User manual

Code: ENIGMA III User Manual
Edition: 1 Revision: 4
Date: 19/12/2008
Page: 26/97
2.5 Pulse-pair processing.
The basis for time domain moment estimation is the transform relationship of the autocorrelation function
of the complex signal to the power spectrum.
The estimate of the autocorrelation can be calculated from the complex input time series at the given
range as following:
T
0
=
1
N
∑
k=0
N −1
s
k
*
s
k
R
m
=
1
N −m
∑
k=0
N −m −1
s
k
' *
s
k
'
Where:
M number of pulses for averaging
s
k
represents unfiltered I and Q samples
s'
k
represents filtered I and Q samples
* complex conjugation
g system gain
S signal power
C clutter power and N is a noise power.
T
0
unfiltered signal power = g(S+C)+N
R
0
filtered signal power = gS+N
R
1
first lag of a filtered signal power =g S exp[j π V'-π
2
W
2
/2]
R
2
second lag of a filtered signal power = g S exp[j 2π V'-2π
2
W
2
]
It is well known that the first few lags of the autocorrelation function are sufficient to find a Doppler
velocity and spectrum width. So, it is enough to calculate T
0
, R
0
, R
1
, R
2.
V' is the mean velocity in the sampling volume and W is the mean spectrum width. Radial velocity in the
normalized Nyquist interval from -1 to 1 and spectrum width in the normalized Nyquist interval [0,1].
Parameter: AcfMode
GAMIC Proprietary