MATHEMATICS NOTATION

The radar and Electronic Warfare communities generally accept some commonly used notation for the various parameters used in radar and EW calculations. For instance, "P" is almost always power and "G" is almost always gain. Textbooks and reference handbooks will usually use this common notation in formulae and equations.

A significant exception is the use of "a" or (alpha) for space loss. Most textbooks don't develop the radar equation to its most usable form as does this reference handbook, therefore the concept of "a" just isn't covered.

Subscripts are a different matter. Subscripts are often whatever seems to make sense in the context of the particular formula or equation. For instance, power may be "P", "P_T", "P_t", or maybe "P₁". In the following list, generally accepted notation is given in the left hand column with no subscripts. Subscripted notation in the indented columns is the notation used in this handbook and the notation often (but not always) used in the EW community.

= Space loss: ₁ = One way space loss, transmitter to receiver; ₂ = Two way space loss, transmitter to target (including radar cross section) and back to the receiver; _1t = One way space loss, radar transmitter to target, bistatic; _1r = One way space loss, target to radar receiver, bistatic

Other notation such as

_tm may be used to clarify specific losses, in this case the space loss between a target and missile seeker, which could also be identified as

_1r.


A = Antenna aperture (capture area): A_e = Effective antenna aperture; Å = Angstrom

B = Bandwidth (to 3dB points): B_IF = 3 dB IF bandwidth of the receiver (pre-detection); B_J = Bandwidth of the jamming spectrum; B_MHz = 3 dB bandwidth in MHz; B_N = Equivalent noise bandwidth, a.k.a. B; B_V = 3 dB video bandwidth of the receiver (post-detection) (subscript V stands for video)

BF = Bandwidth reduction factor (jamming spectrum wider than the receiver bandwidth)

BW = Beamwidth (to 3 dB points)

c = Speed of Light

f = Frequency (radio frequency): f_c = Footcandle (SI unit of illuminance); f_D = Doppler frequency; f_R = Received frequency; f_T = Transmitted frequency

G = Gain: G_t = Gain of the transmitter antenna; G_r = Gain of the receiver antenna; G_tr = Gain of the transmitter/receiver antenna (monostatic radar); G_J = Gain of the jammer; G_JA = Gain of the jammer antenna; G_JT = Gain of the jammer transmitter antenna; G_JR = Gain of the jammer receiver antenna; G = Gain of reflected radar signal due to radar cross section

h = Height or Planks constant: h_radar = Height of radar; h_target = Height of target

J = Jamming signal (receiver input): J₁ = Jamming signal (constant gain jammer); J₂ = Jamming signal (constant power jammer)

J/S = Jamming to signal ratio (receiver input)

k = Boltzmann Constant

K_1,2,3,4 = Proportionality constants

= Lambda, Wavelength or piosson factor

L = Loss (due to transmission lines or circuit elements)

N = Receiver equivalent noise input (kT_oB)

NF = Noise figure

P = Power: P_d = Probability of detection; P_D = Power Density; P_J = Power of a jammer transmitter; P_n = Probability of false alarm; P_r = Power Received; P_t = Power of a transmitter

Pi = ( 3.141592654+)


R = Range (straight line distance): R₁ = Bistatic radar transmitter to target range; R₂ = Bistatic radar target to receiver range; R_J = Range of jammer to receiver (when separate from the target); R_NM = Range in nautical miles

= Sigma, radar cross section (RCS)

S = Signal (receiver input): S_R = Radar signal received by the jammer; S_min = Minimum receiver sensitivity


t = time: t_int = Integration time; t_r = Pulse rise time; t = Pulse width


V = Velocity: V_r = Radial velocity

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