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 is1/Tint for continuous wave (CW) radar, whereTint = integration time, and1/τ for fixed PRF radar, whereτ = 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)