when not to spread spectrum

8/13/2019 When Not to Spread Spectrum

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- _s E s / N oNo 1 ( M - I ) E,/ N o

The ra te a t which real informat ion i s transmit ted, expressed asinformat ion bit s per chip i sr k (chips / baud) E,/ E b (bi t s / chip) k Ts/T b

k R b W , b i t s / b a u dso that , analogously to the previous equat ion:

b E b / oNo' 1 (M-1) ( r l k ) / N o )

Given this value of E b /N o a s a design point to achieve somepresc r ibederror a te , he hermalnoisedensi ty N o m us tbesuch that :

I n T a b l e I for several code ra tes , we give values of specifiedEb/N, for achievingacceptableperformance (BER o p 5 )wi th a pract ica lonvolut ionalodendoftecis iondecoder . '

TABLE IR EQ U IR ED~ / N , FOR P ~ = ~ O - ~ITH C O N V O LU TI O N A L C O D I N G ASOFT ECODING

r(Bits/Bnud) Eb/No (dB)~~

(uncoded) 9.67 / 8 6.4314 5 5l / 2 4.5113 4.0lim (I /n ) 3.4'n-OD

Communicat ion a te l l i te ys temengineers (or l inkbudganalys ts) deal in terms of C / N o the received carrier power-no i se dens i t y r a t i o . B ecpse t he t o t a l t he rm a l no i se i s t he of upl ink and downl ink carr ier - to-noise ra t io , th is is obta if rom com bin ing t he tw o a s :

A l l but the last entry apply to practical decoder implementa(either constraint ength 7 decoders with 3-bit soft Viterbi decod inlong constra int length sequ ential decoders with2-bitsoft decodThe last en try is an asymptotic estimate. Like all other entries it is abo ve he value equired for r ro, whichnhis ase is 1(2 In 2) 1.4 dB. Note that using the atter, without the 2 dB asymptotically yields the results of [1-41

3 April1985 Vol. 23 N

IEEE Communica tions Maga


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dB-HzN o

Each is a func t ion of t h e t r a n s m i t t e d E l R P a n d a n t e n n a g a i na n d t h e r ec ei ve G / T for t h a t l in k . ( F o r a sample l ink budge t seeL y o n [SI). Th e to ta l r ece ived car r ie r power from a l l M ear thstations is :c = M E b Rb

I f t h i s q u a n t i ty i s n o r ma l i z e d b y th e th e r ma l n o i s e in th e to ta lu t i l i z e db a n d w i d t h ,No W,, the esul t is the otal receivedcar r ie r power - to- thermal no ise ra t io

Link per forma nce is measured by the total transmission rateefficiency of t h e t r a n s p o n d e r or l ink as a f u n c t io n of C / ( N O W S ) .M Rb/ W bits /ec /H z

F o r s p r e a d s p e c t r u m mu l t ip le a c c e s s ( S S M A ) s y s te ms , th i s i so b ta in e d f r o m th e s e c o n d , f o u r th , a n d f i f th e q u a t io n s to b e :

Fina l ly , assuming M la rge enough tha t M M , we h

F ig u r e 1 shows ransmission eff iciency of a n S S M A s ysa s a f u n c t io n of C / N , W , for each of t h e c o d e r a t e s s h o wn T a b l e 1.T w o m p o r t a n tc o n c lu s io n sc a n b e d r a wn r o m h ea b o v ee q u a t io n a n d F ig . I .

1 W ith S S M A, th e s a te l l i t e c o mmu n ic a t io n s y s te m i s a lwpower l imited and never bandwidth l imited .2) T h e r a t e e ff ic ie nc y M R b / W , s a t u r a t e s a t ( E b / N o ) - a sC /N , W , b e c o me s v e r y l a r g e . S in c e /No d e c r e a s e s wd e c r e a s in g c o d e r a t e r , t h e lower t h e c o d e r a t e th e b e tth ep e r f o r ma n c e .Lo we r in g h ec o d e a tecos tsn o th in gbecause the sys tem is a l r eady spread and , i t involves or e d u c in g th e v a lu e of k. However , per formance improvme n t d im in i s h e s r a p id lyfor r < / 3 , a s c a n b e n o te d fTa b le 1.


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Other Multiple Access TechniquesF o rT D M Ao rF D M A y s t e m s , h ea b o v ea n a l y s i sa l s oho lds , excep t t ha t t h rough channe l i za t i on use r s do no t i n t e r f e r ewi th each other . Thus N, o he rm a l no i se on ly and t he tw oprevious equ at ions are replaced by:

R b e N o ws M R b < r < I [ T D M A I F D M A ]Ws E b / No WSfo rHere W, is used to denote the to ta l bandwidth ut i l ized for a l lMusers .Figure 1 show s hep rev iousequa t i on o rva r iousr a t e s . T h e l i m i t a t i o n M R b / W ,< is imposed by the bandwidthrequirements of BPSK modulat ion. f QPSK modulation isused, the upper limit is doubled to r < 2 bitslbaud and henceefficiency continues to grow linearly until the new bandwidthlimit is reached.O fcourse , heaboves im pleanalys is gnores neff ic ienciest h r o u g h g u a r d b a n d r e q u i r e m e n t s f o r F D M A a n d g u a r d t i m e sfo r TD M A , bu t hese a r e m ere ly s ca le f ac to r s w h ich do no tinf luence he undam en ta l ehav io r .N o te l soha t ow er

With external interference, as considered in the next section,degradation will be greate r than with BPSK.

backof fo rinear er formance of nonl inearmplifiers r equ i r ed equa l l y fo r SSM A and FD M A sys t em s .Adjacent Satellite or Terrestrial Interference

Supposeexternal n ter ference salso received in heearterminal s main or s idelobe, e i ther f rom an adjace nt sa te l l iby ter res t r ia l means . This can a lso be caused b y another ear thterminals too wide beam, i l luminat ing the des i red sa te l l i te awell asts ntended djacent a te l l i te .Whateverhe ause ,suppose this adjacent in ter ference level , emanat ing f romothe r t e rm ina l s , i s on t he o rde r o f KC watts . I t hen fol loweasi ly that for SSM A, the in ter feren ce i s increased by a fac( I + K ) and the equa t ion i s modif ied to become:

F o r T D M A or FD M A , w e m us t a s sum e s im i la r m odu lain thedjacenta te l l i te . hentol lowshator Bmodulat ion,

fo r R b < r [ T D M A I F D M A ]WS

5 A p r i l 1985-Vol. 23 NIEEE C o m m u n i c a t i o n s M a g


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T husexternal nter ference enders uch ys temsalsopow erlimited at a level I / K Eb/N,) provided thi s does not exceed r.F i gur es 2a , 2b , and 2c show pe r f o r mance f o r bo t h cases f o rcode rates 1/ 2 3/4, a n d 7 / 8 , respectively, and several levels ofex t e r na l i n t e r f e rence ( K 1 / 2, 1/ 4 a n d I / IO-that is, 3, 6 a n dI O dB be l ow the desired carrier level) .

EpilogueBrief ly , we contendha t h e b o v e i m p l e n a l y s e s n d

exam ples teach the fol lowing lessons:1 W h e n C / N U s a t a premium (as w i th smal l ear th s ta tionst r ansmi t t ing t e spec t ab l edata a tes)don t on t r i bu t ef u r t h e r to t he no i se by hav i ng t he use r s j am one ano t he r ,unless bandw idth efficiency is of no conce r n . T h i s app l i e s

3The rationalization that the interference appears as Gaussian noisefor a non-spread spectrum modulation is more tenuous. However, withcoding and soft decision m odulation, everal bauds (proportional to thecode constraint ength) are summed before a decision is made whichmeanshateveralandomariables are summed,upportingGaussian assumption.

only for hermal noise imited (civil) systems. In mili tarysystems, we usual ly have a l ready given up on bandwidthefficiency in order to comb a t a ve r y pow er f u l j ammer , we a r e l r eady s i ngpr eadpec t r umechn i quesmi t igate thi s ef fect . In such a case , the addi t ional mu tualj a m m i n g a m o n g users employing pread pect rummul-t iple access echniques i s of ten nconsequent ia l . In ermsof F ig . w e a r e ope r a t i ng a t ve ry ow C / ( N o W ) r a t iw her eN O Wn o wcons i s t sp r i mar i l y o f j ammi ng p o w eAlso, heremaybe er res t r ia l ys tems uch s e l lularr ad i o w hi ch a r e not pow er limited, and where high extce l l u l a r in t e r f e r ence may make S S M A a m or e r easonab lchoice .2) Netwo rk cont rol i s a smal l pr ice to pay for the efficienca ff or de d b y T M D A o r F D M A . I n f a c t , S S M A is re ano t t o t a l l y uncon t r o l l ed . S ome f o r m of pow er con t r o lusual ly exerci sed; in a two-way sys tem em ploying a hcont rol i s inherent .E ven nnetworkprotocols , wemovi ng aw ay f r om uncon t r o l l ed , ne f f i c i en t, and po t en-t ial lyns tablet ra tegies ,uch as A L O H A ,o w a r dconf l ic t esolut ion rotocolswi th emand ss ignment ;c h a n n e l d e m a n d a s s i g n m e n t i m p l i e s n e t w o r k c o n t r o l achanne l a l l oca t i on . F ur the r mor e , pseudono i se keys mus t


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be d i s t r ibu tedoh e p r e a d p e c t ru m e t w o r k s , n dind iv idua l t a t ionsmus t ynchron ize owi th in mal lf rac t ion of a ch ip t ime .In te r fe rence f rom ad jacen t sa te l l i t e s appears to a f fec t thee ff ic ie n cy o f T D M A o r F D M A l e s s s e v er e ly th a n i t d o e st h a t o f S S M A .T r e a t i n gb a n d w i d t ha sa n n e x p e n s i v ec o m m o d i t ya n dprocess ing as expens ive i s buck ing the power fu l t r end oftechnology. Large-scale-integrat ion for large-scale applica-t ions is rapidly r iving own igi tal rocessing osts .Transmission bandwidth wil l always be at a premium. Asa by-produc t , we have shown tha t e r ro r -cor rec t ing cod ingincreasesandwidthfficiencynllmult ipleccesssys tems; par t i cu la r ly so in SS M A which i s a lways powerl imi ted , u t ign i f ican t ly l son T D M A n dF D M Asys tems . In the l a t t e r , a s C / ( N , W , ) inc reases , h igher coder a t e sa r e e q u i r e d oe x t e n d h e a t e i m i t ,a n d QPSKex tends he inear eg ionu p odouble he ate imit ofBPSK.

T h emyst ique of p read pec t rumcomm unication s is suchtha tc o m m e r c i a len te rpr i ses ,as well asa c a d e m i c s , are of tena t t rac ted by the nove l ty and c leverness o f the t echn ique . Also ,in mall r t i f icial ly idedmarkets, heremaybe emporaryeconom ic advantages . In the long run , th ough , i t i s the au thor sop in ion ha t we mus t s tand back and ques t ion he wisdom ofsquander ing a p rec ious resource such as bandwid th fo r reasonsof expediency.Acknowledgment

The au thor g ra te fu l ly acknowled ges the con t r ibu t ions o f ana n o n y m o u s e v i e w e rw h o s e e c o m m e n d a t i o n sh a v econs ider -ab ly enhanced the c la r i ty o f th i s expos i t ion .References

[ ] J. K. Wolf, Private Communication, 1980.[2] A. J. Viterbi, Presentation at IEEECommunication SocietyWorksh op on Comm unication Theory, Tucson, AZ, April 1982.[3] 0 Yue, Spread spectrum mobile radio, 1977-1982, IEEETransactions on Vehicularechnology. Vol. VT-32, No. IFebruary 1983.[4] J. Y.N. Hui, Through put analysis for code division multipleaccessing f the spread spectrum channel, IEEE Journal onJuly 1984.Selected Areas in C ommunication, Vol. SAC-2, No. 4 . pp. 482-286,

[5] D. L. Lyon, Personal com puter communications viaighperformance micro-earth-stations, to appear in IEEE JournaSelected Areas in Commun ication, 1985.

Dr Andrew Viterbi has devoted app roximately equal segments ocareer to aca demic research, industrial development, and entrepreneactivities.In his first employm ent after g raduating from MI T in 1957, he wmember of the project team at C.I.T . J et Propulsion L aboratory wdesigned and implemented the telemetry equipm ent on theirst succeU.S. satellite, Explorer I. In the early sixties at the same laborato rwas one of th e first commun ication engineers to recognize the potenand propose digital transmission techniques for space and satetelecommunication systems.As a professor in the UCLA School of Engineeringa nd Applied Scfrom 1963 to 1973, he did fundamental work in digital comm unicatheory and wrote twobooks on he subject, for whichhe eceivenumerous professional society awards and international recogniThese include three paper awards, culminating in he 1968 IInformationTheoryGroupOutstandingPaper Award. He has received three major society awards: the 1975 Christopher ColumInternational Award (fromhe talianNational Research Cousponsored by the City of Genoa); the 1980 Aerospace CommunicatAward (from AIAA);and the1984 Alexander Gra ham Bell Medal (fIEEE ponsored by AT T) for exceptional contributions toadvancement of telecommunications.The practical development of hese theoretical principles ed tofounding of LINKABIT Corpo ration, together with Dr. Irwin JacBetween 1968 and 1980 LINKAB IT grew to become a sizable compwith unique expertise and leadership in digital signal procesequipme nt for military an d government satellite comm unication. company has grownt the ame rate ince beingacquired by M/A-C OInc. four years ago,expanding nto commercial telecommunicaequipme nt, terrestrial a s well as satellite, and video scrambling busareas. Dr.Viterbi was Executive Vice President of LINKA BITfro mt o 1982. In 1982, when D r. J aco bs became Executive Vice PresideM/A -COM , h etook overas residentof M/A -COM LINKAB IT, In1984, he was appointed ChiefScientist and S enior Vice PresidenM/A-COM , Inc.He is a member of the U S National Academy of Engineering aFellow of IEEE. He is past Chair man of the Visiting Committee foElectrical Engineering Department of Technion, Israel InstituteTechnology, and he s presently a member of the MIT Corpo ratVisiting Com mittee for Electrical Engineeringand Comp uterScienceis also Chairman of the U . S . Commission on Signal Processing ofInterna tional Radio Scientific Union (UR SI) and a past member ofArmy Science Board. In spite of his corporate administrative dutiehas managed t o remain technically curr ent, having recently proposedspread spectrumprocessing techniques for jam esistant communicaandor digital cellular radio.

7 A p r i l 1985-VOI. 23 NIEEE C o m m u n i c a t i o n s M a g a

when not to spread spectrum

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