Single-Pulse Signal to Noise Ratio | Noise Power | Pulse Integration Equations

Search/Track Radar Constants and Equations

The following constants and equations relate generally to search/track radar systems.

For further background on these and other concepts used in Radar, see generally Skolnik, Merrill I., Radar Handbook, 2nd Ed., New York: McGraw-Hill (1990)

Carrara, Walter G., Goodman, Ron S. and Ronald M. Majewski, Spotlight Synthetic Aperture Radar: Signal Processing Algorithms, Boston: Artech House (1995)

Willis, Nicholas J., Bistatic Radar, Boston: Artech House (1991).

Single-Pulse Signal to Noise Ratio

Single-pulse signal to noise ratio is defined as

where
Pt = peak transmitter power
λ = wavelength,
Gt = transmitter antenna gain,
Gr = receiver antenna gain,
σ = radar cross section (RCS),
Go = other gains/losses,
Rt = transmitter-target range,
Rr = receiver-target range,
Np = noise power,
LAT = transmitter-target path atmosphere attenuation,
LAR = receiver-target path atmosphere attenuation, and
Lr = receiver transmission line loss

Noise Power

Noise power is defined as

Np = K Ts Bw, where

K = Boltzman's Constant (1.38 x 10-23 W/Hz K),
Ts = system temperature, and
Bw = receiver bandwidth, which is
1/Tint for continuous wave (CW) radar, where
Tint = integration time, and
1/τ for fixed PRF radar, where
τ = pulse width

Pulse Integration Equations

The following are equations and constants related to the perfect integrator, constant efficiency and exponent on pulse number.

Perfect Integrator

For a fixed PRF radar, the perfect integrator is defined as

SNRM = M SNR1, where

M = number of pulses, and
SNR1 = per-pulse SNR

For a CW radar, the perfect integrator is defined as

SNRM = Tint SNR1, where

Tint = integration time, and
SNR1 = one-second pulse width SNR

Constant Efficiency

Constant efficiency is defined (for fixed PRF only) as

SNRM = ρMSNR1, where

ρ = integration efficiency

Exponent on Pulse Number

Exponent on pulse number is defined (for fixed PRF only) as

SNRM = MρSNR1, where

ρ = user defined integration exponent (commonly 0.5 for non-coherent integrators)