Noise Ratio Gain due to Range Processing (Gr):** The SNR gain is returned.

#### The Math / Science

The formula for the Signal to Noise Ratio Gain due to range processing (pulse compression) is:

`G_r = (T_(eff) * B_N)/L_r`

where:

- G
_{r}is the Signal to Noise Ratio Gain due to range processing (pulse compression) - T
_{eff}is the effective pulse width of the radar - B
_{N}is the noise bandwidth at the antennae - L
_{r}is the reduction in signal to noise ratio gain due to non-ideal range filtering.

This equation calculates the SNR gain due to range processing (pulse compression)^{1} for monostatic synthetic aperture radar. This equation is most helpful in the context of calculating the Signal-to-Noise of a Synthetic Aperture Radar.

# References

- ^ Performance Limits for Synthetic Aperture Radar - Second Edition. Sandia National Laboratories, Albuquerque, NM. Printed February 2006.

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