3GPP TS 45.004: Modulation

Specification: 45004

🟢Approvedv800
Rel-8
Relevance:7/10

Summary

This document specifies the modulation formats for GSM, including GMSK, 8PSK, 16QAM, and 32QAM. It defines the modulating symbol rate, symbol mapping, start and stop of the burst, differential encoding, filtering, output phase, and modulation for each format.

Specification Intelligence

This is a Technical Document in the Unknown Series series, focusing on Technical Document. The document is currently in approved by tsg and under change control and is under formal change control.

Classification

Type: Technical Document
Subject: Unknown Series
Series: 45.xxx
Target: Technical Implementers

Specifics

Status: Change Control

Version

800.0.0
Release 800
0 technical • 0 editorial

Full Document v800

3GPP TS 45.004 v. 7.3.0

Technical Specification

3rd Generation Partnership Project;

Technical Specification Group GSM/EDGE

Radio Access Network;

Modulation

(Release 8)

 

                                                                          

The present document has been developed within the 3rd Generation Partnership Project (3GPP TM) and may be further elaborated for the purposes of 3GPP.    
The present document has not been subject to any approval process by the 3GPP Organizational Partners and shall not be implemented. 
This Specification is provided for future development work within 3GPP only. The Organizational Partners accept no liability for any use of this Specification.
Specifications and reports for implementation of the 3GPP TM system should be obtained via the 3GPP Organizational Partners' Publications Offices.

 

 

 

Keywords

GSM, radio, Modulation

 

3GPP

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Valbonne - FRANCE

Tel.: +33 4 92 94 42 00 Fax: +33 4 93 65 47 16

Internet

http://www.3gpp.org

 

Copyright Notification

No part may be reproduced except as authorized by written permission.
The copyright and the foregoing restriction extend to reproduction in all media.

 

© 2008, 3GPP Organizational Partners (ARIB, ATIS, CCSA, ETSI, TTA, TTC).

All rights reserved.

 

UMTS™ is a Trade Mark of ETSI registered for the benefit of its members

3GPP™ is a Trade Mark of ETSI registered for the benefit of its Members and of the 3GPP Organizational Partners
LTE™ is a Trade Mark of ETSI currently being registered for the benefit of its Members and of the 3GPP Organizational Partners

GSM® and the GSM logo are registered and owned by the GSM Association

 

Contents

Foreword................................................................................................................................................ 4

1....... Scope........................................................................................................................................... 5

1.1.... References.................................................................................................................................... 5

1.2.... Abbreviations................................................................................................................................ 5

2....... Modulation format for GMSK........................................................................................................ 5

2.1......... Modulating symbol rate..................................................................................................................................................... 5

2.2......... Start and stop of the burst.................................................................................................................................................. 5

2.3......... Differential encoding.......................................................................................................................................................... 6

2.4......... Filtering................................................................................................................................................................................. 6

2.5......... Output phase........................................................................................................................................................................ 7

2.6......... Modulation........................................................................................................................................................................... 7

3....... Modulation format for 8PSK.......................................................................................................... 7

3.1......... Modulating symbol rate..................................................................................................................................................... 7

3.2......... Symbol mapping................................................................................................................................................................. 7

3.3......... Start and stop of the burst.................................................................................................................................................. 8

3.4......... Symbol rotation................................................................................................................................................................... 9

3.5......... Pulse shaping....................................................................................................................................................................... 9

3.6......... Modulation........................................................................................................................................................................... 9

4....... Modulation format for 16QAM and 32QAM at the normal symbol rate.......................................... 10

4.1......... Modulating symbol rate................................................................................................................................................... 10

4.2......... Symbol mapping............................................................................................................................................................... 10

4.3......... Start and stop of the burst................................................................................................................................................ 11

4.4......... Symbol rotation................................................................................................................................................................. 12

4.5......... Pulse shaping..................................................................................................................................................................... 12

4.6......... Modulation......................................................................................................................................................................... 12

5....... Modulation format for QPSK, 16QAM and 32QAM at the higher symbol rate................................ 12

5.1......... Modulating symbol rate................................................................................................................................................... 12

5.2......... Symbol mapping............................................................................................................................................................... 13

5.3......... Start and stop of the burst................................................................................................................................................ 13

5.4......... Symbol rotation................................................................................................................................................................. 13

5.5......... Pulse shaping..................................................................................................................................................................... 13

5.6......... Modulation......................................................................................................................................................................... 14

Annex A (normative):......... Tx filter coefficients for the spectrally wide pulse shape......................... 15

Annex B (informative):....... Change history....................................................................................... 16

 

This Technical Specification has been produced by the 3rd Generation Partnership Project (3GPP).

The contents of the present document are subject to continuing work within the TSG and may change following formal TSG approval. Should the TSG modify the contents of the present document, it will be re-released by the TSG with an identifying change of release date and an increase in version number as follows:

Version x.y.z

where:

x    the first digit:

1    presented to TSG for information;

2    presented to TSG for approval;

3    or greater indicates TSG approved document under change control.

y    the second digit is incremented for all changes of substance, i.e. technical enhancements, corrections, updates, etc.

z    the third digit is incremented when editorial only changes have been incorporated in the document.

The modulator receives the bits from the encryption unit, see 3GPP TS 45.001, and produces an RF signal. The filtering of the Radio Frequency (RF) signal necessary to obtain the spectral purity is not defined, neither are the tolerances associated with the theoretical filter requirements specified. These are contained in 3GPP TS 45.005.

The following documents contain provisions which, through reference in this text, constitute provisions of the present document.

·       References are either specific (identified by date of publication, edition number, version number, etc.) or non‑specific.

·       For a specific reference, subsequent revisions do not apply.

·       For a non-specific reference, the latest version applies.  In the case of a reference to a 3GPP document (including a GSM document), a non-specific reference implicitly refers to the latest version of that document in the same Release as the present document.

[1]                          3GPP TR 21.905: “Vocabulary for 3GPP Specifications”.

[2]                          3GPP TS 45.001: “Physical Layer on the Radio Path (General Description)”.

[3]                          3GPP TS 45.002: “Multiplexing and multiple access on the radio path”.

[4]                          3GPP TS 45.005: “Radio transmission and reception”.

[5]                          3GPP TS 45.010: “Radio subsystem synchronization”.

[6]                          3GPP TS 44.060: “Radio Link Control/ Medium Access Control (RLC/MAC) protocol”.

 

Abbreviations used in this specification are listed in 3GPP TR 21.905.

2.1        Modulating symbol rate

The modulating symbol rate is the normal symbol rate which is defined as 1/T = 1 625/6 ksymb/s (i.e. approximately 270.833 ksymb/s), which corresponds to 1 625/6 kbit/s (i.e. 270.833 kbit/s). T is the normal symbol period (see 3GPP TS 45.010).

2.2        Start and stop of the burst

Before the first bit of the bursts as defined in 3GPP TS 45.002 enters the modulator, the modulator has an internal state as if a modulating bit stream consisting of consecutive ones (di = 1) had entered the differential encoder. Also after the last bit of the time slot, the modulator has an internal state as if a modulating bit stream consisting of consecutive ones (di = 1) had continued to enter the differential encoder. These bits are called dummy bits and define the start and the stop of the active and the useful part of the burst as illustrated in figure 1. Nothing is specified about the actual phase of the modulator output signal outside the useful part of the burst.

Figure 1: Relation between active part of burst, tail bits and dummy bits. For the normal burst the useful part lasts for 147 modulating bits

2.3        Differential encoding

Each data value di = [0,1] is differentially encoded. The output of the differential encoder is:

                                                                      

where Å denotes modulo 2 addition.

The modulating data value ai input to the modulator is:

                                                                   

2.4        Filtering

The modulating data values ai as represented by Dirac pulses excite a linear filter with impulse response defined by:

                                                                                

where the function rect(x) is defined by:

                                                                          

                                                                          

and * means convolution. h(t) is defined by:

                                                                                 

 

where                                                            

where B is the 3 dB bandwidth of the filter with impulse response h(t). This theoretical filter is associated with tolerances defined in 3GPP TS 45.005.

2.5        Output phase

The phase of the modulated signal is:

                                                                          

where the modulating index h is 1/2 (maximum phase change in radians is p/2 per data interval).

The time reference t' = 0 is the start of the active part of the burst as shown in figure 1. This is also the start of the bit period of bit number 0 (the first tail bit) as defined in 3GPP TS 45.002.

2.6        Modulation

The modulated RF carrier, except for start and stop of the TDMA burst may therefore be expressed as:

                                                              

where Ec is the energy per modulating bit, f0 is the centre frequency and j0 is a random phase and is constant during one burst.

3.1        Modulating symbol rate

The modulating symbol rate is the normal symbol rate which is defined as 1/T = 1 625/6 ksymb/s (i.e. approximately 270.833 ksymb/s), which corresponds to 3*1 625/6 kbit/s (i.e. 812.5 kbit/s). T is the normal symbol period (see 3GPP TS 45.010).

3.2        Symbol mapping

The modulating bits are Gray mapped in groups of three to 8PSK symbols by the rule

where l is given by table 1.

Table 1: Mapping between modulating bits and the 8PSK symbol parameter l.

Modulating bits

d3i,, d3i+1, d3i+2

Symbol parameter l

(1,1,1)

0

(0,1,1)

1

(0,1,0)

2

(0,0,0)

3

(0,0,1)

4

(1,0,1)

5

(1,0,0)

6

(1,1,0)

7

 

This is illustrated in figure 2.

Figure 2: Symbol mapping of modulating bits into 8PSK symbols.

3.3        Start and stop of the burst

Before the first bit of the bursts as defined in 3GPP TS 45.002 enters the modulator, the state of the modulator is undefined. Also after the last bit of the burst, the state of the modulator is undefined. The tail bits (see 3GPP TS 45.002) define the start and the stop of the active and the useful part of the burst as illustrated in figure 3. Nothing is specified about the actual phase of the modulator output signal outside the useful part of the burst.

Figure 3: Relation between active part of burst and tail bits. For the normal burst the useful part lasts for 147 modulating symbols

 

3.4        Symbol rotation

The 8PSK symbols are continuously rotated with 3p/8 radians per symbol before pulse shaping. The rotated symbols are defined as

3.5        Pulse shaping

The modulating 8PSK symbols  as represented by Dirac pulses excite a linear pulse shaping filter. This filter is a linearised GMSK pulse, i.e. the main component in a Laurant decomposition of the GMSK modulation. The impulse response is defined by:

where

                                                           

                                                    

and

                                                                               .

The base band signal is

                                                                     

The time reference t' = 0 is the start of the active part of the burst as shown in figure 3. This is also the start of the symbol period of symbol number 0 (containing the first tail bit) as defined in 3GPP TS 45.002.

3.6        Modulation

The modulated RF carrier during the useful part of the burst is therefore:

where Es is the energy per modulating symbol, f0 is the centre frequency and j0 is a random phase and is constant during one burst.

4.1        Modulating symbol rate

The modulating symbol rate is the normal symbol rate which is defined as 1/T = 1625/6 ksymb/s (i.e. approximately 270.833 ksymb/s), which corresponds to 4*1625/6 kbit/s (i.e. approximately 1083.3 kbit/s) for 16QAM and to 5*1625/6 kbit/s (i.e. approximately 1354.2 kbit/s) for 32QAM. T is the normal symbol period (see 3GPP TS 45.010).

4.2        Symbol mapping

The modulating bits are mapped to symbols according to Table 2 for 16QAM and Table 3 for 32QAM.

Table 2: Mapping between modulating bits and 16QAM symbols.

Modulating bits

d4i, d4i+1, d4i+2, d4i+3

16QAM symbol

si

I

Q

(0,0,0,0)

(0,0,0,1)

(0,0,1,0)

(0,0,1,1)

(0,1,0,0)

(0,1,0,1)

(0,1,1,0)

(0,1,1,1)

(1,0,0,0)

(1,0,0,1)

(1,0,1,0)

(1,0,1,1)

(1,1,0,0)

(1,1,0,1)

(1,1,1,0)

(1,1,1,1)

 

 

Table 3: Mapping between modulating bits and 32QAM symbols.

Modulating bits

d5i, d5i+1, d5i+2, d5i+3, d5i+4

32QAM symbol

si

I

Q

(0,0,0,0,0)

(0,0,0,0,1)

(0,0,0,1,0)

(0,0,0,1,1)

(0,0,1,0,0)

(0,0,1,0,1)

(0,0,1,1,0)

(0,0,1,1,1)

(0,1,0,0,0)

(0,1,0,0,1)

(0,1,0,1,0)

(0,1,0,1,1)

(0,1,1,0,0)

(0,1,1,0,1)

(0,1,1,1,0)

(0,1,1,1,1)

(1,0,0,0,0)

(1,0,0,0,1)

(1,0,0,1,0)

(1,0,0,1,1)

(1,0,1,0,0)

(1,0,1,0,1)

(1,0,1,1,0)

(1,0,1,1,1)

(1,1,0,0,0)

(1,1,0,0,1)

(1,1,0,1,0)

(1,1,0,1,1)

(1,1,1,0,0)

(1,1,1,0,1)

(1,1,1,1,0)

(1,1,1,1,1)

 

4.3        Start and stop of the burst

Before the first bit of the bursts as defined in 3GPP TS 45.002 enters the modulator, the state of the modulator is undefined. Also after the last bit of the burst, the state of the modulator is undefined. The tail symbols (see 3GPP TS 45.002) define the start and the stop of the active and the useful part of the burst as illustrated in figure 4. Nothing is specified about the actual phase of the modulator output signal outside the useful part of the burst.

 

Figure 4: Relation between active part of burst and tail symbols. For the normal burst the useful part lasts for 147 modulating symbols.

4.4        Symbol rotation

The symbols are continuously rotated with φ radians per symbol before pulse shaping, where φ  = π/4 and -π/4 for 16QAM and 32QAM respectively. The rotated symbols are defined as

4.5        Pulse shaping

The modulating symbols  as represented by Dirac pulses excite a linear pulse shaping filter. This filter is the linearised GMSK pulse as defined in 3.5.

4.6        Modulation

The modulated RF carrier during the useful part of the burst is:

where y(t') is the base band signal (see 3.5),, Es is the energy per modulating symbol, f0 is the centre frequency and j0 is a random phase and is constant during one burst.

5.1        Modulating symbol rate

The modulating symbol rate is the higher symbol rate which is defined as 1/T = 325 ksymb/s, which corresponds to 650 kbit/s for QPSK, to 1300 kbit/s for 16QAM and to 1625 kbit/s for 32QAM. T is the reduced symbol period (see 3GPP TS 45.010).

5.2        Symbol mapping

The modulating bits are mapped to symbols according to Table 4 for QPSK, Table 2 for 16QAM and Table 3 for 32QAM..

Table 4: Mapping between modulating bits and QPSK symbols.

Modulating bits

d2i, d2i+1

QPSK symbol

si

I

Q

(0,0)

(0,1)

(1,0)

(1,1)

 

5.3        Start and stop of the burst

Before the first bit of the bursts as defined in 3GPP TS 45.002 enters the modulator, the state of the modulator is undefined. Also after the last bit of the burst, the state of the modulator is undefined. The tail symbols (see 3GPP TS 45.002) define the start and the stop of the active and the useful part of the burst as illustrated in figure 5. Nothing is specified about the actual phase of the modulator output signal outside the useful part of the burst.

Figure 5: Relation between active part of burst and tail symbols. For the higher symbol rate burst (see 3GPP TS 45.001) the useful part lasts for 176 modulating symbols.

5.4        Symbol rotation

The symbols are continuously rotated with φ radians per symbol before pulse shaping, where φ  = 3π/4, π/4 and -π/4 for QPSK, 16QAM and 32QAM respectively. The rotated symbols are defined as

5.5        Pulse shaping

The modulating symbols  as represented by Dirac pulses excite one of the following linear pulse shaping filters:

·       A spectrally wide pulse shape c'(t), where c'(t) is the continuous time representation of a discrete time pulse shape cn = c'((n-1)Ts), which is defined in Annex A, where Ts is the sampling period which for the purpose of the pulse shape definition, is T/16, and n = 1, 2, ..., 97.

The base band signal is

NOTE:      A closed-form expression of c'(t) is not available because the spectrally wide pulse shape was numerically optimised based on a set of discrete filter coefficients. The continuous time function can be obtained by:

- low-pass filtering the discrete time function with a pass-band of 400 kHz and a stop-band beginning at 2600 kHz and;

- truncating the duration to the time interval [0, 6T].

An example for such a low-pass filter is a raised cosine filter with the impulse response

r(t) = si(2πt•2600 kHz)•cos(2πt•2200 kHz)/(1–(4 t•2200 kHz)²)

with si(x)=sin(x)/x,

resulting in c'(t) = for 0 £ t £ 6T and c'(t) = 0 for t < 0 or t > 6T.

·       A spectrally narrow pulse shape, c0(t), which is the linearised GMSK pulse as defined in subclause 3.5 for the normal symbol period.

NOTE:      The linearised GMSK pulse is not scaled to the reduced symbol period. Hence its duration in terms of the reduced symbol period is 6T.

The base band signal is

The time reference t' = 0 is the start of the active part of the burst as shown in figure 3. This is also the start of the symbol period of symbol number 0 (containing the first tail bit) as defined in 3GPP TS 45.002.

For the uplink, the pulse shape that shall be used when transmitting a burst is dependent on the parameter 'Pulse format' that is sent during assignment (see 3GPP TS 44.060). For the downlink the spectrally narrow pulse shape shall be used.

5.6        Modulation

The modulated RF carrier during the useful part of the burst is:

where Es is the energy per modulating symbol, f0 is the centre frequency and j0 is a random phase and is constant during one burst.

For an oversampling factor of 16, i.e. 5200 ksamples/s, there are 97 Tx filter coefficients c1 to c97 for the spectrally wide pulse shape. The coefficients are symmetric to c49, i.e. c49–k = c49+k.  The coefficients of c1 to c49 are listed:

   0.00225918460000

   0.00419757900000

   0.00648420700000

   0.00931957020000

   0.01259397500000

   0.01605878900000

   0.01959156100000

   0.02292214900000

   0.02570190500000

   0.02767928100000

   0.02852115300000

   0.02791904300000

   0.02568913000000

   0.02166792700000

   0.01579963100000

   0.00821077000000

  -0.00089211394000

  -0.01114601700000

  -0.02201830600000

  -0.03289439200000

  -0.04302811700000

  -0.05156392200000

  -0.05764086800000

  -0.06034025400000

  -0.05876224400000

  -0.05209962100000

  -0.03961692000000

  -0.02072323500000

   0.00496039200000

   0.03765364500000

   0.07732192300000

   0.12369249000000

   0.17639444000000

   0.23478700000000

   0.29768326000000

   0.36418213000000

   0.43311409000000

   0.50316152000000

   0.57298225000000

   0.64120681000000

   0.70645485000000

   0.76744762000000

   0.82295721000000

   0.87187027000000

   0.91325439000000

   0.94628290000000

   0.97030623000000

   0.98493838000000

   0.99006899000000

 

 

SMG#

SPEC

VERS

NEW_VERS

PHASE

SUBJECT

S27

05.04

5.0.1

6.0.0 (Ph.2)

R97

Conversion to Release 97 EN

S28

05.04

6.0.0

8.0.0

R99

Introduction of 8PSK for EDGE

S30b

05.04

8.0.0

8.1.0

R99

Correction of mistake for range alpha-sub-i in Clause 2.3

 

 

8.1.0

8.1.1

 

Figure 3 replaced (as it was corrupted)

G03

05.04

8.1.1

8.2.0

R99

Correction of symbol period notation

G04

45.004

8.2.0

4.0.0

Rel-4

New version for Release 4

G05

45.004

4.0.0

4.1.0

Rel-4

Correction of Timing Alignment for GMSK and 8-PSK Signals

 

 

Change history

Date

TSG #

TSG Doc.

CR

Rev

Subject/Comment

Old

New

2001-11

07

GP-012359

002

 

Correction of tail bits for 8PSK normal burst

4.1.0

4.2.0

2001-11

07

GP-012372

004

 

Correction of references to relevant 3GPP TSs

4.1.0

4.2.0

2001-11

07

GP-012360

003

 

Correction of tail bits for 8PSK normal burst

4.2.0

5.0.0

2002-06

10

GP-021436

005

 

Corrections and clean up

5.0.0

5.1.0

2003-09

 

 

 

 

Correction of wrong Release number in the front page

5.1.0

5.1.1

 

 

 

 

 

 

 

 

2005-01

23

 

 

 

Version for Release 6

5.1.1

6.0.0

2007-08

35

GP-071544

0006

2

Introduction of QPSK, 16QAM and 32QAM for RED HOT and HUGE

6.0.0

7.0.0

2007-11

36

GP-072015

0008

 

Spectrally wide pulse shape for HUGE B

7.0.0

7.1.0

2008-02

37

GP-080105

0009

 

Spectrally wide pulse shape for HUGE B

7.1.0

7.2.0

2008-08

39

GP-081068

0010

 

Correction of modulating bit rate for 32QAM at the higher symbol rate

7.2.0

7.3.0

2008-12

40

 

 

 

Version for Release 8

7.3.0

8.0.0

 

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Technical Details

AI Classification

Category: 7. Testování a interoperabilita
Subcategory: 7.1 Conformance Testing
Function: Test specification

Version Information

Release: Rel-8
Version: 800
Series: 45_series
Published: 2008-12

Document Info

Type: Technical Specification
TSG: GSM/EDGE

Keywords & Refs

Keywords:
MACGSMRLC

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Contributors:
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File: 45004-800
Processed: 2025-06-22

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