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DIGISONDE-4D
SYSTEM MANUAL
VERSION 1.2.11
SECTION 1 - GENERAL SYSTEM DESCRIPTION 1-25
where f
D
is the Doppler shift in Hz and T is the time between pulses.
The Doppler shift can be calculated as:
f
D
= (f
0
v
r
)/c (or for a 2-way radar propagation path)
f
D
= (2f
0
v
r
)/c
where f
0
is the operating frequency and v
r
is the radial velocity of the reflecting surface toward or away from
the sounder transceiver. The radial velocity is defined as the projection of the velocity of motion (v) on the unit
amplitude radial vector (r) between the radar location and the moving object or surface, which in the iono-
sphere is an isodensity surface. This is the scalar product of the two vectors:
A phase change of 10 in 5 msec would require a Doppler shift of about 5.5 Hz, or 160 m/sec radial velocity
(roughly half the speed of sound), which seldom occurs in the ionospheric except in the polar cap region. The
16-chip complementary phase code pulse compression and coherent summation of the two echo profiles pro-
vides a 32-fold increase in signal amplitude, and a 8-fold increase in noise amplitude for a net signal processing
gain of 15 dB. The Doppler integration, as described later can provide another 21 dB of SNR (signal to noise
ratio) enhancement, for a total signal processing gain of 36 dB, as shown by the following discussion.
Coherent Spectral Integration
1:49. In ionospheric sounding, the motion of the ionosphere often makes it impossible to integrate by simple
coherent summation for longer that a fraction of a second, although it is not rare to receive coherent echoes for
tens of seconds. However, with the application of spectral integration (which is a byproduct of the Fourier
transform used to create a Doppler spectrum) it is possible to coherently integrate pulse echoes for tens of sec-
onds under nearly all ionospheric conditions [Bibl and Reinisch, 1978]. The integration may progress for as
long a time as the rate of change of phase remains constant (i.e., there is a constant Doppler shift, Δf). The
Digisonde-128PS, and all subsequent versions perform this spectral integration.
1:50. The pulse compression described above occurs with each pulse transmitted, so the SNR improvement
for 16-bit complementary phase codes is achieved without even sending another pulse. However, if the meas-
urement can be repeated phase coherently, the multiple returns can be coherently integrated to achieve an even
more detectable or “cleaner” signal. This process is essentially the same as averaging, but since complex sig-
nals are used, signals of the same phase are required if the summation is going to increase the signal amplitude.
If the phase changes by more than 90
during the coherent integration then continued summation will start to
decrease the integrated amplitude rather than increase it. However, if transmitted pulses are being reflected
from a stationary object at a fixed distance, and the frequency and phase of the transmitted pulses remain the
same, then the phase and amplitude of the received echoes will stay the same indefinitely.
1:51. The coherent summation of N echo signals causes the signal amplitude, to increase by N, while the in-
coherent summation of the noise amplitude in the signal results in an increase in the noise amplitude of only
√
𝑁. Therefore with each N pulses integrated, the SNR increases by a factor of
√
𝑁 in amplitude which is a fac-
tor of N in power. This improvement is called signal processing gain and can be defined best in decibels (to
avoid the confusion of whether it is an amplitude ratio or a power ratio) as:
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