Aircraft Wake Detection Using Bistatic Radar: Analysis of ...

R. J. IANNUZZELLI ET AL.
in which the transmitter and receiver are spatially
separated, can be shown to be
P
R
2
PGG T T R
= v(
VC ∩VV),
3 2 2
( 4)
R R
T R
(1)
where
PT = transmitter power,
GT and GR = transmitter and receiver antenna gains,
respectively,
= wavelength,
RT and RR = ranges from the transmitter and receiver
to the intersection of the two antenna beams,
respectively,
v =reflectivity of volume clutter (expressed in m2 /
m3 ),
VC = the common volume, which is contained within
the intersection of the transmitter’s and
receiver’s conical beams, and
VV = vortex volume.
For a monostatic radar, the ranges are identical.
From Ref. 2, clear air turbulence reflectivity v can
be expressed as
4
= 2k [ 2k sin( / 2)]
, (2)
v S
where k = 2/ is the radar wavenumber, and S is the
scattering angle, i.e., the angle at which the radar
energy is bent at the common volume from the transmitter
toward the receiver (180° for the monostatic
case). The spectral representation of the turbulence is
given by
2 −11/
3
n
( ) = 0. 033C ,
(3)
where is the spatial wavenumber, and 2
C is a struc-
n
ture parameter that measures the intensity of turbulent
fluctuations. For the special case of homogeneous isotropic
turbulence, 2
C can be expressed in terms of the
n
more general structure Dn(r) using
where
2 2/ 3
Cn = r Dn() r
− , (4)
[ ] 2
Dn() r ≡ n( x + r) − n() x
(5)
is the structure function, and r is a spatial increment. The
variable n in Eq. 5 is the refractive index of air, which
is related to meteorological variables (temperature,
pressure, humidity). The overbar indicates an ensemble
average. Values of 2 16 2/3
C can range from 10 m n
for weak turbulence to 10 12 m 2/3 for very strong
turbulence. 3,4
Vortex detection by radar poses several challenges
to the radar designer. Most of the problems arise because
the vortex provides little radar return. Since
most of the refraction will be away from the radar
transmitter (Ref. 1), a bistatic arrangement is favored.
The biggest problem with the bistatic continuouswave
radar is the performance degradation due to
phase noise from the spillover signal. Unlike pulse
radars, a continuous-wave radar is both transmitting
and receiving all the time. Time gating, which isolates
a pulse radar receiver from the transmitter, does not
apply with a continuous-wave radar, so other means of
isolating the high spillover signal from the transmitter
into the receiver must be used. We applied several
techniques to reduce spillover at BWI, including construction
of fences around the transmitter and receiver
shelter and separation and pointing of the receiver/
transmitter so that sidelobe patterns could help null
out as much of the direct spillover as possible. In
addition, we experimented with an active nuller 1 and
adaptive processing, which will be described later in
this article. Figure 1 depicts a hypothetical received
signal spectrum, with a finite-passband noiselike vortex
signal component, a receiver noise component,
and a spillover component with phase noise.
RADIOACOUSTIC DETECTION
OF AIRCRAFT WAKES:
ACOUSTIC PUMPING
In 1961, the Midwest Research Institute developed
a radioacoustic detection system, later known as RASS
(radioacoustic sounding system), as a means for
measuring the temperature profile of the lower
300 JOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 19, NUMBER 3 (1998)
Power received (dBm/Hz)
–60
–80
–100
–120
–140
–160
–180
Vortex signal
Receiver noise
Spillover
Phase noise
–200 –150 –100 –50 0 50 100 150
Doppler frequency (Hz)
Figure 1. Illustration of received vortex signal spectrum showing the
major components. Turbulent fluctuations, C n 2 , were 10 12 , 10 14 ,
and 10 16 m 2/3 for strong, moderate, and weak turbulences,
respectively. Radar specifications were transmitter power = 400 W,
beamwidth = 1.6°, transmitter/receiver separation = 1620 m, and
vortex height = 61 m.