+---------------+---------------------------+-------------------------+
| ![](media/im  | GODDARD TECHNICAL         | GSFC-STD-9001           |
| age1.jpeg){wi | STANDARD                  |                         |
| dth="1.165972 |                           |                         |
| 2222222222in" |                           |                         |
| heig          |                           |                         |
| ht="0.8840277 |                           |                         |
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+---------------+---------------------------+-------------------------+
| Goddard Space |                           | Approved: 11-20-2007    |
| Flight Center |                           |                         |
+---------------+---------------------------+-------------------------+
| Greenbelt, MD |                           | Expiration Date:        |
| 20771         |                           | 11-20-2012              |
+---------------+---------------------------+-------------------------+
|               |                           |                         |
+---------------+---------------------------+-------------------------+
| **SPREAD      |                           |                         |
| SPECTRUM      |                           |                         |
| MODULATION    |                           |                         |
| FORMATS FOR   |                           |                         |
| NASA LINKS**  |                           |                         |
+---------------+---------------------------+-------------------------+
| November 20,  |                           |                         |
| 2007          |                           |                         |
|               |                           |                         |
| DO NOT USE    |                           |                         |
| PRIOR TO      |                           |                         |
| APPROVAL.     |                           |                         |
+---------------+---------------------------+-------------------------+
|               |                           |                         |
+---------------+---------------------------+-------------------------+

DOCUMENT HISTORY LOG

  ---------- -------------- ---------------- -----------------------------
  Status     Document       Approval Date    Description
             Revision                        

  Baseline                  05-22-2007       Initial Release
  ---------- -------------- ---------------- -----------------------------

FOREWORD

This standard is published by GSFC, National Aeronautics and Space
Administration (NASA) to provide uniform engineering and technical
requirements for processes, procedures, practices, and methods that have
been endorsed as standard for NASA programs and projects, including
requirements for selection, application, and design criteria of an item.

This standard establishes uniform requirements for applying pseudo-noise
(PN) spreading in NASA links and describes the existing links that use
PN spreading.

*Original signed by:* *Original signed by:*

George Alcorn Steven Scott

Goddard Technical Standard Coordinator Chief Engineer

*Original signed by:* *Original signed by:*

Orlando Figueroa Marcus Watkins

Director of Applied Engineering Director of Office of Systems Safety

and Technology and Mission Assurance

  ---------------------- ----------------- ------------------------------------------------- ---------------
  [\                                       TABLE OF CONTENTS                                 [\
  SECTION]{.underline}                                                                       PAGE\
                                                                                             \
                                                                                             ]{.underline}

  DOCUMENT HISTORY LOG                                                                       2

  FOREWORD                                                                                   3

  TABLE OF CONTENTS                                                                          4

  LIST OF FIGURES                                                                            5

  LIST OF TABLES                                                                             6

  1\.                    SCOPE                                                               7

  1.1                    Purpose                                                             7

  1.2                    Applicability                                                       7

                                                                                             

  2\.                    APPLICABLE                                                          7
                         DOCUMENTS                                                           

  2.1                    General                                                             7

  2.2                    Government                                                          8
                         Documents                                                           

  2.3                    Non-Government                                                      8
                         Documents                                                           

  2.4                    Order of                                                            8
                         Precedence                                                          

                                                                                             

  3\.                    ACRONYMS AND                                                        9
                         DEFINITIONS                                                         

  3.1                    Acronyms and                                                        9
                         Abbreviations                                                       

  3.2                    Definitions                                                         9

                                                                                             

  4\.                    REQUIREMENTS                                                        13

  4.1                    Introduction to                                                     13
                         Spread Spectrum                                                     
                         Modulation                                                          
                         Concepts                                                            

  4.1.1                  Basic Definition                                                    13
                         of Spread                                                           
                         Spectrum                                                            

  4.1.2                  Different Types                                                     14
                         of SS Modulations                                                   

  4.1.3                  Advantages and                                                      14
                         Applications of                                                     
                         DSSS                                                                

  4.2                    Direct Sequence                                                     17
                         Spread Spectrum                                                     
                         Modulation                                                          

  4.2.1                  DSSS System                                                         18
                         Architecture                                                        

  4.2.2                  PN Code Basics                                                      20

  4.2.3                  Generation of PN                                                    21
                         Codes                                                               

  4.3                    Use of Spread                                                       25
                         Spectrum in NASA                                                    
                         Links                                                               

  4.3.1                  Capabilities and                                                    25
                         Characteristics                                                     
                         of Existing NASA                                                    
                         Systems                                                             

  4.4                    Requirements of                                                     29
                         PN Spread                                                           
                         Modulations for                                                     
                         NASA Systems                                                        

  4.4.1                  System Level                                                        29
                         Requirements for                                                    
                         PN Spread Links                                                     

  4.4.2                  Network Element                                                     36
                         Requirements                                                        

  4.4.3                  User Element                                                        36
                         Equipment                                                           
                         Requirements for                                                    
                         PN Spreading                                                        

                                                                                             

  Appendix A NASA                                                                            
  Specific PN Code                                                                           
  Requirements 43 8                                                                          

  Appendix B Algorithm                                                                       
  for Selecting                                                                              
  Primitive Polynomials                                                                      
  56                                                                                         
  ---------------------- ----------------- ------------------------------------------------- ---------------

  ---------------------- ------------------------------------------------------ --------------------
  LIST OF FIGURES                                                               

  [FIGURE]{.underline}                                                          [PAGE]{.underline}

  1                      Spread Spectrum Digital Communication Model            13

  2                      DSSS Spectral Occupancy Before and After Spreading     15

  3                      Spectral Usage of Multiple Users                       16

  4                      Interference Susceptibility Reduction with DSSS        16

  5a                     DSSS System Network Element Architecture               18

  5b                     DSSS System User Element Architecture                  19

  6                      Direct-Sequence Spreading                              20

  7                      Fibonacci Implementation                               22

  8                      Maximal Length Code Generator                          24

  9                      Gold Code Generator                                    25

  10                     Time Transfer Interface                                39

  11                     Time Transfer Interface Timing Diagram                 40

  12                     Command Link Gold Code Generator                       44

  13                     Command Link Gold Code Generator Initial Conditions    45

  14                     Return Mode 2 Link Gold Code Generator                 46

  15                     Octal Conversion Example                               48

  16                     Code Generator Configuration and Initial Conditions    48

  17                     Range Channel Code Generator                           49

  18                     Range Channel Code Feedback Tap Example                50

  19                     Return Modes 1 and 3 Link Code Generator               51

  20                     Return Modes 1 and 3 Link Feedback Tap Example         52

  21                     Shuttle S-band Command Code Generator                  54

  22                     Shuttle S-band Feedback Tap Example                    55
  ---------------------- ------------------------------------------------------ --------------------

  --------------------- ------------------------------------------------------ --------------------
  LIST OF TABLES                                                               

  [TABLE]{.underline}                                                          [PAGE]{.underline}

  1                     Forward I Channel PSK Service Signal Parameters        30

  2                     Salient Characteristics of PN Codes for Forward        32
                        Services                                               

  3                     Forward Q Channel PSK Service Signal Parameters        32

  4                     Shuttle Forward I (Command) Channel Requirements       33

  5                     Return Service Signal Parameters                       34

  6                     Bi-level Telemetry Involving PN Codes                  41

  7                     NASA Unique Initial Conditions for PN Code Generation  44
                        for Command Link                                       
  --------------------- ------------------------------------------------------ --------------------

**SPREAD SPECTRUM MODULATION FORMATS FOR NASA LINKS**

1\. SCOPE

This standard describes the use of spread spectrum modulation in RF
satellite communications systems and presents a detailed specification
of the particular PN spread formats implemented in the low rate data
transmission and PN range tracking services currently used by NASA
systems. The functions and required capabilities of each element of PN
spread links are also provided, including the typical signal flow and
equipment characteristics and constraints involved.

Relevant information on the specification of PN sequences for use in
NASA systems is also provided.

1.1 Purpose

This standard is intended to provide a comprehensive description of the
PN spread spectrum modulation formats used in NASA links and to give
associated technical requirements from the system level to the component
level. The document is organized to support a range of uses, from
providing basic system description, capabilities listing, and
theoretical background for readers seeking a general understanding of
existing systems to documenting the detailed technical requirements
necessary for implementing hardware that is compatible with the current
NASA systems.

1.2 Applicability

This standard is applicable to programs/projects planning to use and/or
implement NASA compatible spread spectrum systems.

This standard may be cited in contract, program, and other Agency
documents as a technical requirements document for NASA specific spread
spectrum links. Tailoring of this standard for application to a specific
program or project shall be approved by the Technical Authority for that
program or project.

2\. APPLICABLE DOCUMENTS

2.1 General

The documents listed in this section describe the performance and
compatibility requirements for NASA's Space Network (SN) and compatible
user equipment systems. The characteristics and requirements in Section
4 of this standard are constituted largely of a subset of these
requirements. The applicable documents are accessible via the NASA
Technical Standards System at
[**http://standards.nasa.gov**](http://standards.nasa.gov/), directly
from the Standards Developing Organizations, or from other document
distributors. The latest issuances of cited documents shall be used
unless otherwise approved by the assigned Technical Authority.

2.2 Government Documents

1.  450-SNUG, Space Network Users' Guide (SNUG), Revision 9, April 2007

2.  451-PN CODE-SNIP, Space Network Interoperable PN Code (SNIP)
    Libraries, Revision 1, November 1998

3.  531-RSD-IVGXPDR Performance and Design Requirements and
    Specification for the Fourth Generation TDRSS User Transponder,
    Review Copy, February 1996

4.  530-RSD-WSC Requirements Specification for the White Sands Complex
    (WSC), Revision 1, June 1997

2.3 Non-Government Documents

1.  Glas, Jack P.F. (December 1996). *[**Non-Cellular Wireless
    Communication Systems**](http://cas.et.tudelft.nl/~glas/thesis),*
    PhD- thesis. Delft University of Technology. ISBN: 90-5326-024-2
    Non-Cellular Wireless Communication Systems

2.  Choi, Byoung Jo. (**December 1997).** *Spreading Sequences.*

2.4 Order of Precedence

When this standard is applied as a requirement or imposed by contract on
a program or project, the technical requirements of this standard take
precedence, in the case of conflict, over the technical requirements
cited in applicable documents or referenced guidance documents.

3\. ACRONYMS AND DEFINITIONS

3.1 Acronyms and Abbreviations

DSSS Direct Sequence Spread Spectrum

ESA European Space Agency

JAXA Japan Aerospace Exploration Agency

MA Multiple Access

MOC Mission Operations Center

PN Pseudo-random Noise

PFD Power Flux Density

PSD Power Spectral Density

RF Radio Frequency

SQPN Staggered Quadrature Pseudo-random Noise

SN Space Network

SS Spread Spectrum

TCXO Temperature Compensated Crystal Oscillator

VCO Voltage Controlled Oscillator

3.2 Definitions

> [Acquisition:]{.underline} In RF communications systems, the process
> by which the receiver tracking loops lock to estimates of the received
> signal phase and timing as a necessary precursor to data detection.
>
> [Acquisition Time:]{.underline} The time interval required for a
> receiver in an RF communications system to complete the acquisition
> process.
>
> [Bandwidth (BW):]{.underline} The difference between the limiting
> frequencies of a continuous frequency band, or the range of contiguous
> frequencies within which the performance of a device, in respect to
> some characteristic, falls within specified limits.
>
> [Baseband:]{.underline} The original band of frequencies which contain
> the information in a data signal prior to modulation.
>
> [Baseband Signaling:]{.underline} Transmission of a digital or analog
> signal at its original frequencies; i.e. a signal in its original
> form, not changed by modulation.
>
> [Baud:]{.underline} A unit of modulation rate. One baud corresponds to
> a rate of one unit interval per second, where the modulation rate is
> expressed as the reciprocal of the duration in seconds of the shortest
> unit interval.
>
> [Baud Rate:]{.underline} Rate at which a characteristic (i.e., phase,
> frequency, amplitude) of a carrier wave is changed by the modulating
> signal.
>
> [Bit (Binary Digit)]{.underline}: The basic unit of information in a
> binary communications system (holding a value of 0 or 1).
>
> [Bit Error Ratio (BER):]{.underline} In a communications system, the
> ratio of data bits which are erroneously detected by the receiver to
> the total number of data bits received.
>
> [Bit Synchronization:]{.underline} Synchronization in which the
> decision instant is brought into alignment with the received bit, i.e.
> the basic signaling element.
>
> [Carrier Frequency:]{.underline} The frequency of the signal onto
> which the baseband signal is modulated.
>
> [Channel]{.underline}: Any medium that a communication link uses to
> transport the electromagnetic waves which includes data.
>
> [Chip:]{.underline} The most elemental component of the time domain
> representation of a PN sequence; that is, the longest duration portion
> of the PN sequence during which the signal parameters are
> approximately constant.
>
> [Chip Rate:]{.underline} In direct-sequence-modulation spread-spectrum
> systems, the rate at which the information signal bits are transmitted
> as a pseudorandom sequence of chips.
>
> Note: The chip rate is usually at least ten times the information bit
> rate.
>
> [Coherent:]{.underline} In an RF communications system, Signal A is
> considered to be coherent with Signal B if their carrier frequencies
> are related by a known, fixed ratio.

[Correlator:]{.underline} The SS receiver component that demodulates a
Spread Spectrum signal.

[Customer:]{.underline} See User.

> [De-spreading:]{.underline} The process used by a correlator to
> recover narrowband information from a spread spectrum signal.
>
> [Detection:]{.underline} In a communications system, the process by
> which the receiving equipment produces an estimate of the transmitted
> sequence based on the noisy received signal.
>
> [Direct Sequence Spread Spectrum (DSSS):]{.underline} See Section 4.2.
>
> [Forward Link:]{.underline} An RF communication link starting from the
> NASA network to the user of that network. A forward link can have
> multiple hopping points along the path.
>
> [Modulation:]{.underline} The process, or result of the process, of
> varying a characteristic of a carrier, in accordance with an
> information-bearing signal.
>
> [Network:]{.underline} The element of a two-way RF link responsible
> for initiating and managing the contact and performing range
> calculation functions (if applicable). A network may include one or
> more ground stations.
>
> [Pseudo-Random Noise Sequence:]{.underline} A Pseudo-random Noise (PN)
> sequence is a sequence of binary numbers, +1 and -1 (or 1 and 0),
> which appears to be random; but is in fact perfectly deterministic.
>
> [PN Chip Jitter:]{.underline} PN code chip jitter is defined as the
> unwanted phase variations of the PN code chip clock measured in
> degrees RMS.

[PN Chip Rate:]{.underline} See definition for Chip Rate above.

> [PN Chip Skew:]{.underline} PN chip skew is the deviation of the chip
> transitions between the I (or command channel for forward) and the Q
> (or range channel for return) from the ideal time delay.
>
> [PN Code:]{.underline} See Section 4.2.
>
> [PN Epoch:]{.underline} The PN Epoch is a repeating reference pattern
> within the code used for the acquisition process and ranging.
>
> [PN Sequence:]{.underline} See Section 4.2.
>
> [PN Spreading:]{.underline} PN spreading is a process used to
> distribute or spread the power of a signal over a bandwidth which is
> much greater than the bandwidth of the signal itself. PN de-spreading
> is the process of taking a signal in its wide PN spread bandwidth and
> reconstituting it in its own much narrower bandwidth.
>
> [Power Flux Density (PFD):]{.underline} The rate of flow of
> electromagnetic energy per unit area is used to measure the amount of
> radiation at a given point from a transmitting antenna. This quantity
> is expressed in units of watts per square meter (W/m^2^) or milliwatts
> per square cm (mW/cm^2^).
>
> [Power Spectral Density (PSD):]{.underline} PSD is the average power
> in the signal per unit bandwidth.
>
> [Quadrature Phase Shift Keying Modulation:]{.underline} Quadrature
> Phase Shift Keying (QPSK) is a form of Phase Shift Keying in which two
> bits are modulated at once, selecting one of four possible carrier
> phase shifts (0, 90, 180, or 270 degrees). QPSK allows the signal to
> carry twice as much information as ordinary PSK using the same
> bandwidth. In QPSK modulation, a cosine carrier is varied in phase
> while keeping a constant amplitude and frequency.
>
> [Return Link:]{.underline} An RF communication link from the user of
> the NASA network to the NASA network. A return link may have multiple
> hopping points along the path.
>
> [Shift Register:]{.underline} A storage device consisting of a data
> input port, a clock input port, an output port, and a single bit
> memory storage; the shift register retains the value currently stored
> in memory at its output port until such time as an input clock pulse
> is received. At this time, the register sets the value in memory to
> the value on its input port.
>
> [Spread Spectrum:]{.underline} A wideband modulation which imparts
> noise-like characteristics to an RF signal.
>
> [Staggered Quadrature PN (SQPN) Modulation:]{.underline} A modulation
> format wherein the PN spread data sequence is modulated onto an RF
> carrier using a variation of QPSK modulation in which one channel is
> delayed by one half of a modulation symbol period (in this case, one
> half of a PN chip period) with respect to the other channel.
>
> [User:]{.underline} The element in an RF communications link which
> exchanges data with the network element. The user is responsible for
> any required transponder/transceiver operations (i.e. generation of
> coherent return link carrier and synchronized PN sequence).

4\. REQUIREMENTS

This section provides the technical information and requirements
associated with implementing PN Spread modulation modes in NASA links.
Section 4.1 provides a basic introduction to Spread Spectrum (SS)
modulation concepts, emphasizing the Direct Sequence Spread Spectrum
(DSSS) approach addressed in this standard. Section 4.2 discusses
implementation of DSSS modulation at the system level, including also a
discussion of PN code selection. Section 4.3 provides relevant
information concerning the PN Spread modulation modes used in NASA's
Space Network. These Sections form the basis for the PN Spread
modulation system and sub-system level requirements given in Section
4.4.

1.  Introduction to Spread Spectrum Modulation Concepts

This section presents an introduction to Spread Spectrum concepts.
Section 4.1.1 presents a basic definition of Spread Spectrum modulation.
Section 4.1.2 describes several means of implementing SS modulation.
Section 4.1.3 expands upon these concepts by detailing some of the major
advantages of DSSS.

1.  Basic Definition of Spread Spectrum

Spread Spectrum (SS) is a family of communications techniques in which
the RF bandwidth used to transmit a given data signal is much wider
(typically several times wider) than what would normally be used with
non-SS modulation techniques.

There are a number of ways to implement spread spectrum modulation. In
each of these techniques, a pseudo-random signal is used to control /
modulate some characteristic of the data signal transmission. This
process is called the spreading operation. Although the spreading signal
is deterministic, periodic, and known by both the transmitter and
receiver; it is independent of the data signal and is chosen to appear
as random as possible.

The effect of the spreading operation is to distribute the information
in the data signal over a significantly larger bandwidth. At the
receiver, a similar algorithm is used, employing the identical periodic
pseudo-random signal (which must be synchronized to that of the
transmitter), to isolate or extract the desired lower bandwidth data
signal from the received higher bandwidth spread signal. This is called
the de-spreading operation. These processes are illustrated generically
in Figure 1.

![](media/image2.wmf){width="5.9944444444444445in"
height="0.9458333333333333in"}

Figure 1---Spread Spectrum Digital Communication Model

A key parameter in all spread spectrum systems is the spreading factor
given in Equation 1 (also equivalent to the processing gain in DSSS)
which can be expressed as the ratio of transmission bandwidth (the
bandwidth of the spread signal) and the information bandwidth (the
bandwidth of the baseband data signal):

$\text{SF} = G_{p} = \frac{\text{BWt}}{\text{BWi}}$ (1)

This factor impacts each of the SS advantages discussed below. For
spread spectrum systems it is, in general, advantageous to have the
largest Spreading Factor / Processing Gain that is possible, subject to
bandwidth constraints.

2.  Different Types of SS Modulations

Some commonly used spread spectrum techniques include DSSS, frequency
hopping spread spectrum and time hopping spread spectrum.

In frequency hopping SS systems, the data signal is modulated directly
onto an RF carrier (using a traditional non-SS technique such as QPSK)
and the frequency of this carrier jumps rapidly between a number of
defined frequencies as a function of the pseudo-random spreading signal.
At the receiver, the carrier tracking loop reference also shifts between
the defined frequencies following the same unique pattern.

In time hopping spread-spectrum the information-bearing signal is not
transmitted continuously. Instead the signal is transmitted in short
bursts where the times of the bursts are decided by the spreading code.
To achieve an equivalent information transfer rate as would be realized
with a non-spread system (where the data transfer is continuous), the
instantaneous data rate (when the system is transmitting) is
significantly increased. This is the mechanism by which the bandwidth
expansion occurs.

In Direct Sequence Spread Spectrum (DSSS), the spreading signal is a
pseudo-random noise (PN) sequence. The bits in the data signal are
modulo-two added with the much higher rate PN code. This effectively
increases the bandwidth of the transmitted signal to that of the
modulated PN sequence. At the receiver, the received sequence is
multiplied by the same PN sequence to remove the spreading.

The DSSS implementation employed by NASA is described in this standard.

3.  Advantages and Applications of DSSS

Systems incorporating the DSSS modulation format described in this
standard offer a number of advantages over non-spread techniques. These
include reduced Power Flux Density (PFD), capability of supporting
multiple simultaneous users via Code Division Multiple Access (CDMA),
reduced susceptibility to interference (including intentional jamming)
and multi-path fading, and decreased probability of signal interception.

[Reduced PFD:]{.underline} Figure 2 demonstrates the Power Spectral
Densities (PSDs) of a data signal before and after spreading. The effect
of the spreading is to increase the signal bandwidth (by the spreading
factor given in Equation 1). However, since the energy *per bit*
required for data transmission is fixed, the magnitude of the PSD (and
thus the associated PFD) of the spread signal is reduced by the same
ratio. At the receiver side, de-spreading has the opposite effect --
transforming the wideband, low-power spread signal into the original
narrow-band high power data signal PSD. The terminology "processing
gain" defined above refers to the relative increase in the PSD level
realized by de-spreading.

![](media/image3.wmf){width="5.186111111111111in"
height="3.5493055555555557in"}

Figure 2--- DSSS Spectral Occupancy Before and After Spreading

[Multiple Simultaneous Users]{.underline}: One of the key applications
for NASA PN Spread systems is the SN multiple access service. In CDMA
systems, multiple users utilize the same frequency band simultaneously
to transmit PN spread signals. As depicted in Figure 3, the composite RF
signal in this band then is the sum of the multiple RF DSSS signals plus
any noise or external interference. Each of the N users is assigned a
unique PN spreading sequence. The properties of these sequences are such
that when a data signal is spread using one sequence, de-spreading with
another sequence produces little, if any processing gain. This allows
receivers operating on the composite signal to pull out the data signal
corresponding to their assigned PN sequence. After de-spreading, the
composite PSD consists of the desired data signal narrow-band high power
component plus the wideband, low power contributions from the other
users' signals and noise. Since the wideband low power PSD contributions
from other users are mostly flat over the narrow desired signal
frequency band, they are often described as "noise-like" interference,
and the effect of adding more users is characterized as "increasing the
noise floor".

![](media/image4.wmf){width="3.5708333333333333in"
height="1.2395833333333333in"}

Figure 3 --- Spectral Usage of Multiple Users

[Reduction in Interference Susceptibility:]{.underline} Another major
advantage of DSSS techniques is a reduction in the susceptibility to RF
interference, whether that interference is accidental or due to
deliberate jamming efforts. Figure 4 demonstrates the mechanism through
which this occurs. In Panel 1, a high power narrow band interferer is
shown with its PSD superimposed upon that of the desired PN spread
signal. The noise floor is shown to provide a context to compare the
relative power levels. In Panel 2, the effects of the de-spreading
operation at the receiver are shown. It is important to note that in the
receiver, the entire composite signal (noise, intended signal and
interferer) are all modulo-two added to the high rate PN sequence. This
has two effects. First, it re-constitutes the original high power
narrowband desired signal. Second, and more importantly, it effectively
spreads the power in the interfering signal over the wider PN sequence
bandwidth. In Panel 3, after the receiver filtering, it can be seen that
the desired signal to interference signal power ratio is significantly
improved (by a factor approximately equal to the processing gain).

![](media/image5.wmf){width="5.591666666666667in"
height="2.7715277777777776in"}

Figure 4 --- Interference Susceptibility Reduction with DSSS

A related benefit of DSSS modulation techniques is the reduction in
susceptibility to multi-path effects. In this case, the mechanism is
more direct. Multi-path is a narrowband phenomenon. By spreading the
energy in a data signal uniformly over a wide bandwidth, the impact of
multipath degradation is effectively reduced.

[Decreased Probability of Signal Interception:]{.underline} The
noise-like properties of the spreading sequences used in a DSSS system,
and the relatively low PSD of the RF signal make it very difficult for
receivers to detect the presence of a PN spread signal without knowing
the PN code in use. This same characteristic also decreases the
probability that a PN spread signal will interfere with other systems in
the same frequency band.

[Capability of Supporting PN Ranging Operations:]{.underline} In a
system where RF links between two elements employ PN spread modulation
formats, it is possible to calculate range estimates using the PN
sequences. The mechanism by which this is accomplished is described in
the series of steps below:

1.  The element functioning as the network generates a PN sequence, uses
    this sequence to spread forward link data and transmits the signal
    to the second element.

2.  The second element (generally a transponder or tranceiver) generates
    the same PN sequence and uses it to de-spread the forward link data.
    Note that in order to do this, it must align (in time) its generated
    sequence with that of the received signal.

3.  It then generates a second PN sequence (to spread the return link
    data), aligns the epoch of this sequence with that of the received
    signal, spreads the return link data and transmits the resulting
    spread signal to the first element (network).

4.  The first element receives the return link signal, generates a
    matching PN code, aligns it to the epoch of the received signal, and
    de-spreads the return link data.

5.  The offset between the epochs of the transmitted forward link PN
    sequence and the received return link sequence is a function of the
    total round trip delay time. By removing the processing time delays
    and dividing by the speed of light, estimate of the (2 way) range is
    obtained.

    1.  Direct Sequence Spread Spectrum Modulation

This section describes issues and approaches relative to the
implementation of DSSS techniques in RF communications systems. Section
4.2.1 provides a basic overview of the architecture of an RF
communications system employing DSSS modulations, and addresses some of
the relevant terminology. Section 4.2.2 discusses significant
characteristics of the PN sequences used, including correlation
properties. Section 4.2.3 discusses the particular PN code families used
for NASA PN Spread systems and their significant properties and
applicability to various types of links.

The descriptive material presented in these sections provides a more
thorough understanding of PN spread modulation systems and also is
useful in defining the requirements provided in Section 4.4.

1.  DSSS System Architecture

Figures 5a and 5b contain block diagrams of the network and user
elements in a DSSS RF communications system. The network element
transmits forward service data to the user element and the user element
transmits return service data back to the network. In these Figures, a
QPSK type modulation format is used to transmit the PN spread signals.
This modulation format is typically referred to as Quadrature PN (QPN)
modulation, or Staggered Quadrature PN (SQPN) modulation if the QPSK
symbols are staggered. However, a BPSK modulation format could also be
used to transmit the PN spread data.

![](media/image6.wmf){width="4.70625in" height="5.3694444444444445in"}

**Figure 5a -- DSSS System Network Element Architecture**

In both the network and the user transmitters, data bits (or coded data
symbols) are split into I and Q channels which are spread separately by
modulo-2 adding the data to PN sequences. The spreading operation is
depicted conceptually in Figure 6. In these Figures, distinct and
potentially different PN sequences (with a common clock and a
synchronized epoch) are used on the I and Q channels for both the
forward and return signals. Again, this approach is not a requirement
for DSSS (for example, one could use the same spreading sequences on
both channels), but it does represent how some NASA PN spread links are
implemented.

Spread data sequences are input to BPSK modulators on each channel, and
the outputs of these are combined to produce the QPN/SQPN signal. At the
receiver side, carrier acquisition, PN acquisition, de-spreading, and
symbol timing recovery are depicted as separate operations although they
are often performed in tandem.

![](media/image7.wmf){width="5.026388888888889in"
height="5.942361111111111in"}

**Figure 5b -- DSSS System User Element Architecture**

![](media/image8.png){width="3.5208333333333335in"
height="1.6666666666666667in"}

Figure 6 --- Direct-Sequence Spreading

PN acquisition is accomplished using a correlator to compute the timing
offset between the reference PN sequence generated internally and the
received sequence. Once this offset, or epoch, is computed, it is used
to de-spread the data signals on the I and Q channels.

The user element in Figure 5b is configured to synchronize the epoch of
the return signal spreading sequences with the detected forward signal
epoch. This facilitates the ranging calculation depicted in Figure 5a.

2.  PN Code Basics

This section presents an overview of pseudo-random noise codes. In
Spread Spectrum systems, the spreading signal is formed by continually
repeating a finite length PN code. To be usable for direct-sequence
spreading, this PN code (composed of N~DS~ binary units called chips)
should exhibit the following characteristics:

-   Codes must have a sharp (1-chip wide) autocorrelation peak to enable
    code-synchronization. (See discussion of autocorrelation below).

-   The codes must have a low cross-correlation value. The lower this
    cross-correlation, the more users that can be allowed in the system.
    This holds for both full-code correlation and partial-code
    correlation. (See discussion of cross-correlation below).

-   The codes should be "balanced", meaning that the difference between
    the number of ones and zeros in the code may be no greater than 1.
    This requirement is necessary for good spectral density properties
    (spreading the energy equally over the whole frequency-band).

[Autocorrelation]{.underline}

The autocorrelation of a signal is a measure of how easy it is to
differentiate between the signal and every time-shifted variant of
itself (over successive time intervals). Autocorrelation for a finite,
discrete signal is defined in Equation 2 where T is a time delay and L
is the sequence length.

$r_{\text{xx}}(T) = \sum_{n = 0}^{L}{x(n)x(n - T)}$ Un-normalized (2)

A signal with an autocorrelation of zero is said to be orthogonal to a
time-shifted version of itself. PN sequences used for DSSS systems
should have a sharp autocorrelation property (meaning that the value of
the autocorrelation, which should be maximal at T=0, should diminish
sharply as the magnitude of T increases. This property simplifies the PN
acquisition process.

[Cross Correlation]{.underline}

Cross correlation is similar to an autocorrelation except that it is
computed between two different signals, for example -- between two
particular PN codes that are members of a PN code family. As with the
autocorrelation, it is computed as the sum of the cross products between
the two signals at different lags. Cross correlation for finite length
discrete signals is defined in Equation 3.

$r_{\text{xy}}(T) = \sum_{n = 0}^{L}{x(n)y(n - T)}$ Un-normalized (3)

Cross correlation is generally used when measuring information between
two different time series.

If the cross correlation is:

-   1 The second sequence matches the first sequence

-   0 There is no relation at all between the sequences

-   -1 The second sequence is an inverted form of the first sequence.

The signals are said to be orthogonal when all pair-wise cross
correlations of two signals are 0.

1.  Generation of PN Codes

PN codes are typically generated using Linear Feedback Shift Register
(LFSR) circuits. These circuits can be described by a generator
polynomial, which uniquely describes the circuit. For a given generator
polynomial, there are two ways of implementing LFSR. One is called the
Galois Feedback Generator. This circuit uses only the output bit to add
several stages of the shift register. It is most desirable for high
speed hardware implementations, as well as when the generator is
implemented in software.

The other implementation structure is known as the Fibonacci feedback
generator. This approach is used in maximal length sequences and Gold
code generators. Figure 7 shows an example of a PN code generator based
on the Fibonacci feedback approach, and gives the associated polynomial.

![](media/image9.wmf){width="6.28125in" height="2.0208333333333335in"}

Figure 7 --- Fibonacci Implementation

[Relation of Polynomial to Shift Register Tap Locations]{.underline}

The combination of taps and their location is specified by the generator
polynomial. An example polynomial is given as:

P(x) = X^17^ + X^4^ + 1

Various conventions are used to map the polynomial terms to register
stages in the shift register implementation. The convention used for
NASA applications is explained below.

In the polynomial P(x) = X^17^+ X^4^ + 1, the trailing \"1\" represents
X^0^, which is the output of the last stage of the shift register. X^4^
is the output of register stage 4 and X^17^ the output of the XOR.

Some key points to note about LFSRs and the polynomial used to describe
them are:

-   The last tap of the shift register is the leading \"1\" and always
    used in the shift register feedback path.

-   The length of the shift register can be deduced from the exponent of
    the highest order term in the polynomial.

-   The highest order term of the polynomial is the signal connecting
    the final \"XOR\" output to the shift register input. It does not
    feed back into the parity calculation along with the other taps
    identified in the polynomial.

    1.  PN Code Families

Among the various families of PN codes used for DSSS applications, there
are some which exhibit perfect (orthogonal) cross-correlations between
component codes and others which exhibit very low cross-correlations. An
example of a code family with orthogonal codes is the set known as Walsh
codes. Examples of PN codes with low-cross correlation are Maximal
Length codes and Gold codes. These are explained in detail below. Other
codes in this category include M-sequences and Kasami-codes.

Code-selection has a large impact on the performance of the system. Code
selection and cross-correlation properties are key performance factors.
Orthogonal codes offer the advantage of minimizing mutual interference
in multiple access systems. They are best used in systems where the PN
sequence is synchronous with the data sequence. However, in systems
where the data and PN sequences are asynchronous (as in NASA PN spread
links), PN codes with low (bit non-zero) cross correlation properties
are sometimes preferable.

NASA systems use shift-register sequences. Shift register codes are not
orthogonal but they have a narrow autocorrelation peak. When the length
of such a shift-register used to generate a PN code is given by N, the
period N~DS~ of the shift-register code will be:

N~DS~ = 2^N^ - 1

The code families used in NASA Spread Spectrum systems include Gold
codes and Maximal Length codes. All of the codes in a particular family
are generated from a single circuit or a related set of circuits.
Circuits to generate PN codes belonging to the class of Gold codes
differ only in the initial conditions of the shift registers. Circuits
to generate Maximal Length Codes differ only in the feedback taps of the
circuit.

There are a finite number of codes in each of these families. These are
further allocated between the different space agencies (e.g., NASA, ESA
and JAXA) in order to allow for interoperability between agencies
without mutual interference. There is also a library of unassigned PN
codes which NASA can use in case the need emerges. Within NASA, the
codes are currently used in the Space Network for a number of services
which are detailed in Section 4.3. These include:

-   Gold Codes: Forward Command Channel (I Channel) and Return DG1 Mode
    2

-   Maximal Length Codes: Forward Range Channel (Q Channel), Return DG1
    Modes 1 and 3, and Forward Shuttle S-band Command Links.

[Maximum Length Codes]{.underline}

A maximal length sequence for a shift register of length N is referred
to as an M-sequence. Such sequences can be created by applying a single
shift-register with a number of specially selected feedback-taps. An
18-stage shift register is shown in Figure 8 with N selectable taps.

![](media/image10.wmf){width="5.625in" height="1.7895833333333333in"}

Figure 8 --- Maximal Length Code Generator

The number of possible codes is dependent on the number of possible sets
of feedback-taps that produce an M-sequence. These sequences have a
number of special properties. Some of those properties which will be
used in the code selection process are:  

-   M-sequences are balanced: the number of ones exceeds the number of
    zeros by only 1.

-   The spectrum of an M-sequence has a *sync^2^* envelope.

-   The   shift-and-add property can be formulated as follows:

> T^k^ u = T^i^ u T^j^ u
>
> where u is an M-sequence, by combining two shifts of this sequence
> (relative shifts i and j) we obtain again the same M-sequence, yet
> with another relative shift.

-   The auto-correlation function is two-valued:

> $$R_{u}(\tau) = \begin{array}{r}
> \left\{ N\tau = \text{kN} \middle| \right.\ 
> \end{array}$$
>
> where k is an integer value, and τ is the relative shift.

There is no general formula for the cross-correlation of two
M-sequences, only some rules can be formulated. A so called "preferred
pair\'" is a combination of M-sequences for which the cross-correlation
only shows 3 different values: -1, -2^\[(N+2)/2\]^ and 2^\[(N+2)/2\]^.
Preferred pairs for shift-registers with a length equal to 4k, where k
is an integer, do not exist.

See Appendix B for Maximum Length sequence algorithm for selecting the
primitive polynomial for NASA links.

[Gold Codes Basics]{.underline}

Gold sequences form a large class of sequences that have good periodic
cross-correlation properties. Gold codes are not orthogonal, but have
low cross correlation at arbitrary delay. Hence, Gold codes perform well
for asynchronous systems. Gold Codes contain fixed feedback tap
locations and user specific initial conditions.

Gold (and Kasami) showed that for certain well-chosen *m*-sequences, the
cross correlation only takes on three possible values, namely -1, -*t*
or *t*-2. Two such sequences are called preferred sequences. Here *t*
depends solely on the length of the LFSR used. In fact, for a LFSR with
N memory elements,

   if N is odd, *t* = 2^(N*l*+1)/2^ + 1, and

   if N is even, *t* = 2^(N+2)/2^ + 1.

Gold codes are constructed by EXOR-ing two m-sequences of the same
length with each other as shown in Figure 9. Thus, for a Gold sequence
of length *m* = 2*^N^*-1, two LFSRs are used, each of length 2*^N^*-1.
If the LSFRs are chosen appropriately, Gold sequences have better
cross-correlation properties than maximum length LSFR sequences.

![](media/image11.wmf){width="3.122916666666667in"
height="0.8222222222222222in"}

Figure 9 --- Gold Code Generator

1.  Use of Spread Spectrum in NASA Links

NASA employs Direct Sequence Spread Spectrum (DSSS) modulation in the
Space Network for low rate data transfer, ranging services, and to
support multiple access modes. PN spreading is performed on both forward
and return services. Capabilities and characteristics of the Space
Network are explained briefly in Section 4.3.1 including coherent, PN
acquisition, and different service modes. 450-SNUG may be consulted for
a complete understanding of these subjects.

1.  Capabilities and Characteristics of Existing NASA Systems

The Space Network provides forward and return data communication
services and tracking services. PN spreading is used in S-band and
Ku-band forward and return services and in Ka‑band forward data
services. Note that S-band services include both Multiple Access (MA)
and Single Access (SSA) services. Tracking services that use PN codes
are Range and Customer Time Transfer. Tracking services are not stand
alone services rather they are integrated into the forward and return
services. Only the SN services that use DSSS and their requirements
relating to the PN coding are provided in the following sections. The
450-SNUG may be consulted for a complete understanding of SN services
and requirements. Note that other agencies (ESA and JAXA) utilize
similar terminology to define PN spread services with identical
characteristics.

The following PN spread signal formats are used in NASA's Space Network:

-   Low Data Rate Forward I Channel Signal Format

-   Low Data Rate Forward Q Channel Signal Format

-   Low Rate Return DG1 Mode 1 Channel Signal Format

-   Low Rate Return DG1 Mode 2 Channel Signal Format

-   Low Rate Return DG1 Mode 3 Channel Signal Format

-   Shuttle S-band Forward I Channel Signal Format.

[Coherent and Non-coherent Modes:]{.underline}

In a coherent RF link, the user element transmitted return link carrier
frequency and PN code clock frequency (if applicable) are derived from
the forward link carrier frequency received from the network element.
For coherent PN spread return links, the return PN code length is
identical to the length of the received forward service range channel PN
code. The customer return I channel PN code epoch is synchronized with
the epoch of the received forward service range channel PN code.

For non-coherent modes, the customer platform transmitted return link
carrier frequency and PN code clock frequency (if applicable) are
derived from an on-board local oscillator.

A customer transponder is required for coherent service whereas a
transceiver may be used for non-coherent service.

[PN Acquisition:]{.underline}

The forward link carrier frequency and PN chip rate are usually Doppler
compensated on a continuous basis in order to minimize the Doppler
resolution requirements of the customer receiver and to facilitate
reacquisition by customer platform in the event of loss of lock of the
forward service signal. The Doppler compensation is performed at the
start of service so it arrives at the customer platform receiver at the
center frequency specified in the customer schedule. The customer
platform receiver then acquires the forward link PN codes (Command I
Channel \[PN Short Code\] and Range Q Channel \[PN Long Code\]).

During the customer platform receiver acquisition period no commands
should be sent via the forward link. The customer platform initially
searches for the PN Short code (I channel) to acquire the forward
signal. If the customer sends commands and thus command modulation there
is an increased possibility of false PN lock within the customer
platform receiver. In the event of a false lock the customer platform
will not be able to correlate the PN long code.

Once the customer equipment is locked to the forward link command I
channel PN code, two functions take place:

The receiver PN correlation process autocorrelates the forward spread
spectrum signal to allow recovery of the forward carrier. This carrier
is then used to coherently generate the return carrier for the return
link acquisition at a transmit frequency of 240/221 times the received
(network forward) frequency.

The customer equipment locally generated PN Long Code will be
synchronized with the correlated network PN Long Code (Q-Range Channel)
by using the PN-Epoch. The PN Epoch is a repeating reference pattern
within the code used for the acquisition process and ranging. The
modified customer platform transmitter Long PN code, containing the I
and/or Q channel data and PN Epoch synchronized with the received PN
Epoch from network, is then used to modulate the now coherent carrier
for network return link acquisition.

Return signal Doppler compensation is performed to allow implementation
of receivers with narrow acquisition and tracking bandwidths.

[Forward Services PN Spread Signal Formats:]{.underline}

SN forward services with data rates equal to and below 300 kbps are
recommended to incorporate spread spectrum modulation techniques to
satisfy NTIA power flux density restrictions. 300 kbps is the achievable
data rate limit for PN spread links with a PN chip rate of 3 Mcps; based
on the general PN spreading requirement of 10:1 ratio of PN chip rate to
symbol rate. This modulation scheme employs a non-staggered QPSK format
with PN spread data on the I channel, also known as the Command channel,
and a ranging PN sequence with no data on the Q channel, also known as
the Range channel. Spread Spectrum BPSK (SS-BPSK) is also possible for
forward services.

The command channel makes use of a shorter (and thus rapidly acquirable)
PN code. The Range channel contains a longer PN code which satisfies the
range ambiguity resolution requirements. The length of the command
channel PN code is 2^10^-1, where the length of the range channel PN
code is exactly 256 times the command channel PN code length. Also, the
codes are synchronized (the first chip in the command channel code
occurs at the same point in time as the first chip in the range channel
code). Once the customer platform acquires the command channel epoch,
acquisition of the range channel PN code timing is greatly simplified
and thus the overall acquisition time is reduced.

The PN code chip rate is coherently related to the transmit frequency in
all cases except for shuttle services. This feature permits the customer
platform receiver to use the receiver PN code clock to predict the
received carrier frequency, thereby minimizing receiver complexity and
further reducing acquisition time. Shuttle PN chip rate and carrier
frequency are independent. Further information on shuttle services is
provided in 530-RSD-WSC.

For data rates [\<]{.underline} 300 kbps, the forward service data is
directly modulo‑2 added to the command channel PN code sequence. The
forward service data will be asynchronous with the carrier and the PN
code. When the command channel does not contain any actual forward
service data, the forward service command channel signal is the command
channel PN code sequence. A 10 to 1 power ratio (command channel to
range channel power) is normally used.

Shuttle forward services use PN coding for I (command channel). The
range channel does not use PN codes.

[Return Links Using Spread Spectrum:]{.underline}

Return services that use PN spread modes are called Data Group 1 (DG1).
For all DG1 modes, the PN code clock must be coherently related to the
transmitted carrier frequency. This feature permits the customer
platform transmitter to use a common source for generating the carrier
and the PN code clock frequencies. For return service DG1 Modes 1 and 3,
the carrier frequency is coherently derived from the received forward
link frequency and the epoch of the return service PN code (the longer
ranging code) is synchronized with the received forward service range
channel PN epoch. The three DG1 modes are summarized below:

-   DG1 Mode 1 service supports up to 300 kbps uncoded on the I and Q
    channels (600 kbps uncoded total) using SQPN modulation with the a
    PN spreading code (ranging code - length 256 \* 2^10^ -1) whose
    epoch is synchronized to that of the received forward service range
    channel code. It supports ranging and 2-way Doppler tracking
    services. Spread Spectrum BPSK can also be used in this mode of
    operation.

### DG1 Mode 2 is a non-coherent service. It supports the same data rates as DG1 Mode 1 but provides only 1 way Doppler. There is no requirement for coherent turn around or synchronization of the PN code. DG1 Mode 2 links use the short PN code (length 2^10^ -- 1) on both I and Q channels. Spread Spectrum BPSK can also be used in this mode of operation.

### DG 1 Mode 3 is a coherent combination service. Up to 300 kbps (uncoded) can be placed on the I channel, which is PN spread in a manner identical to that used with DG1 Mode 1. This allows PN ranging. Coherent turnaround of the carrier frequency also facilitates support for 2-way Doppler. Unlike mode 1, however, the Q channel in mode 3 is unspread, high rate data. The maximum data rate for the Q channel is 3 Mbps (uncoded) for MA service, 6 Mbps (uncoded) for S-band single access service, and 6 Mbps (uncoded) for Ku-band single access. Note that S-band signals requiring bandwidths greater than 6 MHz may be difficult to obtain.  Please contact the GSFC Spectrum Manager.

[Tracking Services Using Spread Spectrum:]{.underline}

The tracking services that use PN spreading are range measurements and
customer time transfer. Note that tracking services are not stand alone
services; rather they are integrated into the forward and return
services.

Range measurement can be achieved during DG1 modes1 and 3 operations by
measuring the time elapsed between the transmission of a PN code epoch
on the forward link and the reception of the turned-around PN code epoch
on the return link. Only two-way range measurements are provided. When
channel delays are subtracted; the result provides a resolution of 1
nanosecond.

Customer (User) Time Transfer is performed during DG1 modes 1 and 3
operations. The time transfer function provides a method to acquire the
data necessary to update a customer platform clock. It gives the
customer Mission Operations Center (MOC) the ability to determine the
time difference between the on-board platform clock and Universal Time
Coordinated (UTC). To facilitate the time transfer measurement, the
customer must cause the platform to note and store the platform clock
reading at the time of arrival of the epoch portion of the PN range
code. The clock reading must be included in the platform telemetry for
processing by the MOC. It is the MOC's responsibility to make the
necessary adjustment to the customer clock using the SN-supplied data.

1.  Requirements of PN Spread Modulations for NASA Systems

This section details the functional and performance requirements of NASA
systems employing the PN spread modulation formats covered by this
standard. Section 4.4.1 provides system level requirements. Section
4.4.2 and 4.4.3 provide network and user element requirements
respectively. The basis for these requirements is the objective of
ensuring compatibility between equipments developed to this standard and
existing SN infrastructure / SN customer platform.

1.  System Level Requirements for PN Spread Links

This section provides requirements that are applicable on a system level
for NASA links using Spread Spectrum modulation. Section 4.4.1.1
provides service availability requirement and Section 4.4.1.2 provides
requirements on each of the service modes.

The system shall support PN code assignments to specific platforms as
assigned by the GSFC Spectrum Manager.

1.  Service Availability Requirements

Systems designed to support NASA PN spread modulation format shall
provide forward and return data transfer services. Forward services
shall be capable of supporting data transfer and range data. Return
services shall be capable of supporting coherent mode of operation if PN
ranging is necessary. These services shall be compatible with NASA's
existing Space Network system PN spread modes. Systems using PN spread
modulations on forward links shall comply with the requirements
specified in Section 4.4.1.2.1. Systems using PN spread modulations on
the return service shall comply with requirements specified in Section
4.4.1.2.2.

2.  Service Mode Requirements

    1.  Forward Services

NASA Forward link services using spread spectrum shall meet the
requirements specified in Sections 4.4.1.2.1.1 and 4.4.1.2.1.2 below.
These Sections detail the signal format requirements applicable to the
Command and Range channels respectively. Shuttle forward link
specifications are provided in Section 4.4.1.2.1.3. These sections
provide only those parameter requirements relating to signal
compatibility with existing PN spread modulation systems. Note that
there are many other types of requirements, not specifically related to
PN spread modulation signal formats, which must be met to ensure system
compatibility with existing SN hardware. Examples would include forward
error correction coding format, data signal formats, etc. Consult
450-SNUG for additional requirements that are not specific to PN spread
formats. NASA Space Network utilizes I channel for command data and Q
channel for range service.

1.  I (Command) Channel

I (Command) channel shall include a rapidly acquirable PN code and
contain the forward service data. PN code enabled Forward I channel
shall meet the requirements specified in Table 1. In addition, Forward I
channel shall meet the requirements specified in Table 2. These
requirements are based on the current SN hardware constraints.

Table 1 --- Forward I channel PSK Service Signal Parameters

+----------------------------------+-----------------------------------+
| **Parameter**                    | **Definition**                    |
+==================================+===================================+
| Transmit carrier frequency (Hz)  | F                                 |
+----------------------------------+-----------------------------------+
| QPSK (PN modulation enabled)     |                                   |
+----------------------------------+-----------------------------------+
| > QPSK Command Channel           |                                   |
+----------------------------------+-----------------------------------+
| > Carrier frequency (Hz)         | Transmit carrier frequency (F)    |
+----------------------------------+-----------------------------------+
| > PN code modulation             | Phase Shift Key (PSK), + π/2      |
|                                  | radians                           |
+----------------------------------+-----------------------------------+
| > Carrier suppression            | 30 dB minimum                     |
+----------------------------------+-----------------------------------+
| > PN code length (chips)         | 2^10^ -- 1                        |
+----------------------------------+-----------------------------------+
| > PN code epoch reference        | Refer to Appendix A               |
+----------------------------------+-----------------------------------+
| > PN code family                 | Gold codes                        |
+----------------------------------+-----------------------------------+
| > PN code chip rate (chips/sec)  | $\frac{\text{31}}{\text{221} \ti  |
|                                  | mes \text{ 96}} \times \text{ F}$ |
|                                  | (S-band)                          |
|                                  |                                   |
|                                  | $                                 |
|                                  | \frac{\text{31}}{\text{1469 } \ti |
|                                  | mes \text{ 96}} \times \text{ F}$ |
|                                  | (Ku-band)                         |
|                                  |                                   |
|                                  | $                                 |
|                                  | \frac{\text{31}}{\text{1469 } \ti |
|                                  | mes \text{ 96}} \times (\frac{F}{ |
|                                  | {}^{\text{10}^{9}}}\text{-8}\text |
|                                  | {.}\text{78-0}\text{.}\text{005 K |
|                                  | }) \times \text{10}^{9}$(Ka-band) |
|                                  |                                   |
|                                  | Where K =                         |
|                                  | $\f                               |
|                                  | rac{\left( \frac{f_{0}}{\text{10} |
|                                  | ^{6}} - \text{22555} \right)}{5}$ |
|                                  |                                   |
|                                  | > Rounded to the nearest integer  |
|                                  | > if K ≠ integer and 0 \< K \<    |
|                                  | > 198. fo is the nominal center   |
|                                  | > frequency in Hz of customer     |
|                                  | > platform receiver as defined by |
|                                  | > the customer MOC.               |
+----------------------------------+-----------------------------------+
| > Data modulation                | Modulo‑2 added asynchronously to  |
|                                  | PN code                           |
+----------------------------------+-----------------------------------+
| > Data format (note 1)           | Not Applicable                    |
+----------------------------------+-----------------------------------+
| > Data rate restrictions (note   | 0.1 ‑ 300 kbps (S-band)           |
| > 1)                             |                                   |
|                                  | 1 kbps ‑ 300 kbps (Ku-band &      |
|                                  | Ka-band)                          |
+----------------------------------+-----------------------------------+
| BPSK (PN modulation enabled;     |                                   |
| also referred to                 |                                   |
|                                  |                                   |
| as Spread Spectrum BPSK          |                                   |
| (SS-BPSK)) (note 2)              |                                   |
+----------------------------------+-----------------------------------+
| > Command Channel                |                                   |
+----------------------------------+-----------------------------------+
| > Carrier frequency (Hz)         | Transmit carrier frequency (F)    |
+----------------------------------+-----------------------------------+
| > PN code modulation             | Phase Shift Key (PSK), + π/2      |
|                                  | radians                           |
+----------------------------------+-----------------------------------+
| > Carrier suppression            | 30 dB minimum                     |
+----------------------------------+-----------------------------------+
| > PN code length (chips)         | 2^10^ -- 1                        |
+----------------------------------+-----------------------------------+
| > PN code epoch reference        | Refer to Appendix A               |
+----------------------------------+-----------------------------------+
| > PN code family                 | Gold codes                        |
+----------------------------------+-----------------------------------+
| > PN code chip rate (chips/sec)  | $\frac{\text{31}}{\text{221} \ti  |
|                                  | mes \text{ 96}} \times \text{ F}$ |
|                                  | (S-band)                          |
|                                  |                                   |
|                                  | $                                 |
|                                  | \frac{\text{31}}{\text{1469 } \ti |
|                                  | mes \text{ 96}} \times \text{ F}$ |
|                                  | (Ku-band)                         |
|                                  |                                   |
|                                  | $                                 |
|                                  | \frac{\text{31}}{\text{1469 } \ti |
|                                  | mes \text{ 96}} \times (\frac{F}{ |
|                                  | {}^{\text{10}^{9}}}\text{-8}\text |
|                                  | {.}\text{78-0}\text{.}\text{005 K |
|                                  | }) \times \text{10}^{9}$(Ka-band) |
|                                  |                                   |
|                                  | Where K =                         |
|                                  | $\f                               |
|                                  | rac{\left( \frac{f_{0}}{\text{10} |
|                                  | ^{6}} - \text{22555} \right)}{5}$ |
|                                  |                                   |
|                                  | > Rounded to the nearest integer  |
|                                  | > if K ≠ integer and 0 \< K \<    |
|                                  | > 198. fo is the nominal center   |
|                                  | > frequency in Hz of customer     |
|                                  | > platform receiver as defined by |
|                                  | > the customer MOC.               |
+----------------------------------+-----------------------------------+
| > Data modulation                | Modulo‑2 added asynchronously to  |
|                                  | PN code                           |
+----------------------------------+-----------------------------------+
| > Data format (note 1)           | Not Applicable                    |
+----------------------------------+-----------------------------------+
| > Data rate restrictions (note   | 0.1 ‑ 300 kbps (S-band)           |
| > 1)                             |                                   |
|                                  | 1 kbps ‑ 300 kbps (Ku-band &      |
|                                  | Ka-band)                          |
+----------------------------------+-----------------------------------+
| Notes:                           |                                   |
|                                  |                                   |
| 1.  The forward data rate in     |                                   |
|     this table is the baud rate  |                                   |
|     that will be transmitted by  |                                   |
|     the SN (includes all coding  |                                   |
|     and symbol formatting).      |                                   |
|     Forward data conditioning is |                                   |
|     transparent to the SN. These |                                   |
|     transparent operations       |                                   |
|     should be performed by the   |                                   |
|     customer prior to            |                                   |
|     transmission to the SN data  |                                   |
|     interface.                   |                                   |
|                                  |                                   |
| 2.  Customer's that operate in a |                                   |
|     SS-BPSK mode for one service |                                   |
|     cannot reconfigure any of    |                                   |
|     their Forward Services       |                                   |
|     (i.e., MAF, SMAF, SSAF,      |                                   |
|     KuSAF, or KaSAF) to an UQPSK |                                   |
|     mode. Contact Code 450 if    |                                   |
|     additional flexibility is    |                                   |
|     required.                    |                                   |
+----------------------------------+-----------------------------------+

Table 2 --- Salient Characteristics of PN Codes for Forward Services

  ----------------------------------- -----------------------------------
  **Parameter**                       **Description**

  PN chip jitter (rms) (including     [\<]{.underline}1 degree
  effects of Doppler compensation)    

  Command/range channel PN chip skew  [\<]{.underline}0.01 chip
  (peak)                              

  PN chip asymmetry (peak)            [\<]{.underline}0.01 chip

  PN chip rate (peak) relative to     [\<]{.underline}0.01 chips/sec at
  absolute coherence with carrier     PN code chip rate
  rate                                
  ----------------------------------- -----------------------------------

1.  Q (Range) Channel

Forward Q channel (range) shall meet the requirements specified in Table
2. Forward Q channel shall also meet requirements specified in Table 3
for PN code enabled services. These requirements are based on the
current SN hardware constraints.

Table 3 --- Forward Q channel PSK Service Signal Parameters

+----------------------------------+-----------------------------------+
| **Parameter**                    | **Definition**                    |
+----------------------------------+-----------------------------------+
| Transmit carrier frequency (Hz)  | F                                 |
+----------------------------------+-----------------------------------+
| QPSK (PN modulation enabled)     |                                   |
+----------------------------------+-----------------------------------+
| QPSK Range Channel               |                                   |
+----------------------------------+-----------------------------------+
| PN code modulation               | PSK, + π/2 radians                |
+----------------------------------+-----------------------------------+
| > Carrier suppression            | 30 dB minimum                     |
+----------------------------------+-----------------------------------+
| PN code chip rate                | Synchronized to command channel   |
|                                  | PN code chip rate                 |
+----------------------------------+-----------------------------------+
| PN code length                   | (2^10^ ‑ 1) x 256                 |
+----------------------------------+-----------------------------------+
| PN code epoch reference          | All 1\'s condition synchronized   |
|                                  | to the command channel PN code    |
|                                  | epoch                             |
+----------------------------------+-----------------------------------+
| PN code family                   | Truncated 18‑stage shift register |
|                                  | sequences                         |
+----------------------------------+-----------------------------------+

2.  Shuttle Forward Service

Shuttle forward service using PN spreading for I (command) channel shall
meet requirements specified in Table 4.

Table 4 --- Shuttle Forward I (Command) Channel Requirements

+----------------------------------+-----------------------------------+
| **Parameter**                    | **Definition**                    |
+----------------------------------+-----------------------------------+
| TDRS transmit carrier frequency  | F                                 |
| (Hz)                             |                                   |
+----------------------------------+-----------------------------------+
| QPSK (PN modulation enabled)     |                                   |
+----------------------------------+-----------------------------------+
| > QPSK Command Channel           |                                   |
+----------------------------------+-----------------------------------+
| > Carrier frequency (Hz)         | Transmit carrier frequency (F)    |
+----------------------------------+-----------------------------------+
| > PN code modulation             | Phase Shift Key (PSK), +/- π/2    |
|                                  | radians                           |
+----------------------------------+-----------------------------------+
| > PN code length (chips)         | 2^10^ -- 1                        |
+----------------------------------+-----------------------------------+
| > PN code epoch reference        | Refer to Appendix A               |
+----------------------------------+-----------------------------------+
| > PN code family                 | Truncated 18‑stage shift register |
|                                  | sequences                         |
+----------------------------------+-----------------------------------+
| > PN code chip rate (chips/sec)  | 11.232 Mcps (S-band)              |
|                                  |                                   |
|                                  | ≈ 3 Mcps (Ku-band)                |
+----------------------------------+-----------------------------------+
| > Data modulation                | Modulo‑2 added asynchronously to  |
|                                  | PN code                           |
+----------------------------------+-----------------------------------+
| > Data format                    | Not Applicable                    |
+----------------------------------+-----------------------------------+
| > Data rate restrictions         | 32 kbps & 72 kbps (S-band)        |
|                                  |                                   |
|                                  | 1 kbps ‑ 216 kbps (Ku-band)       |
+----------------------------------+-----------------------------------+

1.  Return Services

Return services shall meet signal parameters relating to spread spectrum
modulation provided in Table 5.

1.  DG1 Mode 1

DG1 mode 1 shall be used when range and two-way Doppler measurements
(coherent transponder operations) are required concurrently with return
service low-rate data transmission.

For DG1 mode 1 operation, the I and Q channel PN codes shall be
identical but offset by at least 20,000 chips. This separation is
adequate to identify each data channel unambiguously without requiring a
unique PN code for each channel. SS-BPSK is also a possible modulation
for DG1 Mode 1.

2.  DG1 Mode 2

DG1 mode 2 shall be used when return service signal acquisition is
necessary without the requirement for prior user platform signal
acquisition of the forward service (noncoherent transponder/transceiver
operation).

For DG1 mode 2, the I and Q channel PN codes shall be unique 2^11^ - 1
Gold Codes. There is no channel ambiguity in this mode since the PN
codes on I and Q channels are different. SS-BPSK is also a possible
modulation for DG1 Mode 2.

3.  DG1 Mode 3

DG1 Mode 3 can be used when range and two-way Doppler measurements
(coherent transponder operations) are required concurrently with return
service high-rate data transmission.

Restrictions on DG1 mode 3 signal acquisition are identical to those for
DG1 mode 1. In DG1 mode 3, the Q channel must contain only data and no
PN code. MA services are unavailable for DG1 Mode 3.

There is no channel ambiguity in this mode since I/Q channel resolution
is achieved by using PN correlation in addition to knowledge of I/Q
power ratio.

Table 5 --- Return Service Signal Parameters

+----------------------------------+-----------------------------------+
| **Parameter**                    | **Definition**                    |
+==================================+===================================+
| [DG1]{.underline} (note 1)       |                                   |
+----------------------------------+-----------------------------------+
| > Transmit carrier frequency     | F1                                |
| > (Hz)                           |                                   |
+----------------------------------+-----------------------------------+
| > DG1 mode 1                     | $\frac{\tex                       |
|                                  | t{240}}{\text{221}} \times F_{R}$ |
|                                  | (S-band)                          |
|                                  |                                   |
|                                  | $\frac{\text{                     |
|                                  | 1600}}{\text{1469}} \times F_{R}$ |
|                                  | (Ku-band)                         |
+----------------------------------+-----------------------------------+
| > DG1 mode 2                     | Customer platform transmitter     |
|                                  | oscillator                        |
+----------------------------------+-----------------------------------+
| > PN code modulation             |                                   |
+----------------------------------+-----------------------------------+
| > DG1 modes 1 and 2              | SQPN, SS-BPSK (Refer to 450-SNUG) |
+----------------------------------+-----------------------------------+
| > DG1 mode 3, I channel          | PSK [+]{.underline}π/2 radians    |
+----------------------------------+-----------------------------------+
| > PN code chip rate (chips/sec)  | $\frac{\text{31}                  |
|                                  | }{\lbrack\text{240} \times \text{ |
|                                  | 96}\rbrack} \times F_{1}$(S-band) |
|                                  |                                   |
|                                  | $\frac{\t                         |
|                                  | ext{31}}{\lbrack\text{1600} \time |
|                                  | s \text{96}\rbrack} \times F_{1}$ |
|                                  | (Ku-band)                         |
+----------------------------------+-----------------------------------+
| > PN code length (chips)         |                                   |
+----------------------------------+-----------------------------------+
| > DG1 modes 1 and 3              | (2^10^ ‑ 1) x 256                 |
+----------------------------------+-----------------------------------+
| > DG1 mode 2                     | 2^11^ -- 1                        |
+----------------------------------+-----------------------------------+
| > PN code epoch reference        |                                   |
+----------------------------------+-----------------------------------+
| > DG1 mode 1                     |                                   |
+----------------------------------+-----------------------------------+
| > I channel                      | Epoch (all 1\'s condition)        |
|                                  | synchronized to epoch (all 1\'s   |
|                                  | condition) of received forward    |
|                                  | service Q (range) channel PN code |
+----------------------------------+-----------------------------------+
| > Q channel (note 2)             | Epoch delayed x + 1/2 PN code     |
|                                  | chips relative to I channel PN    |
|                                  | code epoch                        |
+----------------------------------+-----------------------------------+
| > DG1 mode 2                     | Not Applicable                    |
+----------------------------------+-----------------------------------+
| > DG1 mode 3, I channel          | Same as DG1 mode 1 (I channel)    |
+----------------------------------+-----------------------------------+
| > PN code family                 |                                   |
+----------------------------------+-----------------------------------+
| > DG1 mode 1                     | Truncated 18‑stage shift register |
|                                  | sequences                         |
+----------------------------------+-----------------------------------+
| > DG1 mode 2                     | Gold codes                        |
+----------------------------------+-----------------------------------+
| > Data modulation:               |                                   |
+----------------------------------+-----------------------------------+
| > DG1 modes 1 and 2              | Modulo‑2 added asynchronously to  |
|                                  | PN code                           |
+----------------------------------+-----------------------------------+
| > DG1 mode 3:                    |                                   |
+----------------------------------+-----------------------------------+
| > I channel                      | Modulo‑2 added asynchronously to  |
|                                  | PN code                           |
+----------------------------------+-----------------------------------+
| > Q channel                      | PSK [+]{.underline}π/2 radians    |
+----------------------------------+-----------------------------------+
| Notes:                           |                                   |
|                                  |                                   |
| 1.  Customer platform data       |                                   |
|     configurations, including    |                                   |
|     specific data rate           |                                   |
|     restrictions for coding and  |                                   |
|     formatting, are defined in   |                                   |
|     450-SNUG for TDRSS return    |                                   |
|     services (refer also to      |                                   |
|     Appendix B of SNUG Rev 9).   |                                   |
|     Unless otherwise stated, the |                                   |
|     data rate restrictions given |                                   |
|     in this table assume rate    |                                   |
|     1/2 convolutional encoding   |                                   |
|     and NRZ formatting.          |                                   |
|                                  |                                   |
| ```{=html}                       |                                   |
| <!-- -->                         |                                   |
| ```                              |                                   |
| 3.  The Q channel PN code        |                                   |
|     sequence must be identical   |                                   |
|     to the I channel PN code     |                                   |
|     sequence; but, offset x +    |                                   |
|     1/2 PN chips, where x        |                                   |
|     \>20,000 (to avoid channel   |                                   |
|     ambiguity). The value of x   |                                   |
|     is defined by the PN code    |                                   |
|     assignment for a particular  |                                   |
|     customer platform.           |                                   |
|     Offsetting Q channel PN      |                                   |
|     sequence by ½ chip achieves  |                                   |
|     SQPN modulation to prevent   |                                   |
|     simultaneous transitions of  |                                   |
|     the I and Q PN sequences.    |                                   |
|     For data configurations that |                                   |
|     use two PN spread channels,  |                                   |
|     SQPN modulation must be      |                                   |
|     used.                        |                                   |
+----------------------------------+-----------------------------------+

1.  Tracking Services

If PN ranging services are provided, the range estimate shall be derived
by determining the time differences between the forward PN code and the
coherent return PN code. When channel delays are subtracted; the result
shall provide a resolution of 1 nanosecond.

When time transfer services are provided, the system shall provide PN
epoch data to the user MOC for user time transfer.

1.  Network Element Requirements

This section provides requirements relating to network elements.
Sections 4.4.2.1 and 4.4.2.2 states requirements on transmit and receive
function of the PN spread links. Section 4.4.2.3 states requirements for
PN ranging.

There shall be no data transitions during the signal acquisition process
if the transponder is NASA Fourth Generation Transponder compatible. In
some cases the data transition during signal acquisition would result in
longer acquisition times.

1.  Transmit Requirements

The network element transmitter shall be capable of generating PN codes
in accordance with Appendix A and 451-PN CODE SNIP. The network element
shall be capable of spreading forward link data as described in Section
4.4.1.2.1.

2.  Receive Requirements

The network element shall be capable of receiving the return link signal
using the formats described in sections 4.4.1.2.2. The network element
shall perform PN acquisition to obtain the epoch of the received code.
The network element shall provide PN epoch synchronization to the
transmitter for ranging turnaround.

Network element shall be capable of supporting users employing PN codes
allocated to other agencies.

3.  PN Ranging Requirements

If the system employs PN ranging, the network element shall be capable
of computing correlation to estimate total delay. If the system employs
PN ranging, the network element shall be capable of resolving delay
ambiguity. The network element shall also be capable of performing range
zero set functions to precisely calculate and account for processing
delays through network element equipment and other related requirements.

2.  User Element Equipment Requirements for PN Spreading

This section provides functional and performance requirements for user
element equipment in a system employing NASA standard PN Spread
modulation formats relating to the PN spread signal formats used in
Space Network compatible customer platform. The requirements discussed
in this section are based on the [NASA Fourth Generation TDRSS User
Transponder]{.underline} specification which is compatible with the
Space Network. The NASA Fourth Generation TDRSS User Transponder
requirements and parameter values are provided as an example
implementation. These requirements ensure compatibility with existing
Space Network PN spread modes; however, SN compatibility may be achieved
with other implementations. Customer platform/equipment should be a
transponder when coherent mode of operation is required; if non-coherent
operation is used the user equipment may be a transceiver. Note that
this section provides only those parameter requirements relating to
signal compatibility. As indicated above, there are other types of
requirements, not specifically related to PN spread modulation signal
formats, which must be met to ensure system compatibility with existing
SN hardware. Consult 450-SNUG for additional requirements that are not
specific to PN spread formats.

1.  Receive Requirements

The customer platform receiving system shall search for and acquire the
I channel PN codes (short code). The receiving system shall be capable
of de-spreading short PN codes. When using coherent mode of operation,
the transponder shall be capable of providing coherent turnaround
capability to the transmitter.

The customer platform receiving system shall search for and acquire the
range channel PN code (long code) upon acquisition of the I (command)
channel PN code and carrier. The receiving system shall be capable of
de-spreading the long PN code. The customer platform shall be capable of
providing PN epoch synchronization to the transmitter for ranging
turnaround.

External Programming Connector shall include the state "PN code" (The
user's assigned PN code address (1 of 85 codes) must be specified) as
one of the programming parameters.

2.  Transmit Requirements

The customer platform shall be capable of spreading data on I channel
and on Q channel using generated PN codes. The customer platform shall
be capable of synchronizing the epoch of the transmitted PN code to that
of the received code.

3.  Transmitter Requirements for PN Spreading

Both long and short return link codes shall be produced in the customer
platform in accordance with Appendix A and 451-PN CODE-SNIP with
characteristics specified in Table 3.

The transmitter PN code and carrier shall be coherent with respect to
each other for all modes of operation. For coherent forward link/return
carrier operation, the transmitter shall be phase modulated by a long
code PN sequence synchronized to the forward link. For noncoherent
forward link/return link operation, the transmitter shall be phase
modulated by a short code PN sequence synchronized to the Temperature
Compensated Crystal Oscillator (TCXO). In either case, code modulation
shall be capable of ground command disable.

1.  PN Chip Rate

The PN chip rate shall meet the requirements specified in Table 3 for
each of the services.

4.  Receiver Requirements for PN Spreading

    1.  Dual Mode Search

The customer platform receiver shall simultaneously search for PN code
correlation and a carrier wave (CW) signal greater than the detection
threshold. Upon acquisition of one signal type, the other mode shall be
inhibited until loss of initial signal and subsequent return to search
mode occurs.

2.  Receiver Lock Detectors

The receiver shall be capable of providing the following lock detectors:

a.  Sync Detect: It indicates the receiver has detected energy in the
    receive bandwidth and it has initiated the PN code main lobe
    verification routine.

b.  Main Lobe Detect: It indicates the receiver has concluded
    successfully the PN code main lobe verification routine.

c.  PN Lock: It indicates the receiver is locked to and tracking the
    short PN code.

d.  Long Code Detect: It indicates synchronization has been established
    with the long PN code.

    1.  PN Chip Rate

The customer platform receiver shall be capable of acquiring signals
with chip rates specified in Table 1 and Table 2.

1.  Performance Requirements

    1.  Short Code Acquisition Time

The customer platform receiver shall acquire short code PN lock with a
probability of 90 percent or greater within 20 seconds after arrival of
the forward link transmission.

2.  Long PN Code Acquisition Time

The receiver shall establish synchronization with the long PN code with
a probability specified for the system.

2.  Ranging Performance

Each customer platform shall synchronize its return link PN Code epoch
to the received forward link long PN code epoch for ranging. The
transponder must meet the timing requirements between these epochs
specified in paragraphs 4.4.3.4.4.1 through 4.4.3.4.4.4.

1.  Absolute Time Delay

The nominal absolute time delay (To) between transmit and receive epochs
shall be 325 nsec, which is the reciprocal of the PN chip rate,
[+]{.underline}100 nsec.

2.  Time Delay Variation

The customer platform shall be designed such that the time delay, when
averaged over a 100-second interval, between transmit and receive epochs
(To) does not vary from its nominal value more than that specified for
the network as a function of signal strength, carrier frequency, chip
rate, or primary power supply voltage, either individually or in
conjunction with the environmental parameters.

3.  Time Delay Repeatability

The time delay for any specific set of signal and/or environmental
parameters must be repeatable

within [+]{.underline}10 nsec.

4.  Short-Term Time Delay Jitter

The time delay jitter shall not exceed 10 nsec rms.

3.  Time Transfer Interface Requirements

    1.  General

The customer platform shall provide two redundant PN code epoch outputs
as shown in Figure 10 which coincide in time with the all 1's or epoch
state of the forward link long code as defined in 451- PN CODE - SNIP.

![](media/image12.wmf){width="5.872916666666667in"
height="2.183333333333333in"}

Figure 10 --- Time Transfer Interface

2.  Rise and Fall Times

The epoch signal rise and fall times shall not exceed 30 nsec as
measured at the 10 to 90 percent points.

3.  Epoch Period

The period of the epoch will nominally be determined by the equation
(see Figure 11):

![](media/image13.wmf){width="2.5729166666666665in"
height="0.6770833333333334in"}

where: fpn = PN chip rate in chips/sec as determined from the received
signal. The duration of the epoch signal will be nominally one PN chip.

![](media/image14.wmf){width="4.75in" height="3.145138888888889in"}

Figure 11 --- Time Transfer Interface Timing Diagram

4.  Epoch Timing Accuracy

The timing uncertainty between the epoch output and actual epoch
transition of the receiver long code must be as specified for the
network. The jitter component or sample-to-sample variation must not
exceed assigned time period.

1.  PN Code Performance

    1.  Code Modulation Coherency

The transmitter PN code and carrier shall be coherent with respect to
each other for all modes of operation. For noncoherent forward
link/return link operation, the transmitter shall be phase modulated by
a short code PN sequence synchronized to the Temperature Compensated
Crystal Oscillator (TCXO). In either case, code modulation shall be
capable of ground command disable.

1.  PN Chip Rate

The PN chip rate requirements provided in tables 2 and 5 shall be met
for forward and return services respectively.

2.  PN Code Skew

The skew between the 50 percent transition points of the I and Q channel
PN codes shall be ½ chip +0.01 chip at the modulator input.

3.  PN Code Asymmetry

The percent asymmetry between the 50 percent points of a high-to-low PN
transition versus a

low-to-high transition shall not exceed 1 percent.

Percent asymmetry =
$\frac{T(\text{LH}) - T(\text{HL})}{T(\text{LH}) + T(\text{HL})} \times \text{ 100}$
percent

4.  PN Chip Jitter

a\. In transmitter modes 1 and 3 the PN chip jitter must not exceed 10
nsec rms.

b\. For transmitter mode 2, the PN chip jitter must not exceed 4 nsec
rms.

2.  Bilevel Status Telemetry

The customer platform shall provide the bilevel status signals in RT
Subaddress 2 as specified in Table 6 for PN codes.

Table 6 --- Bilevel Telemetry Involving PN Codes

+-------+----+------+-------+------------+----------------+----------+
| RT    | Wo | Bit\ | Fun   | False      | True State\    | Update   |
|       | rd | Ass  | ction | State\     | (Bit = 1)      |          |
| S     |    | ign- |       | (Bit = 0)  |                | f        |
| ub-ad |    | ment |       |            |                | requency |
| dress |    |      |       |            |                |          |
|       |    |      |       |            |                | (upda    |
|       |    |      |       |            |                | tes/sec) |
+=======+====+======+=======+============+================+==========+
| 2     | 1  | 01   | PN    | PN code    | PN code        | 5        |
|       |    |      | Lock  | loop is    | tracking is    |          |
|       |    |      | (PNL) | not locked | locked to      |          |
|       |    |      |       |            | TDRSS forward  |          |
|       |    |      |       |            | link code      |          |
+-------+----+------+-------+------------+----------------+----------+
| 2     | 1  | 03   | Long  | No         | Indicates      | 5        |
|       |    |      | Code  | synch      | s              |          |
|       |    |      | d     | ronization | ynchronization |          |
|       |    |      | etect | with the   | has been       |          |
|       |    |      |       | long code  | established    |          |
|       |    |      | (L    |            | with the range |          |
|       |    |      | CDET) |            | code           |          |
+-------+----+------+-------+------------+----------------+----------+
| 2     | 1  | 05   | Sync  | Receiver   | Indicates      | 5        |
|       |    |      | d     | is in      | s              |          |
|       |    |      | etect | search     | ynchronization |          |
|       |    |      | (     | mode       | has been       |          |
|       |    |      | SYNC) |            | established    |          |
|       |    |      |       |            | with the short |          |
|       |    |      |       |            | forward link   |          |
|       |    |      |       |            |                |          |
|       |    |      |       |            | PN code        |          |
+-------+----+------+-------+------------+----------------+----------+
| 2     | 1  | 13   | I PN  | I PN code  | I PN code is   | 5        |
|       |    |      | di    | has been   | enabled        |          |
|       |    |      | sable | inhibited  |                |          |
|       |    |      | (     | from       |                |          |
|       |    |      | INHI) |            |                |          |
|       |    |      |       | modulating |                |          |
|       |    |      |       | the return |                |          |
|       |    |      |       | link       |                |          |
|       |    |      |       | carrier    |                |          |
+-------+----+------+-------+------------+----------------+----------+
| 2     | 1  | 14   | Q PN  | Q PN code  | Q PN code is   | 5        |
|       |    |      | di    | has been   | enabled        |          |
|       |    |      | sable | inhibited  |                |          |
|       |    |      |       | from       |                |          |
|       |    |      | (     |            |                |          |
|       |    |      | INHQ) | modulating |                |          |
|       |    |      |       | the return |                |          |
|       |    |      |       | link       |                |          |
|       |    |      |       | carrier    |                |          |
+-------+----+------+-------+------------+----------------+----------+

APPENDIX A

NASA SPECIFIC PN CODE REQUIREMENTS\
(Properties, Criteria and Selection Requirements)

NASA systems designed to be Space Network compatible shall meet the
requirements specified in this appendix when implementing PN codes.
451-PN CODE-SNIP provides libraries of PN codes that NASA systems can
use which meets all the requirements specified in this appendix.

NASA services use Gold codes and Maximal Length Codes for various
services. This appendix provides details on specific PN code properties,
generation criteria, and code selection for each of the services that
use PN spread modulation.

1.  Gold Codes for NASA Systems

Gold Codes are used by NASA in the Forward I channel (Command Link) and
Return Mode 2 links. The codes differ only in the initial conditions of
the shift registers. The following sections explain Gold Codes used in
these links in detail.

1.  Command Link Gold Codes

Figure 12 provides the Gold code generator circuit used in the Forward
Command Link. Command link circuit uses two single-shift registers of
length 10. The feedback taps are the same for each agency and the codes
only differ in the initial conditions of Register A. For NASA Command
link the initial conditions are given in table 1.

1.  Command Link Properties

The set of Gold codes corresponding to this circuit hold the following
properties:

a.  A total of 2^10^ + 1 = 1025 sequences (codes) can be generated by
    altering the initial conditions of only one of the shift registers

b.  Each code is 2^10^ -- 1 = 1023 symbols long

c.  Of the 1025 codes, 355\* are balanced codes, i.e. each code has
    precisely 512 ones and 511 zeros.

It should be noted that the circuit of Figure 12 for which this property
holds contains a "zero" in stage 1 of register A. A detailed discussion
of this constraint is provided in 451- PN CODE - SNIP.

Table 7 --- NASA Unique Initial Conditions for PN Code Generation for
Command Link

  ------------- ------- ------------ ------------- ------------- -------------
  Initial               Agency       Balanced      Assigned      Unassigned
  Conditions\                        Codes         Codes         Codes
  Register A\                                                    
  Stage Number:                                                  

  10            9                                                

  0             0       NASA         85            85            0
  ------------- ------- ------------ ------------- ------------- -------------

![](media/image15.wmf){width="5.121527777777778in"
height="3.201388888888889in"}

Figure 12 --- Command Link Gold Code Generator

1.  Command Link Code Criteria

Balance and low cross correlation values are considered as the selection
criteria for the Forward Command Link PN code libraries. A balanced code
is one in which the number of \"ones\" is one more than the number of
\"zeros\". This type of code is preferable due to its smooth transmitted
spectrum. It is also desirable to use codes that are \"unique\", which
is accomplished by choosing codes with low cross correlation values.
Because Command Codes are Gold Codes, they have minimum cross
correlation values. Not only are the side lobes small compared to the
maximum auto correlation value (2^N^ - 1), but the frequency of
occurrence is also relatively small.

2.  Command Link Code Selection

The Command Link Code Libraries were modeled after the circuit shown in
Figure 13. Figure 14 depicts an example of a forward command channel
code generator configuration with initial conditions. During the
selection, stage 1 of register A contains a \"zero\".

Each Forward Command Link library consists of only 85 codes. NASA\'s
initial conditions for stages 10 and 9 of register A produce only 85
balanced codes, therefore no selection method needed to be established
and there will be no unassigned codes.

The Command Link code assignments are listed in 451-PN CODE-SNIP. The
GSFC Spectrum Manager shall assign PN codes for each user.

![](media/image16.wmf){width="6.495138888888889in"
height="4.477777777777778in"}

Figure 13 --- Command Link Gold Code Generator Initial Conditions

1.  Return Mode 2 Link Gold Codes

    1.  Return Mode 2 Link Properties

Figure 14 shows the Gold code generator for Return Mode 2 link
(non-coherent turnaround mode).

![](media/image17.wmf){width="5.364583333333333in"
height="3.2888888888888888in"}

Figure 14 --- Return Mode 2 Link Gold Code Generator

This circuit is composed of three single-shift registers of length 11.
The feedback taps are the same for each agency\'s library. The codes
only differ in the initial conditions of Registers A and

C for each agency. The set of Gold Codes associated with this circuit
has the following properties:

a.  There are 2^11^ + 1 = 2049 codes generated by altering the stage
    contents of one of the two shift registers (register A for the I
    channel codes and register C for the Q channel codes)

b.  Each code is 2^11^ - 1 = 2047 symbols long

c.  Of the 2049 codes, there are 2^10^ + 1 = 1025 balanced codes in the
    set

    1.  Return Mode 2 Link Code Criteria

The following four criteria are considered in the selection of the
Return Mode 2 Link PN code libraries: balance, low cross correlation
values, no duplicate code assignments, and minimized spurious code
effects. A balanced code is preferable because it will have a smooth
transmitted spectrum. It is also desirable to use codes that are
\"unique\", which is accomplished by choosing codes with low cross
correlation values. Because these codes are Gold Codes, they have
minimum cross correlation values. Not only are the side lobes small
compared to the maximum auto correlation value (2^N^ - 1), but the
frequency of occurrence is also relatively small. To avoid interference,
I or Q code assignments should not be duplicated. Spurious codes are
caused by the filtering and hard-limiting of a staggered quadriphase PN
(SQPN) signal. If a spurious code matches an assigned code, false lock
may occur and thus cause interference. To avoid this type of
interference, codes are selected to ensure that such spurious code
matches are not generated.

It has been shown that if the Q channel sequence is delayed 1/2 chip
(SQPN) then the spurious sequences generated on the I and Q channels due
to filtering and hard-limiting are:

> I channel spur = i ⊕ q ⊕ q1
>
> Q channel spur = q ⊕ i-1 ⊕ i

where i and q are the binary sequences on the I and Q channel
respectively, q1 is the q sequence delayed by one chip and i-1 is the i
sequence advanced by one chip.

In Figure 14, registers A and C are identical, so i and q are members of
the same Gold code set.

Term by term modulo 2 addition of two members of a set of PN codes
results in another member of the same PN code set. From the equations
above, it is obvious that the spurious codes which occur on the I and Q
channels are also members of the same set of Gold codes and therefore
are capable of causing \"false lock\". To avoid the possibility of false
lock, the choice of I and Q channel code pairs must be made so that the
spurious codes on the I and Q channels do not duplicate any of the 510
gold codes assigned to NASA, ESA or JAXA\'s Return Mode 2 Link
libraries. A detailed analysis of spurious codes is found in 451- PN
CODE - SNIP.

2.  Return Mode 2 Link Code Selection

The Return Mode 2 Link Code Libraries were modeled after the circuit
shown in Figure 14. There are no restrictions on the initial conditions
of Register A and C. The initial conditions are expressed as four digit
octal numbers. Each octal digit is converted to its three bit binary
representation, giving a twelve digit binary number. Since the circuit
design has only eleven registers, the most significant digit is
truncated. Figure 15 demonstrates an initial condition conversion from
octal to binary. Figure 16 shows the initial conditions of registers A
and C for the example shown in Figure 15.

![](media/image18.wmf){width="5.434722222222222in"
height="1.2909722222222222in"}

Figure 15 --- Octal Conversion Example

![](media/image19.wmf){width="6.239583333333333in" height="4.96875in"}

Figure 16 --- Code Generator Configuration and Initial Conditions\
for Octal Conversion Example

The NASA Return Mode 2 Code library (previously assigned) employs the
fact that if the initial condition of the spurious code is all zeroes,
then the spurious code is a maximal length code and not a Gold Code.
Therefore, interference due to false lock is minimized since the
spurious maximal length code would not be mistaken for an assigned Gold
Code. This criteria was applied to the spurious Q codes of the NASA,
ESA, and JAXA Return Mode 2 code libraries.

The Return Mode 2 Link code assignments are listed in 451-PN CODE-SNIP.
The GSFC Spectrum Manager shall assign PN codes for each user.

1.  Maximal Length Codes for NASA Systems

NASA uses Maximal Length Codes for Forward Range Channel, Return Modes 1
and 3 Links, and Forward Shuttle S-band Command Links.

Sets of maximal length codes (M-sequences) are produced by varying the
feedback tap locations, given the constraints on the total number of
taps. The set from which the Return Modes 1 and 3 Link Code libraries
are selected contains code possibilities with eight or fewer taps, and
the set from which the Ranging Code libraries are selected is restricted
to the possible tap combinations with six or fewer taps. The NASA
specific Shuttle S-band Forward Command Link library is selected with
two or four feedback taps.

1.  Forward Range Channel Codes

    1.  Forward Range Channel Properties

The circuit used to generate the Range Channel Codes is an 18 stage
register with as many as six

tap connections, as shown in Figure 17.

![](media/image20.wmf){width="5.127777777777778in"
height="1.4270833333333333in"}

Figure 17 --- Range Channel Code Generator

The initial conditions for the Ranging Code circuit depicted above are
the same for each code. The codes differ in their unique feedback tap
assignments. Libraries of codes were selected from the set having the
following properties:

a.  Codes are of length 2^18^ - 1 = 262143

b.  Codes are truncated to an integer multiple (256) of the command code
    length, (2^10^ - 1)\*256 = 261888. The all 1\'s initial condition of
    the register is synchronized to the 1001001000 state of the B
    register of the Command Channel Code generator as shown in
    Figure 12. Thus, the last 262143-261888=255 bits of the code are not
    generated before the shift register is reset to its initial all 1\'s
    condition. This synchronization and truncation process permits rapid
    acquisition of the longer code using the short code.

c.  792 maximal length codes are possible with six or fewer taps.

    1.  Forward Range Channel Code Criteria

The following criteria were considered in the selection of the Forward
Ranging Channel PN Code libraries: maximal length and balance. Maximal
length codes are required to ensure that the full transmitted sequence
of 262143 (truncated to 261888) bits is not a repeated periodic
subsequence, thus avoiding false lock. Maximal length codes are produced
by corresponding primitive polynomials, as shown in Figure 18. See
Appendix B for a detailed description of the criteria for producing
maximal length codes.

![](media/image21.wmf){width="6.061111111111111in"
height="3.9805555555555556in"}

Figure 18 --- Range Channel Code Feedback Tap Example

Additionally, maximal length codes exhibit the favorable property of
balance, which ensures a smooth transmitted spectrum. Balance is defined
as having one more \"one\" than \"zero\". For the Ranging Codes,
however, the full code is not transmitted; thus the truncated balance is
of interest. The balance of the truncated code produced for the Forward
Ranging Channel is at most off by a factor of 255/262143, approximately
0.1%. Thus, it is assumed that all codes are \"essentially\" balanced.

2.  Forward Range Channel Code Selection

The Range Channel Code libraries were modeled after the circuit in
Figure 18. This figure also shows the relationship between the octal
definition of the code, as listed in the libraries, and the
corresponding shift register feedback tap locations. NASA has been
assigned 85 codes meeting the above described criteria.

The Forward Range Link code assignments are listed in 451-PN CODE-SNIP.
The GSFC Spectrum Manager shall assign PN codes for each user.

1.  Return Modes 1 and 3 Link Codes

    1.  Return Modes 1 and 3 Link Properties

Figure 19 shows the circuit used to generate the Maximal Length Codes
for the Return Mode 1 and Mode 3 Links.

![](media/image22.wmf){width="6.250694444444444in"
height="2.2430555555555554in"}

Figure 19 --- Return Modes 1 and 3 Link Code Generator

The above circuit is an eighteen-stage linear shift register utilized
for the Return Modes 1 and 3 Link Codes. Mode 1 uses both the I and the
Q Channels, while Mode 3 uses only the I-Channel code. The Q-Channel
code is generated by modulo two summing the ninth and eighteenth stages,
as shown in the figure above. The assigned codes differ in their unique
feedback tap assignments. The maximum number of feedback taps is eight.
The initial conditions are the same for each code, an all 1\'s
condition. Libraries of codes were selected from the set having the
following properties:

a.  Codes are of length 2^18^ - 1 = 262143

b.  Codes are truncated to 261888 to synchronize the shift register with
    the Forward Range channel. Thus, the last 262143 - 261888=255 bits
    of the code are not generated before the shift register is reset to
    its initial all 1\'s condition

c.  3088 maximal length codes are possible with eight or fewer taps.

    1.  Return Modes 1 and 3 Link Code Criteria

The following criteria were considered in the selection of the Return
Modes 1 and 3 Link PN Code libraries: maximal length, balance, a channel
offset in excess of 20000 chips, and minimized spurious code effects.
Maximal length codes are produced by shift registers with corresponding
primitive polynomials as depicted in the Return Modes 1 and 3 Feedback
Tap Example of Figure 20. Maximal length codes assure certain favorable
properties. See Appendix B (Algorithm for Selecting Primitive
Polynomial) for a detailed description of the maximal length codes.

![](media/image23.wmf){width="6.499305555555556in"
height="3.7576388888888888in"}

Figure 20 --- Return Modes 1 and 3 Link Feedback Tap Example

A balanced code is desired due to its smooth transmitted spectrum. In
the case of maximal length codes, the balance is assured when there is
one more \"one\" than \"zero\". The full code is not transmitted; rather
it is the truncated balance that is of interest. The balance of the
truncated code produced for the Return Modes 1 and 3 Link Channel is at
most off by a factor of 255/262143, approximately 0.1%. Thus it is
assumed that all codes are \"essentially\" balanced. Since dual channels
are used for Mode 1 operations, assigned codes must have an I to Q (or Q
to I) channel difference greater than 20,000 chips to avoid channel
ambiguity. As depicted in Figure 19, the I and Q Channel codes are
simultaneously generated by the same shift register. The Q-channel code
is the modulo two addition of two phase shifted versions of the
I-Channel code. Employing a basic property of binary maximal length
sequences, the Q-Channel is simply a shifted version of the I Channel.

In order to minimize the spurious code effects created by filtering and
hard limiting, a minimum offset of 5000 chips is imposed between the
codes and the spurious codes generated. This is necessary to avoid
interference, because the spurious codes are simply a shifted version of
the channel codes. This is obvious by the shift and add property given
in the equations below:

> I channel spur = i ⊕ q ⊕ q1
>
> Q channel spur = q ⊕ i-1 ⊕ i

where i and q are the binary sequences on the I and Q channels
respectively, q1 is the q sequence delayed by one chip and i-1 is the i
sequence advanced by one chip. A detailed analysis of spurious codes is
found in 451- PN CODE - SNIP.

2.  Return Modes 1 and 3 Link Code Selection

The Return Modes 1 and 3 Link Code libraries were modeled after the
circuit in Figure 19. The relationship between the octal definition of
the library codes and the corresponding shift register feedback tap
locations is seen in Figure 19. NASA has been assigned 85 codes. Due to
an inconsistency in the derivations of the spurious code offsets, six of
the NASA codes do not meet the above stated 5000 chip requirement. All
remaining code assignments adhere to the specified criteria.

A Forward Range Code could meet all of the criteria imposed on the Modes
1 and 3 Link codes.

However, any assigned Forward Ranging Codes were eliminated from the
possible codes for the

Return Modes 1 and 3 Link libraries to be used by ESA and JAXA.

The Return Modes 1 and 3 Link code assignments are listed in 451-PN
CODE-SNIP. The GSFC Spectrum Manager shall assign PN codes for each
user.

1.  Shuttle S-band Forward Command Link Codes

    1.  Shuttle S-band Forward Command Link Properties

The circuit used to generate the Shuttle S-band Command Codes is a 10
stage register with two or four tap connections, as shown in Figure 21.

![](media/image24.wmf){width="5.072916666666667in" height="1.71875in"}

Figure 21 --- Shuttle S-band Command Code Generator

The initial conditions for the Shuttle S-band Command Code circuit
depicted above are the same for each code. The codes differ in their
unique feedback tap assignments. The NASA specific library of codes was
selected based upon the following properties:

a.  Codes are of length 2^10^ - 1 = 1023

b.  The initial condition of the register is all 1\'s

c.  Two or four feedback taps.

    1.  Shuttle S-band Forward Command Link Code Criteria

The following criteria were considered in the selection of the Shuttle
S-band Forward Command PN Code libraries: maximal length and balance.
Maximal length codes are required to ensure that the full transmitted
sequence of 1023 bits is not a repeated periodic subsequence, thus
avoiding false lock. Maximal length codes are produced by corresponding
primitive polynomials, as shown in Figure 22.

![](media/image25.wmf){width="6.497222222222222in"
height="4.104861111111111in"}

Figure 22 --- Shuttle S-band Feedback Tap Example

Additionally, maximal length codes exhibit the favorable property of
balance, which ensures a smooth transmitted spectrum. Balance is defined
as having one more \"one\" than \"zero\".

2.  Shuttle S-band Forward Command Link Code Selection

The Shuttle S-band Command Code libraries were modeled after the circuit
in Figure 22. This figure also shows the relationship between the octal
definition of the code, as listed in the libraries, and the
corresponding shift register feedback tap locations. The NASA specific
Shuttle Forward Link Command library consists of 4 codes meeting the
above described criteria.

The Shuttle S-band Command Link code assignments are listed in 451-PN
CODE-SNIP. The GSFC Spectrum Manager shall assign PN codes.

APPENDIX B

Algorithm for Selecting Primitive Polynomials

Although much work has been done on maximal length codes, of the
published tables available, a complete listing of primitive polynomials
of order 18 was not found. It is the property of primitiveness of the
characteristic polynomial that assures maximal length of the generated
code.

Therefore, software was written to test all possible codes meeting
system requirements for primitiveness following the procedure described
herein.

Two basic facts about shift registers producing maximal length codes can
be employed to eliminate codes and decrease the set to be studied:

1.  There must be a tap in the register corresponding to the highest
    order coefficient of the characteristic polynomial; and,

2.  There must be an even number of taps.

Using these criteria alone, combinational analysis will show that it is
possible to construct 6885 codes using two, four, or six taps, and to
construct 19448 codes using eight taps. However, these will not
necessarily guarantee M-sequences or exhibit other desirable properties.

For a shift register to produce a code of maximal length, the
corresponding characteristic polynomial must be primitive. That is to
say, given an irreducible characteristic polynomial of degree n, the
polynomial is primitive if and only if it divides x^m^ -1 for no m less
than 2^n^ -1. In using this condition to test for primitiveness, a
polynomial must be irreducible. A polynomial is irreducible if it is not
divisible by any polynomial of order less than itself, except the
polynomial, p(x) = 1. Software was written to test each possible
polynomial for irreducibility. It was found that 1503 polynomials of 9
terms (corresponding to a shift register of 8 taps) were irreducible,
and that 4316 polynomials of 3, 5, or 7 terms (corresponding to a shift
register of 2, 4, or 6 taps) were irreducible.

Consider the set of irreducible polynomials of degree n; if n is a prime
number, then the polynomial is said to be primitive. In this study, n is
equal to eighteen, which is not prime; therefore, further investigation
is necessary. Thus, the following definition applies:

> Given an irreducible characteristic polynomial of degree n, the
> polynomial is primitive if and only if it divides x^m^ - 1 for no m
> less than 2^n^ - 1.

An algorithm used to determine if a given polynomial is primitive is
described below:

1.  Compute residues, or remainders, of 1, x, x2, x4, x8, \..., x2n-1
    modulo the characteristic equation, f(x).

2.  Multiply and reduce to form the residue of x2^n^ - 1. If the result
    is not 1, the polynomial is rejected. If the result is 1, the test
    is continued.

3.  For each factor r of 2^n^ - 1, compute the residue of xr by
    multiplying the appropriate combination of residues from step (1).
    If none of these is 1, the polynomial is primitive.

The above algorithm does not assume that the polynomials are
irreducible; in fact, step (2) is always true for irreducible
polynomials. Restricting the polynomial test set to those proven to be
irreducible, as was done in this case, enables the two approaches to be
combined.

The procedure used for this analysis is as follows:

1.  Compute factors of 2^n^ -1 = 2^18^ - 1 = 262143. There are a total
    of 29 factors, excluding 1 and 262143.

2.  Eliminate all factors less than 18, i.e., 3,7,9. This can be done
    since the algorithm tests for residues and the remainder in these
    cases would be the factor itself, thus passing the condition
    outlined in step (3). A total of 26 factors remain.

3.  For each of the 26 factors, r, show that the remainder of xr divided
    by the characteristic equation, f(x), is not equal to 1. If this
    fails for any of the factors, then f(x) is not primitive. Otherwise
    f(x) is primitive and will produce a maximal length code.

Software was developed, implementing the above algorithm, and used to
test each of the irreducible polynomials in the test set for
primitiveness.