Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 48
Weather Radar: Operation and Phenomenology
Pr =
2 2
PG
λ
t
( 4π )
3
Ls
σi
R L (R ),
i
4 2
i
(7)
i
Key WSR-88D Parameters [10]
where the equation sums over the contributions of several scatters
within a resolution volume. Most often, the weather radar range equation is written as a function of reflectivity, or RCS per unit volume:
η=
1
ΔV
σ i ,
Table 1.
Antenna Subsystem
Gain
45 dB
(8)
Polarization
Simultaneous HH and
VV
where ΔV is the radar resolution volume and η is given in units of
square meters per cubic meters. For further simplification, a common assumption is that the range and propagation losses throughout a resolution volume are approximately equal and thus may be
moved outside the summation in (7).
In the case of the WSR-88D, the beam is axis symmetric [10],
i.e., θ3 = ϕ3; thus, the resulting resolution volume is roughly cylindrical [2], [11]. Therefore, using (4) and (5), the resolution volume
is approximated as [2]
Beamwidth
0.93°
i
2
Rθ cτ
ΔV ≈ π 3 .
2 2
(9)
Using (8) and (9), the final form of the weather radar range equation is
2 2
1 PG
λ ηθ32cτ
t
Pr =
,
(10)
2ln ( 2 ) 512π 2 R 2 L2 ( R ) Ls
1
where a factor of
has been included to account for the non2ln ( 2 )
uniform Gaussian directivity pattern of the radar over the radar
resolution cell volume [2].
E. THERMAL NOISE
All target echoes received by the radar compete with receiver thermal noise. The total observed signal at sample i is
yi = si + ni ,
(11)
where ni is the receiver noise and si is the received signal. Thermal
noise is modeled as a white, circular, zero-mean complex Gaussian
process. The noise power of the radar receiver is
Pn = kbTs B = kbT0 FB,
(12)
where kb = 1.38 × 10−23 J/K is Boltzmann's constant, T0 is the standard temperature of 290 K, F is the receiver noise figure, Ts = T0F
is the system equivalent noise temperature1 in kelvins, and B is the
instantaneous receiver bandwidth. Under most circumstances, it is
assumed that B = β.
Accurate estimates of the system noise power are essential to
properly estimate the power of the received signal. For example,
1
48
Ts, in (12), refers to the system equivalent noise temperature, a
term common in radar literature, which is related to the standard
temperature To and the system effective temperature Te by the
equation Ts = To + Te.
First sidelobe level
Elevation steerability
−29 dB
+0.5° to +19.5°
Maximum rotation rate
30 ° s−1
Transmitter Subsystem
Transmit frequency
2.7-3.0 GHz
Peak power
750 kW
Short pulse width
1.57 μs
Long pulse width
4.5 μs
Short pulse PRF
318-1,304 Hz
Long pulse PRF
318-452 Hz
Receiver Subsystem
Noise temperature
450 K
Receiver bandwidth
0.63 MHz
HH, horzontal transmit [emdash] horizontal receive;
VV, vertical transmit [emdash] vertucak receive.
WSR-88D specifications require the capability to estimate reflectivity and velocity at signal-to-noise ratios (SNRs) as low as −3
dB [12]. Based on the preceding equation and the parameters in
Table 1, the WSR-88D receiver noise power is expected to be −114
dBm. Measurements have yielded a comparable value of −113
dBm [11].
F. DOPPLER FREQUENCY
Most weather radars have a coherent quadrature receiver [10],
which can measure the phase of a received sinusoidal wave relative to the radar's stable local oscillator (STALO). Coherence over
multiple transmitted pulses yields two main advantages. First, it
offers an increased SNR, where the exact gain in SNR is a function
of the number of pulses in a coherent processing interval (CPI)
and the rate at which the signal decorrelates over the duration of
the CPI. Second, coherence facilitates measurement of the Doppler
frequency:
fd ≡
2Vr
λ
,
(13)
where Vr is radial velocity of the target in meters per second. The
Doppler frequency is measured over a series of pulses in a CPI,
which is called a slow-time sequence. The time between consecu-
IEEE A&E SYSTEMS MAGAZINE
JULY 2017, Part II of II
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