Two-way coherent Doppler errors resulting from phase scintillations induced on the uplink by the solar corona are considered. It is shown that this error can be estimated by taking statistics on the differential Doppler measurements. Typical estimates for the error are given for four Sun-Earth-probe angles and for integration times ranging from 1 second to 1 minute. These results are based on data collected during the 1985 Voyager 2 conjunction

Asmar, S. W.

Kinman, P. W.

English

NASA Technical Reports Server

TDA Progress Report 42-95 
N89 - 2033 2 
July-September 1988 
Two-way Coherent Doppler Error Due to Solar Corona 
P. W. Kinman and S. W. Asmar 
Telecommunications Systems Section 
This report considers two-way coherent Doppler error resulting from phase scintilla- 
tions induced on the uplink by the solar corona. It is shown that this error can be esti- 
mated by taking statistics on the differential Doppler measurements. Typical estimates 
for the error are given for four Sun-Earth-probe angles and for integration times ranging 
from I second to I minute. These results are based on data collected during the 1985 
I Voyager 2 solar conjunction. 
I I. Introduction 
When a spacecraft is in the same area of the sky as the Sun 
and beyond it, the radio beams to and from that spacecraft 
experience phase scintillations due to passage through the solar 
corona. These scintillations will dominate all other sources of 
error for two-way coherent Doppler measurement when the 
Sun-Earth-probe angle is small. Thus, for those missions that 
feature numerous or long-lasting solar conjunctions, especially 
inner planetary missions, it is important to characterize this 
source of Doppler error. Unfortunately, the relevant param- 
eters of the solar corona are highly variable, and adequate 
statistical characterizations do not exist. It has, however, been 
possible to measure the phase scintillations induced on 2.3- 
and 8.4-GHz downlinks by the solar corona. It is in fact possi- 
ble to  make this measurement using any Sun-encountering 
spacecraft with two downlinks of different but related fre- 
quencies. The phase scintillations induced on the downhks ,  
once measured, can be removed from the Doppler phase 
record. The phase scintillations induced on the uplink, on the 
other hand, remain. These cannot be measured or removed 
unless two simultaneous uplinks are available. 
This report considers two-way coherent Doppler error 
resulting from phase scintillations induced on the uplink by 
the solar corona. This error is estimated by taking statistics 
on phase scintillations induced on the downlinks of Voyager 2 
during a 1985 solar conjunction. 
II. Measuring Phase Scintillations Induced 
on the Downlinks 
Whenever a two-way coherent Doppler measurement is 
being performed, the downlink frequencies fi and f 2  are 
related to  the uplink frequency fo  by the transponding ratios 
G, and G, and the relative velocity of the spacecraft and the 
deep space station. In addition, there are noise terms that 
represent the phase scintillations picked up in transit through 
the solar corona. These frequency relationships may be ex- 
pressed by 
Gi v,' vd" 
f, f ,  Gi ' 
r;: = Cif0 (1 - 2P/c) + - t - . i = 1 , 2  (1) 
The nonrelativistic Doppler shift has been indicated here; it is 
proportional to  the ratio of the range rate to  the speed of 
light, c. 
28 
https://ntrs.nasa.gov/search.jsp?R=19890010961 2020-03-20T03:53:33+00:00Z
The parameter v,', in units of Hz2, represents the level of 
phase scintillations induced on the uplink by the solar corona. 
It depends only on the physical properties of that part of the 
corona through which the uplink radio beam passes. It is an 
implicit function of time. By taking the integral of the square 
of the local plasma frequency along the uplink ray path, then 
taking a time derivative and dividing by twice the speed of 
light, one could calculate v i .  Unfortunately, the local plasma 
frequency is generally not known. The parameter v i  is the 
downlink analog of u,'. 
Using Eq. (l),  we can obtain an expression for v j  : 
The phase scintillations induced on the downlinks contribute 
a frequency noise term that can be identified if the differential 
Dopper shift, fl - (G,/G,) fi, is measured. Once identified, 
this frequency noise term is easily subtracted out of the Dop- 
pler record. At this point, the only error due to solar corona 
remaining in the Doppler record is the term involving v,' . The 
Doppler error E ,  in velocity units, is 
(3) 
The brackets ( *  )T indicate a time average over an integration 
time T .  
The statistics of v,' and v: are the same. This is in fact the 
key to being able to estimate the error E .  In the writing of 
standard deviations u( * ), then, the subscripts u and d may be 
ignored. 
(4) 
C 
U ( f )  = - o ( ( v 2 ) T )  
2 f,2 
As suggested by Eq. (2), the required coronal statistics can be 
obtained by taking a statistical measure of the differential 
Doppler shift, viz., 
The required coronal statistics can also be obtained from a 
pair of one-way downlinks of different but related frequencies. 
This is, in fact, how the data appearing in this report were ob- 
tained. In this case, Eqs. (4) and (5) still hold, but some terms 
in Eq. (5) need proper interpretation. The term GI fo is the 
frequency of the first downlink, and the term Gl/G, is the 
ratio of the downlink frequencies. 
111. Voyager 2 Results 
During the 1985 solar conjunction for Voyager 2, differen- 
tial Doppler data were collected from a pair of one-way down- 
links. The downlinks originated with an ultrastable oscillator 
aboard the spacecraft, and the 64-m subnet was used for recep- 
tion. Estimates were made of what the observed level of phase 
scintillations would do to a two-way coherent Doppler mea- 
surement. These estimates were obtained by applying the dif- 
ferential Doppler statistics to Eqs. (4) and (5). The frequency 
of the first downlink was approximately 2296 MHz. The ratio 
of the downlink frequencies, C,/C,, was 3/11. 
The standard deviation of the two-way coherent Doppler 
error, as expressed in Eq. (4) and based on Voyager 2 differen- 
tial Doppler measurements, has been compiled in Table 1 and 
plotted in Fig. 1. The statistics have been calculated for inte- 
gration times ranging from 1 second to 1 minute. For the 
longer integration times, the error is less. Four example Sun- 
Earth-probe angles have been included. It must be understood 
that the properties of the solar corona are highly variable and 
that the results shown in Table 1 and Fig. 1 do not represent 
a characterization of the error as a function of Sun-Earth- 
probe angle. Such a characterization must be based on a larger 
set of data. 
The Doppler error due to solar corona can be reduced by 
using a higher frequency on the uplink. For 7.2-GHz and 
34.3-GHz uplinks, the errors shown in Table 1 and Fig. 1 are 
divided by 11.5 and 263, respectively. For some missions, this 
is an important advantage for the higher frequencies. 
IV. Conclusions 
This report has explained how phase scintillations induced 
on the downlinks can be measured. It has been shown that 
taking statistics on these measured phase scintillations leads to 
estimates of the Doppler error due to uplink phase scintilla- 
tions. Typical estimates for the error have been calculated 
based on differential Doppler data collected during the 1985 
Voyager 2 solar conjunction. 
29 
Table 1. Two-way coherent Doppler error for 2.1CHz uplink and 
dual-frequency calibrated downlink' 
Doppler error (mm/sec) for several 
Integration Sun-Earth-probe angles 
time, sec 
1.3" 1.7" 2.1" 2.5" 
1 172.0 137.2 99.4 41.3 
5 161.7 98.2 65.7 31.2 
10 152.6 78.1 54.2 27.2 
15 142.7 67.1 47.9 24.3 
20 137.1 64.7 45.3 23.2 
25 131.7 57.9 40.2 22.8 
30 127.7 53.5 41.1 21.7 
35 123.9 52.9 37.9 21.3 
40 122.3 51.5 37.2 19.4 
45 117.7 48.7 33.9 19.6 
50 117.9 47.6 34.0 20.5 
55 116.5 45.9 34.1 19.2 
60 112.4 43.5 33.4 18.4 
*These results are based on phase scintillation measurements made 
using the Voyager 2 spacecraft during its 1985 solar conjunction. 
The time and place at which the measurements were made are 
indicated below. 
1.3": 2030 to 2135 on 12-8-85 at Goldstone 
1.7": 0440 to 0640 on 12-12-85 at Canberra 
2.1": 0435 to 0545 on 12-8-85 at Canberra 
2.5": 2015 to 2120 on 12-12-85 at Goldstone 
30 
LL 
w 
0 10 20 30 40 50 60 
INTEGRATION TIME, sec 
Fig. 1. Doppler error due to solar corona for various 
Sun-Earth-probe angles. 
31 


Two-way coherent Doppler error due to solar corona

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