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MINIMUM SHIFT KEYING:

A SPECTRALL\r EFFICIENT MO DUL A TION

Subb arayan Pasupathy

Compact power spectrum, good error rate performance, andeasy synchronization make MSK an attractive digital

modulation technique.

The ever increasing dem and for digital transmissionchan nels, in the radio frequenc y (RF) band presents apotentially serious problem of spectral congestion ands

likely to cause severe adjacentnd cochannelinterference problems. This has, in recent years, led to

the investigation of a wide variety of techniques forsolving the roble m of spectralongestion. omesolutions to this problem include: 1) new allocations athigh frequencies; 2) bettermanagement of existing

allocations; 3) the use of frequency-reuse echniquess u c ha s h e u se of narrow-beamantennasanddualpolarizing syste ms ; )he se of efficient sourceencoding techniques; and ) he useof spectrally efficientmodulation techniques [l]. his article will consider thelast app roa ch and analy ze, in particular, a modulationsch em e known a s minimum shift keying MSK). Th e

MSK signal format will be explained and its relation toother schem es such as quadra ture phase shif t keying(QPSK ), offse t QPSK (OQPS K), and frequency shi ftkeying (FSK) pointed out . Themain at tributes of MSK,

such as constant envelope, spectralfficiency, err or rateperformance of binary SK, and self-synchronizingcapab ility will all b e exp laine d on hebasis of the

modulation format.

The u thor is with theDepar tmen t of ElectricalEngineering,University of Toron to , Toron to , On t . , Canada .

SPECTRAL EFFICIENCY AND MSK

In any omm unication ystem, . th e two rimarycommunicat ion esourcesare he ransmittedpower

an dhannelandwidth. A generalystem-designobjective would be ouse hese wo esources sefficiently a s possible. In man y comm unication channels,

o n e of the resources may be more precious than theother nd encemo st hanne ls an e classifiedprimarily a s power-limited or band-lim ited. (The voice-gradeelephone ircuit, with approximately 3 kHzbandwidth, is a typical band-limited chan nel, whe reassp ac e comm unication links are typically power limited).In power-limited channels, coding schemes would begenerally usedoave ower the xpense of

bandw idth, wherea s n band-limited chann els “spectrallyefficient modulation” techniqueswould be used to save

bandwidth.

The primary objective of spectrally efficient

modulation is to maximize the bandwidth

efficiency, measured i n b its/s/Hz.

Th e primary objective of spectrally efficient modula-tion is to maximize the bandw idth efficiency, defined as

the ratio of data ra te to channel bandwidth (in units of

bits/s/Hz). A secon dary objective of suc h m odulation

14

0163-6804/79/0700-0014$00.75 @ 1979 IEEE

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7/15/2019 MSK-paper


sch em es may be'to achieve this bandw idthfficiency a t aprescribedverage bit erro rate with minimumexpendi ture of s ignal pow er . S ome channels may haveother restrictions and limitations which may force othercons traints on the modulat ion techniques . For example,comm unication systems using certain typesof nonlinearchannels call for an additional feature, namely,constantnvelope, which makesheodulationimpervious to suc h mpairments. Thisis needed because

a memoryless nonlinearity prod uce s extra neo us side-bands whenpassing a signal with amplitude fluctuations.Such s idebands int roduce out-of-band inter ferenceithother communication systems.

A typical examplewhere uchconsiderationsareappropriate is in time-division multiple access (TDMA)satelli te co mm unic ation, wh ere the raveling wave tu be(TWT)amplifiers are operated near powe r saturationorhigh efficiency. For freq uen cy division multiple acc es s(FDMA) application also, constant e nvelope propertiesare useful at each ground terminal, if the high poweramplifier is operated near power saturation like a class"C" device, where the respo nse would be nonlinear. In

this article, we will be con ce rne d with these an d similarapplications which call foi a constantnvelope,bandw idth-efficient, igital-modulationechnique. Re-

cent investigations into signaling schemes for suchapplications have centered upon MSK.

Modulation. studies during the late 1960's led to thedevelopment of MSK [2], [3].MSK was used y the DataTransmission Co.Da tran ) for i ts prop osed a tanetwork in 1972 [4]. Other applications which havecons idered nd/orused MSK since then include a

proposedA T & Tom estic satellite syste m [5],[6],

military tactical radio [7], extremely low frequen cy (ELF)underwater commu nication systems [8], and Canadiancommu nications technology atell ite (CTS ) exp erim ents[9]. We will exa mi ne the major attr ibutes of MSK whichma ke it a suitable candid ate for su ch applications. W ebegin with a brief review of some related modulationtechn iques such as FSK, PSK, QPSK, and OQPSK.

FSK and PSK

The cons traintof a constant envelope feature for themodulation scheme narrows he search o wo majorsignaling tech niqu es, namely, FSK and PSK . Consid erbinarycommunication-transmittingapulseevery T

seconds (at theignaling rate of 1/T baud) to deno te oneof two equally likely information sym bols , +1 r -1. FS Kden otes he wo tates by transmitting a sinusoidalcarrier at o n e of tw opossible requencies, wh erea sbinary PSK (BPSK) uses the two opposite phasesf thecarrie r (i.e., 0 and 180").Fig. 1 ho ws typical signals in th etw oypes of modulation.Notehat BPSK is alsoequivalent to amp litude modulating the carrie r wit.h theinformation bit stre am , i.e. , multiplication with +1or -1.

The two schemes can be compared on theasis of theirbit error ate (BER) performance i .e. , he veragenumber of errors in transmittinga long bit str ea m )

. .

"1". . . . . " . . " . I

' I -1 "

" 1 " "-1"

Fig. 1. (a ) Binary phase shift keying; b) Frequencyshi ft keying.

through an deal channel. The deal channel is taken to bea linear all-passcha nne l, corru pted nly by additive whiteGaussian oise with a constant one-s ided) ower

spectral density of N o W/Hz. T he required ratio, € , /No ,of signal energy per bit (E,) and noise evel N o o achievea given BER (su ch as1error in l o 5 bits) is the quantityof

interest .

It can be shown hat optimum receivers for binarysignals in such cha nne ls call for match ed filters (alsoknown as correlator-detectors) with perfect arrierphase eference available at he receiver.For uchcoherent receivers, which base their bit decisions afterobserving the signal over Tsec ond s, there exists classof signals, of which PSK. is one, which turns out to beoptimum in the sense of requiring the minimum am oun tof €,/No for aspecified BER. Thisoptimum class of

signals is called "antipodal," i.e., the twoignals denotingthe two possible information symbols have exactly thesame shape but opposite polarity. On the othe r hand ,from the viewpoint of simpler receiver implementation,noncoh erent detection schem es, hich do not make useof the carrier phase reference, can also be used. Forexample, a noncoherent detector for FSK can use twoban dpas s f i lters tuned to the two frequencies, followedby e nvelop e detectors and bit-rate samplers, and basethe binary ecision o n which of th ewo ampledenvelopes is the larger. It can be show n that for suchnoncoherent detect ion, the opt imum class of signals is

the class of noncoherently orthogonal signals. (Orthog-onalsignals are hose hat do not nterfere with on eanother in the process of detection. If the demodulationprocess is coherent , hey anbe called oherentlyor thogonal and if noncoherent detect ion is employed,noncoherently orthogonal. For example,n noncoherentFSK signaling using enve lope dete ctors, the two FSKsignals at frequencies' f l and fz are said to b enoncoherently rthogonal, i f , when tone t f, is

transmitted, the sampled e nvelope of t he ou tpu t of th ereceiving filter tuned tof2 is zero, i .e. , no cross alk.) Inthe case of FSK, the minimum separation between the

J uly 1979 15

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two frequencies qualshe signaling ra te /T o rnoncoherent orthogonality. The performance of such a

noncoherently orthogonal FSK scheme is much poorerthanhe oherent ntipodal PSK sche me . Even if

coherentlyorthogonal FSK is usedanddetected bycoheren t methodsn an effort to improve performance,tis still poor er by 3 -dB (in term s of E,/&) than PSK.

The poorer performancef FSK has been responsiblefor restricting the usef FSK mainly to low -da ta-rat eow -

efficiency app lication s, while PSK has been the prefer redscheme for efficient higher-data-rateapplications.W ew i l l show later that thiss not a fair assessment of FSK . Infact , MSK,a coherentlyorthogonal FSKmodulationscheme, requires only 1/2T H z f requency separat ionand achievesa performance equivalent to that ofPSK,

when oherenteceiver asests ecision fterobserving theignal over 2 it per iods (2Tseconds)ratherthan just one. Beforee view MSK as a particular case of

FSK, it is helpful tounders tand everalother PSKschemes , such as QPSK and OQPSK, and toiew MSK

as a particular variation of OQ PS K signaling.

QPSK and OQPSK

Theopt imum E,/& performance chievable withBPSK led to a search for mechan isms to impro ve thebandw idth efficiency of PSK sche me s wi thout any oss of

perform ance. It was ound hat ince os2rfct nd

s in2rfct (wheref , s the car r ier f requency) are coherent lyorthogonal signals, two binary bit s tre am s modulatingthe two carrier s ignalsn quadrature can be demodulated

separately . (In analog comm unication, this idea has beenused for a long time to multiplex two signals on the sam ecarrier , so as to occupy the sam e bandwidth, e .g . , the

tw ohrominanceign als in color television ar e

modulated onto the color subcarrier this way). S u c h a

modulation scheme, increasing the bandwidthfficiencyof binary PSK by two, is known as QPSK ands show n inFig. 2 (a).

I'a,(t)

The input binary bit stre am € a k > , ( a k+1)k Oj1,2,. . .arrives at a ratef 1/Tbaud ands separated into twos t r eams a , ( t ) and aQ(t) onsisting of even and odd bi ts ,respectively, as shownn the ex ample waveforms f Fig.2(a) . The wo pulse rains modulate he nphase andqua dratu re com pon ents of the carrier and the sum ( t ) ,the m odulated Q PSK signal, can be represente d as

The two terms in (1) represent two binary PSK signalsandaneetectedndependentlyueohe

orthogonality of cos(2rfCt+ a ) nd sin (27~f,t+x)4 '

Using a well-known trigonometric identity, (1) can also

be written as

s ( t )=COS(2frj't +O ( t ) ) (2 )

where, as shown in Fig. 3, O ( t )=0; k 90" or 180"corresponding to the four combinations of a , ( t ) a n d

The OQ PSK signaling can also be represented by (1)

and (2) and the di f ference between the two m odulat iontechniques is only in the a lignmen t of the two it s tream s.The odd and evenit s treams, transmitted at the ratef

1/2Tbaud ,are ynch ronously aligned in QP SK asshow n in Fig. 2(a)] such that their transitions coin cide.OQPSK modulation is obtain ed by a shift or offset in th e

relative alignments of a , ( t ) nd aQ(t) ata s t reams by anamount equa l to . Fig. 2(b) shows the offset. (OQ PSKs

also somet imes refer red to as s taggered QPSK.)Th e difference in time alignment in the bit stre am s

does not change the power spectral dens i ty and hence

bothQ P S K n dO Q P S K pect r a aveheam e(s in2~ fT/2rfT )2 sh ape, assoc iated i th the rectangularpulse used for signaling. However, the two modulationsrespond differently when they undergobandlimiting an d

a&).

a0 a6>t

0 2T 4T 6T -8T

a0 ! a6 1 .t

-T 0 T 3T 5T TI

Dernuiti-

0 T 2T 3TT 5T 6T 7T 8T &iin (2Tfct + n/4)

0 2T 4T 6T 8T

Fig. 2. (a) QPSK modulator; (b ) Staggeringof data streams in OPQSK.

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Fig. 3. Signal space diagram or OPSK and OPOSK.

hardlimiting operat ions,. nco unte red in applicationssuc h as satel li te com municat ions . Thedifference in thebehavior of the two modulations can be understoody astudy of the phase changes- in he car r ier in the wo.modulations.

In QPSK, due to the coincidentlignment of a , ( t ) ndaQ ( t ) t reams, the car r ier phase can change only on ceevery 2T . The carrier phase over any 2T interval is anyo n e of the four phases show n n Fig. 3 depending on thevalues of IaQ(t) , , ( t )> .n the next 2Tinterva1, if neitherbit s tream chan ges sign, the carrier phase remains the

same. If o n e c o m p o n e n t ( a , ( t ) r a a ( t ) ) hanges sign, aphase shift of 290" occurs . A change in bothcom pon ents results in a phas e shift of 180". Fig. 4(a)

shows a typical QPSK signal waveform, for the samplesequence a , ( t )a nd aQ ( t ) ho wn in Fig. 2( a). In a satellitecomm unication system, the modulated signal shown in

Fig. 4(a) is' bandlimited by a bandpass filter so a s t oconform to out-of-band pectral emission standa rds.The bandlimitedQPSK will no longerhave constantenvelope an d in fact, the occasion al phasehifts of 7r radin the carrie r will make the envelo pe go t o ze ro [IO].Atth e satellite rep ea ter, this ignal will un de rgo hardlimitingwhich, while resto ring heconstantenvelope to thesignal, will a t the sam e time res tore essentially all thefrequency sidelobes back to their original level prior tofiltering. These undesiredidebandsegatehebandlimiting of the QPSK signal carriedoutat hetransmitter and introduce out-of-band radiation on th esatellite downlink that maynterfere with oth ercommunication sys tems. On the othe r h and ,andlimit-ins and hardlimiting operati ons do not seem o produce

the middle of th eothersymbolandhence only on ecomp onent can switch at a ime.Thiseliminates thepossibility of 180"phase changes and phase changes arelimited to O", ? 90" every T seco nds. Fig. 4(b) s how s atypical OQP SK waveform for the exam plebit stream s inFig. 2(b). When a OQPSK signal undergoes bandlimit-ing, the resulting intersymbol interference (smearing of

adjacent pulses on one anoth er) cause s th envelope to

droop slightly in the region of 7r/2 rad phase transitions.

Sincephase shifts of 180" havebeen voided,heenvelope does not go t o ze ro s it do es in th e bandlimitedQPSKase.Whenhe bandlimited OQPSK goesthrough a hard limiter, the slight envelopedroop is

removed by the limiting process.However, limitingaffects only the envelope and the phase is preserved.Consequent ly , he absence of rapid phase shifts (andhen ce high frequency conten t) in the region of a 7r/2phase change means thatimiting will not rege nera te thehigh freque ncy com pon ents originally removed by thebandlimiting filter. T hus , ut-o f-ba ndnterference is

avoided.Tes ts [lo] indicate that unlike QPSK, the spectrumof

OQ PSK after imiting remains essentially unchanged nds e e m s to retain its bandlimited nature in almost itsentirety. OQPSK signals also see m to perform betterthan QPS K in the presence of phase j it ter a ssociatedwith noisy referencecarriers [ l l ] .Fur thermore, heoffset of T s betwee n the 2 bit s tream s in OQ PSK hasbeenshown to beoptimum in terms of phase jitterimmunity in the prese nce f additive Gau ssian noise 12].All these advantages possessed y OQPSK s t em mainly

from the act that OQ PSK avoids thearge phase changeof 180"associated with the QPSK format. This suggeststhat further suppression of out-of-band interference inbandlimiting-hardlimiting applications can be obtained,f

the OQ PSK ignal format canbe m odified to avoid phasetransitionsaltogether.Thisca nbe hought of a sa nobviousmotivation for designing constant nvelop e

modulation sche me s with continuous phase.MSK is o n esuc h sc hem e, a s will be discussed nex t.

-~

t h e sam e deleterious effect on an O QP SK signal. 0 TT 3T 4TT 6T 7T

s tates s imul taneous ly. One com pone nt hasransitions in Fig. 4. (a) OPSK waveform; (b) OPOSK waveform.

In OQPSK,he binary comp onentsannothange (b)

J uly 1979 17

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-T T 3T 5T 7T

al t ) cos (vt/PT) (b )

. os 27rf,t t

' 0 2TTT ST

aa(t) sin (d)

. in 2rrfct t

0 T 2T 3T 4TTTT (f)

b k -1 -1

f

0 T 2T 3T 4T 5T 6TT

Fig. 5. MSK waveforms.

~

M SK can b e viewed as a form of offset quadrature

phase shift keying with a half-sinusoidal rather

than rectangular weighting.

M SK

MSK can be thought of as a special ca se of OQ PSKwith sinusoidal pulse weighting [13],[141. Consider theOQPSK signal, with the bit streams offset as shown inFig. 2(b). If sinusoidal pulses ar e employed nstead ofrectangular shapes, the odified signal can be efined as

MSK and eq ualss ( t ) =a, ( t )cos("f )cos2rfct +aQ( t ) s in ( r ' ) s in2r fc t .

2 T

(3)

Fig. 5 shows the various comp onents f the MSK signaldefined by (3). Fig. 5(a) show s th emodified in-phase bitstream waveform, for the sample a , 3 s t r eam shown nFig. 2(b). Th e c orresponding values f the e ven-bits ares h o w n a s k 1 inside the waveform. The in-phase carrier[the first term in (3)], btained bymultiplying thewaveform in Fig. 5(a) by c o s2 ~ f , t ,s show n in Fig. 5(b).

Similarly, the sinusoidally shap ed odd ibit stream and thequadrature carrier are shown in Fig. 5(c ) and (d) . Thecomposite MSK signal s ( t ) , he addition of Fig. 5(b ) and(d) , s shown in Fig. 5(e ). Th e aveform in Fig. 5(e) can bebetter understood if we use a well-known.trigonometricidentity to rewrite (3) a s

(4)( t ) =COS[2Tfctf bk(f)ITt+ $ k ]2 T

where bk i s+1 when a, and aQ have oppos i te s igns and

bk is -1when a , and aQhave the sameign and $ k is 0orT corresponding to a , =1or - .Note thatb k ( t ) an alsobe written as -a,(t)aQ(t).

From Fig. 5(e)an d (4), we ded uce he followingproperties of MSK.

1) It has cons tant envelope.2) There is phase continuity n the RF carrier at theit

transition instants.3) The signal is an FSK signal with signaling

frequencies f+= c + 1/4Tandf - = c - 1/4T.Hence thefrequencyeviationquals half the bit rat e,.e. ,

This is the minimum frequency spacingwhich allows he

two FSKsignals tobecoherently orthogon al, in thesense discussed in the section on FSK and PSK; hencethe name "minimum shift" keying. Since the frequencyspacing is only half a s muc h as he conve ntional 1/Tspacing used in non coh eren t dete ction of FSK signals,MSK is also referred to as Fast FSK [3].1

4) The exce ss phase f the MSK signal, referenced tothe carrier phase, is given by the term

A f =f +- - =1/2T.

@( t )= bk( t )- k-t 7rt

2 TTin (4), which increa ses or dec reasesinearly during eachbit period of T seconds . A bit bkof +1cor responds to anincrease of the carrier phaseby 90" and corresponds to

a n FSK signal at hehigher requency j+ . Similarly,bk =- mplies a linear de cr ea se of ph ase by 90"over Ts , corresp ond ing to th e lower frequency f-. (In order tomake the phase cont inuous atit transitions, the carrierfrequency f , should be chosen such that c is an integralmultiple of 1/4T, ne-fourth h e bit rate.) The exce ssphase O(t) is show n in Fig. 5(f), with th e corre spon dingfrequencies and values of b, shown below.

Th us MSK can be viewed either as an OQ PSK ignalwith sinusoidal pulse weightingr as cont inuous phase(CP FS K) signal witha frequency separation equal oone-half the bit rate.

PULSE SHAPING AND POWER SPECTRA

Th e powe r pectra of QP SK,O Q P S K ,and MSK(shifted tobaseb and ) an all be expre ssed by themag nitude squared of P(f) ,he Fourier transformof thesymbol haping unction p(f). Thus, for QPSKandOQP SK [ see ( l )]

'There re everal orms of MSK described in the i terature;

howe ver, all of them arespectrally equivalent to the version described

here. Most of the m differ in details, such s bit-to-symbol precoding and

the use of differential encoding.

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1

(7t1 <T

P ( t ) = (5)elsewhere.

and for MSK [see (3)]

c o s (g) I t I d T.

P ( t ) = (6 )elsewhere.

Thus the spectral density G(f ) for QPSK and OQPSK(normalized to have the same power) is given by

and for MSK is given by

The spec tra are sket che d in Fig. 6.

The difference in th e rates of falloff of these spectracan be explained on the basis of the smoothnes s of the

pulse shape p ( t ) . The smoother he pulse shape, hefas ter is t h e d r o p of spectral tails to zero. Thus , MSK,

having a smoother pulse, hasower sidelobes than QPSK

an dO Q P S K . A measure of thecompac tnes s of amodulation spectrum is the bandwidth B which contain s

99 percent of the total power. For MSK, B =(1 .2/T)while for Q P S KandO Q P S K , B =( 8 / T ) [13]. This

10

0

-10

OQPSK

-20

N

r

Im

F

(3

-30.

-40

-50

-60

- 00

7

0.5

iK

1.5

fT

2.5

Fig. 6. Spectral density of OPSK, OPOSK, and MSK.

J uly 1979

indicateshat in relatively wide-ba ndatellite links

(whe re, or xam ple, filtering is not used fter henonlinearities), MSK may bespectrally mo re efficientthan QPSK or OQPSK. However , as can be seen romFig. 6 , the MSK spec trum has a wider mainlobe than

QPSK and OQPSK. This suggests that in narrow-bandsatellite links, MSK may not 6e the preferre d meth od.Computer simulations [151, which take into account allrelevant parts of typical ' wide-band and narrow-band

TDMA satellite links, tend to suppor theboveconclusions.Assumingheransm itter nd satelliteamplifiers to be operating at pow er saturation, results

[15] show hat MSK gives supe riorper fo rmance to

QPSK when a , theproduct of channel pacingandsymbol duration exceeds .8 n d toOQP SK only when a

exceeds 2.3. OQPSK is shownoaveuper iorperformance to QPSK except when a is less than 1.4.However , it should bepointed out that n realistic systemapplications [13], [15], . the difference in th e require d( € , / N o )or the three schem es seemso be less than 1d B

and the cho icef modulat ion method depen ds o n o ther ,less obvious, criteria.

MSK has someexcellent special propertie s that mak eit anttractivelternative when otherhannelconstraints equireband width efficiencies below 1.0bit/s/Hz. For examp le, the continuou s phase nature ofMSK makes it highly desirable for high-power

transmitters driving highly reactiveoads [8]. Sinceintersymbol switching occurs when the nstanta neou samplitude of p(t) is zer o, the finite rise and fall times anddat a asy mm etry nevitably pre sent in practical situationshave a minimal effect on the MSK performance [16]. Inaddition, as we shall see below, MSK has simpledemodulation and synchronization circuits .

MSK TRANSMITTER A ND RECEIVER

A typical MSK modu lator is sho wn in Fig. 7 [6],[9 ],[ 161.The multiplier produ ces two phase ' coherent signals atf requencies f+ and f-. T he advan tage of this method of

forming the binary FSK signals is thathe signalcoherence and thedeviation ratio ar e largely unaffectedby variations in the data rate9]. Th e binary FSKsignals,after being separated by means of narrowbandpassfilters, ar e properly com bined. to form the in-p hase a nd

quadra tu re a r r i e r omponen ts .These arr iers remultiplied with the odd and even bit s trea ms a , ( t )and

aQ(t) which are offset by T , as in Fig. 2(b) J to producethe MSK modulated signal s ( t ) as defined in (3 )].

Th e block diagram of a typical MSK receive r is shownin Fig. 8. The received signal (equal to s ( t )of (3) n theabsence of noisendntersymbolnterference) is

multiplied by the respectiv e n-ph ase and quad rature

carriers x( t ) and y ( t ) followed by integrate and .dumpcircuits. Th e multiplier-integrator cons titutes correla tiondetect ionorma tch ed filtering, anoptimumcoherentreceiver in the abse nce f intersymbol interference.N o t ethe integration interval of 2T s . T he emodula tion worksa s follows: if s ( t ) of (3 ) is multiplied by x( t ) (= COSAf/2TC O S ~ A ~ , ~ ) ,he low frequency compone nt of the result

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BpF st(t) = % C O S 27rfct+d 2 T )

f +

> x (t)

co s 27rf,t fcztl/4T)o

COS [7rt/2T] I

BP F

>Y (t)f - S z (t) =‘h COS (27rf ct - 7rt/2T)

BandpassFilter

Fig. 7 . MSK modulator: x ( t ) =cos( r t /2T)cos2r fc t ;y ( t )=s in( r t /ST)s in2r f , t .

Integrator

Fig. 8. MSK receiver: x ( t )=cos(nf/2T)cos2nfc1;y(f) =sin(r1/2T)sin2rl,t.

FrequencyDivider

MS K Sunde’s FSK

BandpassFilter

clock

. .

Fig. 9. Synchro nization circuits for MSK: I+ =& +1/4T;

f- & - 1/4T.

( the output f the integrator) equals,(t)(l+cos r t /T) /4and hence theolarity of the sampler output determines

the value of a,(t). T h eopera t ionon hequadra tu re

20

channel is similar and determines the valuesof the odd-bits.

The reference waveforms x( t ) and y ( t ) and the clocksignal at )$ the bit rateneededat hesamplersarerecovered from s ( t ) as sho wn in Fig. 9. Although theMSK signal s ( t )has no discrete com ponents which canbe used for synchronization, it produ ces strong discretespectra l components a t f+and 2f- when passed througha squarer .T hequa rer, in effect, dou ble shemodula t ion ndexandproducesan FSK signal withAf = 1/T, known as Sunde ’s SK [171. Sunde’s FSK h as50 percent of its total power in line components at the

two ransmitter requencies.)Thesecomponentsareextracted by bandpass filters (in practice, by phase-locked. loops) andhenrequ ency division circuitsprodu ce the signals

s , ( t )= )$cos(27rfct+“t )27- (9)

and

s2 ( t )=Wcos(27rfct--2T)’ (10)7Tt

respectively. Th e s um an d ifference s, +s2and sp- s1

produce the reference carr iers(t)and y ( t ) , respectively.

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If s l ( t ) n d sP ( t ) re multiplied a nd low-pass filtered, t heoutput is '/4 cos2 r t / 2T (asignal at '/2 the bit r ate) which is

th edesire d timing waveform. Th us he MSK formatlen ds itself to very easy self-synchronization.

Th e natu ral 80" ambiguity produ ced by the divide-by-two circuits i .e., wh ethe r the outp utsa re? l ( t ) , t sq ( t ) ]ca nbe emov ed by differential enco ding ndothertechniques [14],[ 181. (Differential encoding is a t ech-nique in which changes or ransitions in bit stre am s,

rather than the absolute values themselves, are encodeda s $1 and -1.At the receiver, a differential de co de r willbe employed to generate the original bit stream.)

".

y . (b) ? C O S (27rfctf nt/2T) ii

' i

! 1 %i

Fig. I O . Signal space diagrams for (a) B PSK (antip odal);

and (b ) FSK (orthogonal) .

ERROR RATE PERFORMANCE

In addition to it5 bandwidth efficiency and self-synchronizing capabilities, the error rate perf orm ancefMSK in an ideal cha nne l, as efined in the section onSKand PSK is also of intere st. It is relevant at th is point to

summarizehe erfo rma nce capabilities of relatedbinary and quadrature modulations. inary PSK (BPSK)with k c o s 2 ~ r f ~ tepresenting "1" and "- ," s , as wementioned before, an exa mp le f antipodal signaling an dcanbe epr esen ted s how n in Fig. 10(a) with anormalized distance of two between them.n QPSK, thetwo ca rr ie r s u sed (c os (2 ~ r f ~ t7r/4) and sin(2-rrft +T /

4)) are orthogonal and hence the two bit stream s a r ( t )

and aQ(t) an be demodulated independently. Henceor

t he same ( € ( , / N o ) ,he e rro r probabilities of coherentlydetec ted BPSK andQ P S Kreheame .incestaggeringhe bit stre am soes not changeheorthogonality of th ecarriers,OQPSKhas hesameperformance a s BPSK and QPSK.

MSK ( 3 ) usesantipodal symbol sha pes (t o s &2 T

and t sin&) over 2T to modulate the two orthogonal

carriers jus t as was the casen QPSK. Also, the energynthe two shapes p ( t ) in (5 ) and (6) are the same. Thus,when match ed filtering is used to recover the data (as

2 T

was the case n Fig . 8) , MSK has the same performance

as BPSK, QPSK, and OQ PSK.Note, howev er, hat it is the detection of the MSK

signal on the basis of observation over 2 T secon ds t .hatresults in this good perform ance. If MSK is coherentlyde t ec t ed a s anSK signal with bit decision mad e ove r anobse rvation interval of T secon ds, MSK would be poore rthan BPSK by 3 dB. This s because the coherent perfor-mance of equal energy binary signals in white Gau ssian

noise depen ds only on the "distance" between the twosignals in the signal space-the larger the dista nce , theless the probability of error . (Thiss intuitively appea lingsince the larger the distance, the less the possibility of

mistaking on e signal for the other .) AsFig. 10(b) shows,MSK, viewed as an example of orthogo nal FSK ignaling,has only a distance of a etween the twoignals. Thisdecrease in the distance in FSK as compared toBPSKtranslates into an ( € , / N o ) ncrease of 3 dB needed to

mainta in the same error ra te asn a BPSK scheme . ThisdB disadvantage of FSK overBPSK vanishes n the caseof MSK, whe re bit decisions are made after observing thewaveform over two bit periods.

Even though T is the duration of one .b i t and onedecision per ransm itted bit is needed,betterperfor-mance may beobtained by observing he receivedwaveform over a ongerperiod, thus giving us m oreknowledge abou t he underlying signal and/ornoiseprocess. In MSK, thephasesare elatedove r 2 bitperiods and hence by observing over 2T seconds andusing the continuous phase nature of MSK, we know

mo re abo ut the signal. In fact, as is evident from theOQPSK format of M S K (3), we know that over2 T sec-onds , it is o n e of two antipodal signals which h as b eentransmittedandhence heequivalence in theperfor-mance of MSK and BPSK.

Since MSK is a type of FSK, it can also benoncohe rently detected (e.g., by means of a discrimina-

tor)whereas QPSK systemsequ ire ither a fullycoh ere nt or differentially coh erent detec tion schem e.

This possibility of noncoherentetectionermitsinexpensive demodulation of MSK 'when the received( € , / N o ) is adeq uate and provides a low-cost flexibilityfeature in some systems.

EXTENSIONS A ND GENERALIZATIONSMSK or cont inuous phase SK (CPFSK ) may be gen-

eralized to include other values of Af, the requencyseparation, and a longer bit memory before the decision

has t obe made. For arger observation intervals uch as3T or 5T , a maximum improvement of 0.8 dB has ,beenreported for Af =0.715/T [18]-[20]. However,hecomplexity of the circuits involved doe s not see m to

favor these schemes over the simple yet efficient MSKmodulation.

Similarly, while retaining the adv ant age of good biterrora te erformance,hepectral ropert ies of

MSK canbe mproved by shaping hedatapulsesfurther.Note hat in MS K, he symbolpulse shapep ( t ) is c o s [ ~ t g ( t ) / 2 T ] w h e r e ( t )= 1, 0 d d T. 'O the r

J uly1979 21

7/15/2019 MSK-paper


choices of g(t) ar e possible with the sp ectral falloffratedepending on he nd-pointbehavior of the hape

cho sen [21],[22]. For xam ple, aunction su ch sg(t)=s i n ( 2 ~ t / T ) / ( 2 ~ t / r ) k n o w n s si nu so id al fre-

qu enc y shift keying [23]) results n a muchsmoo the rp ( t )

and produces an asymptotic spectralalloff that is twiceas fast a s in MSK. Unfortunately, all the se generaliza-tions tend to produce a broader (main lobe) spectrumthan MSK thusworsening heperform ance t low

bandwidth/bit rate values. MSK has been extended tomultiple level pulses, know n a s multiple amplitude MSK(MAM SK) [24]. Othe r rec ent wo rks [25],[26] indicatethat application of an efficient baseband coding schemesuc h as correlative coding [27] to MSK may be th e an-swer to fur ther spectra l economyandgood performance.

SUMMARY

The MSK schem e was shown to be a special ca se of

continu,oushase FSK signaling with frequen cydeviation equal to the bit rate . MSK ca n also be viewedas a form of offset QPSK signaling in which the symbol

pulse is a half-cycle sinusoid rathe r han heusualrectangular form. It com bine s in on e modulation form atmany attractive attributes such as constant envelope,compact spectrum, the error ra te performancef BPSK,and simple demodulation and synchronization circuits.

MSK is an excellent modulation technique for

digital inks when bandwidth conservation and

the use of efficient amplitude-saturating

transmitters are mportant requirements.

These ea turesmake MSK an excellentmodulation

techn ique for digital links in which bandw idth conserva -tion and the use of efficient transmitters with nonlinear

(amplitudeaturated) evices remportant designcriteria.

REFERENCES

[ l] J. G. Sm ith, “Spectra lly efficient m odulation,” in Pro c. IEEE Int.

Conf. Commun. (ICC ’77), Jun e 1977, pp. 3.1-37-3.1-41.[2] M. L. Doelz an d E. H. Heald, Collins Radio Co., “Minimum-shift

data communicat ion system,” U.S. Patent 2 977 417, Mar. 28,1961.

[3 ] R . D eBuda, “Coheren t demodulat ion of frequency shift keyingwith low deviation ratio,” IEEE Tran s. Comm un., vol. C O M -2 0 ,pp. 429-435, Ju ne 1972.

[4] W . A. Sullivan, “High capacity microwave syste m f or digital dat a

transmission,” I€€€ Trans. Commun., vol. C O M -2 0 , pp. 466-470, Jun e 1972.

[5 ] D. M. Brad y, “FM-C PSK: Na rrowband digital FM with co herentphase de tection,” in Proc. IEEE Conf. C omm un. ( ICC 72). Ju ne

[6 ] -, “A cons tant enve lope digital modulation techniq ue for milli-meter-wave satellite system ,” in Pro c. IEEE Int. Conf. Commun.(ICC ’74), Minneapolis, MN, Ju ne 1974.

[7] E. J. S a s s a n d J . R. Hannum, “Minimum shift keying modem fordigitized vo ice comm unication s,” J . RCA, pp . 80-84, 1974.

[SI S. L. Bernstein et a/. , A signaling schem e fo r ext rem ely low fre-quency ELF) ommunic ation,” IEEE Trans .Commun. , vol.

C O M -2 2 , pp . 508-528, Apr. 1974.[9 ] D. P. Taylor et a/.,“A high sp eed digital mode m for experimental

work on he communications echnology satellite,” Can. Elec.Eng. J . , vol. 2, no. 1, pp. 21-30, 1977.

1972, pp . 44-12-44-16.

22

[ l o ] S . A. Rhodes, “Effects of hardlimiting on bandlimited transmis-sions with conventional and offset QPSK modulation,” in Proc .Nat . TeIecommun. Conf . , Houston , TX, 1972, PP . 20F/1-20F/7.

[11] -, “Effect of noisy phase reference on coherent detection of

offse t QP SK signals,’’ IEEE Tra ns. C omm un., vol. COM-22, PP.

1046-1055, Aug. 1974.[121 R . D. Gitlin and E . H. H o, “Th e per forma ncef taggered quadra-

ture amplitude modulation in the prese nce of phase jitter,” IEEETrans. Commun. , vol. COM-23 , pp. 348-352, Mar. 1975.

[13] S . A. Grone meye r and A. L. McBride, “MSK and offset QPSKmodulation.” IEEE Trans . Com mun., v01. COM-24 , pp. 809-820,Aug. 1976.

H. R. Mathwich, J. F. Balcewicz, and M. Hec h t , “The effect oftandem band and amplitudeimiting on the Eb/No perform ancefminimum frequency) shift keying MSK),” IEEE Tran s. Com-mun. , vol. C O M -2 2 , pp. 1525-1540, Oct.. 1974.M. Atobe, Y . Matsumoto , and Y . Tagash ira , “One so lu t ion fo rconstantenvelopemodulation,” in Proc. 4th Int.Conf.DigitalSatellite Commun. , Montreal, P.Q., Canada, Oct. 1978, pp. 45 -50 .R. M. Fielding e t a/., Perfo rmance character izat ionof a highdatarate MSK and QPSK channel,” inProc. IEEE Int. Conf. Com mun.(ICC ’77), Ju ne 1977, pp . 3.2-42-3.2-46.W. R . Bennet t andS.0 .Rice. “Spectral density and autocorrela-tion functions associated with binary frequencyhift keying,” BellSyst. Tech. J. , vol. 42 , pp. 2355-2385, Se pt . 1963.R . DeBuda,“FastFS Ksignalsand heirdemodulation,”Can.Elec. Eng. J. , vol. 1, no . 1, pp. 28-34, 1976.W . B. Os borne and M. B. Lun tz , “Coheren t and noncoheren tdetection of CPFSK,” IEEE Trans. Comm un. , vol. COM-22 , pp .

R. DeBuda, “About optimal propertiesf fast frequency-shift key-ing,” IEEE Trans. Com mun. (Cor resp.), vol. COM-22 , pp. 1726-1728, Oc t. 1974.M. K. Simon, “A generalization of minimum-shift-keying (MSK)-type signaling based upon input data symbol pulse shaping,”IEEETrans. Commun. , vol. COM-24 , pp . 845-856, Aug. 1976.M. Rabzel and S. Pasupathy, “Spectral shaping n MSK-type sig-

nals,” IEEE Trans.Cornmun. vol. COM-26 , pp. 189-195, Jan .1978.F. Amoroso, “P ulse and spec trum man ipulation in the minimum(frequency) shift keying (MSK) format,” IEEE Tr ans. Com mun.(Corresp . ) , vol. COM-24 , pp. 381-384, Mar. 1976.W . J. Web er , I l l , e t al., “A bandwidth compressive modulationsystem using multiamplitude minimum shift-keying (MAM SK),”

I€€€ Trans. Cornrnun. , vol. C O M -2 6 , pp. 543-551, May 1978.

IEEE Trans. Commun.. vol . COM-23 , pp. 1228-1243, Nov. 1975.G . J . Garr ison , “A power spectral densityanalysis for digital F M , ”

F . d e Jag e r an dC. B. Dekker, “Tamed frequency modulation, Anovel method to achieve spectrum economy in digital transmis-sion,’’ IEEE Trans. Comrnun. , vol. COM-26 , pp. 534-542,May1978.S. Pasupathy, “Correlative coding; A bandwidthfficient signalingscheme,”lEEE Comrnun .SOC. ag . , vol. 17 , pp. 4-11, July 1977.

SubbarayanPasupathy w asborn in Ma-dras, India. He eceived heB.E.degree in

Madras, India, n 1963, theM. Tech . degree ntelecommunications rom heUniversity of

electrical engineering from the Indian Instituteof Technology, Madras, India,n 1966, and theM. Phil. and Ph.D. degre esn engineering and

applied cience romYaleUniversity,Ne wHav en, CT, in 1970 an d 1972, respectively.

From 1965.1967, heas a ResearchScho lar and par t - t ime Lectu rer a t the Ind ianInstitute o f Technolosv.Madras. ndia.an d

1023-1036, Aug. 1974.

he worked as Teaching Assistant atYale University , CT; from968-1971. F rom 1972-1973, he was a Postdoc toral Fellow at the Univer-s i ty of Toronto, Toronto, Ont. , Canada, working in the area of arrayprocessing of sonar signals. Since 1973, he has beenwith the Depart-ment of Electrical Engineering, Universityof Toron to , Toron to , Ont . ,Canada, where hes now an Associate Professor and Chairmanf th eCommunications Group. His current research interestsie in the are asof digital communications, sonar-rad ar systems, and communica tiontheory.

Dr. Pasupathy is a registered Professional Engineer in the Provinceof Ontar io , Canada, and a me mber of the IEEE.

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