| As |
Azimuth sample spacing along the azimuth or y axis, meters |
| α |
Frequency change rate for LFM signal, hertz per second (Hz/s) |
| β |
Frequency change rate for LFM signal along azimuth direction, Hz/s |
| B, Bt |
Frequency bandwidth, Hz |
| BD, BDop |
Doppler frequency bandwidth, Hz |
| BDs |
Doppler frequency bandwidth in terms of slow time s, Hz |
| BDu |
Doppler frequency bandwidth in terms of radar position μ, Hz |
| Bku |
Spatial frequency bandwidth in the ku domain, Hz |
| c |
Speed of light, 3 × 108 meters per second (m/s) |
| f |
Frequency, Hz |
| fb |
Baseband frequency, Hz |
| f0 |
Reference frequency, Hz |
| fc |
Carrier frequency, Hz |
| fs |
Sampling frequency, Hz |
| fm |
Maximum frequency, Hz |
| fPRF |
Pulse repetition frequency, Hz |
| fD |
Doppler frequency, Hz |
| fDr |
Doppler frequency in terms of slant range r, Hz |
| fDs |
Doppler frequency in terms of slow time s, Hz |
| fDu |
Doppler frequency in terms of radar position u, Hz |
| fDc |
Centroid of Doppler frequency, Hz |
| fDcr |
fDc with respect to slant range r, Hz |
| fDcs |
fDc with respect to slow time s, Hz |
| fDcu |
fDc with respect to radar position u, Hz |
 Dcs |
Derivative of fDcs, or slope of fDcs, Hz/s |
| Dc |
Derivative of fDc, or slope of fDc, Hz/s |
| D |
Derivative of fD, or slope of fD, Hz/s |
| fDU |
Upper bound of Doppler frequency bandwidth, Hz |
| fDL |
Lower bound of Doppler frequency bandwidth, Hz |
| fDUr |
fDU with respect to slant range r, Hz |
| fDLr |
fDL with respect to slant range r, Hz |
| fDUs |
fDU with respect to slow time s, Hz |
| fDLs |
fDL with respect to slow time s, Hz |
| f0(x) |
Ideal target function along range or x axis |
| f0(y) |
Ideal target function along azimuth or y axis |
| f(x) |
Target function along range or x axis |
| f(y) |
Target function along azimuth or y axis |
| F0(k) |
Fourier transform of f0(x) |
| F0(ky), F0(ku) |
Spatial Fourier transform of f0(y) |
| F(k) |
Fourrier transform of f(x) |
| F (ky), F (ku) |
Spatial Fourier transform of f (y) |
| hr (t) |
Range matched filter |
| haz(s) |
Azimuth matched filter |
| haz(t, s) |
2D azimuth matched filter |
| Haz(ω, ωD) |
2D spatiotemporal Fourier transform of haz(t,s) |
| Im(ku) |
Gating function in wavenumber ku domain due to mth target |
| im(u) |
Inverse spatial Fourier transform of Im(ku) |
| kx |
Spatial wavenumber, corresponding to spatial Fourier transform of x, 1/meter (m−1; reciprocal meter) |
| ku |
Spatial wavenumber, corresponding to spatial Fourier transform of u, m−1 |
| kum |
Spatial wavenumber, corresponding to mth target |
| k′u |
Spatial wavenumber changing rate |
| ky |
Same as ku, m−1 |
| k |
Wavenumber, corresponding to f, m−1 |
| kb |
Wavenumber in baseband corresponding to fb, m−1 |
| k0 |
Wavenumber, corresponding to f0, m−1 |
| kc |
Wavenumber, corresponding to fc, m−1 |
| λ |
Wavelength of electromagnetic wave, m |
| L |
Antenna length, m |
| Ls |
Synthetic aperture length, m |
| Lsa |
Ls for target located at range R0a, m |
| Lsa2 |
Half size of Lsa, m |
| Lsx |
Ls for target located at range R0x for x = b, c, d ..., m |
| Lsx2 |
Half size of Lsx, m |
| Lsai |
Lsa for ith target |
| Lsxi |
Lsx for ith target |
| Ltotal |
Sum of Lsx from all targets, m |
| M |
Number of rows in a 2D data array |
| Mamb |
Doppler ambiguity |
| N |
Number of columns in a 2D data array |
| Naz |
Number of azimuth lines within the synthetic aperture length Ls |
| Nazi |
Number of azimuth lines within Ls for target located at range R0i |
| Nr |
Number of samples within the transmitter pulse duration |
| Nrx |
Number of sample difference between range Rx, for x = b, c ..., and range reference Ra |
| p(t) |
Transmitted radar signal |
| P(ω) |
Fourier transform of p(t) |
| pb(t) |
Baseband transmitted radar signal |
| psf(t) |
Pont spread function in time domain |
| psf(ω) |
Fourier transform of psf(t) |
| R0 |
Shortest distance between target and radar, m |
| R0a |
R0 with target located at range x = a, m |
| R0i |
R0 with target located at range x = b, c ..., m |
| Ruin |
Slant range between target n and radar located at ui, m |
| Rc |
Distance between target and radar when target is under illunination of radar center beam, m |
| R1 |
Distance between target and radar when radar starts to illuminate the target, m |
| R3 |
Distance between target and radar when radar stops to illuminate the target, m |
| Rs |
Slant range sample spacing, m |
| RS |
shortest distance from radar to ground along the range (x-axis) direction, m |
| RL |
Longest distance from radar to ground along the range (x-axis) direction, m |
| R(s) |
Slant range in terms of slow time s, m |
| R(u) |
Slant range in terms of radar position u, m |
| Δ R |
Slant range difference with respect to R0 (broadside SAR case) or R3 (squint SAR case), m |
| Δ Rr |
Slant range resolution, m |
| Δ Rgr |
Ground range resolution, m |
| Δ Ra |
Angular resolution, m |
| s |
Slow time variable along radar moving direction, seconds (s) |
| sc |
Slow time when target is illuminated by center beam of radar, s |
| s(t) |
Target reflected signal |
| sb(t) |
Baseband signal of s(t) |
| S(ω) |
Fourier transform of s(t) |
| Sb(ω) |
Fourier transform of sb(t) |
| S(t,u) |
Target reflected signal when radar is at location y = u |
| S(ω, ωD) |
2D Spatiotemporal Fourier transform of s(t,u) |
| sm(t,u) |
mth target reflected signal when radar is at location y = u |
| Sm(ω, ωD) |
2D spatiotemporal transform of sm(t,u) |
| sbm(t,u) |
Baseband version of sm(t,u) |
| Sbm(ω, ωD) |
Baseband version of Sm(ω, ωD) |
| sr0(u) |
Range reference fouction for radar located at (0, u) |
| Sr0(ku) |
Spatial Fourier transform of sr0(u) |
| τ |
Pulse duration time or echo delay time, s |
| τui |
Echo delay time when radar is located at ui, s |
| τuin |
Echo delay time due to target n and when radar is located at ui, s |
| T, T0 |
Period of periodic signal, s |
| Ta |
Time duration when target is under illumination of radar beam, s |
| Tp |
Pulse duration time, s |
| u |
Radar position variable along the azimuth or y axis, m |
| ui |
Radar position at u = ui, m |
| u2 |
Radar location when target is under illumination of radar center beam, m |
| u1 |
Radar location when radar begins to illuminate target, m |
| u3 |
Radar location when radar ceases to illuminate target, m |
 |
Radar velocity, a vector along azimuth direction m/s |
| Vr |
Radar's radial velocity, a scalar along the target direction, m/s |
| W |
Antenna width, m |
| Xc |
Centerpoint of target area along x axis, m |
| X0 |
Half size of target area along range (x-axis) direction, m |
| Y0 |
Half size of target area along azimuth (y-axis) direction, m |
| Yc |
Centerpoint of target area along y axis, m |
| yi |
Target location along y axis, m |
| <rn> |
2D signal array corresponding to target n |
| ω |
Angular frequency, Hz |
| ωb |
Angular baseband frequency, Hz |
| ω0 |
Angular reference frequency, Hz |
| ωc |
Angular carrier frequency, Hz |
| σi |
Reflection coefficient from ith target |
| θ |
Angle, radians, or degrees |
| θH |
Horizontal beamwidth = λ/L, radians or degrees |
| θV |
Vertical beamwidth = λ/W, radians or degrees |
| θ3dB |
Antenna 3-dB beamwidth, radians or degrees |
| θm(u) |
Aspect angle with respect to mth target when radar is at location y = u, radians or degrees |
| θu |
Equal to θm(u) for single target |
| θq |
Radar squint angle, radians or degrees |
| Δ(t) |
Delta or impulse function |
| sinc(t) |
Sampling or interpolation filter function |
| Rect(t) |
Time-domain rectangular pulse with duration |t| ≤ ½ |
| |χ (τ, fD)| |
Radar ambiguity function |
 |
Fourier transform operator |
| −1 |
Inverse Fourier transform operator |
| J(u) |
Jacobian of transformation |
