810-005, Rev. E
DSMS Telecommunications Link
Design Handbook

202, Rev. A
34-m and 70-m Doppler
December 15, 2002

Document Owner:              Approved by:

-----------------------      --------------------------
C.J. Ruggier        Date     J.B. Berner          Date
Tracking System Engineer     Tracking and Navigation Services
                             Development Engineer

Prepared by:                 Released by:
                             [Signature on file in TMOD Library]
------------------------     ---------------------------
P.W. Kinman        Date      TMOD Document Release  Date


Change Log
Rev           Issue Date               Affected Paragraphs       Change Summary
Initial       1/15/2001                All                       All



Note to Readers 
There are two sets of document histories in the 810-005 document, and these
histories are reflected in the header at the top of the page. First, the entire document is
periodically released as a revision when major changes affect a majority of the modules. For
example, this module is part of 810-005, Revision E. Second, the individual modules also
change, starting as an initial issue that has no revision letter. When a module is changed, a
change letter is appended to the module number on the second line of the header and a summary
of the changes is entered in the module's change log.


Contents
Paragraph                                                                                             Page
1. Introduction......................................................................................... 4
1.1 Purpose............................................................................................. 4
1.2 Scope............................................................................................... 4
2. General Information ................................................................................. 4
2.1 Doppler Measurement Error .......................................................................... 7
2.1.1 Measurement Error for One-Way Doppler............................................................. 9
2.1.2 Measurement Error for Two-Way and Three-Way Doppler .............................................. 9
2.2 Carrier Tracking .................................................................................. 10
2.2.1 Carrier Loop Bandwidth .......................................................................... 10
2.2.2 Static Phase Error in the Carrier Loop........................................................... 10
2.2.3 Carrier Phase Error Variance .................................................................... 11
2.2.4 Carrier Power Measurement ....................................................................... 12
2.3 Doppler Measurement With Small Sun-Earth-Probe Angles ............................................. 12
2.3.1 Doppler Measurement Error ....................................................................... 13
2.3.2 Carrier Phase Error Variance .................................................................... 14
Appendix A References.................................................................................. 20

Illustrations
Figure                                                                                                Page
1. One-Way Doppler Measurement ......................................................................... 6
2. Two/Three-Way Doppler Measurement.................................................................... 6
3. Doppler Measurement Error Due to Solar Phase Scintillation: S-Up/S-Down............................. 15
4. Doppler Measurement Error Due to Solar Phase Scintillation: S-Up/X-Down ............................ 16
5. Doppler Measurement Error Due to Solar Phase Scintillation: X-Up/X-Down............................. 17
6. Doppler Measurement Error Due to Solar Phase Scintillation: X-Up/S-Down ............................ 18
7. Doppler Measurement Error Due to Solar Phase Scintillation: X-Up/Ka-Down............................ 19

Table
Table                                                                                                 Page
1. Static Phase Error ................................................................................. 12


1. Introduction

1.1 Purpose
This module provides sufficient information for the telecommunications engineer
to understand the capabilities and limitations of the equipment used for Doppler measurement at
the Deep Space Network (DSN) 34-m and 70-m stations.

1.2 Scope
The scope of this module is limited to those features of the Downlink Channel at
the 34-m High-efficiency (34-m HEF), 34-m Beam Waveguide (34-m BWG), and 70-m stations
that relate to the measurement of and reporting of the Doppler effect. This module does not
discuss the capabilities of the equipment used for Doppler measurement at the DSN 34-m Highspeed
Beam Waveguide (HSB) station.


2. General Information

The relative motion of a transmitter and receiver causes the received frequency to
differ from that of the transmitter. This is the Doppler effect. In deep space communications it is
usual to define Doppler as the transmitted frequency (the uplink) minus the received frequency
(the downlink) divided by the ratio that was used onboard the spacecraft (the transponding ratio)
to generate the downlink frequency. For the receding spacecraft that are typical of deep space
exploration, the Doppler so defined is a positive quantity. Since the frequency of a carrier equals
the rate-of-change of carrier phase, the Downlink Channel supports Doppler measurement by
extracting the phase of the downlink carrier (Reference 1).
There are three types of Doppler measurement: one-way, two-way, and threeway.
In all of these cases, the accumulating downlink carrier phase is measured and recorded.
When the measurement is one-way, the frequency of the spacecraft transmitter must typically be
inferred. A much more accurate Doppler measurement is possible when the spacecraft coherently
transponds a carrier arriving on the uplink. In such a case, the downlink carrier frequency is
related to the uplink carrier frequency by a multiplicative constant, the transponding ratio. Also,
the downlink carrier phase equals the uplink carrier phase multiplied by this transponding ratio.
Thus, when an uplink signal is transmitted by the DSN and the spacecraft coherently transponds
this uplinked signal, a comparison of the uplink transmitter phase record with the downlink
receiver phase record gives all the information necessary for an accurate computation of the
combined Doppler on uplink and downlink. When one Deep Space Station (DSS) both provides
the uplink and receives the downlink, so that there are two "nodes" (the DSS and the spacecraft)
present, then it is a two-way measurement. When one DSS provides the uplink and another
receives the downlink, so that there are three nodes present, then it is a three-way measurement.
Figure 1 illustrates one-way Doppler measurement. The measurement is
referenced to the signal originating on the spacecraft. The frequency stability of the spacecraft
oscillator used to generate the downlink carrier will, in general, limit the performance of this
Doppler measurement. Usually, only Ultra-Stable Oscillators (USOs) are used for one-way
Doppler measurement.
Figure 2, Two/Three-Way Doppler Measurement, illustrates the more usual
means of measuring Doppler. The measurement originates at a DSS. The uplink carrier
frequency is synthesized within the exciter from a highly stable frequency reference provided by
the Frequency and Timing Subsystem (FTS). Since this reference is much more stable than
anything that a spacecraft-borne oscillator could provide, a two-way or three-way Doppler
measurement is more accurate than a one-way measurement. The uplink carrier may be either
constant or varied in accord with a tuning plan. In either case, the phase of the uplink carrier is
recorded for use in the computation of a Doppler effect.
For all Doppler measurements (one-, two-, and three-way), the downlink signal is
routed from the Antenna Feed/Low Noise Amplifier (LNA) to the Downlink Channel. This is
reflected in Figures 1 and 2. Within the Radio-frequency to Intermediate-frequency
Downconverter (RID), which is located at the antenna, a local oscillator is generated by
frequency multiplication of a highly stable frequency reference from the FTS and the incoming
downlink signal is heterodyned with this local oscillator. The Intermediate-Frequency (IF) signal
that results is sent to the Signal Processing Center (SPC).
In the SPC, the IF to Digital Converter (IDC) alters the frequency of the IF signal
by a combination of up-conversion and down-conversion to a final analog frequency of
approximately 200 MHz and then performs analog-to-digital conversion. The final analog stage
of down-conversion uses a local oscillator supplied by the Channel-Select Synthesizer (CSS),
which is also part of the Downlink Channel. The CSS is adjusted before the beginning of a pass
to a frequency appropriate for the anticipated frequency range of the incoming downlink signal.
During the pass, the frequency of the CSS remains constant. The local oscillator frequencies of
the CSS (and, indeed, of all local oscillators in the analog chain of down-conversion) are
synthesized within the Downlink Channel from highly stable frequency references provided by
the FTS. All analog stages of down-conversion are open-loop, and so the digital signal coming
out of the IDC reflects the full Doppler effect on the downlink carrier.
The Receiver and Ranging Processor (RRP) accepts the signal from the IDC and
extracts carrier phase with a digital phase-locked loop (Reference 2). The loop is configured to
track the phase of a phase-shift keyed signal with residual carrier, a suppressed carrier, or a
QPSK signal. Since every analog local oscillator is held at constant frequency during a pass, the
downlink carrier phase at sky frequency (that is, the phase that arrives at the DSS antenna) is
easily computed from the local oscillator frequencies and the time-varying phase extracted by the
digital phase-locked loop.
Since Doppler is a difference of frequencies and a frequency is a derivative of
phase, a record of phase transmitted on the uplink and of phase received on the downlink is
sufficient to compute the combined uplink/downlink Doppler. It is important to note that these

Figure 1. One-Way Doppler Measurement
(Figure omitted in text-only document)
Figure 2. Two/Three-Way Doppler Measurement
(Figure omitted in text-only document)

phase records must account for integer as well as fractional cycles. (This is unlike many
telecommunications applications where it is necessary to know the carrier phase only modulo
one cycle.) The data are uplink and downlink phase counts at sky frequency (only downlink
phase counts in the case of a one-way measurement). The downlink phase counts are available at
0.1-second intervals. The uplink phase counts are available from the Uplink Processor Assembly
(UPA) at 1.0-second intervals.

2.1 Doppler Measurement Error
Only errors in measuring the rate-of-change of the distance between phase centers
of the antennas are considered here. There are other errors that must be considered in any
navigation solution, such as those introduced by propagation through the troposphere, the
ionosphere, and the solar corona. Additional information on the effect of the solar corona on
Doppler measurement is contained in paragraph 2.3.
Each error is characterized here as a standard deviation of range-rate sigma_V and is in
units of velocity. To translate any of these errors to a standard deviation of frequency sf, the
following equation can be used.
sigma_f = 2f_c/c * sigma_v   (1)
where
f_c = the downlink carrier frequency and
c = the speed of light in vacuum.

Equation (1) is for two-way and three-way Doppler measurement. (The factor of 2 is absent for
one-way Doppler measurement.)
When tracking a residual carrier, the carrier loop signal-to-noise ratio is
rho_L = P_c/N_0 |_D/L * 1/B_L   (2)
where P_C/N_0 |_D/L is the downlink carrier power to noise spectral density ratio, Hz.

There is an additional loss to the carrier loop signal-to-noise ratio when tracking a
residual carrier with non-return-to-zero symbols in the absence of a subcarrier. This loss is due to
the presence of data sidebands overlaying the residual carrier in the frequency domain and
therefore increasing the effective noise level for carrier synchronization. In this case, rho_L must be
calculated as (Reference 3)
rho_L = P_C/N_0 |_D/L * (1/B_L) * 1/(1 + 2E_S/N_0)     (4)

where 
P_T/N_0|_D/L = downlink total signal power to noise spectral density ratio, Hz
S_L = squaring loss of the Costas loop (Reference 4),

S_L = (2E_S/N_0)/(1 + 2E_S/N_0)    (5)

When tracking QPSK, the carrier loop signal-to-noise ratio is
rho_L = P_T/N_0|_D/L * S_LQ/B_L    (6)
where S_LQ is the squaring loss of the QPSK Costas loop (Reference 5),

S_LQ = 1/(1 + 9/(2E_SQ/N_0) + 6/(E_SQ/N_0)^2 + 3/(2(E_SQ/N_0)^3))  (7)
where E_SQ/N0 is the energy per quaternary channel symbol to noise spectral
density ratio.

When telemetry data in a non-return to zero (NRZ) format directly modulate the
carrier (that is, no subcarrier) and there is an imbalance in the data (that is, an unequal number of
logical ones and zeros), a residual-carrier loop will experience an additional jitter. This jitter
represents an additional error source for Doppler measurement. The size of this error
contribution is strongly dependent on the statistics of the telemetry data.

2.1.1 Measurement Error for One-Way Doppler
Measurement error for one-way Doppler is normally dominated by the relative
instability of the spacecraft oscillator and by the lack of knowledge of the exact frequency of this
oscillator. Associated with one-way Doppler measurement is an unknown bias due to uncertainty
in the transmitted frequency. In addition, there is a random error due to instability of the
spacecraft oscillator. This latter error may be roughly modeled as
sigma_V = sqrt(2)c * sigma_y
where
sigma_v = the standard deviation of range-rate in velocity units,
c = the speed of light in vacuum, and
sigma_y = the Allan deviation of the spacecraft oscillator.

The Allan deviation is a function of integration time.

2.1.2 Measurement Error for Two-Way and Three-Way Doppler
Measurement errors for two-way coherent and three-way coherent Doppler must
include the effect of jitter introduced by the spacecraft receiver. The two-way or three-way
coherent Doppler measurement error due to thermal noise is approximated by

sigma_v = c/(2sqrt(2)(pi)f_c * T) * sqrt(1/rho_L + G^2B_L/(P_C/N_0|_U/L))
where
T = measurement integration time, s
f_C = downlink carrier frequency, Hz
c = speed of light in vacuum, mm/s
G = transponding ratio
B_L = one-sided, noise-equivalent, loop bandwidth of downlink carrier loop, Hz
P_C/N_0|_U/L = uplink carrier power to noise spectral density ratio, Hz
rho_L = downlink carrier loop signal-to-noise ratio.

Equation (9) assumes that the transponder (uplink) carrier loop bandwidth is large compared
with the DSS (downlink) carrier loop bandwidth, which is typically the case.

2.2 Carrier Tracking
The Downlink Channel can be configured to track phase-shift keyed telemetry
with residual carrier or a suppressed carrier or a QPSK signal. In order to achieve good Doppler
measurement performance, it is important to characterize the phase error in the carrier loop.

2.2.1 Carrier Loop Bandwidth
The one-sided, noise-equivalent, carrier loop bandwidth is denoted B_L.The user
may choose to change B_L during a tracking pass, and this can be implemented without losing
phase-lock, assuming the change is not too large.
There are limits on the carrier loop bandwidth. B_L can be no larger than 200 Hz.
The lower limit on B_L is determined by the phase noise on the downlink. In addition, when
operating in the suppressed-carrier mode, B_L is subject to the following constraint.
B_L = R_SYM/20, suppressed carrier,   (10)
where R_SYM is the telemetry symbol rate.

In general, the value selected for B_L should be small in order to maximize the
carrier loop signal-to-noise ratio. On the other hand, B_L must be large enough that neither of the
following variables becomes too large: the static phase error due to Doppler dynamics and the
contribution to carrier loop phase error variance due to phase noise on the downlink. The best B_L
to select will depend on circumstances. Often, it will be possible to select a B_L of less than 1 Hz.
A larger value for B_L is necessary when there is significant uncertainty in the downlink Doppler
dynamics, when the downlink is one-way (or two-way non-coherent) and originates with a less
stable oscillator (such as an Auxiliary Oscillator), or when the Sun-Earth-probe angle is small (so
that solar phase scintillations are present on the downlink).
When tracking a spinning spacecraft, it may be necessary to set the carrier loop
bandwidth to a value that is somewhat larger than would otherwise be needed. The loop
bandwidth must be large enough to track out the variation due to the spin. Also, the coherent
AGC in the receiver must track out the amplitude variations.
The user may select either a type 2 or type 3 carrier loop. Both loop types are
perfect, meaning that the loop filter implements a true accumulation.

2.2.2 Static Phase Error in the Carrier Loop
The carrier loop, with either a type 2 or type 3 loop, has a very large tracking
range; even a Doppler offset of several megahertz can be tracked. With a finite Doppler rate,
however, there will be a static phase error in a type 2 loop.

Table 1, Static Phase Error (rad), shows the static phase error in the carrier loop
that results from various Doppler dynamics for several different loops. These equations are based
on the work reported in Reference 6. The Doppler dynamics are here defined by the parameters
alpha and beta.
alpha = Doppler Rate (Hz/s)
beta = Doppler Acceleration (Hz/s^2)

In the presence of a persistent Doppler acceleration, a type 2 loop will periodically slip cycles.
The equations of Table 1 are valid when tracking phase-shift keyed telemetry with
either residual or suppressed carrier or a QPSK signal. These equations are exactly the same as
those appearing in Appendix C of module 207, 34-m and 70-m Telemetry.

2.2.3 Carrier Phase Error Variance
When the spacecraft is tracked one-way, the carrier phase error variance sigma_phi^2 is given by
sigma_phi^2 = 1/rho_L + sigma_S^2    (11)

When the spacecraft is tracked in a two-way or three-way coherent mode, the
carrier phase error variance sigma_phi^2 is given by
sigma_phi^2 = 1/rho_L + G^2(B_TR-B_L)/(P_C/N_0|_U/L) + sigma_S^2   (12)

where
B_TR = one-sided, noise-equivalent, transponder carrier loop bandwidth, Hz
sigma_phi^2 = contribution to carrier loop phase error variance due to solar phase
scintillations, rad^2 (see paragraph 2.3.2)
and the other parameters are as defined in paragraph 2.1.2.
It is recommended that the following constraint on carrier phase error variance be observed.
sigma_phi^2 <= {  0.10 rad^2,  residual carrier       (13)
               {  0.02 rad^2,  suppressed carrier


Table 1. Static Phase Error (rad)


Loop             Range-Rate                 Derivate of Range-Rate      Second Deriviate of Range-Rate
                 (Constant Doppler Offset)  (Constant Doppler Rate)     (Constant Doppler Acceleration)
type 2,          0                          9(pi)/(16B_L^2) * alpha     (9(pi)beta/(16B_L^2))t - 27(pi)beta/(64B_L^3)
standard
underdamped

type 2,          0                          25(pi)/(32B_L^2)            (25(pi)beta/(32B_L^2))t - 125(pi)beta/(128B_L^3)
supercritically
damped

type 3,          0                          0                           12167(pi)/(8000B_L^3) * beta
standard
underdamped

type 3,          0                          0                           35937(pi)/(16384B_L^3) * beta
supercritically
damped

2.2.4 Carrier Power Measurement
When the downlink is residual-carrier, an estimate of the downlink carrier power
P_C is available. When the downlink is suppressed-carrier, an estimate of the total downlink
power P_T is available. This is done by first estimating P_C/N_0|_D/L (with a modified version of the
algorithm described in Reference 7) or P_T/N_0|_D/L (with the split-symbol moments algorithm
described in Reference 8). An estimate of the noise spectral density N0 comes from continual
measurements made by a noise-adding radiometer. This information is used to compute absolute
power P_C or P_T. The results are reported once per second.

2.3 Doppler Measurement With Small Sun-Earth-Probe Angles
When the Sun-Earth-probe angle is small and the spacecraft is beyond the Sun,
microwave carriers pick up phase scintillations in passing through the solar corona. There is a
resulting contribution to Doppler measurement error and also an increase in the carrier loop
phase error variance. The magnitudes of these effects are highly variable, depending on the
activity of the Sun.

2.3.1 Doppler Measurement Error
Equations (14) and (15), below, based on the work reported in Reference 9, offer
a coarse estimate of the average solar contribution to the standard deviation of Doppler
measurement error. Equation (14) is valid when tracking phase-shift keyed telemetry with either
residual or suppressed carrier or a QPSK signal, but only for Sun-Earth-Probe angles between 5 degrees
and 27 degrees. In general, the standard deviation of Doppler measurement error will be the root-sumsquare
of the error standard deviation due to thermal noise, which is given in Equation (9), and
the error standard deviation due to solar phase scintillations, which is given in Equation (14).
sigma_V = (0.73c * sqrt(C_band) * [sin(theta_SEP)]^-1.225)/(f_C * T^0.175)     (14)
where
T = the measurement integration time in seconds,
fC = the downlink carrier frequency in hertz,
c = the speed of light in vacuum (~= 3 x 10^11 mm/s), and
?_SEP = the Sun-Earth-probe angle.
The result, sigma_V, will have the same units as c.

The constant C_band depends on the uplink/downlink bands; it is given by
Cband = { 6.1 x 10-5, S-up/S-down             (15)
        { 4.8 x 10-4, S-up/X-down
        { 2.6 x 10-5, X-up/S-down
        { 5.5 x 10-6, X-up/X-down
        { 5.2 x 10-5, X-up/Ka-down
        { 1.9 x 10-6, Ka-up/X-down
        { 2.3 x 10-7, Ka-up/Ka-down

Figure 3 shows sigma_V as a function of Sun-Earth-probe angle for two-way or threeway
Doppler measurement with an S-band uplink and an S-band downlink. The vertical axis is in
units of mm/s. The three curves in that figure correspond to measurement integration times of 5,
60, and 1000 seconds. Figure 4 shows sigma_V for an S-band uplink and an X-band downlink. Figure
5 shows sigma_V for an X-band uplink and an X-band downlink. Figure 6 shows sigma_V for an X-band
uplink and an S-band downlink. Figure 7 shows sigma_V for an X-band uplink and a Ka-band
downlink.

2.3.2 Carrier Phase Error Variance
Equation (16), below, based on the work reported in Reference 9, offers a coarse
estimate of the average solar contribution, in units of rad^2, to carrier loop phase error variance.
Equation (16) is valid when tracking phase-shift keyed telemetry with either residual or
suppressed carrier or a QPSK signal, but only for Sun-Earth-Probe angles between 5 degrees and 27 degrees.
sigma_S^2 = (C_band * C_loop)/(sin(theta_SEP)^2.45 * B_L^1.65), 5 degrees <= theta_SEP <= 27 degrees  (16)

In Equation (16), ?_SEP is the Sun-Earth-probe angle and B_L is the carrier loop bandwidth. C_band is
given by Equation (15) for two-way and three-way coherent operation and by
C_band = { 2.6 x 10^-5, S-down           (17)
         { 1.9 x 10-6, X-down
         { 1.3 x 10-7, K_a - down

for non-coherent operation.
C_loop is a constant depending on the type of carrier loop selected.
C_loop = { 5.9, standard underdamped type 2 loop      (18)
         { 5.0, supercritically damped type 2 loop 
         { 8.2, standard underdamped type 3 loop
         { 6.7, supercritically damped type 3 loop

Equation (16) together with Equations (15), (17), and (18) give the contribution of
solar coronal phase scintillation to carrier loop phase error variance. It is used in Equation (12) to
compute the total carrier loop phase error variance.


Figure 3. Doppler Measurement Error Due to Solar Phase Scintillation: S-Up/S-Down
(Figure omitted in text-only document)
Figure 4. Doppler Measurement Error Due to Solar Phase Scintillation: S-Up/X-Down
(Figure omitted in text-only document)
Figure 5. Doppler Measurement Error Due to Solar Phase Scintillation: X-Up/X-Down
(Figure omitted in text-only document)
Figure 6. Doppler Measurement Error Due to Solar Phase Scintillation: X-Up/S-Down
(Figure omitted in text-only document)
Figure 7. Doppler Measurement Error Due to Solar Phase Scintillation: X-Up/Ka-Down
(Figure omitted in text-only document)


Appendix A
References
1. P. W. Kinman, "Doppler Tracking of Planetary Spacecraft," IEEE Transactions
on Microwave Theory and Techniques, Vol. 40, No. 6, pp. 1199-1204, June 1992.
2. J. B. Berner and K. M. Ware, "An Extremely Sensitive Digital Receiver for Deep
Space Satellite Communications," Eleventh Annual International Phoenix
Conference on Computers and Communications, pp. 577-584, Scottsdale,
Arizona, April 1-3, 1992.
3. J. Lesh, "Tracking Loop and Modulation Format Considerations for High Rate
Telemetry," DSN Progress Report 42-44, Jet Propulsion Laboratory, Pasadena,
CA, pp. 117-124, April 15, 1978.
4. M. K. Simon and W. C. Lindsey, "Optimum Performance of Suppressed Carrier
Receivers with Costas Loop Tracking," IEEE Transactions on Communications,
Vol. COM-25, No. 2, pp. 215-227, February 1977.
5. J. H. Yuen, editor, Deep Space Telecommunications Systems Engineering,
Plenum Press, New York, pp. 94-97, 1983.
6. S. A. Stephens and J. B. Thomas, "Controlled-Root Formulation for Digital
Phase-Locked Loops," IEEE Transactions on Aerospace and Electronic Systems,
Vol. 31, No. 1, pp. 78-95, January 1995.
7. A. Monk, "Carrier-to-Noise Power Estimation for the Block-V Receiver," TDA
Progress Report 42-106, Jet Propulsion Laboratory, Pasadena, CA, pp. 353-363,
August 15, 1991.
8. S. Dolinar, "Exact Closed-Form Expressions for the Performance of the Split-
Symbol Moments Estimator of Signal-to-Noise Ratio," TDA Progress Report 42-
100, pp. 174-179, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1990.
9. R. Woo and J. W. Armstrong, "Spacecraft Radio Scattering Observations of the
Power Spectrum of Electron Density Fluctuations in the Solar Wind," Journal of
Geophysical Research, Vol. 84, No. A12, pp. 7288-7296, December 1, 1979.