BSTJ 50: 7. September 1971: Data Transmission by Combined AM and PM. (Salz, J.; Sheehan, J.R.; Paris, D.J.)

9 MB·English

coven eerie
Mi SL Se

Data Transmission by Combined
AM and PM

Hy J. SALZ, J.R, SHEEHAN, and D. J. PARIS
(tnt wove Bara 2,100)

{This paper preety tortie analges and experimental seriaion
of the perormanes af «gtd tata mode which wae combined amplitude
Gd phe mariiation (AAE-BPM), The ters! wot aes operation
beer the unilinited additive Gauerion cheonel The resiver aac the
tern fr whioh tortie rele are peace, wee an xsl
set i paral wh m pues det caer tho deta, The eer
ferme cule at eommisniotion econey tmoraced 8 Bite per cel vf
Geol) a6 itina af vera oinal fo noe ratio (SAM) are wk
fa male couparnane it tien wneattice schon. Te theory pede &
Sefer fae tte dT poer ther ok! cs by race! fom angle

orion We present experiwovin! raul hich
vesent it the ar

‘Vhonstice! investigations of the pasformaice of womined amplic
tude ard pheee modition sysioms have been reported on by ©. R.
Catt (ba), A.C, Tswock ol R. W. Taek 1960), Lueky and
HLoneook® (1982), and aoe sesently by M. Later end M. B, Talhot®
(1957). These investigators foun! thal on the adative white Gnursian
anos, combined AM wd PM vielde a better error rate wt ned
Sius-to-neice ratio than PM of AQ slone when the nutter of toca)
evel is = 8,

ere we vigorously establish (hese elaine for & peutic system
Instend of ting ineae matebed Ble detetion (Ref. 2), we use ui
event] or cohevenr pasa ceteetien Wo etna he plise and a cone
‘ventional envelope deiesoe co estimate cc amplitude. Wil theoreti
ely aptiznum signa! [ocetone fn frditensiens apgce ars general's
Dob quatiiaed bre eubjces nly es fied poser huuitien, we onsider
Pate sign st ehh ave quantized,
2400 re meus ssn nugeMoN SORA, SEPNIBNUEE RL

“The cuestions we answer in Us paper exe the followings Given an
[X-love! svat ase he sling e use Fra idea and AF pee eel,
‘Hat = EX, what isthe value e° such Uh
le rior tei euglest fora fire! aroun ef S/N’ when simeling
cover the bandlinited adestive Griaerion shane? How docs thie cox
Vine latices eehere eomprr with anly PM a> AM nice: S/N
“How eilient i his mowulalign orien in texas of attaneble bite per
‘eyele of barvidth of xed error rile? And fnally how elose oem theeo
‘theorciedl raul be setizd im the nhoratery with aetual hardware?

We eptesent se rena signal by the time eres

St) — LU + Any caveat | lett — WD) o
lore Dy = sb (Bh — 1), dt = 1,2, ,b/2, for alls see the amplitude
Spmbois ord (Gq) i862 of aq apd phanen Tae signal pte)
ib barllinitel ideal pulse such that goT} — 1, when x= O-apd

(© for ull otlnr w. Poe she enlealutions that follow we leke

fin (fet /P];[ G8) /7] without lee oF geoealy. Th possive
fonetante Fy Ay ain ay 190s far arsitrery. The coal amount of
‘onmation ened by StCh i 177 Hog L 1 log, APs ~ 1/P logs 1
Iie A= ATL, We roeard Se eampituce symbols {and Dre phase
smb (8) a8 Selegercert wenéom variables. By ftrodueine &
forw’y stituted hace in Ze arms. of te 208 (+) funetion in
‘quition (1) nd ase nandoriang te cpoe: of (7 rene te signs]
SUH sutionasy, A sasigatorwand eulen'ction® reveals Pat he etal
average power in SU)

‘whens - anetes the enstable neers
Ror the ede mise ewe te santa} resentation

WO) ~ x0 emo + 9 sina
where a(t) andy) are glavionery tov mean independent baseband
{Guassian onosea poseeing decal variance 0

"The dla roeriver pesresecs tho sum sil $0) + TP() to ots
cetimutes of (Ee) amd (6c). Resp is wp ihe to paraliel

TEBE eins a var a ia ty fd Re 6
stern nam masses 2401

deieetne, Paosedzectars willbe denoted reawetively by B- the en-
Yelopesetecton wed g-—the phase een.

Tee E detewor eprvates hy Fos comping the envelope ct S48 +
Wt and thon ernclonans's sem iny Ube eel st every 7 econds
‘Phe a delee-oe compas the pane ef sil Pts ise Ge Re. fo
fade'si'el dseussion ef pause moduli aad cemoculetion) be i
then synelrouoysly purple to derive resimetre of {5} In al these
fperetione we asset comet timing fvoruation is ella at
the recive.

We begin by suelyeing the J detcetor fst. The envelope ofthe sum
Seuulis

oO =CE0

+(EW saben ego e960r

Ag 6m fale — 09) + OP

snd cumple teen at =

Wo abg en FH a

‘wha wo han use sae abvionsnotatoni shorthand, Tn ale shal
£ gemne exvelge exit we ral ave V+ Aby > O forall shies of
‘The oe. the soliton

vee ba o
ino ma by = (E — 1h. Ove tsk in the next seston ill be to wrel-
tute Uhr err ete iy Die Beer ine sr etn of toe probably

tiettbution of E*
"The detent compres either

forthe artual phuse. AS lng as 8

teeeeursments are wnambsons

ps teat of 82) = TEC
han 8 nang envelope these

‘The error rate of the B detector is doversinel from the conditioned
toil prebabiliee of B® (equation [21]

P= Pur Sele al
at

Fe = Bie La a
ate

f= aby 0 6
2K rH SuLL sre sREMERTEAY, sOWMNAL, SLEDS

avd

W = angen,
Tis diffe to ane}vze che exank ropresernaticn of these probubilicee
nd therefore we renee to expaneeAs ak: upper bound

"Phe laver tal prebaPiity i appee bur yy

* a

[owe pyaras < [one
~My, 580 ®

howe (the anit step funeton, P i te probably dst

UE and MnO) — (oF) ete momect geaeratng Fastin of

Tin ke masa an upper bound tthe pps tl probability Is

Bee Mol o

ince B*feaustion (4 i the sum of wquaes of to independent
Gaus renown vabibles wih met , :
the moment youersting fantion i rei elated om Bef. 5. 270),
The mol 2

oo
where
o
where
I) art =
ad
Fele way he
‘The mer hound jose derived Hele for wily por

in thee euouinious there sxite sw apiriom ar eaeh af a
ster nena raassouseca aus

hom: exporestially tightest To find thoee ae ae st the
Ccorivativw o Bat Bo ro bla

4 Pees nay
Beam 05 =8$# ae | ony =o
Ping eo rot
1 (—1+4)

‘Fer o postive st to exit i: Ss custo thn? > a Gu phawion' ly
reeeonablr sonsiticn) cine the aptsnune is thereore

D)

‘When thie vane of A ie subsite into 0) we get the final rel

res ton{ i 06
Siiely hn fh BAG) eto a0 we oes wo ret fo A
Tani er =a (1 af, Hoe jg rasan
tim shat 3/2 <M iving sie no pose rete When aro
tics an subned n Ba eloe habog? =172 =
2/8) sk the all elo, Using (rot in ego) mule
inthe Ba! unser fr nue Dut on he ues tl probs

rexfop{-sha or} av

We now have ail te ingredients ts yen ero este eallstions
Symbol delewion is abtaived hy eamparing the recived envelope
to fixed :tesho.ds. The recived envelupe iz the absereo of noise ie
Vp) = Aige =O 1,2,--- L/2 ane the shesbolds
ave sob ta F = 248, We soe ftom agtaone (10) om (11) Lal the wee
Fetem af Leth upper ard lew wil prosabistiee dapend ex the dif-
{sense beteen tae seseved auplte value ard the threshold, Taz
tmaxinmm of tbe aMtoronee ie srypy ik Cnnaeesiontge when one
lgcent errors are ranscere, she etror sei er howe hy

ay

‘ehere the consent ( is of minor msertonee. Move general techniques!
for udsiny the bebaviar of to! probabilities of aebicary Gauceian
2404 rus wets, wyeOmae TReeMNEAL SOCRS2, BOTENEH TL

imadoatic forma sex at. euustion (12) is elo an asymptotic
onl, approaching the wetunl evar vete ae af — 0. We Cetefore
toe exp! Ae/Be") as good erat for he eto vate ir eubsequent

"The probity of error for phace desectors is well knw (se Ref
45). The esl onmala for diferent have desetion ie

MN ay
Wie for coherent phase dtertinn

F (Berl

Py = om {Pest Gp oa

Tile whee 2 ie the nism wate ofthe eavloze in th eleence of
p-v-ag— 0, 45)

Tei reasonable vo requis hae th eror tutes in Une P ae deter
tors fw exponersillientjet. Phi ruiremenuds to Ue coniion

acy = AL-+ aitwie’ Sz, ilfereutal detetion (D. D.)

ee

(and avant
Saiving for V explicitly give

= Abd, MO, DD. on

y
Abily MCD.
whore
41 pp
wha
ran
and

iL Web 1d en,
[sh

‘These formulas indicate aow dhe power ito be partitioned Between
the ena Ute cartes phase information sd the signe! that earies
pene ok maxourscos 2405

she emplltde inorzantion cx concen ently deermine Ube tberbole
‘in the B te

Using equation (17) in equssion (2) we obsain a formuly for the

‘otal average teansaital pater as Tunetion 9? the number af ara

fe levels Lend the muaner of hice

Pee

iF ¢
(re, an a8)

where fie ether fg or f. depending on th upp of ph detactar em
loved

‘Ww now wish to compare the probability of orror exposeaty of the
mixed modeletion -ysiem with ut oyun: phase al pre and
todulation st fved sigsl-tnswiwe alin. For the mited moduletion
sycem we fest expnose 472 new fanotien of Ike pier us eeustion
[U8] and then sabatiite Inia equation (12). Negieating the ennstent
cosfeiert-ve obtain

{Poa a
rawoolPi yah yh ow

nese

sii, an = ye St
Whe on'y phone madultion is used wie total numberof eves Y=
MEL, the error rate become

(oP oaanegt bh
cop (oS Bein ager fe PP.

nat “
{Ps sigh 1.

4 3}

Powe ST 1

WF eh ree std i poe

en
2408 rem aera avsrmse Tarstea sounra, saNEM 1671

ei ea funetion of the Fratton Biller ie wea at
We therefore wee Ue alana

af Sh top 23

ms,
©. Seeman

rote oy = Bef
‘Assuring Lua dhe added wise hs Aat dooblesided spectral dene

es)

sud the comer footer i all ho erorerateexpreevons hesomes

Pi TP. _ enevgyih
— eM ay, nauaeyele

‘The fectoe wiping 4 in equations (10), (20), and (21) are all
‘qual to les than unity and tuereony may be rope degra
tion over Bina-y aysinms. (These tasters recuse to unity for binwy
stems

‘Compsvinna hetstmn tarse avatome ean conveniontly be oud by
poting the wluise sins n? these eoeisiens as Seaotina of Zand Me
fuck that 8 = BMF Towanl [ois cx the foloring defirsions one
nak,

Drs

1

ID toga sits.

By

p= tbe (st)

= hee =) eo

A naturel ction hich mew ates is the fllowing: for fcc s
there an L whieh auiniminy Dpy(Z, NI? The snswe> ie yes and the
sompavisons we present are base ot this wplimnum eoie of F— the
uber ef saulitude level,

‘Or fst reuite ane eonsatciau in ‘able T for types) values of
For instance, na level aystem all phase wodaltion yields beter
perforimses Uns eoaings eystam etree Dy i lem than Dg 17
snr beta “RaSSEGATON 210%

“Pant e T— Panta nis of Prmarsmsr Paretrrens

mij Ong

ecto en

EB, hore ino advantage here in gpliting the levels, On he order
Dbond for an S-level system, 2 axpliudes ud 4 plore pears pre
fevable than jost @phasos or 8 amples und che advantages gained

sce 1.) dE hen § thases are ueed nd 3.8 a8 wen 8 azplitiades are
ted. Te is alvays advantages to ane the level when JV = 8, The
sudvuntage becomes mare prououpead as 3 Socom: lac.

‘Weaow turn acteation tote comrsimiestion eicierey af she vavone

veodulation schemes cossiered. The Hare of mer. sedis the wtaine
Able sinner of bite per evel for q given agncl-tosnoiee ratio ra
fue err ate, Tho rite 17m bite pov epee aleve hy tae ste

= Blaze en

sete ie the symbol sgnsling sue atl Rid reguned ond
‘For alee doubieerdsband systems sich as PMC ane. AMGBM, 9/7? is
aqal to unity wile fr baosbard sr! single sdb myetems, o/c
fqual tate, We thereto have

Bove
we

loz. bitefeyele ey
2 ogy 3 bieeete

Since wo are comparing eyscms opening ever unequal bandwidths,
{tw anpropriat ta give sn alternative mnterprctation af the eonetant

1 ie tempting ta eel a che signal-to-noise ratio. Lowever the quantity
2Nqu snr acess te toise omer in the physiee! hanna, ‘he
um! nae power can only be deoeunes ence & evetionsiy be-
208 nam suLL Srounat aRONRACAT. ForRNAL, SERENE WF

‘con che wienaing rats ad he plgies: lanai ie given, Por
Aloublesileound sgeten-s A's fn fate the eto igus Tso-ueiae rai
binee p= B. Hose for hnsehendl and SB, 4 = LSM, We dell
tr th pein, heen afte she parameter ie wot Ia make samp!
ona ia very ein la sol The BB Sue-oe when wh ig often
of interes: inthe eetakl S/N, Fur vcan pie, we ate trom Table T th
‘Level AM he 1.7 UB woot chon level PM We mot bear in mind
however that the AM system for wat the figures ave given in the
table are double edd AM. 17, however, the comparicon is soul
for bavebend. AM or 98D-AAT vlan 2 ul wore ravet bo aldo tothe
TAB.

{We se from eto (20) oF (21) thet im oder to mnintain Fixed
‘ewor rate in BAI onl AM tbe signa-to-povee ratio must vary as the
Equare of the nuzber of lok when the Ieter is longe, When S/N it
fexpressed in dB i chun is dine» proportional tothe logarithm ofthe
Dumber of levels anc nenee to the eisieacy expressed in bits per eyele,
Dlcts af efisieney ve 8/2 in os for ANT and PM will chenefore appess
linear sith intel aloe, i eset ra’ be difere) A six
Tae argument coplns tS modletion t Uve rosalinda i twice
a lege compared wits PBI aad AM, THis ident trom the Tort hat
'2 SSE bviee as neny bies por eee cane allsine ae fy PME oF
ese siebual AY with she same rsonber u lvee,

‘We shall now skuvy toute eircey of eombined AMC and PME cea
fuevon of 378 expcuted i) alan nour an Fliows the sa
lope st the efficney uf SSD, In order to prove thie lam we mb
Alsnonsteate that in eombiond AN and PM S/N wares lincory with
tie numberof levels (ors ba ereoe eae, T's variation eam be
Aleduoed by eonedering the aerapretio bezawior of CL, 2) fqion
{i0)) Disvegaring ll wbiyicaivefaators af and and romping

sretaitne ata oe at
pu (; NV ay
gan ~(o~ 3 oe
meee! on

"The optinsan Lie proportvnal ln V/V since

age MM
3b rn

implies that

eo)