ETSI TS V ( )

Transcription

1 TS V ( ) TECHNICAL SPECIFICATION Dgtal cellular telecommuncatons system (Phase 2+) (GSM); GSM/EDGE Modulaton (3GPP TS verson Release 15) GLOBAL SYSTEM FOR MOBILE COMMUNICATIONS R

2 3GPP TS verson Release 15 1 TS V ( ) Reference RTS/TSGR vf00 Keywords GSM 650 Route des Lucoles F Sopha Antpols Cedex - FRANCE Tel.: Fax: Sret N NAF 742 C Assocaton à but non lucratf enregstrée à la Sous-Préfecture de Grasse (06) N 7803/88 Important notce The present document can be downloaded from: The present document may be made avalable n electronc versons and/or n prnt. The content of any electronc and/or prnt versons of the present document shall not be modfed wthout the pror wrtten authorzaton of. In case of any exstng or perceved dfference n contents between such versons and/or n prnt, the only prevalng document s the prnt of the Portable Document Format (PDF) verson kept on a specfc network drve wthn Secretarat. Users of the present document should be aware that the document may be subject to revson or change of status. Informaton on the current status of ths and other documents s avalable at If you fnd errors n the present document, please send your comment to one of the followng servces: Copyrght Notfcaton No part may be reproduced or utlzed n any form or by any means, electronc or mechancal, ncludng photocopyng and mcroflm except as authorzed by wrtten permsson of. The content of the PDF verson shall not be modfed wthout the wrtten authorzaton of. The copyrght and the foregong restrcton extend to reproducton n all meda All rghts reserved. DECT TM, PLUGTESTS TM, UMTS TM and the logo are trademarks of regstered for the beneft of ts Members. 3GPP TM and LTE TM are trademarks of regstered for the beneft of ts Members and of the 3GPP Organzatonal Partners. onem2m logo s protected for the beneft of ts Members. GSM and the GSM logo are trademarks regstered and owned by the GSM Assocaton.

3 3GPP TS verson Release 15 2 TS V ( ) Intellectual Property Rghts Essental patents IPRs essental or potentally essental to normatve delverables may have been declared to. The nformaton pertanng to these essental IPRs, f any, s publcly avalable for members and non-members, and can be found n SR : "Intellectual Property Rghts (IPRs); Essental, or potentally Essental, IPRs notfed to n respect of standards", whch s avalable from the Secretarat. Latest updates are avalable on the Web server ( Pursuant to the IPR Polcy, no nvestgaton, ncludng IPR searches, has been carred out by. No guarantee can be gven as to the exstence of other IPRs not referenced n SR (or the updates on the Web server) whch are, or may be, or may become, essental to the present document. Trademarks The present document may nclude trademarks and/or tradenames whch are asserted and/or regstered by ther owners. clams no ownershp of these except for any whch are ndcated as beng the property of, and conveys no rght to use or reproduce any trademark and/or tradename. Menton of those trademarks n the present document does not consttute an endorsement by of products, servces or organzatons assocated wth those trademarks. Foreword Ths Techncal Specfcaton (TS) has been produced by 3rd Generaton Partnershp Project (3GPP). The present document may refer to techncal specfcatons or reports usng ther 3GPP denttes, UMTS denttes or GSM denttes. These should be nterpreted as beng references to the correspondng delverables. The cross reference between GSM, UMTS, 3GPP and denttes can be found under Modal verbs termnology In the present document "shall", "shall not", "should", "should not", "may", "need not", "wll", "wll not", "can" and "cannot" are to be nterpreted as descrbed n clause 3.2 of the Draftng Rules (Verbal forms for the expresson of provsons). "must" and "must not" are NOT allowed n delverables except when used n drect ctaton.

4 3GPP TS verson Release 15 3 TS V ( ) Contents Intellectual Property Rghts... 2 Foreword... 2 Modal verbs termnology... 2 Foreword Scope References Abbrevatons Modulaton format for GMSK Modulatng symbol rate Start and stop of the burst Dfferental encodng Flterng Output phase Modulaton Overlad CDMA Modulaton format for 8PSK Modulatng symbol rate Symbol mappng Start and stop of the burst Symbol rotaton Pulse shapng Modulaton Modulaton format for 16QAM and 32QAM at the normal symbol rate Modulatng symbol rate Symbol mappng Start and stop of the burst Symbol rotaton Pulse shapng Modulaton Modulaton format for QPSK, 16QAM and 32QAM at the hgher symbol rate Modulatng symbol rate Symbol mappng Start and stop of the burst Symbol rotaton Pulse shapng Modulaton Modulaton format for AQPSK Modulatng symbol rate Symbol mappng Start and stop of the burst Symbol rotaton Pulse shapng Modulaton Annex A (normatve): Annex B (nformatve): Tx flter coeffcents for the spectrally wde pulse shape Change hstory Hstory... 20

5 3GPP TS verson Release 15 4 TS V ( ) Foreword Ths Techncal Specfcaton has been produced by the 3 rd Generaton Partnershp Project (3GPP). The contents of the present document are subject to contnung work wthn the TSG and may change followng formal TSG approval. Should the TSG modfy the contents of the present document, t wll be re-released by the TSG wth an dentfyng change of release date and an ncrease n verson number as follows: Verson x.y.z where: x the frst dgt: 1 presented to TSG for nformaton; 2 presented to TSG for approval; 3 or greater ndcates TSG approved document under change control. y the second dgt s ncremented for all changes of substance,.e. techncal enhancements, correctons, updates, etc. z the thrd dgt s ncremented when edtoral only changes have been ncorporated n the document.

6 3GPP TS verson Release 15 5 TS V ( ) 1 Scope The modulator receves the bts from the encrypton unt, see 3GPP TS , and produces an RF sgnal. The flterng of the Rado Frequency (RF) sgnal necessary to obtan the spectral purty s not defned, nether are the tolerances assocated wth the theoretcal flter requrements specfed. These are contaned n 3GPP TS References The followng documents contan provsons whch, through reference n ths text, consttute provsons of the present document. - References are ether specfc (dentfed by date of publcaton, edton number, verson number, etc.) or non-specfc. - For a specfc reference, subsequent revsons do not apply. - For a non-specfc reference, the latest verson apples. In the case of a reference to a 3GPP document (ncludng a GSM document), a non-specfc reference mplctly refers to the latest verson of that document n the same Release as the present document. [1] 3GPP TR : "Vocabulary for 3GPP Specfcatons". [2] 3GPP TS : "Physcal Layer on the Rado Path (General Descrpton)". [3] 3GPP TS : "Multplexng and multple access on the rado path". [4] 3GPP TS : "Rado transmsson and recepton". [5] 3GPP TS : "Rado subsystem synchronzaton". [6] 3GPP TS : "Rado Lnk Control/ Medum Access Control (RLC/MAC) protocol". [7] 3GPP TS : "General Packet Rado Servce (GPRS)". [8] 3GPP TS : "Channel Codng". 1.2 Abbrevatons Abbrevatons used n ths specfcaton are lsted n 3GPP TR In addton to abbrevatons n 3GPP TR the followng abbrevaton apply: AQPSK EC ESAB Adaptve Quadrature Phase Shft Keyng Extended Coverage Extended Synchronzaton Access Burst 2 Modulaton format for GMSK 2.1 Modulatng symbol rate The modulatng symbol rate s the normal symbol rate whch s defned as 1/T = 1 625/6 ksymb/s (.e. approxmately ksymb/s), whch corresponds to 1 625/6 kbt/s (.e kbt/s). T s the normal symbol perod (see 3GPP TS ).

7 3GPP TS verson Release 15 6 TS V ( ) 2.2 Start and stop of the burst Before the frst bt of the bursts as defned n 3GPP TS enters the modulator, the modulator has an nternal state as f a modulatng bt stream consstng of consecutve ones (d = 1) had entered the dfferental encoder. Also after the last bt of the tme slot, the modulator has an nternal state as f a modulatng bt stream consstng of consecutve ones (d = 1) had contnued to enter the dfferental encoder. These bts are called dummy bts and defne the start and the stop of the actve and the useful part of the burst as llustrated n fgure 1. Nothng s specfed about the actual phase of the modulator output sgnal outsde the useful part of the burst. In case of EC operaton, the phase durng the useful part of contguous bursts, belongng to the same blnd physcal layer transmssons wthn a TDMA frame, has a fxed relaton, see subclauses 2.6 and 2.7. dummy bts tal bts 3 tal bts dummy bts Output phase The useful part 1/2 bt 1/2 bt The actve part Fgure 1: Relaton between actve part of burst, tal bts and dummy bts. For the normal burst the useful part lasts for 147 modulatng bts 2.3 Dfferental encodng Each data value d = [0,1] s dfferentally encoded. The output of the dfferental encoder s: where denotes modulo 2 addton. The modulatng data value α nput to the modulator s: $ d = d d ( d {, }) Flterng $ α = 1 2d ( α { 1, + 1}) The modulatng data values α as represented by Drac pulses excte a lnear flter wth mpulse response defned by: t g() t = h()* t rect T ¹ where the functon rect(x) s defned by: t 1 T rect = for t < T¹ T 2

8 3GPP TS verson Release 15 7 TS V ( ) t rect = 0 T ¹ otherwse and * means convoluton. h(t) s defned by: ht () = 2 t exp 2 2 2δ T ¹ ( 2π). δt where ln( 2) δ = and BT = 03. 2πBT where B s the 3 db bandwdth of the flter wth mpulse response h(t). Ths theoretcal flter s assocated wth tolerances defned n 3GPP TS Output phase The phase of the modulated sgnal s: t' T ϕ(') t απh g( u) du = where the modulatng ndex h s 1/2 (maxmum phase change n radans s π/2 per data nterval). The tme reference t' = 0 s the start of the actve part of the burst as shown n fgure 1. Ths s also the start of the bt perod of bt number 0 (the frst tal bt) as defned n 3GPP TS Modulaton The modulated RF carrer, except for start and stop of the TDMA burst or ESAB (see 3GPP TS [3]) may therefore be expressed as: 2E xt (') = c. cos( 2π f0t' + ϕ(') t + ϕ 0) T where E c s the energy per modulatng bt, f 0 s the centre frequency and ϕ 0 s a random phase and s constant durng one burst or ESAB (see 3GPP TS [3]). In case of EC operaton when usng blnd physcal layer transmssons (see 3GPP TS [7]) the modulated RF carrer, except for start and stop of the burst may, for each blnd physcal layer transmsson of a burst for whch phase and ampltude coherency s requred (see 3GPP TS [4]), be expressed as: where 2Ec x( t') =. cos(2π f0( t' + t0 ) + ϕ( t') + ϕ157 + ϕ0 ) T - t 0 s a burst-specfc tme offset, constant durng one burst, and s defned as the tme dfference between tme nstant t' = 0 for the current burst and t' = 0 for the frst transmsson of the same burst n the current TDMA frame. - ϕ 157 s a phase shft of ether 0 or h, and s constant durng one burst.

9 3GPP TS verson Release 15 8 TS V ( ) - ϕ 0 s a random phase and s constant durng all blnd physcal layer transmssons of the same burst wthn the same TDMA frame. For EC-GSM_IoT, only nteger tmeslot lengths are allowed (see 3GPP TS [5]). If any blnd physcal layer transmsson s transmtted n the uplnk on tmeslot 0 or tmeslot 4, whch are 157 symbols long, all followng blnd physcal layer transmssons of the same burst n that TDMA frame shall be shfted n phase by h,.e. ϕ 157 = h, otherwse ϕ 157 = 0. For the downlnk ths phase shft shall not be appled,.e. ϕ 157 = Overlad CDMA In the case of Overlad CDMA the modulated RF carrer may be expressed wth an addtonal term compared to subclause 2.6 representng the Overlad CDMA code: 2Ec x( t') =. cos(2π f ( t' + t0 ) + ϕ( t') + ϕ157 + ϕ0 + OC T 0 π ) where OC equals 0 or 1 n accordance wth the appled Overlad CDMA code (see 3GPP TS [3]) and s constant durng one burst. For each blnd physcal layer transmsson wthn a TDMA frame, OC equals ts respectve Overlad CDMA code element. For example for Overlad CDMA code 0,0,1,1, OC equals 0 for the frst two blnd physcal layer transmssons and 1 for the last two blnd physcal layer transmssons wthn a TDMA frame. NOTE: If the blnd physcal layer transmssons wthn a TDMA frame are contnuously modulated, a phase shft of π between two bursts can be well approxmated by nvertng all the bts of the second burst, ncludng three to fve guard bts precedng and followng the tal bts, respectvely. 3 Modulaton format for 8PSK 3.1 Modulatng symbol rate The modulatng symbol rate s the normal symbol rate whch s defned as 1/T = 1 625/6 ksymb/s (.e. approxmately ksymb/s), whch corresponds to 3*1 625/6 kbt/s (.e kbt/s). T s the normal symbol perod (see 3GPP TS ). 3.2 Symbol mappng The modulatng bts are Gray mapped n groups of three to 8PSK symbols by the rule where l s gven by table 1. s = e j 2πl / 8 Table 1: Mappng between modulatng bts and the 8PSK symbol parameter l. Modulatng bts Symbol parameter l d 3,, d 3+1, d 3+2 (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 Ths s llustrated n fgure 2.

10 3GPP TS verson Release 15 9 TS V ( ) Q (d 3, d 3+1, d 3+2 )= (0,0,0) (0,0,1) (1,0,1) (0,1,0) (0,1,1) (1,1,1) (1,1,0) (1,0,0) I Fgure 2: Symbol mappng of modulatng bts nto 8PSK symbols. 3.3 Start and stop of the burst Before the frst bt of the bursts as defned n 3GPP TS enters the modulator, the state of the modulator s undefned. Also after the last bt of the burst, the state of the modulator s undefned. The tal bts (see 3GPP TS ) defne the start and the stop of the actve and the useful part of the burst as llustrated n fgure 3. Nothng s specfed about the actual phase of the modulator output sgnal outsde the useful part of the burst. 9 tal bts 9 tal bts Output phase The useful part 1/2 symbol 1/2 symbol The actve part Fgure 3: Relaton between actve part of burst and tal bts. For the normal burst the useful part lasts for 147 modulatng symbols 3.4 Symbol rotaton The 8PSK symbols are contnuously rotated wth 3π/8 radans per symbol before pulse shapng. The rotated symbols are defned as sˆ = s e j3π / Pulse shapng The modulatng 8PSK symbols ŝ as represented by Drac pulses excte a lnear pulse shapng flter. Ths flter s a lnearsed GMSK pulse,.e. the man component n a Laurant decomposton of the GMSK modulaton. The mpulse response s defned by:

11 3GPP TS verson Release TS V ( ) 3 + = S( t T ), for 0 t 5T c0 ( t) = 0 0, else where S( t) t sn( π g( t ) dt ), for 0 0 t 4T π = sn( π g( t ) dt ), for 2 0 0, else t 4T 4T < t 8T 1 t 5T /2 t g( t) = Q(2π 0.3 ) Q(2π 0.3 2T T loge (2) T 3T /2 ) log (2) e ¹ and Q t) τ = e 2π t ( dτ. The base band sgnal s y ( t' ) = sˆ c0 ( t' T + 2T ) The tme reference t' = 0 s the start of the actve part of the burst as shown n fgure 3. Ths s also the start of the symbol perod of symbol number 0 (contanng the frst tal bt) as defned n 3GPP TS Modulaton The modulated RF carrer durng the useful part of the burst s therefore: x ( t') = 2E T s Re j( 2π f0t' +ϕ0 ) [ y( t') e ] where E s s the energy per modulatng symbol, f 0 s the centre frequency and ϕ 0 s a random phase and s constant durng one burst. 4 Modulaton format for 16QAM and 32QAM at the normal symbol rate 4.1 Modulatng symbol rate The modulatng symbol rate s the normal symbol rate whch s defned as 1/T = 1625/6 ksymb/s (.e. approxmately ksymb/s), whch corresponds to 4*1625/6 kbt/s (.e. approxmately kbt/s) for 16QAM and to 5*1625/6 kbt/s (.e. approxmately kbt/s) for 32QAM. T s the normal symbol perod (see 3GPP TS ). 4.2 Symbol mappng The modulatng bts are mapped to symbols accordng to Table 2 for 16QAM and Table 3 for 32QAM.

12 3GPP TS verson Release TS V ( ) Table 2: Mappng between modulatng bts and 16QAM symbols. Modulatng bts d 4, d 4+1, d 4+2, d QAM symbol s 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)

13 3GPP TS verson Release TS V ( ) Table 3: Mappng between modulatng bts and 32QAM symbols. Modulatng bts d 5, d 5+1, d 5+2, d 5+3, d QAM symbol s 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) Start and stop of the burst Before the frst bt of the bursts as defned n 3GPP TS enters the modulator, the state of the modulator s undefned. Also after the last bt of the burst, the state of the modulator s undefned. The tal symbols (see 3GPP TS ) defne the start and the stop of the actve and the useful part of the burst as llustrated n fgure 4. Nothng s specfed about the actual phase of the modulator output sgnal outsde the useful part of the burst.

14 3GPP TS verson Release TS V ( ) Fgure 4: Relaton between actve part of burst and tal symbols. For the normal burst the useful part lasts for 147 modulatng symbols. 4.4 Symbol rotaton The symbols are contnuously rotated wth radans per symbol before pulse shapng, where = /4 and - /4 for 16QAM and 32QAM respectvely. The rotated symbols are defned as 4.5 Pulse shapng sˆ = s e The modulatng symbols ŝ as represented by Drac pulses excte a lnear pulse shapng flter. Ths flter s the lnearsed GMSK pulse as defned n Modulaton The modulated RF carrer durng the useful part of the burst s: jϕ x ( t') = 2E T s Re j( 2π f0t' +ϕ0 ) [ y( t') e ] where y(t') s the base band sgnal (see 3.5),, E s s the energy per modulatng symbol, f 0 s the centre frequency and ϕ 0 s a random phase and s constant durng one burst. 5 Modulaton format for QPSK, 16QAM and 32QAM at the hgher symbol rate 5.1 Modulatng symbol rate The modulatng symbol rate s the hgher symbol rate whch s defned as 1/T = 325 ksymb/s, whch corresponds to 650 kbt/s for QPSK, to 1300 kbt/s for 16QAM and to 1625 kbt/s for 32QAM. T s the reduced symbol perod (see 3GPP TS ). 5.2 Symbol mappng The modulatng bts are mapped to symbols accordng to Table 4 for QPSK, Table 2 for 16QAM and Table 3 for 32QAM..

15 3GPP TS verson Release TS V ( ) Table 4: Mappng between modulatng bts and QPSK symbols. Modulatng bts d 2, d 2+1 QPSK symbol s I Q (0,0) (0,1) (1,0) (1,1) Start and stop of the burst Before the frst bt of the bursts as defned n 3GPP TS enters the modulator, the state of the modulator s undefned. Also after the last bt of the burst, the state of the modulator s undefned. The tal symbols (see 3GPP TS ) defne the start and the stop of the actve and the useful part of the burst as llustrated n fgure 5. Nothng s specfed about the actual phase of the modulator output sgnal outsde the useful part of the burst. Fgure 5: Relaton between actve part of burst and tal symbols. For the hgher symbol rate burst (see 3GPP TS ) the useful part lasts for 176 modulatng symbols. 5.4 Symbol rotaton The symbols are contnuously rotated wth radans per symbol before pulse shapng, where = 3 /4, /4 and - /4 for QPSK, 16QAM and 32QAM respectvely. The rotated symbols are defned as 5.5 Pulse shapng sˆ = s e The modulatng symbols ŝ as represented by Drac pulses excte one of the followng lnear pulse shapng flters: - A spectrally wde pulse shape c'(t), where c'(t) s the contnuous tme representaton of a dscrete tme pulse shape c n = c'((n-1)t s), whch s defned n Annex A, where T s s the samplng perod whch for the purpose of the pulse shape defnton, s T/16, and n = 1, 2,..., 97. The base band sgnal s jϕ y ( t' ) = sˆ c' ( t' T + 2.5T ) NOTE: A closed-form expresson of c'(t) s not avalable because the spectrally wde pulse shape was numercally optmsed based on a set of dscrete flter coeffcents. The contnuous tme functon can be obtaned by:

16 3GPP TS verson Release TS V ( ) - low-pass flterng the dscrete tme functon wth a pass-band of 400 khz and a stop-band begnnng at 2600 khz and; - truncatng the duraton to the tme nterval [0, 6T]. An example for such a low-pass flter s a rased cosne flter wth the mpulse response r(t) = s(2 t 2600 khz) cos(2 t 2200 khz)/(1 (4 t 2200 khz)²) wth s(x)=sn(x)/x, 97 resultng n c'(t) = c r( t ( n 1) T ) n n= 1 s for 0 t 6T and c'(t) = 0 for t < 0 or t > 6T. - A spectrally narrow pulse shape, c 0(t), whch s the lnearsed GMSK pulse as defned n subclause 3.5 for the normal symbol perod. NOTE: The lnearsed GMSK pulse s not scaled to the reduced symbol perod. Hence ts duraton n terms of the reduced symbol perod s 6T. The base band sgnal s y ( t' ) = sˆ c0 ( t' T + 2.5T ) The tme reference t' = 0 s the start of the actve part of the burst as shown n fgure 3. Ths s also the start of the symbol perod of symbol number 0 (contanng the frst tal bt) as defned n 3GPP TS For the uplnk, the pulse shape that shall be used when transmttng a burst s dependent on the parameter 'Pulse format' that s sent durng assgnment (see 3GPP TS ). For the downlnk the spectrally narrow pulse shape shall be used. 5.6 Modulaton The modulated RF carrer durng the useful part of the burst s: x ( t') = 2E T s Re j( 2π f0t' +ϕ0 ) [ y( t') e ] where E s s the energy per modulatng symbol, f 0 s the centre frequency and ϕ 0 s a random phase and s constant durng one burst. 6 Modulaton format for AQPSK 6.1 Modulatng symbol rate The modulatng symbol rate s the normal symbol rate whch s defned as 1/T = 1 625/6 ksymb/s (.e. approxmately 270,833 ksymb/s), whch corresponds to 2*1 625/6 kbt/s (.e. 541,666 kbt/s). T s the normal symbol perod (see 3GPP TS ). 6.2 Symbol mappng The modulatng bts are mapped to the quaternary symbols accordng to Table 5.

17 3GPP TS verson Release TS V ( ) Table 5: Mappng between modulatng bts and quaternary symbols. Modulatng bts for a, b AQPSK symbol n polar notaton s (0,0) jα e (0,1) jα e (1,0) jα e (1,1) jα e Ths s llustrated n Fgure 5. α α Fgure 5: Mappng of modulatng bts to AQPSK symbols The rato of power between the Q and I channels s defned as the Subchannel Power Imbalance Rato (SCPIR). The value of the SCPIR s gven by SCPIR 20 log10 ( tan( α ))db =. The value of α shall be chosen such that SCPIR 10dB. 6.3 Start and stop of the burst Before the frst bt of the burst as defned n 3GPP TS enters the modulator, the state of the modulator s undefned. Also after the last bt of the burst, the state of the modulator s undefned. The tal symbols (see 3GPP TS ) defne the start and the stop of the actve and the useful part of the burst as llustrated n Fgure 6. Nothng s specfed about the actual phase of the modulator output sgnal outsde the useful part of the burst.

18 3GPP TS verson Release TS V ( ) Fgure 6: Relaton between actve part of burst and tal symbols. For the normal burst (see 3GPP TS ) the useful part lasts for 147 modulatng symbols. 6.4 Symbol rotaton The symbols are contnuously rotated wth radans per symbol before pulse shapng, where = /2. The rotated symbols are defned as sˆ = s e jϕ 6.5 Pulse shapng The modulatng symbols ŝ as represented by Drac pulses excte the followng lnear pulse shapng flter: c0(t), whch s the lnearsed GMSK pulse as defned n subclause 3.5 for the normal symbol perod. The base band sgnal s y ( t' ) = sˆ c0 ( t' T + 2T ) The tme reference t' = 0 s the start of the actve part of the burst as shown n fgure 6. Ths s also the start of the symbol perod of symbol number 0 (contanng the frst tal bt) as defned n 3GPP TS Modulaton The modulated RF carrer durng the useful part of the burst s: x ( t') = 2E T s Re j( 2π f0t' +ϕ0 ) [ y( t') e ] where E s s the energy per modulatng symbol, f 0 s the centre frequency and ϕ 0 s a random phase and s constant durng one burst.

19 3GPP TS verson Release TS V ( ) Annex A (normatve): Tx flter coeffcents for the spectrally wde pulse shape For an oversamplng factor of 16,.e ksamples/s, there are 97 Tx flter coeffcents c 1 to c 97 for the spectrally wde pulse shape. The coeffcents are symmetrc to c 49,.e. c 49 k = c 49+k. The coeffcents of c 1 to c 49 are lsted:

20 3GPP TS verson Release TS V ( ) Annex B (nformatve): Change hstory SMG SPEC VERS NEW_VE PHA SUBJECT S R97 Converson to Release 97 EN S R99 Introducton of 8PSK for EDGE S30b R99 Correcton of mstake for range alpha-sub- n Clause Fgure 3 replaced (as t was corrupted) G R99 Correcton of symbol perod notaton G Rel-4 New verson for Release 4 G Rel-4 Correcton of Tmng Algnment for GMSK and 8-PSK Sgnals Change hstory Date TSG # TSG Doc. CR Rev Subject/Comment Old New GP Correcton of tal bts for 8PSK normal burst GP Correcton of references to relevant 3GPP TSs GP Correcton of tal bts for 8PSK normal burst GP Correctons and clean up Correcton of wrong Release number n the front page Verson for Release GP Introducton of QPSK, 16QAM and 32QAM for RED HOT and HUGE GP Spectrally wde pulse shape for HUGE B GP Spectrally wde pulse shape for HUGE B GP Correcton of modulatng bt rate for 32QAM at the hgher symbol rate Verson for Release Verson for Release GP Introducton of VAMOS modulaton Verson for Release Verson for Release Verson for Release 12 (frozen at SP-65) Verson for Release 13 (frozen at SP-70) GP Introducton of EC-EGPRS GP Correctons to Overlad CDMA Change hstory Date Meetng TDoc CR Rev Cat Subject/Comment New verson GP F Clarfcatons and mscellaneous correctons to EC-GSM IoT (ncludng name change) RP F Correctons to EC-GSM-IoT RP F Correcton to Overlad CDMA realsaton Release 14 verson (frozen at TSG-75) RP B Introducton of ESAB Release 15 verson (frozen at TSG-80)

21 3GPP TS verson Release TS V ( ) Hstory V July 2018 Publcaton Document hstory