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

203
Sequential Ranging
Effective November 30, 2000

Document Owner:              Approved by:

-----------------------      -----------------------
C.J. Ruggier        Date      A. Kwok           Date
Tracking System Engineer      Tracking and Navigation Services
                             System Development Engineer

Prepared by:                 Released by:
                             [Signature on file in TMOD Library]
------------------------     ------------------------
R.W. Sniffin        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.

Module 203 supersedes module TRK-30, Rev. E, dated January 15, 1998, in 810-005.
Contents                                        

Contents 
Paragraph                                                                                             Page
1 Introduction.......................................................................................... 6
1.1 Purpose ............................................................................................ 6
1.2 Scope .............................................................................................. 6
2 General Information................................................................................... 6
2.1 Network Simplification Project Ranging.............................................................. 7
2.2 System Description.................................................................................. 7
2.3 Parameters Specified for Ranging Operations ........................................................ 9
2.3.1 Transmit Time and Receive Time ................................................................... 9
2.3.2 Clocks and Components ............................................................................ 9
2.3.3 Square-Wave and Sine-Wave Ranging ............................................................... 11
2.3.4 Integration Times ............................................................................... 12
2.3.4.1 T_1............................................................................................ 12
2.3.4.2 T_2............................................................................................ 14
2.3.4.3 T_3............................................................................................ 17
2.3.4.3 Cycle Time .................................................................................... 17
2.3.5 Modulation Index ................................................................................ 18
2.3.6 Frequency Chopping............................................................................... 19
2.3.7 Other Parameters ................................................................................ 20
2.3.7.1 Tolerance ..................................................................................... 20
2.3.7.2 Servo ......................................................................................... 20
2.3.7.3 Pipe........................................................................................... 21
2.4 Range Measurement Process ......................................................................... 22
2.4.1 Range Measurement Technique ..................................................................... 22
2.4.2 P_r/N_0.......................................................................................... 24
2.4.2 Figure of Merit ................................................................................. 25
2.4.3 Differenced Range Versus Integrated Doppler ..................................................... 28
2.5 Ratio of Downlink Ranging Power to Total Power .................................................... 28
2.6 Range Corrections ................................................................................. 30
2.6.1 DSS Delay........................................................................................ 31
2.6.2 Z-Correction..................................................................................... 32
2.6.3 Antenna Correction .............................................................................. 32
2.7 Error Contributions................................................................................ 35
Appendix A, The Current DSN Ranging System............................................................. 36
A1.0 System Description Using the Sequential Ranging Assembly ......................................... 36
A2.0 Range Measurement Process Using the SRA .......................................................... 37
A3.0 Performance Differences .......................................................................... 38
A3.1 Integration Times ................................................................................ 38
A3.1.1 T_1............................................................................................. 38
A3.1.2 T_2............................................................................................. 40
A3.1.3 T_3............................................................................................. 40
A3.2 Other SRA Ranging Parameters...................................................................... 40
A3.3 SRA Calculations ................................................................................. 40
A3.3.1 Cycle Time ..................................................................................... 40
A3.3.2 P_r/N_o ........................................................................................ 40
A4.0 Range Corrections Using the SRA................................................................... 44
A4.1 DSS Delay......................................................................................... 44
A4.2 Antenna Calibration............................................................................... 44
A5.0 Error Contributions for Ranging Using the SRA..................................................... 45

Illustrations
Figure                                                                                                Page
1. The NSP Era DSN Ranging System Architecture ......................................................... 8
2. Integration Time T_1 Versus P_r/N_o, Clock Frequency Fc = 1 MHz, for Sine-Wave Ranging.............. 14
3. Integration Time T_1 Versus P_r/N_o, Clock Frequency Fc = 500 kHz, for Square-Wave Ranging.......... 15
4. Code Component Integration Time T_1 Versus P_r/N_o for Various Probabilities of Error and n = 5..... 16
5. Code Component Integration Time T_1 Versus P_r/N_o for Various Probabilities of Error and n = 10.... 16
6. Code Component Integration Time T_1 Versus P_r/N_o for Various Probabilities of Error and n = 20.... 17
7. Chopping of C5, C6, and C7 (by C4).................................................................. 21
8. Component Acquisition Process ...................................................................... 23
9. Figure of Merit, with T_2 = 5 sec for Various Frequency Components. ................................ 26
10. Figure of Merit, with T_2 = 50 sec for Various Frequency Components ............................... 27
11. Figure of Merit, with T_2 = 500 s for Various Frequency Components................................. 27
12. Pr/Pt as a Function of (gamma)RNG/DN for Selected Values of Modulation Index theta DN ............. 30
13. DSN Range Measurement.............................................................................. 31
14. Typical DSS Delay Calibration...................................................................... 33
15. Measuring the Z-Component ......................................................................... 34
A-1. Current DSN Ranging System ....................................................................... 37
A-2. Integration Time T_1 Versus P_r/N_o, Clock Frequency F_c = 1 MHz, 
     for Sine-Wave Ranging Using the SRA .............................................................. 41
A-3. Integration Time T_1 Versus P_r/N_o, Clock Frequency F_c = 500 kHz, for
     Square-Wave Ranging Using the SRA ................................................................ 42
A-4. Code Component Integration Time T_1 Versus P_r/N_o for Various Probabilities of Error and n = 5 .. 42
A-5. Code Component Integration Time T_1 Versus P_r/N_o for Various Probabilities of Error and n = 10 . 43
A-6. Code Component Integration Time T_1 Versus P_r/N_o for Various Probabilities of Error and n = 20 . 43
A-7. Typical Range Calibration Signal Path for DSS Using SRA and MDA Ranging Equipment ................ 45

Tables
Table                                                                                                 Page
1. Range Code Resolving Capability .................................................................... 11
2. One-Sigma Range Error for NSP Era Ranging System.................................................... 35
A-1. One Sigma Range Error for SRA/MDA-Equipped Ranging System ........................................ 46


1 Introduction

1.1 Purpose

This module describes the Ranging capabilities of the Network
Simplification Project (NSP) and provides the performance parameters of the Deep
Space Network (DSN) Sequential Ranging equipment for the 70-m, the 34-m High
Efficiency (HEF), and the 34-m Beam Waveguide (BWG) subnets. Appendix A gives a
description of the ranging architecture and performance for the 26-m subnet and
the 34-m High-speed Beam Waveguide (HSB) antenna that are not included in the
NSP implementation scheme, and for the 70-m, 34-m HEF, and 34-m BWG subnets
prior to the NSP implementation.

1.2 Scope
The material contained in this module covers the sequential ranging
system that is utilized by both near-Earth and deep space missions. This
document describes those parameters and operational considerations that are
independent of the particular antenna being used to provide the
telecommunications link.  For antenna-dependent parameters, refer to the
appropriate telecommunications interface module, modules 101, 102, 103, and 104
of this handbook. Other ranging schemes employed by the DSN include the tone
ranging system, described in module 204 and the pseudo random noise (PN) and
regenerative ranging, described in module 214.


2 General Information

The DSN ranging system provides a sequentially binary-coded ranging
scheme to measure the round-trip light time (RTLT) between a Deep Space Station
(DSS) and a spacecraft.  An uplink signal is transmitted to a spacecraft where
it is received by the on-board transponder, then demodulated, filtered, and
remodulated onto the downlink carrier. The downlink signal received at the DSS
is correlated with a Doppler-modified replica of the transmitted codes that were
sent to the spacecraft approximately one RTLT earlier. Using Doppler rate-
aiding, the RTLT is determined by measuring the phase difference between the
received code and the transmitted code.

The three basic tracking modes are one-way, two-way, and three-way. In
the one-way tracking mode, the spacecraft generates a downlink signal that is
received by the Earth-based station without a transmission being made to the
spacecraft. Two-way tracking consists of transmitting an uplink to a spacecraft
where it is received and coherently transmitted as a downlink to the same Earth
station. For the three-way tracking mode, two-way tracking is performed by an
Earth station, while another station tracks the downlink signal using a
different antenna and possibly a different frequency standard.
The parameters to be specified for ranging operations are explained in Paragraph
2.3. Paragraph 2.4 presents the process of range measurement that includes the
evaluation of RTLT, ranging-power-to-noise ratio (P_r/N_o), figure of merit (FOM), and
differenced range versus integrated Doppler (DRVID). The relationship of
downlink ranging power over total power is given in Paragraph 2.5. Paragraph
2.6 provides the corrections required to determine the actual range to a
spacecraft. Error contributions of the ground system are discussed in
Paragraph 2.7.


2.1 Network Simplification Project Ranging
The Deep Space Network is undergoing a redesign of the uplink and
downlink architecture to achieve simplified operations and increased
performance. A major feature of the modification is the splitting of the
ranging and Doppler uplink and downlink functions, allowing recovery from
anomalies on one without affecting the other.

In contrast to the previous design that employed a separate piece of
equipment called the sequential ranging assembly (SRA), the new ranging system
does not require a real-time interface between the uplink and downlink
elements. There is a connection between the uplink and downlink in the sense
that both elements must send data to a common node. However, the digital time-
tagged data can be passed to the common node in non-real time, without loss of
range measurement accuracy. The lack of a hardware connection to between the
uplink and downlink elements of single antenna to the ranging equipment makes
it possible to perform range measurements in the three-way tracking mode.

NSP ranging replaces the SRA with separate uplink and downlink
ranging processors. Local code models are generated that match the SRA
sequential tone ranging. The Tracking Data Delivery Subsystem (TDDS) replaces
the Metric Data Assembly (MDA) and the Radio Metric Data Conditioning (RMDC)
function of preparing the data for delivery to the user.

Ranging code components cover 1 MHz to 1 Hz in steps of powers of 2
provided by software local code models. Correlation of the ranging signal to
determine clock phase and range ambiguity is handled using software algorithms.

2.2 System Description
The NSP architecture for the DSN ranging system is shown in Figure 1.
It consists of a front end portion, an uplink portion, and a downlink portion.
The front-end portion consists of the microwave components, including a Low-
noise Amplifier (LNA) and the antenna. The uplink portion includes the Uplink
Ranging Assembly (URA), an exciter, the transmitter, and the controller,
referred to as the Uplink Processor Assembly (UPA). The downlink portion
includes the RF-to-IF Downconverter (RID), the IF-to-Digital Converter (IDC),
the Receiver and Ranging Processor (RRP) and the Downlink Channel Controller
(DCC). The Downlink Telemetry and Tracking Subsystem (DTT) and the Uplink
Subsystem (UPL) provide the essential functional capability for NSP ranging.
                                        
                                        
Figure 1. The NSP Era DSN Ranging System Architecture
(Figure omitted in text-only document)                                        
                                        
                                        
Control of the ranging function is within the DTT. Control signals
from the DTT are coupled to the URA in the UPL via the Reliable Network Service
(RNS) and the UPA. The URA generates the sequential ranging codes for two-way
and three-way ranging and forwards them to the exciter where they are modulated
onto the uplink. It also monitors the uplink ranging phase and forwards this
data to the TDDS.

The amplified downlink signal from the microwave is downconverted by
the RID (located on the antenna) and fed to the IDC where it is sampled at 160
Msamples/s into an 8-bit digital signal at the RRP. After processing, the
downlink range phase data are delivered to the TDDS by the Downlink Channel
Controller (DCC), via the station RNS and a similar function at JPL. The TDDS
formats the ranging data and passes the uplink and downlink phase information to
the Navigation subsystem (NAV). Subsequently, the NAV provides the ranging data
to projects.

Each DTT Controller Processing Cabinet (DCPC) is equipped with a
single channel, which includes a single RRP. For spacecraft with multiple
channels (for example, S-band and X-band), or for multiple spacecraft within
a single antenna beamwidth, multiple DCPCs will be assigned to that antenna.

In addition to producing downlink phase information, the RRP
generates a 66-MHz ranging reference analog signal with a Numerically
Controlled Oscillator (NCO). The ranging reference frequency F_RNG (ref), is
computed from the received frequency, f_r, as follows:

               F_RNG (ref ) = F_r/(32K)    (1)        
where:
F_r = received carrier frequency
K = normalization factor (independent of uplink frequency)
                     240/221 (S-down)
                     880/221 (X-down)
                     3344/221 (Ka-down).

2.3 Parameters Specified for Ranging Operations

The following paragraphs present the parameters that are required
in ranging operations.

2.3.1 Transmit Time and Receive Time
The rabging system needs a transmit time (XMIT) and an a-priori
estimate of the RTLT, truncated to the nearest second, in order that the code
sequence sent by the UPL can be correlated for measuring the phase shift through
the round-trip-time delay. When a XMIT and an approximate RTLT are specified,
the DTT automatically calculates the receive time To by adding the two
quantities, T_o = XMIT + RTLT. This T_o is also called the start time of the
correlation process for the code sequence. The two time quantities must be
specified to the nearest second.

2.3.2 Clocks and Components
A range measurement begins with the highest frequency code followed
by subsequent codes each having a frequency exactly half of the previous one.
The first code in the sequence is called the clock component and determines the
resolution of the measurement. The lower frequency codes that follow are used
to resolve the ambiguity (uncertainty) of the a-priori range estimate.

1 shows the clocks and components used in ranging operations. A
total of 21 code components are available. They are referred to as component
numbers 4 through 24 as shown in the Table. The first 7 components (numbered 4
through 10) are called the clock components or simply clocks. The approximate
ambiguity resolving capability of a component is listed for reference. The
approximate frequencies and periods of the codes are also shown.
The exact clock frequency (Fc) to replace the approximate
frequency in the second column is computed by the relationship:
F_C = F_66/2^(2+n)    (2)                    
where n is an integer from 4 to 24 that represents a code component or a
component number and F_66 is the exciter reference frequency.

The value of F_66 used to produce Table 1 was exactly 66.000 MHz. In
ranging operations, this frequency varies depending upon the transmitting
(uplink) carrier frequency. F_66 is denoted by F_66S or F_66X depending on whether
it was derived from an S-band or X-band uplink frequency and can be expressed in
terms of the uplink frequency as follows:
          S-band uplink:
          F_66S = F_ts/32 (3)
          
          X-band Uplink
          F_66X = 221/749 * F_tx/32    (4)
where, F_ts and F_tx are the S- and X-band transmitting (uplink) frequencies.

The third column (approximate period) shows the periods of the
corresponding frequencies in the second column. The fourth column (ambiguity
resolving capability) lists the products of the periods and the speed of
light (299,792.5 km/s), divided by a factor of 2 to determine the one-way
distance.

Depending on the uncertainty of the range estimate, a flight project
determines the number of components needed for ranging operations. An example in
choosing the clock and components is given as follows:

Example: Suppose the spacecraft is known to be at a 10-minute RTLT
from Earth to within +/-100,000 km. If it is desired to resolve the ambiguity to
about 40,000 km, and if the distance is desired to be resolved to within 150 m,
then components 4 through 22 should be defined for ranging. That is, clock 4
(about 1 MHz) is used with the subsequent 18 components (5 through 22).


Table 1. Range Code Resolving Capability
                                        
Component Approximate    Approximate   Approximate
 Number   Frequency      Period (s)    Ambiguity Resolving
          (Hz)                         Capability (km)
   4*     1,030,000.000   9.700E-07          0.1450
   5*      516,000.000    1.940E-06          0.2910
   6*      258,000.000    3.880E-06          0.5810
   7*      129,000.000    7.760E-06           1.160
   8*      64,500.000     1.550E-05           2.330
   9*      32,200.000     3.100E-05           4.650
  10*      16,100.000     6.210E-05           9.30
   11       8,060.000     1.240E-04           18.60
   12       4,030.000     2.480E-04           37.20
   13       2,010.000     4.960E-04           74.40
   14       1,010.000     9.930E-04           149.0
   15        504.000      1.990E-03           298.0
   16        252.000      3.970E-03           595.0
   17        126.000      7.940E-03          1,190.0
   18        62.900       1.590E-02          2,380.0
   19        31.500       3.180E-02          4,760.0
   20        15.700       6.360E-02          9,530.0
   21         7.870       1.270E-01         19,100.0
   22         3.930       2.540E-01         38,100.0
   23         1.970       5.080E-01         76,200.0
   24         0.983       1.020E+00         152,000.0
* available clocks                     

2.3.3 Square-Wave and Sine-Wave Ranging
The DTT may process the received codes in two ranging modes. They are
referred to as square-wave and sine-wave operation. For square-wave operation,
the DTT processes all harmonics of the received codes. For sine-wave operation,
only the fundamental (the first harmonic) is processed. Square-wave operation is
the default because, with the exception of the higher frequency clock
components, the codes are received as square waves. However, sinewave operation
may be desirable if non-linearities or other processes exist that may delay the
range code fundamental and its harmonics differently. The two modes can be
summarized by:

          Square-wave operation: transmit          square waves
                                 correlate as      square waves
                            
          Sine-wave operation:   transmit          square waves
                                 correlate as      sine waves
                            
Ranging with the 500-kHz and 1-MHz clocks are special cases due to the
limited ranging bandwidths of most spacecraft and an intentional 1.2 MHz
bandwidth limit in the DSN ranging modulators. This limit has been installed to
prevent interference with services adjacent to the DSN uplink allocations . The
ranging equipment presently requires the 1 MHz clock to be processed using sine-
wave correlation. If square-wave correlation is specified, the 500 kHz code will
be processed using the square-wave correlation algorithm although only its
fundamental will have been transmitted to the spacecraft.

2.3.4 Integration Times
Three integration times must be specified for ranging operations.
They are: T_1 for clock integration, T_2 for each lower-frequency component
integration, and T_3 for DRVID measurement(s).

2.3.4.1 T_1
T_1 is the total time used to integrate the correlation samples for
the clock component. It is a function of the clock frequency, the desired
variance of RTLT measurements, and the ranging signal to noise spectral density
and can be calculated by the following expressions:
          Sine-wave operation:            
          T_1 = 1/64 x 1/F_c^2 x 1/(sigma^2(t)) x 1/(P_r/N_o), s     (5)
where
F_c = the clock frequency, Hz
sigma^2(t) = the desired variance of the RTLT measurements, s^2
P_r/N_o = the ranging signal to noise spectral density, Hz

The factor 1/64 has been derived empirically from the most probable
variance of a range point when using sine-wave correlation.

          Square-wave operation:
          T_1 = 1/49 x 1/F_c^2 x 1/(sigma^2(t)) x 1/(P_r/N_o), s     (6)
where
F_c , sigma^2(t), and P_r/N_o are as above and the factor 1/49 has been
derived empirically from the upper bound variance of the 1 MHz sine-wave
ranging when using square-wave correlation.
          The above equations can be rewritten in terms of the uncertainty sigma(r)
in meters, by multiplying the uncertainty sigma(t) in seconds by the speed of light
and dividing by a factor of 2. This provides:


          Sine-wave operation:
          sigma(r) = sqrt(352/(F_c^2(MHz) x T_1 x P_r/N_o)), m   (7)
          
          Square-wave operation:
          sigma(r) = sqrt(458/(F_c^2(MHz) x T_1 x P_r/N_o)), m   (8)
where:
F_c = the clock frequency, MHz
T_1 = the clock component integration time, s
P_r/N_o = the ranging signal to noise spectral density, Hz.

Note: The uncertainty, sigma, here is only due to thermal noise. Other
errors must be added to this to get the total uncertainty (see Paragraph 2.7).
Figure 2 plots integration time (T_1) as a function of P_r/N_o for sine-
wave operation using a 1 MHz clock component with sigma(r) as a parameter. For a
desired sigma(r), the user may find the proper integration time, T_1, for an
estimated P_r/N_o (in dB-Hz). Figure 3 is a similar graph for square-wave
operation using a 500-kHz clock component. This figure may also be used for
lower frequency square-wave clocks by recognizing that dividing F_c by 2 will
result in T_1, being multiplied by 2^2, etc.
                                        
Figure 2. Integration Time T_1 Versus P_r/N_o, Clock Frequency F_c = 1 MHz, for Sine-Wave Ranging
(Figure omitted in text only document)  
               
Ranging is possible as long as the receiver remains in lock over the measurement
time. However, there is a practical lower limit for P_r/N_o (usually about -10 dB-
Hz) determined by the combination of integration times (cycle time) and the
minimum number of range points needed by the project. See Cycle Time in
Paragraph 2.3.4.4 for further details.

2.3.4.2  T_2
T_2 is the integration time for each of the lower-frequency
components. It is a function of P_r/N_o and the probability of error in acquiring
all components (excluding the clock). In general, T_2 is given by the following
equation

T_2 = 1/(P_r/N_0) x {InvErf[2(1-P_e)^(1/(n-1)) - 1]}^2,  s    (9)
                                        
Figure 3. Integration Time T_1 Versus P_r/N_o, Clock Frequency F_c = 500 kHz, for Square-Wave Ranging
(Figure omitted in text-only document)
where
Pr_N0 = the ranging signal to noise spectral density, Hz
InvErf[*] = the inverse error fo the * quantity
P_e = the probability of error in acquiring all (n-1) components.
n = the total number of components including the clock being acquired.
Figures 4 through 6 show T_2 versus P_r/N_o for various P_e and n. An appropriate T_2 
for ranging operations can be determined from these curves by choosing the desired n, 
the desired, P_e, and the estimated P_r/N_o.

                                        
Figure 4. Code Component Integration Time T_1 Versus P_r/N_o for Various
Probabilities of Error and n = 5
(Figure omitted in text-only document)

Figure 5. Code Component Integration Time T_1 Versus P_r/N_o for Various
Probabilities of Error and n = 10
(Figure omitted in text-only document)
                                        
Figure 6.   Code Component Integration Time T_1 Versus P_r/N_o for
Various Probabilities of Error and n = 20
(Figure omitted in text-only document)

2.3.4.3 T_3
T_3 is the integration time for differenced range versus integrated Doppler
(DRVID) measurements (see Paragraph 2.4.3 for a further discussion of
DRVID). Since the phase information is already available from the clock
acquisition, T_3 can be less than T_1 (typically 7/8 T_1).

2.3.4.3 Cycle Time
Cycle time is the total time that the DTT spends to perform
measurements for the clock, the (n-1) components, and the DRVIDs. It also
includes some dead time between component integrations to accomodate the 1-
second inaccuracy permitted in specifying the estimated RTLT. In other words, it
is the time required to complete one range acquisition. The cycle time (CYC) is
automatically calculated by the DTT, and it is given by the following formula:
 CYC= (2+T_1) + (1+T_2)(n-1) + DRVN(2+T_3) + 1, s       (10)
where
T_1 = clock integration time
T_2 = component integration times
T_3 = DRVID integration time
n = the total number of components including the clock
DRVN= the number of DRVIDs specified for the acquisition.

For a typical 8-hour tracking pass, it is recommended that CYC be
less than the following limits:

          Soft limit: CYC <= 30 minutes

          Hard limit: CYC <= 55 minutes.

The chance of getting a desired number of good range points decreases
substantially as the cycle time approaches the 55-minute limit. Any glitch
occurring in the system during the time of measurement will cause a range point
to become invalid. It is better to stay closer to, or within the soft limit.

2.3.5 Modulation Index
In ranging operations, square-wave codes are modulated on the uplink
carrier by the exciter phase modulator. This results in an attenuation of
carrier power and a corresponding increase of power spread into the sidebands.
The phase displacement of the carrier due to modulation is referred to as the
modulation index and may be specified as a peak-to-peak or root mean square
(RMS) value. That is, if the modulation waveform is specified as peak-to-peak
value, the modulation index will define the peak-to-peak phase modulation. If,
on the other hand, the modulation waveform is specified as an RMS value, the
modulation index will define the RMS phase modulation The expressions for
carrier power and ranging power are given in terms of the modulation index as
follows:

          P_c = P_t (cos^2(theta)), numeric, units of power (11)

          P_r = P_t (sin^2(theta)), numeric, units of power (12)
          
where:
P_c= the carrier power
P_r= the ranging power
P_t= the total power before ranging modulation (that is, P_t = P_c + P_r)
theta = the modulation index in radians (or degrees).

Therefore, the carrier suppression in dB is given by:
P_c/P_t = 10log(cos^2(theta)) . (13)

The modulators used in the DSN operate over the range of 0.1 to 1.5
radians, peak. It should be noted that equation 13 assumes ideal conditions,
and variations between the calculated and that measured values of carrier
suppression may occur depending on the amplitude, frequency, and phase
responses of the modulator in use.

Example: An unmodulated signal is received by a spacecraft with Pt = -100 dBm.
When this signal is modulated by square waves of a 30-deg modulation index,
the carrier power (P_c) becomes -101.25 dBm (suppressed by 1.25 dB) and the
ranging (sidebands) power (P_r) is -106.0 dBm (P_r = -100 dBm + 10log(sin(30)^2)).

2.3.6 Frequency Chopping
Separation between the ranging modulation products and the carrier
frequency decreases as a ranging acquisition steps through the code components
of the lower frequencies. If this were allowed to continue, 1) the receiver
tracking loop would follow the waveform and track out the code(s); or 2)
interference occurs to the telemetry or command modulation. A frequency chopping
modulation function can be enabled to prevent these problems. The function is
defined by:
C=C_m # C_c
where:
C = modulation
C_m = the square-wave modulation of the component, m, being chopped
C_c = the square-wave modulation of the clock component
# = modulo 2 addition

The chopping process results in a power spectrum for a sideband pair relative to
the ranging power as follows:
P_k/P_r = 10log{8 x [tan(k(pi)/(2^(m-n+1)))/(k(pi))]^2}, dB   (15)
where  
P_k = the power of the k-th odd sideband pair (a perfect square wave will not have any even harmonics)
P_r = the total ranging power (all sidebands)
m = the component number being chopped
n = the number of the clock (2 to 10)
k = the odd sideband-pair number of the component being chopped.

The physical meaning of chopping can best be illustrated by Figure 7,
which shows components C5, C6, and C7 being chopped by the 1-MHz clock, C4. The
dotted lines indicate where the edges of the components would be without
chopping. Note that C4 # C5 is the same as C5 shifted 1/4 cycle to the left.
This occurs when a component is chopped by another component at twice its
frequency.

In the chopping-disabled mode, no components are chopped until 1 kHz
(C14) and the remaining lower frequency components (C15 to C24) are reached.
The chopping component must be of the same or lower frequency than the clock
component, and it should be no lower than 16 kHz (C10). The chopping function
is handled by the ranging default software and can be overridden by directive
if necessary.

2.3.7 Other Parameters
There are four other parameters that must also be specified for
ranging operations. Their meaning and usage are briefly summarized below.

2.3.7.1 Tolerance
Tolerance is used to set the acceptable limit of the FOM -- an
estimate of the goodness of an acquisition, based on the P_r/N_0 measurement (see
Paragraph 2.4.3 for additional discussion).

Tolerance may be selected over the range of 0.0% to 100.0%. As an
example, if the tolerance is set to 0.0%, all range acquisitions will be
declared valid. Alternately, if the tolerance is set to 100.0%, all range
acquisitions will be declared invalid. A typical value set for tolerance is
99.9%. This value will flag acquisitions that have a 99.9% or better chance of
being good as valid, and the rest as invalid.

An acquisition is declared valid or invalid depending upon the
following criteria:


       FOM >= Tolerance  results  Acquisition declared valid
                          in
       FOM <  Tolerance  results  Acquisition delcared invalid.
                          in
2.3.7.2  Servo                     
Servo is used to correct distortions of the data due to charged
particle effect using DRVID information (See Paragraph 2.4.3 for a discussion of
DRVID). When Servo is enabled, the local Doppler-corrected components will be
shifted back into phase with the received components. The correction is made by
setting a proper Servo value.

Figure 7. Chopping of C5, C6, and C7 (by C4)
(Figure omitted in text-only document)             

Servo has a value between 0 and 1.0. It should be set to 1.0 with a
noiseless signal, but if the noise level is too high, no DRVID refinement is
possible and Servo should be set to 0. Note that if Servo is 1.0, the correction
is made immediately; however, if Servo is set to a fractional value between 0
and 1.0, that fraction of the correction will be done on any one DRVID
measurement.

2.3.7.3 Pipe
The Pipe parameter (for pipelining) specifies the number of range
acquisitions to be made. This parameter enables multiple measurements to be
initiated before the first measurement is completed. Only one acquisition is
made if Pipe is disabled. If it is enabled, range measurements will be made
until the total number of acquisitions reaches (2^15 - 1) or until the specified
number of acquisitions. In other words, the number of range acquisitions that
can be performed is between 1 and (2^15 - 1).

2.4 Range Measurement Process
The URA uses a reference frequency (denoted by F_66 in this document)
from the exciter to generate a sequence of square waves (or binary codes). This
code sequence is phase-modulated onto the uplink carrier beginning at the transmit time. The
measurement process begins at T_0 which is between 0 and 1 second before this
signal is received by the RRP, one RTLT later.
The RRP contains an identical coder that is driven by a reference
frequency (denoted by F_RNG in this document) that is derived from the received carrier
frequency but scaled to the corresponding uplink frequency as discussed in
paragraph 2.2. Thus, the receiver coder is able to provide a code sequence
that includes compensation for the frequency shift introduced by Earth-
spacecraft relative Doppler.
At T_0, the first (clock) component from the reciever coder is
correlated against the received signal to produce the correlation values V_I and
V_Q. The V_I s and V_Q s are used to compute the angle and amplitude of the
received code; hence, the phase and signal strength are
determined. The following paragraphs provide further detail.

The measurement of the phase (angle) displacement of the clock
provides the resolving capability of the range measurement (See Table 1). Once
the phase displacement is determined, the receiver coder is shifted by this
displacement amount to produce a zero-phase shift in the in-phase channel.
Since the remaining components are phase-coherent with the clock component, it
is only necessary to determine if each component is in or out of phase with the
previous component. This is done by integrating the V_I s and V_Q s for the time
T_2 specified during initialization. If each component is in phase, no action is necessary; if
one is out of phase, that component and the remaining components are shifted by
half its period. This process is repeated for each component. The sum of the
required shifts (plus the clock-phase shift) is the phase delay between the
transmitted and received signals, and the range is determined. The process is
illustrated in Figure 8.

2.4.1 Range Measurement Technique
The RRP measures two-way range, that is, the RTLT, by determining
the phase difference between the transmitted and received modulation. This
phase displacement (tau) is computed by the following expressions:
Sine-wave ranging:
        tau =  atan2 (SIGMA V_Q, SIGMA V_I), radians                     (16)
Square-wave ranging:                                 
        tau =  SGN(SIGMA V_Q) x 1/4 x (1 - (SIGMA V_I)/(abs(SIGMA V_Q) + SIGMA V_I)), cycles.  (17)


Figure 8.  Component Acquisition Process
(Figure omitted in text-only document)
Notes:
1. Assume that the range to the spacecraft results in tau = tau_R and that the
   range uncertainty is in the interval defined by C2 and C3.
2. Measurement of the phase offset of C1 indicates that the correlation
   amplitude is not at a peak value. The receiver coder is shifted (delayed) to
   bring the correlation value to a positive peak, A.
3. At A, the correlation function for C2 is at a negative peak; thus C2
   is out of phase. The reference code is shifted by half the period of C2 (to
   bring it into phase), arriving at B.
4. At B, C3 is out of phase with C2. The reference code is shifted by
   half the period of C3, arriving at D.
5. The sum of the phase shifts required to bring all components into
   phase is tau_R , the range measurement.
where
V_I and V_Q = the in-phase and quadrature correlation values
atan2(y,x)= the arctangent function that produces an angle in the  proper quadrant

SGN(*) = | +1, * >= 0
         | -1, * <  0

For ranging operations, the above tau of different dimensions are
converted to a measurement unit called the range units (RU). RUs have the
dimension of seconds and are defined as 1/16 of the period of the reference
frequency, that is

          RU =1/16 x 1/F_66, s (18)

where F66 is the reference frequency, F66S or F66X  as discussed earlier.

Using the above RU equation, one may convert the measurement obtained in RUs
to physical quantities such as time (nanoseconds) and distance (meters). For
example, if the F66 used in a range measurement is 66.000 MHz and suppose the
measurement obtained is 6,500,000 RU, then the equivalent RTLT delay is 6.155
ms, and the one-way distance is about 923,295 m.

2.4.2 P_r/N_0
The actual ranging power-to-noise spectral density (P_r/N_0) is
evaluated at the end of the integration of all in-phase and quadrature
correlation values for the clock. It combines ranging system performance with
receiver noise. This ratio is given by:
P_r/N_0 = 10log((Ranging Signal Power(P_s))/(Noise Power(P_n)) x Bandwidth(BW)), DB   (19)
where, depending on a ranging operation, P_s is evaluated by two different expressions.
Sine-wave operation:
P_s = ((SUM(V_I, 1, N))^2 + (SUM(V_Q, 1, N))^2)/N^2   (20)

Square-wave operation:
P_s = (SUM(V_I, 1, N) + SUM(V_Q, 1, N))^2/N^2   (21)

where:
V_I and V_Q are the correlation values.
N is the total number of samples collected during the clock acquisition.
Noise power is estimated by adding the variances of the in-phase and
quadrature correlation samples:
P_n = Var_I + Var_Q , (22)
where: Var_x is the variance function:
Var_x = SUM(x^2, 1, N)/N - (SUM(x, 1, N))^2/N^2   (23)
where:
x represents the correlation sample V_I s and V_Q s
N is the number of samples. Finally, because P_n = N_0 x the process bandwith of the RRP,
it is necessary to multiply P_s/P_n by the process bandwidth (1 Hz) to put it in the form of P_r/N_0.

2.4.2 Figure of Merit
The FOM is a probability measure which estimates the chance of
successful acquisition of all lower frequency codes. The probability of
making at least one error in acquiring these codes is:
P_e = 1 - [1/2 + 1/2Erf(sqrt(P_r/N_0 x T_2))]^(n-1)    (24)
where:
n = the number of components including the clock.
Erf(*) = the error function.
P_r/N_0 = the ranging power-to-noise ratio.
T_2 = the integration time for each of the lower frequency components, s.

Therefore, the probability P_c of getting all correct measurements is:
P_c = 1 - P_e   (25)
FOM = 100 x P_c, percent    (26)

The FOM is calculated following the clock phase measurement using the
measured P_r/N_0, the integration time T_2, and the number of lower-frequency
components. The FOM is a valid estimate only if conditions do not change. It
provides a reference by which a user may judge the validity of a range
measurement. Figures 9 to 11 show P_c versus P_r/N_0 for
various values of T_2 and n.
                                        
Figure 9. Figure of Merit, with T_2 = 5 sec for Various Frequency Components.
(Figure omitted in text-only document)

Figure 10. Figure of merit, with T_2 = 50 sec for Various Frequency Components.                                        
(Figure omitted in text-only document)                                     

Figure 11. Figure of merit, with T_2 = 500 sec for Various Frequency Components.                                        
(Figure omitted in text-only document)    

2.4.3 Differenced Range Versus Integrated Doppler
Differenced range versus integrated Doppler (DRVID) may be used to
calibrate the range observable and to study the electron content in the
transmission medium. For a given range observable, charged particles have the
effect of making the spacecraft appear further than its actual distance. As
the signal propagates through the charged-particle medium, the phase velocity
of the carrier increases by a certain quantity, while the group velocity of
the range code decreases by exactly the same quantity.

In the NSP era, DRVID is calculated from tracking data containing the
observed differences between the range measurements affected by the range-code
group velocity, and the delta range measurements derived from the Doppler
measurements influenced by the carrier-phase velocity. A more proper term for
this quantity is pseudo-DRVID (PDRVID); however, the traditional name will be
used in this article.

DRVID (t) = {[phi_u(t) - phi_d(t)]-[phi_u(t - T_cycle) - phi_d(t - T_cycle)]}    (27)
            - 26 * {r_1 * [theta_u(t) - theta_u(t - T_cycle)]
            - r_2 * [theta_d(t) - theta_d(t - T_cycle)]} mod range ambiguity

where
phi_u(t) = uplink range phase, s
phi_d(t) = downlink range phase, s
theta_u(t) = uplink carrier phase, RU
theta_d(t) = downlink carrier phase, RU
T_cycle = anging cycle time, s
r_1 = exciter reference frequency/carrier frequency ratio
   (either 1/32 or 221/(749 x 32) - see Paragraph 2.3)
r_2 = transponder turnaround ratio.

2.5 Ratio of Downlink Ranging Power to Total Power

For the type of currently used turn-around ranging channel, the
ratio of power in the fundamental ranging sidebands to the total signal power
in the downlink is a function of the uplink ranging signal-to-noise ratio. The
P_r/Pt ratio for two-way ranging is given as:
[P_r/P_t]_DN = 2*J_1^2[sqrt(2) * theta_DN sqrt(gamma_(RNG/UP)/(1 + gamma(RNG/UP)))] * 
               exp(- (theta^2_DN/(1 + gamma_(RNG/UP)))   (28)
where:
[P_r/P_t]_DN = the ratio of power in fundamental ranging sidebands to total
                            signal power for downlink
J_1^2[*] = the Bessel function of the first kind of order one
theta_DN = the downlink ranging modulation index, radians rms
gamma_(RNG/UP) = the uplink ranging signal-to-noise ratio at the output of the
   transponder's ranging channel filter, given by:
gamma_(RNG/UP) = 8/(pi)^2[P_r/N_0]_up * 1/B_RNG   (29)

where:
[P_r/N_0]_UP = the ranging power to noise spectral density ratio at input to the
   transponder's ranging channel filter, Hz    
B_RNG = A typical value for B_RNG is 1.5 MHz.


Figure 12 is a plot of equation 28, with [P_r/P_t]_DN versus gamma_(RNG/UP) for
selected values of theta_DN. For deep space missions, the uplink ranging signal-to-noise ratio
is usually quite small, and the operating point lies on the steep curve on the
left side of Figure 12. In this case, equation 28 may be approximated as
follows:
[P_r/P_t]_DN ~= gamma_(RNG/UP) * theta_DN^2 * exp(-theta_DN^2), gamma_(RNG/UP) << 1   (30)



Figure 12. P_r/P_t as a Function of gamma_(RNG/DN) for Selected Values of
Modulation Index theta_DN
(Figure omitted in text-only document)

The presence of uplink noise feeding through onto the downlink has
two effects on ranging performance: loss of ranging power and interference.
Noise affects the ranging performance by dissipating valuable downlink power
from the fundamental ranging signal sidebands. This is characterized by the
above expressions for [P_r/P_t]_DN. Alternately, the potential exists for 
noise to interfere with the fundamental ranging sidebands, causing degradation 
to the ranging signal by raising its noise floor. For most deep space missions, 
the latter effect is not considered to cause significant degradation for 
two-way ranging measurements.

2.6 Range Corrections
The DTT range measurements include delays of equipment within the DSS
as well as those of the spacecraft. These delays must be removed in order to
determine the actual range referenced to some designated location at the
antenna. Figure 13 illustrates the end-to-end range measurement and identifies
the delays that must be removed before an accurate topocentric range can be
established. The DSN is responsible for providing three measurements to the
project. They are the DSS delay, the Z-correction, and the antenna correction.
                                      
Figure 13. DSS Reference S/C Reference Location Location
(Figure omitted in text-only document)
                                        
2.6.1 DSS Delay
The DSS delay is station and configuration dependent. It should be
measured for every ranging pass. This measurement is called precal for pre-track
calibration and postcal for post-track calibration. The former is done at the
beginning of a ranging pass; the latter is only needed when there is a change in
equipment configuration during the track or precal was not performed due to a
lack of time.

The delay is measured by a test configuration, which approximates
the actual ranging configuration. The signal is transmitted to the sky;
however, before reaching the feedhorn, a sample is diverted to a test
translator through a range calibration coupler. The test translator shifts the
signal to the downlink frequency, which is fed into the coupler. The signal
flows through the LNA to the DTT for calibration.
Figure 14 shows the signal path for a typical calibration of DSS
delay when the uplink and downlink are in the same frequency band. The heavy
lines identify the calibration path. When the uplink and downlink are in
different bands, the downlink signal from the test translator is coupled into
the receive path ahead of the LNA and as close to the feed as practical.

2.6.2 Z-Correction
The delay in the microwave components ahead of the coupler and the
airpath (the distance from the horn aperture plane to the subreflector, to the
antenna aperture plane, and finally to the antenna reference location) must be
included in the calibration. Also, the translator delay must be removed. A
measurement called "Z-correction" is made to obtain an adjusted DSS delay.

The Z-correction is given by the difference of two quantities: the
translator delay and the microwave plus air path delay. Figure 15 relates these
quantities to the physical structure of the antenna.

The test translator delay is measured by installing a zero delay
device (ZDD) in place of the test translator. Since the ZDD delay is measured
in the laboratory, the signal delay contributed by the test translator can be
calculated to a known precision. This measurement is made approximately twice
a year or when there are hardware changes in the signal path.

The microwave and air path delays are measured by physically
calibrating the microwave hardware components prior to installing them on the
antenna. The antenna aperture plane, the horn aperture plane, and an antenna
reference location are used to determine the actual air path delay as shown in
Figure 14. The antenna reference location is the perpendicular intersection of
the primary antenna axis with the plane of the secondary axis. Geocentric and
geodetic locations for the antenna reference location can be found in module
301.

2.6.3 Antenna Correction
An antenna correction is required when the antenna reference location
is not at a fixed location with respect to the Earth. Because the NSP ranging
equipment only is being installed at Azimuth-Elevation (Az-El) antennas that
have a fixed reference location, no antenna correction is required. The antenna
correction for the 26-m subnet antennas is described in Appendix A.
                                        
Figure 14. Typical DSS Delay Calibration
(Figure omitted in text-only document)

Figure 15. Measuring the Z-Correction
(Figure omitted in text-only document)

2.7 Error Contributions

The ground system, the media, and the spacecraft contribute errors to
range measurements. The error contributions of the media and spacecraft are
outside the scope of this document and have not been included.

The round-trip one-sigma delay error of the DSN ranging system over a
ranging pass has been estimated for the X-band system as 6.3 nanoseconds (about
0.95 meter one-way). The S-band one-sigma delay error has been estimated as 12.5
nanoseconds (about 1.9 meters one-way).

Table 2 provides a breakdown of long-term error contributions due to
calibration and errors inherent within the equipment of the various subsystems
that constitute the total ground system of the NSP-Era Ranging System.

            Table 2. One-Sigma Range Error for NSP-Era Ranging System
                                        
  Subsystem           X-band                S-band
                Round-     One-way   Round-      One-way
                 trip                trip
                                     Delay
                 Delay    Distance      (ns)     Distance
                 (ns)        (m)                   (m)
     FTS         1.00       0.15        1.00       0.15
   Receiver      2.00       0.30        2.00       0.30
Exciter and      1.33       0.20        5.33       0.80
Transmitter
Microwave and    2.33       0.35        2.33       0.35
Antenna
Uplink Ranging   2.00       0.30        2.00       0.30
Board
Downlink         2.00       0.30        2.00       0.30
Ranging Board
    Cables       1.33       0.20        1.33       0.20
 Calibration     2.66       0.40        2.66       0.40
   Reserve       3.33       0.50        10.0       1.50
Root Sum Square  6.33       0.95       12.47       1.87


Appendix A
The Current DSN Ranging System

The current DSN ranging equipment has the same functional
characteristics as the equipment previously described but does not provide
optimum performance with the newer digital receivers. It is therefore being
replaced at the 70-m, the 34-m HEF, and all 34-m BWG stations except DSS 27.
This appendix describes the architecture and performance of the current
sequential ranging equipment in the 26-m subnet and at the 34-m HSB station, DSS
27. It also identifies the performance differences between the NSP ranging
equipment and the existing ranging equipment when it is used at the 70-m, the 34-
m HEF, and the 34-m BWG stations.

A1.0 System Description Using the Sequential Ranging Assembly
The DSS Tracking Subsystem (DTK) comprises two items of equipment,
the sequential ranging assembly (SRA) and the metric data assembly (MDA). This
equipment performs the range measurement, formats the radiometric data, and
sends it to the NAV at JPL. The NAV processes and provides the data to
projects. The Network Support Subsystem (NSS) provides radiometric predicts to
the DTK. Figure A-1 shows the current DSN ranging system configuration.

The SRA generates a sequence of square-wave frequencies (ranging code
components) that are modulated onto the uplink carrier by the exciter and
transmitted to the spacecraft. The spacecraft on-board transponder receives the
signal , demodulates and filters it, and remodulates it onto the downlink
carrier. The downlink is captured and amplified at the DSS, downconverted by
the RID, and received by either a multi-function receiver (MFR) or Block V
receiver (BVR). The SRA correlates the demodulated downlink signal with a
Doppler-modified replica of the transmitted codes using the same process as was
described earlier.

The SRA has two hardware interfaces with the exciter. The first
provides the reference frequency, F_66, from the exciter to the SRA. The second
supplies the square-wave ranging modulation signal derived from this reference
to the phase modulator in the exciter. The SRA also has two hardware interfaces
with the receiver. The first carries the received ranging codes while the
second provides a representation of the received Doppler. Each SRA has two
receive channels so there are actually two pairs of interfaces between the SRA
and the two receivers at each station. SRA channel 1 is normally used to
process S-band (or receiver 1) data and channel 2 is used to process X-band (or
receiver 2) data.
                 
Figure A-1. Current DSN Ranging System
(FIgure omitted in text-only document)                       
                                        
At the 26-m Subnet stations and the 34-m HSB antenna, the received
ranging codes are provided to the SRA as a 10-MHz analog intermediate frequency
(IF) from the MFR and demodulated within the SRA. At stations employing the BVR
(the 70-m, the 34-m HEF, and the 34-m BWG stations), demodulation of the ranging
codes are done within the receiver and the ranging baseband signal is sent to
the SRA as digital data through an optical-fiber interface.

A2.0 Range Measurement Process Using the SRA
The SRA transmitter coder uses a reference frequency (denoted by
F_66 in this document) to generate a sequence of square waves (or binary
codes). This code sequence is phase-modulated onto the uplink carrier. The
measurement process begins at T_0 which is between 0 and 1 second before this
signal is received by the SRA one RTLT later.
Prior to the receive time, T_0, the SRA receiver coder is referenced to
the same F66 as the tramsnitter coder so it operates at the same frequency and
phase. At T_0, a scaled Doppler reference from the tracking receiver is
introduced to advance or retard the phase of the receiver coder. This has the
effect of adding the frequency shift introduced by Earth-spacecraft relative
Doppler to the receiver coder so the correlation can be accomplished. Having
aligned the receiver coder frequency to the frequecny of the received code, the
correlation to determine the phase of the received code proceeds by the same
process described in paragraph 2.4.

A3.0 Performance Differences

The performance of the SRA and the NSP-era ranging are slightly
different because of improvements incorporated into the new equipment and
interface incompatabilitese between the SRA and digital receivers in 70-m, the
34-m HEF, and the 34-m BWG stations and the SRA. The following paragraphs
summarize these differences.

A3.1 Integration Times
The SRA requires specification of the same three integration times as
discussed in paragraph 2.3.4; however, their calculation and recommendations for
selecting values are somewhat different.

A3.1.1 T_1
T_1, the total time used to integrate the correlation samples for the
clock component, is calculated by the equations provided in paragraph 2.3.4.1
with different constants. The modified expressions are:

      Sine-wave operation:
      T_1   = 1/56 x 1/F_c^2 x 1/(sigma^2(t)) x 1/(P_r/N_0), s   (A-1)

      Square-wave operation:                             
      T_1   = 8/343 x 1/F_c^2 x 1/(sigma^2(t)) x 1/(P_r/N_0), s  (A-2)

where                                                    
F_c = the clock frequency, Hz                
sigma^2(t) = the desired variance of the RTLT measurements, s^2
P_r/N_o =   the ranging signal to noise spectral density, Hz.

The above equations can be rewritten in terms of the uncertainty sigma(r)
in meters, by multiplying the uncertainty sigma(t) in seconds by the speed of light
and dividing by a factor of 2. This provides:
          Sine-wave operation:
          sigma(r) = sqrt(402/(F_c^2(MHz) x T_1 x P_r/N_0), m   (A-3)
          Square-wave operation:
          sigma(r) = sqrt(523/(F_c^2(MHz) x T_1 x P_r/N_0), m   (A-4)
where
F_c = the clock frequency, MHz
T_1 = the clock component integration time, s
P_r/N_o = the ranging signal to noise spectral density, Hz.

Note: The uncertainty s here is only due to thermal noise. Other
errors must be added to this to get the total uncertainty (see paragraph A5.0).

Figure A-2 plots integration time (T_1) as a function of P_r/N_o with sigma(r) as a
parameter for the SRA using sine-wave operation and a 1-MHz clock component.
For a desired sigma(r), the user may find the proper integration time, T_1, for an
estimated P_r/N_o (in dB-Hz). Figure A-3 is a similar graph for square-wave
operation using a 500-kHz clock component. This figure may also be used for lower 
frequency square-wave clocks by recognizing that dividing Fc by 2 will result in 
T_1, being multiplied by 4, etc.

Ranging is possible as long as the receiver remains in lock over the measurement
time. However, there is a practical lower limit for P_r/N_o (usually about -10
dB-Hz) determined by the combination of integration times (cycle time) and the
minimum number of range points needed by the project. See Cycle Time in
Paragraph 2.3.4.4 for further details. A P_r/N_o of -10
dB-Hz is also the recommended limit when the SRA is used with the Block V
Receiver because of inefficiencies in the interface between the two pieces of
equipment.

A3.1.2 T_2
T_2, the integration time for each of the lower frequency components,
is calculated by the equation provided in paragraph 2.3.4.2 (equation 9). The
figures provided there are repeated as figures A-4 through A-6 to emphasize the
recommendation that the SRA should not be operated at a P_r/N_o of less than -10
dB-Hz when using the Block V Receiver.

A3.1.3 T_3
T_2, the integration time for DRVID measurements, is selected by the
same reasoning discussed in paragraph 2.3.4.3 and is usually set at 7/8 x T_1,
rounded to the nearest integer.

A3.2 Other SRA Ranging Parameters
The other SRA ranging parameters are the same as required by NSP-era
ranging. This includes modulation index (paragraph 2.3.5), frequency chopping
(paragraph 2.3.6), tolerance (paragraph 2.3.7.1), servo (paragraph 2.3.7.2),
and pipe (paragraph 2.3.7.3).


A3.3   SRA Calculations

A3.3.  Cycle Time
The cycle time calculated by the SRA uses the same algorithm as the NSP-era
ranging discussed in paragraph 2.3.4.3.

A3.3.2 P_r/N_o
The actual ranging power-to-noise spectral density (P_r/N_0) is
evaluated at the end of the integration of all in-phase and quadrature
correlation values for the clock by the same
proces that was described in paragraph 2.4.2. However, the process bandwidth
of the SRA is 5 Hz as P_r/N_0 is evaluated using pairs of 0.1-second long
correlation samples. Therefore, it is necessary to multiply Pn by the
reciprocal of 2 x 0.1 s, or 5 Hz, in order to put it in the form of P_r/N_0.
                                        
Figure A-2. Integration Time T_1 versus P_r/N_0, Clock Frequency F_c = 1 MHz,
for Sine-Wave ranging using the SRA
(Figure omitted in text-only document)
             
Figure A-3. Integration Time T_1 versus P_r/N_0, Clock Frequency F_c = 500 MHz,
for Sine-Wave ranging using the SRA
(Figure omitted in text-only document)

Figure A-4. Code Component Integration Time T_1 versus P_r/N_0 for various probabilities
of Error and n=5
(Figure omitted in text-only document)

Figure A-5. Code Component Integration Time T_1 versus P_r/N_0 for various probabilities
of Error and n=10
(Figure omitted in text-only document)

Figure A-6. Code Component Integration Time T_1 versus P_r/N_0 for various probabilities
of Error and n=20
(Figure omitted in text-only document)

A4.0 Range Corrections Using the SRA
The following paragraphs discuss the DSS delay and antenna
calibration when using the SRA. The Z-correction (paragraph 2.6.2) is the
same for both types of ranging equipment.

A4.1 DSS Delay
The DSS Delay is measured by the same technique as discussed in
paragraph 2.6.1; however, calibration path is different and is illustrated in
Figure A-7. This figure assumes the uplink and downlink signals are in the
same frequency band. When the uplink and downlink are at different
frequencies, the downlink signal from the Test Translator is coupled into the
receive path ahead of the LNA and as close to the feed as practical.

A4.2 Antenna Calibration
There are two types of structurally different antennas in the DSN.
They are the Azimuth-Elevation (Az-El) mount, and the X-Y mount. The first type
has an azimuth axis that perpendicularly intersects the elevation axis with the
result being that the antenna correction is equal to zero. The DSN 70-m, 34-m
HEF, 34-m BWG, and 34-m HSB antennas are of this type.

The X-Y antennas of the 26-m subnet have a primary axis and a
secondary axis that are offset from each other. This offset causes the
secondary axis (the Y-axis) to move relative to the Earth as the antenna
rotates and adjusts its elevation about the primary axis (the X-axis). The
change of distance is calculated by the following antenna correction
expression:

delta_(rho_A) = -6.706cos(theta), m  (A-5)

where
theta = the angle of the Y-axis.

Figure A-7. Typical Range Calibration Signal Path for DSS Using SRA and MDA Ranging Equipment

A5.0 Error Contributions for Ranging Using the SRA

The round-trip one-sigma-delay error of the DSN ranging system over a
ranging pass has been estimated for the X-band system as 6.3 nanoseconds (about
1.0 m one-way). The S-band system error has been estimated as 14.5 nanoseconds
(about 2.2 m one-way).

Table A1 shows a breakdown of long-term error contributions due to
calibration and errors inherent within the equipment of the various subsystems
that constitute the total ground system using the SRA and MDA ranging equipment.

Table A-1. One-Sigma Range Error for SRA/MDA-Equipped Ranging System
                                        
  Subsystem           X-band                S-band
                Round-    One-way    Round-      One-way
                 trip                trip
                                     Delay
                 Delay    Distance      (ns)     Distance
                 (ns)       (m)                    (m)
Frequency and    1.00       0.15        1.00       0.15
Timing
   Receiver      2.67       0.40        2.67       0.40
Exciter and      1.33       0.20        5.33       0.80
Transmitter
Microwave and    2.33       0.35        2.33       0.35
Antenna
   Tracking      0.67       0.10        0.67       0.10
    Cables       1.33       0.20        1.33       0.20
 Calibration     3.33       0.50        3.33       0.50
   Reserve       3.33       0.50       12.47       1.87
   Root Sum      6.30       0.95       14.52       2.18
    Square