Ground-Based Remote Sensing of Cloud Properties ...
337
A low-pass filter at the output of the demodulators removes the high frequency term containing
cos(a + (3), together with any other frequecies much greater than a - f3 due to nonlinearities
in the mixer, with the result that
I(t) = Low Frequency Part[V(t)v;.~/(t)] = Yo cos [2ker - wmt +
and
Q(t) = Low Frequency Part[V(t)v;.~/(t)] = Yosin[2ker - wmt +
We emphasize that no matter what the nature of the electomagnetic field is at the receiver
antenna output port, the result of the coherent path signal processing is to strip off the carrier
frequency and create the I and Q signal voltages. The voltage amplitudes of I and Q are
always a faithful representation of the electromagnetic field strength at the receiver antenna
output port. If the gains GSYS and losses Lsys from the receiver antenna to the output of the
demodulators are known, then the amplitudes of I and Q can be used to produce estimates of
the electromagnetic field strength at the receiver antenna. Furthermore, the variations in time
of the I and Q signals enable one to produce power density spectra of the signal from which
estimates of the velocities of the scatterers relative to the radar are derived.
13.4.2 Estimating received power from an isolated scatterer
The power in the electromagnetic field at the receiver antenna due to scattering from a single,
isolated particle is proportional to the real part of the electric field squared averaged over a
period Tant = 2rr / (we + W m) ofthe Doppler shifted wave:
_ (As)2 [ 1 la Tan • 2
]
Pant - - - -T.
COS [2ker - (We + wm)t +
ant 0
As before, the factor in brackets is 1/2 so that
(As)2
Pant = -2--' 1'/0
(13.33)
(13.34)
Therefore, apart from a constant of proportionality, the power averaged over a cycle of the wave
is simply the wave amplitude squared and divided by two.
This same power can be estimated from either the I or Q signal voltages. Consider I(t) from
(13.32a). The instantaneous power in I(t) is
(13.35)
where Rre/ is the appropriate impedance. Therefore, the power averaged over the period
Tiq = 2rr /wm is
(13.36)
Assuming that we know Gsys and Lay., as well as the receiver antenna aperture Ae(B,
(13.37)
337
A low-pass filter at the output of the demodulators removes the high frequency term containing
cos(a + (3), together with any other frequecies much greater than a - f3 due to nonlinearities
in the mixer, with the result that
I(t) = Low Frequency Part[V(t)v;.~/(t)] = Yo cos [2ker - wmt +
and
Q(t) = Low Frequency Part[V(t)v;.~/(t)] = Yosin[2ker - wmt +
We emphasize that no matter what the nature of the electomagnetic field is at the receiver
antenna output port, the result of the coherent path signal processing is to strip off the carrier
frequency and create the I and Q signal voltages. The voltage amplitudes of I and Q are
always a faithful representation of the electromagnetic field strength at the receiver antenna
output port. If the gains GSYS and losses Lsys from the receiver antenna to the output of the
demodulators are known, then the amplitudes of I and Q can be used to produce estimates of
the electromagnetic field strength at the receiver antenna. Furthermore, the variations in time
of the I and Q signals enable one to produce power density spectra of the signal from which
estimates of the velocities of the scatterers relative to the radar are derived.
13.4.2 Estimating received power from an isolated scatterer
The power in the electromagnetic field at the receiver antenna due to scattering from a single,
isolated particle is proportional to the real part of the electric field squared averaged over a
period Tant = 2rr / (we + W m) ofthe Doppler shifted wave:
_ (As)2 [ 1 la Tan • 2
]
Pant - - - -T.
COS [2ker - (We + wm)t +
ant 0
As before, the factor in brackets is 1/2 so that
(As)2
Pant = -2--' 1'/0
(13.33)
(13.34)
Therefore, apart from a constant of proportionality, the power averaged over a cycle of the wave
is simply the wave amplitude squared and divided by two.
This same power can be estimated from either the I or Q signal voltages. Consider I(t) from
(13.32a). The instantaneous power in I(t) is
(13.35)
where Rre/ is the appropriate impedance. Therefore, the power averaged over the period
Tiq = 2rr /wm is
(13.36)
Assuming that we know Gsys and Lay., as well as the receiver antenna aperture Ae(B,
(13.37)