User's Manual Part 2

Processing Algorithms (draft)
RVP8 User’s Manual
April 2003
5–12
5.2.3 Autocorrelations for PPP-Mode
The autocorrelations are computed during pulse-pair-processing mode according to the
following algorithms (corresponding physical models are also given):
Parameter and Definition Physical Model
T
o
+
1
M
ȍ
M
n+1
s
n
* s
n
g
r
g
t
(S ) C) ) N
R
o
+
1
M
ȍ
M
n+1
sȀ
*
n
sȀ
n
g
r
g
t
S ) N
R
1
+
1
M * 1
ȍ
M*1
n+1
sȀ
*
n
sȀ
n)1
g
r
g
t
Se
j p VȀ*p
2
W
2
ń2
R
2
+
1
M * 2
ȍ
M*2
n+1
sȀ
*
n
sȀ
n)2
g
r
g
t
Se
j 2p VȀ*2p
2
W
2
where M is the number of pulses in the time average. Here, sȀ denotes the filtered time series, s
denotes the original unfiltered time series and the * denotes a complex conjugate. g
r
and g
t
represent the transmitter and receiver gains, i.e., their product represents the total system gain.
Since the RVP8 is a linear receiver, there is a single gain number that relates the measured
autocorrelation magnitude to the absolute received power. However, since many of the
algorithms do not require absolute calibration of the power, the gain terms will be ignored in the
discussion of these. T
o
for the unfiltered time series is proportional to the sum of the
meteorological signal S, the clutter power C and the noise power N. R
0
is equal to the sum of
the meteorological signal S and noise power N which is measured directly on the RVP8 by
periodic noise sampling. T
o
and R
0
are used for calculating the dBZ values- the equivalent radar
reflectivity factor which is a calibrated measurement. The physical models for R
0
, R
1
and R
2
correspond to a Gaussian weather signal and white noise. W is the spectrum width and V’ the
mean velocity, both for the normalized Nyquist interval [–1 to 1].
The exact value of M that is used for each time average will generally be the “Sample Size” that
is selected by the SOPRM command (See Section 6.3). However, when the RVP8 is in PPP
mode and antenna angle synchronization is enabled, the actual number of pulses used may be
limited by the number that fit within each ray’s angular limits at the current antenna scan rate.
The value of M will never be greater than the SOPRM Sample Size, but it may sometimes be
less. For example, at 1KHz PRF, 20_/sec scan rate, 1_ ray synchronization, and a Sample Size
of 80, there will be 50 pulses used for each ray (not 80). Note, however, that the number of
pulses used in the “batched” (non-PPP) modes will always be exactly equal to the Sample Size,
since those modes are allowed to use overlapping pulses.