Digital modulation and mobile radio. Refresher topic

Transcription

1 igial modulaion and mobile radio Refresher opic

2 igial modulaion and mobile radio When speech is ransmied using digial mobile radio, i is firs of all digiized and hen source- and channel-coded. On he one hand, his ensures ha he daa sream from he source coders has a considerably lower bi rae han he original daa signal and, on he oher, channel coding provides addiional error conrol for ransmissions via he radio channel. The channel-coded daa sream is a sequence of burss which are ransmied using a combined FM/ TM mehod. The modulaion echniques used mus be ailored o he radio channel. Our new refresher opic describes how he informaion o be ransmied is modulaed ono an RF carrier and recovered in he receiver wih special reference o GSM neworks. ue o he naure of he opic, he fundamenal relaionships will be expressed mahemaically using complex numbers where necessary. Rohde & Schwarz has special experise in he field of digial mobile radio. We are involved in an exensive range of aciviies from consulaion on various echnical commiees, in paricular he earlier Groupe Spécial Mobile, which gave is name o he European GSM nework, hrough he developmen of a complee range of es equipmen and sysems o he provision of a wide range of sysem simulaors. Rohde & Schwarz also organizes raining courses ranging from he pracical o he heoreical which are specially ailored o he needs of nework operaors and sysem users. This was he saring poin for his refresher opic. bi T bi. The opposie is an RZ signal (reurn o zero) which only has a non-zero value for a fracion of T bi, for example T bi /, and goes o 0 for he res of he ime. Eiher signal can be unipolar or bipolar. If hey are unipolar, one of he wo logical symbols is represened by a finie (posiive or negaive) volage, he oher by 0 V. Bipolar signals represen he wo logical symbols by volages wih opposie polariies. The sequence a(n) is mapped digially ono he baseband signals. Firs of all, he sequence a(n) is replaced by a sequence of weighed irac dela funcions a(n) δ(nt) {0;}. To produce a unipolar NRZ signal, his sequence is fed ino an inerpolaion filer wih he ransfer funcion: Modulaing signals and RF carriers Iniially he informaion o be ransmied is in he form of a sequence a(n) comprising elemens from he se a {0; }. The modulaor convers his sequence of logical ones and zeros ino a sequence of analog signals which are suiable for ransmission. The conversion of his sequence ino volages in he baseband is referred o as baseband modulaion and he conversion of hese baseband signals ino RF signals is ermed RF carrier modulaion. In general a block of k bis from he sequence a(n) can be represened by one of he M = k possible saes of he baseband signal. For example a block comprising one bi can be represened by one of wo volages, 0 or 5 V, or by one of wo RF frequencies, f + f or f f. block comprising wo bis (a dibi) can be represened by one of four volages or by one of four frequencies and so on. The saes of he baseband signal and he RF signal can be expressed in an even more general form as signals u i and s i respecively. These signals do no necessarily have o remain consan over he duraion of a bi. This means ha digial modulaion is simply he process of selecing one of he M = k possible baseband or RF signals and assigning his signal o a block of k bis. This procedure is referred o as M-ary modulaion (FIG ).. Baseband modulaion n NRZ signal (non reurn o zero) is a signal ha remains a a consan, non-zero value over he duraion of a Modulaor wih 6 RF oupu signals FIG M-ary modulaion (here M = 6) sin f T H(f) = = si( f T) f T or wih he impulse response h = (a) T for T T (sin x/x lowpass filer) 0 elsewhere (b) To generae a bipolar signal, 0.5 is added before filering and he sum signal [(a(n) 0.5) δ(nt)] { 0.5; +0.5} is muliplied by. / conversion (FIG ) is hen performed afer digial filering. However, he NRZ signals generaed in his way are no bandlimied and, heoreically, would give rise o an infiniely wide RF specrum afer carrier modulaion. The sin x/x lowpass filer is, herefore, replaced by a lowpass ha provides more effecive bandlimiing (eg wih a cos rolloff or Gaussian ransfer funcion). fer / conversion he sampling frequency from he digial secion sill has o be removed from he modulaing signal by means of an analog lowpass.

3 Oversampling Oupu signal of sin x/x lowpass filer igial filer needs o be known is how he communicaion channel affecs he envelope of hese wo componens. Inroducing he complex envelope of he complex signal: Oupu signal of lowpass wih Nyquis edge FIG Generaing baseband signals s = e jϕ e jf c, (4) which is relaed o he real RF signal by s = Re[ e jϕ e jf c ] (5) is a good way of doing his.. escripion of RF signal The expression s = l E bi /T bi a cos[f c +ϕ] () represens he RF signal as a real funcion, where E bi is he energy ransmied per bi. Consequenly l E bi /T bi is he volage drop across a - Ω resisor. The erm a gives he ampliude as a funcion of ime, f c he carrier frequency as a funcion of ime and ϕ he insananeous phase. To simplify he noaion, he expression l E bi /T bi a is ofen replaced by or, if a is consan, by ; s is also referred o as he bandpass signal provided is bandwidh is small in comparison wih he carrier frequency f c. case for neworks using modulaion echniques based on he GSM sandard (GSM sands for Groupe Spécial Mobile or Global Sysem for Mobile Communicaions). They can also be hough of as double-sideband ampliude-modulaed RF signals wih suppressed carrier. The modulaing signals are funcions such as cos[ϕ] and sin[ϕ] for example. To deermine he degree o which he signal is disored as i passes hrough he communicaion channel, all ha The complex envelope, which is also referred o as he equivalen baseband signal, hen has he form: u = l Ebi /T e jϕ = cos[ϕ] + j sin[ϕ]. (6) The similariy beween he complex envelopes and he I/Q represenaion of he real signal is sriking. The RF signal can also be described in erms of is I and Q componens (inphase and quadraure). They are: s I = cos[ϕ] cos(f c ) and s Q = sin[ϕ] [ sin(f c )] (3) wih s = cos[f c + ϕ] = s I + s Q. This ype of represenaion, which is of course also valid for unmodulaed RF signals, makes i a lo easier o undersand modulaor operaion. The ampliudes of he wo modulaed I/Q componens are funcions of ime even when = = cons. or a =, in oher words even when he RF signal has a consan envelope as is he igial Radiocommunicaion Teser CM65 for GSM, PCN, PCS and ECT mobile phones 3

4 Basic modulaion echniques The ampliude, frequency and/or phase of he RF or baseband signal described by equaions () o (6) are modified by he daa signal so ha he informaion i represen is impressed on he RF signal. The erms M-ary ampliude, frequency or phase modulaion are used o indicae which parameer is varied o represen he informaion. The erm keying is used for digial modulaion. The abbreviaions SK for ampliude-shif keying, FSK for frequency-shif keying and PSK for phase-shif keying are widely used inernaionally. Sraigh SK has ceased o have any significance in pracice, bu FSK and PSK are widely used in heir binary and M-ary forms. Wih M-ary PSK, he upper limi for M is 8 because noise suscepibiliy rises disproporionally as M increases. combinaion of SK and PSK is used for M >8. This leads o M-ary quadraure ampliude modulaion (QM). In his case he carrier can assume M saes or, as has already been explained, here exiss a se of M ime-domain signals, each of which represens a digial word ld(m) bis in lengh (ld = logs o base ). The acual modulaion process involves muliplying an RF carrier of he form cos[(f c + ϕ], which can also be expressed in complex form as exp(jf c ) exp[jϕ], by he baseband signal. simple ring mixer can be used o perform sraighforward ypes of modulaion like binary SK or PSK. The daa sequence is convered ino a unipolar (SK) or bipolar (binary PSK) NRZ signal. Wih M-ary PSK and QM, he signal o be modulaed mus be spli ino is I and Q componens. Boh componens are modulaed by wo differen ime-domain signals c I and c Q, which are derived from he daa sequence a(n). However, i urns ou ha hese wo ime-domain signals are idenical o he real and imaginary pars of he complex, equivalen baseband signal o wihin he sign of 4 he imaginary par. Modulaion is hen essenially a process of mapping he daa sequence a(n) o be ransmied ono he complex envelope of he modulaed RF signal.. mpliude-shif keying mpliude-shif keying (SK) is he simples way of modulaing digial informaion ono a carrier. Even hough on/off keying (OOK), he original version of SK, is no longer commonly used, i is he key o undersanding he fundamenals of digial modulaion. To simplify he discussion, we shall assume ha he daa sream which modulaes he (real) carrier cos(f c ) is a sequence a(n) wih a {0, } comprising an alernaing sequence of s and 0s, ie a(n) =, 0,, 0,, 0,... This sequence is convered ino a unipolar NRZ signal by a digial inerpolaion filer wih T for T T h = 0 elsewhere fer / conversion, a signal wih he Fourier series 4 u = - + [ [ bi] ] - cos - f 4 3 cos[ [ - f bi] ] + (7) 3 is obained. The C componen is half he ampliude (/) and here are specral lines a odd half-ineger muliples of he bi rae, ie (n +)f bi /. There are no specral lines a whole ineger muliples of he bi rae n f bi (n 0). If he daa sequence is a random, uniformly disribued sequence of s and 0s, a good assumpion for acual daa ransmissions, he discree specrum ends o a coninuous specrum in he limi. gain here is a C componen of / and zeroes a muliples of he bi rae. This signal is fed o he modulaor. I is easy o see ha he carrier is, in effec, urned on and off when i is muliplied by he unipolar NRZ signal. If modulaion is aken o be he assignmen of a symbol a i from an alphabe comprising N symbols o a signal s i from a se of N signals (in his case N = ), he signal s = cos(f c ) is assigned o he symbol and he signal s = 0 o he symbol 0. s he carrier signal and he baseband signal are muliplied ogeher, i follows from he shif heorem for Fourier ransforms ha he specrum of he modulaed RF signal is s = - cos(f c ) + - cos[ [ f c ± - f bi ] 3 cos[ [ f c ± - f bi ] ] + (8) 3 for he sequence a(n) =, 0,, 0,, 0... and a coninuous specrum in he form of a symmerical mapping of he baseband specrum ino he RF band for a random sequence a(n). In boh cases he carrier frequency is presen in he specrum bu a half is original ampliude. The specrum has zeroes a he frequencies f c ± nf bi (FIG 3). Equaion (8) shows ha boh halves of he specrum cenered on he carrier frequency would, in heory, be infiniely wide. Therefore, o ensure efficien use of he RF band, he specrum mus be bandlimied. This is bes done in he

5 baseband. Specifically, all frequencies in he baseband signal up o a leas f bi / mus be allowed hrough. This is equivalen o limiing he bandwidh of he RF signal o fc ± f bi /, in oher words o f bi. Baseband signal 0.5 f bi brup limiing of he baseband a f bi / is counerproducive because large signal delays are inroduced. The filer ha is used should, herefore, have a coninuous ransiion from he passband o he sopband which follows a cosine funcion for example. RF signal ( α) for 0 f T FIG 4 Time-domain signals and specra wih binary phase-shif keying (ft ) ( α) ( α) for < f (9) α T T H(f) = sin ( α) 0 for < f T f bi for SK, is bipolar (binary phase-shif keying, BPSK). If he NRZ signal is used o modulae a carrier of he form cos(f c ), an RF signal which is phase-shifed by 80 as compared o he modulaing signal is obained. This means ha s = s and his ype of modulaion is called anipodal. The (real) specrum of he baseband signal is given by This filer replaces he sin x/x lowpass which was menioned previously. The RF signal now has a bandwidh B which is a funcion of he roll-off facor α and in fac when α = 0, B = f bi and when α =, B = f bi. In pracice roll-off facors beween 0.35 and 0.5 are widely used; his corresponds o RF bandwidhs beween.35f bi and.5f bi. I is hen possible o define a bandwidh efficiency which indicaes wha bi rae per Hz of bandwidh can be ransmied. The heoreical upper limi for SK is bi/s/hz, bu in pracice efficiencies beween 0.65 and 0.8 bi/s/hz are encounered.. Binary phase-shif keying If he daa sequence a(n) is mapped o a sequence of dela funcions a(n) δ (nt) {+; }, an NRZ signal is oupu by he sin x/x lowpass. This signal, unlike he modulaion signal 4 u = - cos[ [ bi] - ] f cos[ [ - f bi] ] +. (0) 3 and has no C componen. The specrum of he modulaed carrier s= - cos[ [ f c ± - f bi ] 3 - cos[ [ f c ± - f bi ] ] +, () 3 FIG 3 Baseband signal 0.5 f bi RF signal Time funcions and specra wih ampliude-shif keying f bi is obained by muliplying he baseband signal and he carrier ogeher. The specrum does no conain he carrier frequency (FIG 4). The occupied bandwidh is he same as ha for SK and has been limied by passing he baseband signal hrough a lowpass filer wih a cos roll-off before modulaion. Consequenly, SK and BPSK have he same heoreical maximum bandwidh efficiency of bi/s/hz and a bandwidh efficiency beween 0.65 and 0.8 bi/s/hz in pracice. 5

6 .3 M-ary quadraure ampliude modulaion Pulse shaping igial filer To increase bandwidh efficiency, wo, hree or in general k consecuive bis from a daa sequence a(n) can be combined o form a new symbol b(m) by means of serial/parallel conversion. s a resul, he symbol rae is reduced o f bi /k. The new symbols are referred o as dibis, ribis, quadbis or k-bi words in general. The modulaion process requires M = k RF signals, each wih a differen phase and/or ampliude. The M = k possible symbols b(m) are mapped ono hese signals. FIG 5 M-ary quadraure ampliude modulaion 6 QM igial filer n I/Q modulaor is he bes ype of modulaor o use. Firs of all, i splis he unmodulaed RF signal ino wo componens. The quadraure or Q componen is phase-shifed by 90 wih respec o he in-phase or I componen. Therefore he unmodulaed I componen is described by cos(f c ) and he unmodulaed Q componen by sin(f c ). Boh componens are fed o mixers, where hey are muliplied wih he modulaing signals c I and c Q ; c I and c Q are derived from he symbol sequence b(m) and o wihin he sign of he Q componen are idenical o he real and imaginary pars of he complex envelope of he modulaed RF signal. The producs c I cos(f c ) and c Q [ sin(f c )] are added ogeher o give he modulaed RF signal. The modulaion process is reduced o mapping he symbol sequence b(m) ono he wo baseband componens. In he case of unfilered quadraure ampliude modulaion (QM), saircase signals in he ime domain wih M/ possible values are produced (FIG 5). By passing he baseband signal hrough a filer wih a cuoff frequency equal o half he symbol rae, he bandwidh of he RF signal is limied o he symbol rae = bi rae/k, which means ha he bandwidh efficiency is k imes beer han for BPSK. Quadraure phase-shif keying (QPSK) is he firs sep in his direcion. Two consecuive FIG 6 Time-domain signal in baseband Unmodulaed carrier I/Q modulaor Quadraure phase-shif keying Bi sequence Modulaed carrier bis are combined o form a dibi which can represen one ou of M = = 4 symbols. These symbols are mapped ono he phases ϕ i {45, 35, 5, 35 } of he RF signal or ono he four ime-domain signals s i = cos[f c + (i + ) /4] wih i {0,,, 3}. TBLE shows how he bi sequences, he dibis, he modulaion signals and he phases of he RF signal are relaed. FIG 6 shows he signals in he ime domain, in he frequency domain and by means of a phase sae diagram. I should be noed ha in his case oo here is no carrierfrequency componen in he specrum. RF ime-domain signal RF specrum Phase sae diagram 0.5 f bi Bi ibi c I c Q ϕ sequence TBLE 00 I 45 0 II 35 III 5 0 IV 35 Modulaion parameer assignmens Theoreically, he bandwidh efficiency can be increased o bi/s/hz and so is wice he maximum bandwidh efficiency for SK and BPSK. In pracice, values beween and.5 bi/s/hz can be obained. 6

7 .4 Frequency-shif keying ll he ypes of modulaion described so far have been linear. The (double sideband) baseband specrum is shifed linearly in he RF range. The modulaors used are memoryless as neiher he insananeous phase ϕ(m) nor he insananeous ampliude a(m) are funcions of previous values ϕ(m-p) or a(m-p). noher way of ransmiing digial signals is mapping he M-ary baseband signals ono RF signals wih M differen frequencies. This ype of modulaion is referred o as M-ary frequency-shif keying (FSK). FSK is no linear and he RF specrum is a Bessel specrum which has frequency componens ha are no presen in he original signal. simple form of frequency-shif keying wih no memory can be implemened by swiching beween M oscillaors each wih a differen frequency. When his is done, he phase of he RF signal is random. The disadvanage of his ype of FSK is ha he RF specrum has large sidelobes. Frequencyshif keying wih coninuous phase shifs (coninuous phase frequencyshif keying, CPFSK) does no have his drawback. CPFSK modulaor can be implemened wih a volageconrolled oscillaor (VCO) or an I/Q modulaor. Binary FSK is he simples form of FSK and is described in erms of he wo signals s = cos[(f c + f)] and () s = cos[(f c f)].5 Correlaion and disance beween signals The parameers used o represen informaion are no he only differences beween he various ypes of modulaion. There are also differences in heir sensiiviy o exernal inerference and, as menioned previously, efficien use of he available RF bandwidh. number of parameers ha indicae how well a modulaion mehod can ransmi informaion on a paricular radio channel have o be considered. In chaper, modulaion was defined as he assignmen of one of he M possible signals ha could be ransmied o a block of k bis. The signal is disored during ransmission. The purpose of demodulaion in he receiver is o deec he signal in he presence of he noise which has been inroduced during ransmission and o disinguish i from he oher M - signals ha could have been sen. I is obvious ha a modulaion echnique based on a se of M signals can bes fulfil is ask if hese M signals are as differen from each oher as possible. Mahemaically, he degree of similariy beween wo signals is expressed in erms of heir correlaion facor s s d T ρ = (3) s d T or in erms of heir Euclidean disance = [s s ] d T = E + E l E E ρ (4) where E is he mean energy over he duraion of he symbol. When E = E, as is he case wih PSK and FSK, his equaion simplifies o = E bi ( ρ). (5) For binary SK (s = 0) his formula gives a disance SK = E l and BPSK = E l for BPSK (s = s ). There are wo disance values for QPSK, max = E l and min = l E ḷ The Euclidean disance for FSK depends on he modulaion index; in he case of CPFSK wih a modulaion index of 0.5 CPFSK = l E ḷ This is he basis for he modulaion echnique used for GSM radio neworks..6 Coheren demodulaion When RF signals are phase-modulaed, he resuling specrum does no have a componen a he carrier frequency. This means ha he relaionship beween he curren phase which carries he informaion and he phase of he unmodulaed carrier is no direcly available. Therefore, a complex mehod is used o regenerae he carrier so ha i has is original frequency and phase. There are several frequency synchronizaion echniques ha can be used, for example squaring he modulaed signal once or wice and hen dividing he doubled frequency by wo (BPSK) or he quadrupled frequency by four (QPSK). noher approach is o periodically ransmi an unmodulaed frequency which he local oscillaors in he receiver can lock ono. Usually he exac phase is obained by means of special sequences (raining sequences) conained in he daagrams. The crosscorrelaion of he received sequences wih idenical sequences sored in he receiver provides phase correcions for he local oscillaors. signal of he form cos(f) and an orhogonal signal of he form sin(f) = cos(f + /) are recovered from he regeneraed carrier. 7

8 Boh componens are muliplied by he received signal cos(f + ϕ) and he following are obained: cos ( f ) cos(f + ϕ) cos(f) = [cos(ϕ) + cos(4f + ϕ)], c l cos(f + ϕ) cos [ f + ] = cos [ ϕ + ] + cos [ 4f + ϕ + ]. (6) cos (f+ϕ) -sin ( f ) c Q FIG 7 Coheren demodulaion The following erms remain when RF componens are filered ou (FIG 7): [cos(ϕ)] and (7) cos [ ϕ + ] = [ sin(ϕ)] However, as equaion (3) shows, hese are he modulaing signals of he I and Q carrier componens o wihin a consan facor and, as equaion (6) shows, hey are he componens of he complex envelope of he modulaed signal o wihin he same consan and he sign of he imaginary par. If he original daa are o be recovered, he inverse of he mapping ono he signals c I and c Q or ono he complex envelope u mus be found. Coheren demodulaion mus be used for sysems using rue phase modulaion, provided ha differenial coding is no used for he daa. When phase shifs and no absolue phases are used o encode informaion, his is referred o as differenial coding. Coheren demodulaion can, however, be used for all oher ypes of modulaion. In general, i performs beer han non-coheren mehods, ie lower bi error rae for he same raio of bi energy o noise power densiy. 3 Modulaion mehods for mobile-radio neworks The las chaper would lead one o conclude ha BPSK has he greaes immuniy o noise inroduced by he ransmission channel. Indeed, afer ransmission hrough a channel ha only adds whie noise o he waned signal, referred o as an WGN channel (added whie Gaussian noise), BPSK is opimal wih respec o he bi error rae as a funcion of he bi energy o noise power densiy raio E bi /N 0. This ype of modulaion is, herefore, used as a benchmark for oher ypes of modulaion. The bandwidh efficiency is inadequae however. lhough M-ary PSK and QM have considerably beer bandwidh efficiencies, hey exhibi small Euclidean disances, which means ha heir suscepibiliy o noise on he ransmission pah increases as he number of signal saes increases. The implemenaion of modulaors and demodulaors also becomes more and more involved as he complexiy of he modulaion echnique increases. Osensibly, when compared wih BPSK, QPSK seems o be a good rade-off beween efficien use of bandwidh, immuniy o noise and echnical complexiy because of is mean minimal difference in Euclidean disance and is bandwidh efficiency, which is wice as good. By conras, CPFSK as implemened in GSM neworks requires far more complex hardware and so on he face of i does no appear o be he opimum choice. However, a more careful analysis of he band-limied RF signals and heir suiabiliy for radio ransmission gives an enirely differen perspecive. Bandlimied M-ary PSK exhibis spurious inciden M modulaion of he RF carrier. The reason for his is ha he magniude of he RF signal vecor changes during phase ransiions which are slower han hose ha occur wih modulaion wihou band-limiing. This effec is paricularly marked when he phase changes by 80 (ransiion from 00 o for BPSK and 0 o 0 for QPSK), he carrier being reduced o zero for a ime. The carrier is reduced o 0.7 of is maximum value when he phase changes by 90 and o 0.38 of is maximum value when he phase changes by 35 (possible phase shif for 8-PSK) his is equivalen o aenuaion of 8.4 db. This precludes he use of effecive bu nonlinear C-class amplifiers in mobile radios and means ha linear -class amplifiers are required for he oupu sage. I also makes i more difficul o recover he carrier from he modulaed signal, which is essenial for coheren demodulaion. 8

9 3. /4 differenial QPSK special form of baseband signal encoding ha only uses phase shifs of 45 and 35 is used for neworks operaing o he Japanese JC sandard and for digial runked-radio neworks in Europe and his is one soluion o he problem. The approach a leas prevens carrier exincion, momenary loss of he carrier. Wih /4 differenial QPSK he informaion is no represened by an absolue phase bu raher in erms of a phase difference. So coheren demodulaion is unnecessary and here is no need o deal wih he difficul problem of reconsrucing a carrier wih exacly he same frequency and phase of he original from he received signal, srongly disored by he mobile-radio channel. TBLE Bi sequence δ δ ibi Phase ransiion 00 ϕ = 0 / + /4 = ϕ = / + /4 = 3/4 = 35 ϕ = / + /4 = 5/4 = 5 = 35 0 ϕ = 3 / + /4 = 7/4 = 35 = 45 Phase ransiions for /4 QPSK 0 0 δ c l Q H(f) = sinx x Square filer (no band limiing) δ l c Q c l The original daa sequence a(n) undergoes serial/parallel conversion, husgeneraing a new symbol sequence b(m) {00; 0; 0; } whose elemens are assigned o he phase ransiions lised in TBLE. This assignmen is essenially a ype of Gray coding, adjacen symbols and signals differing by jus one bi. n approach of his kind reduces bi errors. The /4 offse gives he modulaor a memory funcion. The phase ransiions are modulaed ono he carrier by an I/Q modulaor FIG 9 Filer wih Nyquis edge (band limiing) c Q aa sequence, I/Q signals and phase sae diagrams for /4 QPSK (FIG 8). Firs he curren carrier phase is obained from he sequence of phase differences by means of a feedback loop, hen he wo modulaion signals c I and c Q are calculaed from he carrier phase. his sage he modulaion signals are in he form of dela funcions δ(mt) {+; + / l ; / l ; }. They are hen band limied by passing hem hrough lowpasses (FIG 9). raised cosine filer is used. Moreover, filering is shared beween he ransmier and he receiver. 0 0 S P 0 ϕk T ϕk By spliing up he overall filer response ino equal pars a he ransmier and receiver end δ l PM 0 cos(f) H(f) = sin ( α) for 0 f T (ft ) ( α) (+ α) for < f (8) α T T (+ α) 0 for < f T δ Q PM δ I/Q {+, +/, /, } -sin(f) FIG 8 I/Q modulaor for /4 QPSK i is possible o obain an opimal signal/noise raio when recovering he received symbol sequence b (m). 9

10 3. Minimum shif keying and Gaussian minimum shif keying Modulaion Frequency Phase shif over Correlaion Euclidean index h deviaion f bi duraion T bi facor ρ disance 3.. Mahemaical derivaion of MSK When i formulaed he GSM sandard, he sandards commiee chose a differen approach and sipulaed angle modulaion wih a consan envelope of he RF signal for digial neworks. This means ha he lengh of he vecor represening he RF signal does no change as i urns hrough an angle of ϕ from ϕ( ) o ϕ( ) over a ime inerval equal o he bi duraion. The end of he vecor mus, herefore, describe he arc of a circle wih an angular speed of dϕ ϕ =. fer urning hrough his d T bi angle, during which a symbol is ransmied, he vecor does no remain saionary in he posiion i has reached bu coninues o urn in he same direcion, so repeaing he signal ha has been ransmied, or urns in he opposie direcion, so sending he opposie of he ransmied bi. The phase change of he RF signal wih respec o he arbirary zero phase of he unmodulaed carrier is associaed wih a frequency change of f. The insananeous frequency and he frequency deviaion can be calculaed from he firs derivaive of he carrier phase, in oher words from he derivaive of he argumen of he cosine funcion describing he carrier. 0 3 ϕ ϕ 0 =0 3 f+ f f- f TBLE 3 If he phase change ϕ ha occurs over he duraion of a bi is expressed as a muliple h of, h being referred o as he modulaion index, he following relaions are obained: Φ = f c + ϕ h = f c + ϕ 0 ±, T bi dφ dϕ d d = f c ± f h = f c ± ; T bi h f = ; T bi h ϕ = ϕ 0 ± ; ϕ = h (9) T bi = f c +[ ] The signals represening he symbols 0 and can hen be expressed as: h s = cos [ [ f c + ] ] T bi = cos((f c + f)) and h s = cos [ [ f c ] ] = f bi = 90 0 E bi 4 T bi 4 MSK parameers T bi = cos((f c f)) (0) n-t bi FIG 0 Relaionships beween daa signal, frequency and phase for minimum shif keying These equaions describe frequency keying (see equaion ). Because he phase changes coninuously, his ype of modulaion is referred o as coninuous phase frequency-shif keying (CPFSK). FIG 0 shows he correlaions beween he daa sequence, curren phase and curren frequency. The rellis diagram which shows he possible phase ransiions also explains why a CPFSK modulaor has a memory. I is easy o see how he curren phase depends on previous saes. Equaion 3 gives he following expression for he correlaion facor of he wo signals s and s : sin( h) sin(f c T bi ) ρ = () h f c T bi If f c >>/T bi, he second erm can be negleced. Uncorrelaed signals (ρ = 0) are obained when h = k 0.5 where k {,, 3, }; h = 0.5 is herefore he smalles modulaion index for which he wo signals are uncorrelaed. FSK wih h = 0.5 and f = = f bi is herefore also 4T bi 4 referred o as minimum shif keying (MSK). TBLE 3 summarizes he main parameers for his ype of modulaion once more. 3.. Implemening MSK The simples way of producing an MSK signal would be o conver he daa sequence a(n) ino a bipolar NRZ signal which is hen used o conrol a VCO (FIG ). This approach is in fac adoped for, say, cordless phones where he specificaions for he frequency and angle accuracy of he

11 0 Baseband signal modulaed signal do no have o be so sringen. However, he GSM specificaions for he maximum frequency and angle error during a burs are so igh ha a VCO would be incapable of meeing hem. n I/Q modulaor gives beer resuls under hese resrains. Before analyzing a modulaor of his kind, i will be useful o briefly review he I/Q noaion used for modulaed RF carriers once more. s = cos[f c + ϕ] = [cos(ϕ) cos(f c ) + sin(ϕ) ( sin(f c ))] () The RF signal has wo muually orhogonal componens cos(f) and sin(f) = cos(f + /) which are muliplied by he funcions cosϕ and sinϕ by means of, say, wo doublebalanced mixers. The angle ϕ can be obained from equaion 9 and is given below: ϕ = ϕ(nt bi ) ± 0.5/T bi * (3) wih 0 < * < T bi In pracise, he modulaed carrier can be obained in he following way:. Obain he wo muually orhogonal carrier componens l = cos(f) and Q = sin(f).. Muliply he I componen wih cosϕ and he Q componen wih sinϕ. 3. dd he wo componens. c f ϕ c l c Q FIG MSK VCO f 0 + f f 0 f 0 - f ϕ Modulaion signals and I/Q signals for Oupu frequency Phase of MSK signal The nex problem is he generaion of he modulaing signals cosϕ and sinϕ. This canno be done wih classic analog mehods, he signals have o be calculaed digially using equaion 3 for he ime nt bi < * < (n +)T bi, he polariy of he fracion deermining wheher a or a 0 is sen. FIG 3 I/Q modulaor for MSK If he daa sequence a(n) is mapped ono he daa funcion c = c(nt bi + *) + for a(n + ) = = for a(n + ) = 0 (4) (3) can be rearranged o give 0.5 ϕ = ϕ(nt bi ) + c * (5) T bi This yields: FIG Generaing minimum shif keying wih VCO c I = cos(ϕ(nt bi )) cos [ * T bi ] c sin(ϕ(nt bi )) sin [ * ] T bi and c Q = sin(ϕ(nt bi )) cos [ * T bi ] + c cos(ϕ(nt bi )) sin [ * ] (6) T bi f Calculaion of phase angle ϕ ϕ Calculaion of sinϕ and cosϕ The following approach is used:. Sar wih an iniial phase. If ϕ (0) = 0 is seleced, equaion 6 ges less complex: sin(ϕ(nt bi )) becomes 0, cos (ϕ(nt bi )) becomes ±.. Calculae ϕ (for example by using a digial accumulaor). 3. Calculae he funcions of ime c I and c Q from ables. 4. Calculae he phase ϕ(nt bi ), (las accumulaor value in ). 5. Go o. FIG shows his procedure for eigh consecuive bis; FIG 3 shows how he modulaor operaes. The bipolar NRZ signal is proporional o he insananeous oupu frequency f c ± f of he cos(f) -sin(f) cos(f+ϕ) modulaor. In he accumulaor i is inegraed o give a signal ha is proporional o he insananeous phase of he modulaed carrier. Tables for sinϕ and cosϕ provide he signals c I and c Q in digial form. fer / conversion and analog filering by a lowpass, hese signals are fed o he modulaors a whose RF inpus he orhogonal componens of he carrier have been applied. The wo modulaed carrier componens are added in a power summer o give he oupu signal. If you consider he I/Q modulaor from he poin where he bipolar NRZ signal is fed ino he RF oupu, i acs as a frequency modulaor or a VCO.

12 3..3 Bandwidh reducion by baseband filering The power-densiy specrum of unfilered MSK can be described analyically by he funcion 6 T bi cos f T Φ bi vv(msk) = 6 f T bi (7) he daa funcion is filered before he modulaing signals c I and c Q are calculaed from i by means of a nonlinear operaion. For he ime being i will be convenien o hink of he I/Q modulaor as a frequency modulaor (VCO) as far as he processing of he modulaing signals is or by is ransfer funcion ln f ln ( T bi f) H(f) = e B = e (B T bi ) (9) ln where σ = and B = 3 db B T bi bandwidh of filer. These expressions conain he new erm B T bi, which nor- FIG 4 Specra for QPSK and MSK FIG 6 GMSK specra for various values of bandwidh bi duraion In FIG 4 i is compared wih he QPSK power-densiy specrum funcion. The diagrams show ha he main lobe of he MSK specrum is considerably wider and ha here are no specrum zeroes a f c +/ f bi. On he oher hand, he MSK specrum s ail-off, which is proporional o f 4, is considerably seeper han ha of he QPSK specrum. In boh cases he specrum can be improved by baseband filering, bu wih one big difference in he case of QPSK i is he modulaing signals c I and c Q ha are filered, bu wih MSK concerned, because his simplifies he descripion of filering. Simply imagine he filer conneced o he inpu of he frequency modulaor (FIG 5). GSM specificaions sipulae ha he daa signal should be passed hrough a Gaussian filer, hence he designaion Gaussian minimum-shif keying (GMSK) for his ype of bandlimied modulaion. This filer can be described in erms of is impulse response h = e σ T bi (σ T bi ) (8) malizes he filer bandwidh o he bi frequency f bi and which is used insead of he acual bandwidh of he Gaussian filer o describe he efficiency of he filering process. B T bi = means ha MSK is being implemened, while smaller values of B T bi indicae GMSK wih a correspondingly smaller bandwidh. FIG 6 shows he effec on he RF specrum. GSM neworks use B T bi = 0.3. This means ha he 3 db bandwidh of he baseband signal is 8.5 khz (TBLE 4). u Baseband signal (unfilered) u fil Baseband signal (filered) Filer Modulaor (VCO) ϕ Phase posiion of GMSK signal f Oupu frequency FIG 5 Generaion of GMSK par from he waned effec of bandlimiing ha is obained by filering he daa funcion, here is also an unwaned effec referred o as inersymbol inerference. Theoreically, when a recangular pulse p c = rec(/t bi ) of duraion T bi is filered, is duraion saisfies he inequaliy < < +. To esimae he inerference, he ap-

13 Bi duraion Bi frequency Bandwidh bi duraion 3 db bandwidh T bi f bi B T bi 3.69 µs khz khz BER B T = (MSK) B T = 0.5 B T = 0. TBLE 4 GMSK parameers for GSM 0-3 proximae response of he filer o his pulse can be obained from convoluion wih he impulse response of he filer. The convoluion of p c * h gives rise o inegrals of he form B x e dx, which do no have closed-form soluions bu can be calculaed from he Gaussian error funcion erf(x) using he mehods of numerical analysis (FIG 7). In pracice, when B T bi = 0.3, only an inerval from = 3T bi o = +3T bi, he duraion of 6 bis, needs be considered; ouside his ime inerval he filer response can be assumed o be zero. delay of a leas 3T bi mus be inroduced o preven causaliy from being Ideal anipodal modulaion (BPSK) db 6 E bi /N o FIG 0 Bi error rae, BER, as funcion of E bi /N 0 wih B T as parameer T C 0 T C violaed. ue o pulse spreading and he conservaion of energy, he maximum value of he filered pulse drops o abou 0.7 imes he ampliude of he simulus. FIG 7 Shaping recangular pulse wih Gaussian filer FIG 8 Reinforcemen of wo neighbouring recangular pulses wih same polariy (resuling oupu funcion shown by dashes) Simulus Response + 0 T C T C T C T C - Simulus Response + The responses of he Gaussian filer o neighbouring recangular pulses reinforce and cancel each oher ou. Reinforcemen occurs if neighbouring pulses have he same polariy (FIG 8) and cancellaion, ie he maximum ampliude of he curren pulse is reduced even furher o abou 0.5 imes he value of he original pulse, if neighbouring pulses have opposie polariies (FIG 9). Because of filering, he funcion c fil, which is proporional o he insananeous oupu frequency, is coninuous a he modulaor inpu and he phase funcion ϕ fil loses is breakpoins. This in urn smoohs he modulaing funcions c I and c Q and, as a resul, here is an improvemen in he specrum ha is a funcion of B T; his is shown in FIG 6. FIG 9 Cancellaion of wo neighbouring recangular pulses wih opposie polariy (resuling oupu funcion shown by dashes) 0 - T 0 C T T C T C C - Simulus Response However, because of inersymbol inerference, he improvemen in he specrum has o be raded off agains an error rae ha increases as B T decreases, he raio E bi /N 0 remaining consan (FIG 0). 3

14 3..4 rchiecure of GMSK modulaor Before he daa sream is fed o he modulaor, i is differenially encoded using he rule d(k) = a(k) a(k ), where d(k) {0; }. dding 0.5 and hen muliplying by a facor of gives a sequence of bipolar dela funcions δ(k) { ; +}. The res of he modulaion process depends on he srucure of he hardware and firmware used for he modulaors, he only proviso being ha he olerances saed in TBLE 5 mus be me for burss lasing 56 µs. These parameers depend on he accuracy of he modulaing signals c I and c Q, on he frequency and phase sabiliy of he oscillaor and he exac orhogonaliy of he I and Q carrier componens. The exac soluion involves finding he convoluion of p c h Gauss. The δ(k) are inerpolaed using a bipolar NRZ funcion in a digial filer wih an oversampling rae of up o x6, before hey are ransformed ino he funcion c fil by a furher filer wih Gaussian characerisics. The nex par of he modulaor is he same as he MSK modulaor ha has already been described. In oher words, he insananeous phase is calculaed by inegraing c fil o obain ϕ fil, cos[ϕ fil ] and sin[ϕ fil ] are calculaed and hese funcions are muliplied by he wo orhogonal carrier componens (FIG ). TBLE 5 In pracice, however, here is no need o follow he exac sequence of operaions ha flow from he heory. s here are a large number of mobile saions, i is essenial o adop a cos-effecive approach while a he same ime meeing he requiremens lised above. concep developed by Philips shows how complexiy can be reduced drasically. Wih his approach, differenial encoding no need be performed as a separae operaion and he ables for calculaing cos[ϕ fil ] and sin[ϕ fil ] can be dispensed wih enirely a major improvemen. To do his, he original daa sequence ha has been convered ino a bipolar signal is muliplied by a phasor e jk/. The complex coefficiens c(k) ha resul are fed o a filer wih Gaussian-like characerisics. complex funcion appears a he oupu of he filer. Is real par approximaes he modulaion signal c I, while is imaginary par approximaes he modulaion signal c Q. From he resuling direcion of roaion of he RF vecor, i can be verified ha his form of modulaion and he modulaion produced by he original, differenially encoded signal are idenical (FIG ) emodulaing MSKand GMSK signals s equaion (0) shows, MSK signals are frequency-modulaed RF signals. In Max. frequency error Max. phase error Max. phase error (peak) FIG c Q. Generaing modulaion signals c I and Tolerances for modulaed carrier T sin x/x lowpass (rms) Gaussian filer Oversampling Calculaion of ϕ, sinϕ and cosϕ c I c Q he case of GMSK signals, only he baseband funcion, which is proporional o he oupu frequency, is filered. The RF signal can also be hough of as being frequency-modulaed. Consequenly, simple frequency demodulaion using convenional frequency discriminaors or an indirec approach using FM o pulse frequency modulaion conversion would be sufficien o recover he ransmied daa. Neverheless, he considerably more complex roue of coheren demodulaion, described in chaper.6, is aken. There are wo main reasons for his:. Under he same ransmission condiions, coherenly demodulaed RF signals exhibi lower bi error raes han hose ha are no.. Because of he ransfer funcion of he mobile-radio channel, he RF signal is alered in such a way ha demodulaing he received signals wihou equalizaion would in mos cases lead o unaccepably high error raes. However, equalizaion is only possible if he characerisics of he radio channel over ime are known, in oher words is ransfer funcion mus be coninuously esimaed. s described in chaper.6, coheren demodulaion gives he complex envelope of he RF signal, which is also modified by he radio channel. If he undisored baseband signal is known as well, he ransfer funcion of he channel can be calculaed. sequence of 6 bis, referred o as he raining sequence and a copy of which 4

15 is sored in he receiver, is ransmied in he middle of every burs of 56 bis. By finding he cross-correlaion of he received equivalen baseband signal and he complex envelope ha he raining sequence would generae if recepion were ideal, he characerisics of he radio channel can be esimaed. IF sage Frequecy synchronizaion cos -sin x I x Q igial signal processor for channel esimaion, channel correcion and deriving daa mos likely o be sen To decoder FIG 3 GMSK demodulaor The block circui diagram of he demodulaor is shown in FIG 3. fer recepion, he RF signal is convered o an IF and fed o he wo mixers. The frequency of he superheerodyne oscillaor is synchronized by means of a frequencycorrecion burs ransmied a regular inervals by he base saion. This oscillaor provides he wo orhogonal signals cos(ω) and sin(ω). fer passing hrough he mixers and lowpasses, he wo componens of he equivalen baseband signal undergo / conversion and are fed o a digial signal processor ha, from he disored complex envelope, reconsrucs he sequence ha is mos likely o have been ransmied. c I c Q T = /f IF subsampling: T = (n+/4)t IF sage Sample x Q (i-) Inerpolaed value (-) i (-) Inerpolaion x I (i) x Q (i) FIG 4 Top: demodulaion wih / converer. Boom: signals c I and c Q recovered by IF sampling For he demodulaor oo here are less involved soluions. FIG 4 shows a concep ha uses jus one / converer. Efficien implemenaion of GMSK mod- FIG ulaor The received signal ha has been convered o an IF is undersampled using a sampling period of T s = (n + /4)T, where T is he IF period. The samples x i are muliplied by ( ) i, in oher words he samples wih odd indices have heir signs invered. Samples wih indices of he form i are he I-componen samples of he received signal, hose wih (i ), he Q-componen samples. The delay beween he wo componens is equalized by an inerpolaion filer. Peer Hazold jk e igial filer c I c Q References Mäusl, R.: igiale Modulaionsverfahren. Hühig Verlag, Heidelberg, 988 Proakis, J. G.: igial Communicaions. McGraw Hill, New York, 989 c I Schöffel, P. e al.: rchiekur eines Mobilfunkgeräes für das Nez. Philips Innovaion /99 c Q irecion of roaion of RF vecor Reconsruced differenially encoded daa sequence Picken,.: The GSM mobile-elephone nework: echnical feaures and measuremen requiremens. News from Rohde & Schwarz Nos. 36, 37, 38 Lüich, F., Hech,.: Tesing digial radio receivers wih Signal Generaor SMHU 58. News from Rohde & Schwarz Nos. 36, 37 5

16 Should you wan o deepen your knowledge Rohde & Schwarz is offering a series of seminars which deal in deph wih he following opics: digial modulaion in heory and pracice analysis of digially modulaed signals digial communicaion sysems. Experienced raining saff will make you familiar wih he subjec maer by going ino many examples and, wha is mos imporan, you will be given pleny of opporuniy o pu heory ino pracice using sae-of-he-ar measuring equipmen se up o simulae real operaing condiions. Rohde & Schwarz will arrange hese seminars o be held exclusively for you on he company premises in Munich, bu if you wish he seminars can also be conduced a your premises. This migh be paricularly convenien if large groups of people are o be inroduced ino new subjecs a he same ime, which would oherwise ake up considerable ime and money for ravelling. sk us o submi an offer. You may also obain our comprehensive seminar brochure in English or visi us on he Inerne under hp:// 6

17 Where would you be 7

18 wihou Rohde & Schwarz soluions for mobile communicaions s sysems and user expecaions ge more and more sophisicaed, hose involved in mobile radio need a powerful parner wih experise in measuring echnology. Tha parner is Rohde & Schwarz. Supplier of approval es sysems for GSM, CS 800, CS 900, ECT and TETR in planning, developmen, producion, service and ype approval. Wih esers and sysems for he whole world of mobile radio sandards. Soluions from handheld esers o complee sysem simulaors for all analog and digial mobile radio sandards. When i comes o mobile communicaions whaever you wan o measure Rohde & Schwarz is your parner. Saying ahead of he field Rohde & Schwarz has a long rack record of innovaion. nd a worldwide repuaion for excellence. Consan R& and paricipaion in inernaional sandardizaion ensure ha we say in he forefron of echnology. Engineering sysems o es o he highes sandards. eveloping echnology ha mees your needs. Now and in he fuure. Firs in he field CM family mulimode radio esers for mobile communicaions GSM CS 800 (PCN) CS 900 (PCS) ECT PC CM -MPS Easy o use and packed wih power feaures. 8 ual-mode and muliband esing in one saion wihou add-ons Excellen price/performance raio and low life-cycle coss hrough modular plaform-based concep High-speed remoe conrol for high producion hroughpu evelopmen Qualiy assurance Producion Service Insallaion Mainenance Mobile radio service made easy CTS 55 GSM and CS 800/900 service eser In addiion o simple funcional ess, he new CTS 55 digial radio eser is also used o conduc repairs. I is an excellen ool for repairing mobile elephones quickly and reliably. Paricular aenion was paid o making GSM and CS 800/900 phone esing simple o each and everyone. Value-for-money es soluion Repair ceners Manufacurers Service providers Nework operaors Tesing down o he las bi CRTP/C family digial radio esers The CRTP/C family has paved he way for developmen and coninual engineering of GSM, CS 800 (PCN) and CS 900 (PCS). Realisic precompliance wih suppor of es programs Supporing sofware for he developmen of nex-generaion mobiles available Base saion developmen Chip developmen Compliance Precompliance Qualiy ssurance Manufacurers Nework operaors Tes houses Synonym for superioriy CMS family analog radio esers The leers CMS are synonymous wih he mos successful analog mobile radio eser family on he marke. Powerful, maure and easy-o-use. dvanced feaures include: Transmier and receiver esing of M, FM, ϕm and SSB radios Specrum monior and ransien recorder Opional inegraed signalling uni for all common cellular neworks VOR/ILS avionics es evelopmen Qualiy assurance Producion Service Insallaion Mainenance We have your nework covered Complee range of coverage measuremen sysems Esablishing and mainaining a highqualiy radio nework is a complex ask involving planning of sies, nework insallaion, esing, opimizaion, and mainenance.

19 To mee hese needs, we offer a complee range of sysems and componens embedded in a sandard sofware environmen. Wheher you are looking for a budge-priced porable es sysem or fully equipped es vehicles for measuring field srengh or signalling, we have an esablished soluion. Proven in pracice and feauring innovaion, maximum performance, and ease of use. TS9955 The fas all-round high-performance measuring sysem for insallaion and qualiy assurance. TS995 The porable measuremen sysem for service, mainenance and qualiy assurance. TS9953 Inerim es ransmier sysem for insallaion, sie planning and nework upgrading. Tried and esed The sure way o a ype approval cerificae. Exclusive supplier of full ype approval es equipmen (FT) for GSM mobiles Prescanning and ype approval for CS 800 and CS 900 mobiles and base saions Complee range of ECT ype approval sysems for RF, audio and proocol es of fixed and mobile pars Masers of modulaion Signal generaor family Rohde & Schwarz signal generaors are used worldwide in he developmen, producion and service of mobile communicaions equipmen. From general-purpose analog use o demanding R& applicaions, we have he righ signal generaor for every need. Examples from our exensive range: SME family Universal signal generaors for digial modulaion Mulisandard digial coder including frequency hopping and TM capabiliies Inernal programmable daa generaor SMIQ family High-qualiy I/Q modulaor Universal digial modulaion coder for highes flexibiliy Preprogrammed sandard seings for PHS, IS-95 CM, NC, PC, GSM High-performance fading simulaor opion according o sysem specificaions Power and Reflecion Meer NRT Precision direcional power meer for measuring of power and reflecion on ransmiers, anennas and indusrial power generaors under real operaing condiions. NRT is ideal for mainenance, producion and lab bench use as well. verage power measuremen for all kinds of modulaion Compaible wih digial modulaion sandards like GSM, CS 800, PHS, CS 900, NC, PC, ECT, TETR, MIRS, IS-95 CM, B Measuremen of peak envelope power, peak-o-average raio and burs average power irecional Power Sensor NRT-Z44 for direc use on he serial inerface of any PC Full range, full specrum FSE family of specrum analyzers for analog and digial radio The FSE range of specrum analyzers ses oally new sandards of price/ performance. Wih power for he presen and flexibiliy for he fuure. High dynamic range for burs measuremens and CP High measuring speed Universal analysis of digially modulaed mobile communicaions signals QPSK, /4-QPSK, GMSK, FSK and more. evelopmen Producion Qualiy assurance Type approval Service 9

20 More informaion, please I would like o know more abou Rohde & Schwarz and measuring soluions for mobile communicaions Please check boxes as required. I would like informaion abou Rohde & Schwarz I would like o consul a sales engineer I would like o know more abou Rohde & Schwarz measuring soluions for mobile communicaions Name Posiion ddress Fax CM family mulimode radio esers CTS 55 GSM and CS800/900 service eser CRTP/C family digial radio esers CMS family analog radio esers Coverage measuremen sysems Type approval and precompliance es sysems SME family universal signal generaors SMIQ family vecor signal generaors wih fading simulaor opion Power and Reflecion Meer NRT FSE family specrum analyzers for analog and digial radio Training Company Phone P Prined on chlorine-free paper Subjec o change Prined in Germany 0897 (Pe sö) ROHE& SCHWRZ GmbH & Co. KG Mühldorfsraße München P.O.B München Telephone Fax Inerne: hp://