A Comparison of Modulation Schemes in Bandlimited AWGN Channels

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1 Souhen llinois Univesiy Caondale OpenSUC Coneence Poceedings Depamen o Elecical and Compue Engineeing A Compaison o Modulaion Schemes in andlimied AWGN Channels Ted J. Wolco New Mexico Sae Univesiy - Main Campus William P. Osone osone@eng.siu.edu Follow his and addiional woks a: hp://opensiuc.li.siu.edu/ece_cons Pulished in Wolco, T.J., & Osone, W.P. (1995). A compaison o modulaion schemes in andlimied AWGN channels. EEE Miliay Communicaions Coneence, MLCOM '95, Coneence Recod, v. 2, doi: 1.119/MLCOM EEE. Pesonal use o his maeial is pemied. Howeve, pemission o epin/epulish his maeial o adveising o pomoional puposes o o ceaing new collecive woks o esale o edisiuion o seves o liss, o o euse any copyighed componen o his wok in ohe woks mus e oained om he EEE. This maeial is pesened o ensue imely disseminaion o scholaly and echnical wok. Copyigh and all ighs heein ae eained y auhos o y ohe copyigh holdes. All pesons copying his inomaion ae expeced o adhee o he ems and consains invoked y each auho's copyigh. n mos cases, hese woks may no e eposed wihou he explici pemission o he copyigh holde. Recommended Ciaion Wolco, Ted J. and Osone, William P., "A Compaison o Modulaion Schemes in andlimied AWGN Channels" (1995). Coneence Poceedings. Pape 58. hp://opensiuc.li.siu.edu/ece_cons/58 This Aicle is ough o you o ee and open access y he Depamen o Elecical and Compue Engineeing a OpenSUC. has een acceped o inclusion in Coneence Poceedings y an auhoized adminisao o OpenSUC. Fo moe inomaion, please conac opensiuc@li.siu.edu.

2 A COMPARSON OF MODULATON SCHEMES N ANDLMTED AWGN CHANNELS Ted J. Wolco and William P. Osone New Mexico Sae Univesiy Asac n ecen yeas, as daa aes ise o seemingly deceasing availale andwidhs, a gea deal o eseach has een dieced owad inding andwidh eicien modulaion schemes. Two such mehods ae Paial-Response Signaling and Tellis-Coded Modulaion. oh o which pomise peomance gains in a andlimied channel when compaed o uncoded sysems. This pape will compae he peomance o hese schemes, when applied o a QPSK sysem ove vaious channel andwidhs. QPSK sysem, which also ansmis symols epesening 2 inomaion is, will also e evaluaed. A well known esul o he i eo ae o such an ideal QPSK sysem is / 7\ p = Q[,/?, whee Q(x) is he complimenay eo uncion, E is he enegy pe i and No is he single-sided powe specal densiy o he AWGN [5]. noducion As daa ae demands incease, he need o andwidh eicien modulaion schemes has diven a gea deal o eseach. As a esul, a nume o complex sysems have een developed. Paial-Response Signaling (PRS) [,2,3] and Tellis-Coded Modulaion (TCM) [4,5] ae wo mehods pomising inceased peomance ove andlimied channels, hus allowing highe daa aes hough he channel o ee peomance in he same channel. This pape will invesigae he peomance o elaively simple implemenaions o each o hese echniques - a QPSK PRS and an 8PSK TCM sysem - in channels o dieen andwidhs. y doing so, i will e deemined whehe o no hese implemenaions live up o hei pomised peomance gains. i eo aes ae esimaed hough aseand Mone Calo simulaion using he Signal Pocessing Woksysem@ (SPWTM) sowae package. Each sysem compaed ansmis a a ae o wo inomaion is pe channel symol. Channel andwidh is speciied y a 6h ode uewoh ile wihou phase-equalizaion. Simulaions ae peomed wih no andlimiing and a andwidhs equal o 3, 1.5 and 1. imes he symol ae, geneaing vaying degees o S. oh modulaion schemes ansmi symols epesening wo daa is. Theeoe, hei peomance will e judged o equal symol aes - equal inomaion aes - ove channels o equal andwidh. Fo compaison puposes, he peomance o an uncoded This wok was suppoed y NASA gan NAG Pi,) AWGN Souce (3 The esuls o he simulaions o he uncoded QPSK sysem ae pesened in gaphical om in Figue 2. The poailiies o i eo o dieen channel $ EEE Auhoized licensed use limied o: Souhen llinois Univesiy Caondale. Downloaded on May 29, 29 a 22:37 om EEE Xploe. Resicions apply.

3 andwidhs ae ploed vesus EOo. Alhough his sysem is ale o peom easonaly well - less han 2d o degadaion a an eo ae o lx1m4 - o channel andwidhs o 1.5.R~ o geae, hee is signiican peomance loss as he andwidh appoaches he symol ae. This is he peomance agains which he TCM and PRS sysems will e judged. P a 1E-2. 1 E-l 1E-3 E in 2 - QPSK Theoy ENo (d) *- QPSK, No andlimiing + QPSK, W = 3(Rs) A QPSK, W = 1 5(Rs) QPSK, W = Rs Figue 2 /'Peomance o Uncoded QPSK QPSK wih Paial-Response Signaling (PRS) Duoinay PRS was is pesened y Lende [3] as a nehod o high-speed daa ansmission. The addiion o a Viei pocesso o maximum likelihood sequience esimaion was made y Foney [2], in 1972, And, in 1975, Kaal and Pasupahy [l] pesened a uniied sudy o PRS. PRS sysems opeae ased on he idea o conolled S. Since he S1 is known, is eecs can e emoved y he eceive. This allows he shaping o he signal specum, naowing he signal andwidh o placing nulls in he powe specum o he ansmied signal. This naowe specum will pesumaly e ale o pass hough a naowand channel wih less disoion han is expeienced y he wide specum associaed wih QPSK and TCM signals. The Viei algoihm can hen e used o make he opimum sequence esimaes, iased upon he known S. PRS s:ysems ae usually denoed y hei sysem polynomial F(:D), o he om N-1 F(D) = CnD" 9 n=o whee{,) ae he samples o he desied impulse esponse h(), N is he smalles nume o coniguous samples ha span all he non-zeo samples, and D is he delay opeao [l]. he inpu and oupu sequences ae denoed {x,} and {y,} especively, hen whee m m. X(D) = Exn -D"& (D) = Cyp". n=o n=o The sysem polynomial can e chosen such ha he equency esponse closely maches he channel equency :sponse, heey minimizing he S1 encouneed. Duoinay, wih a sysem polynomial F(D) = 1 + D was chosen o his sudy ecause o is lowpass equency chaaceisics [ 11. The simulaion model consiss o wo independen duoinay PRS channels coesponding o he in-phase and quadaue QPSK channels. The wo daa seams {xi,} and {xqn} ae independen inay symols aking on values {- 1,l } wih equal poailiy. Alhough he sysem consiss o wo Viei pocessos, his choice o sysem polynomial educes hei complexiy o only wo saes. The esuling simulaion model is shown in Figue 3 and is made up o wo daa souces, wo PRS F(D)=l+D iles, a QPSK modulao, he channel ile, a mached ile and he wo Viei pocessos peoming maximum likelihood sequence esimaion. Pocesso Pocesso Figue 3 / QPSK-PRS Model File Auhoized licensed use limied o: Souhen llinois Univesiy Caondale. Downloaded on May 29, 29 a 22:37 om EEE Xploe. Resicions apply.

4 As in he uncoded QPSK simulaions, he inphase and quadaue esimaed daa sequences ae compaed o he coesponding ansmied daa sequences o esimaion o i eo aes. The sysem i eo ae o a given signal -o-noise aio is hen he aveage o he wo independen eo aes. Figue 4 pesens he esuls in gaphical om. The peomance o his sysem degades in a manne simila o ha o he uncoded QPSK sysem - sysem peomance is degaded y aou 1.5d a a andwidh o 1.5.R~ and y close o 2.5d a a andwidh equal o he symol ae. Noe howeve ha he eo aes wee signiicanly wose han ideal QPSK, even when hee was no andlimiing. s...;...-" _-...l... i... i... a E-1 E-2.. <.. e-.,.-. -, TCM sysems can e exemely complicaed, someimes applying mulidimensional ellis diagams wih lage numes o saes and vaying code aes. Complexiy in geneal inceases wih he nume o saes in he ellis. This pape ocuses on a elaively simple 4- sae, ae 2/3 (2 daa is o each 3 i 8PSK symol) XPSK TCM sysem [S, pp Even hough he complexiy o he sysem chosen is low, he heoeical asympoic coding gain ove uncoded QPSK is 3d, showing he powe o TCM. The 8PSK TCM simulaion model (Figue 5) opeaes on a single daa seam, {x,}. The daa is ueed and supplied o he TCM modulao in pais. Fo evey daa pai, one code symol is ansmied y he modulao hough he channel ile. Noise is hen added om an AWGN souce. The eceive sucue consiss o a mached ile and TCM Viei decode, which geneaes paallel daa esimaes. These esimaes ae conveed o a seial seam eoe compaison wih he ansmied daa seam. o E-3 E-4 E QPSK Theoy E/No (d) * QPSK PRS, No andlimiing -' QPSK PRS, W = 3(Rs) -( QPSK PRS, W = 1 51s) i QPSK PRS, W = Rs Figue 4 / Peomance o QPSK-PRS SPSK TCM 3ne ovious mehod o comaing eos geneaed y S1 is he addiion o coding o he sysem. Howeve, in many cases, coding comes a he cos o andwidh expansion. Thus any gains om he coding mus ovecome he loss geneaed y he inceased S. n 1976, Ungeoek [6] demonsaed ha Tellis Coded Modulaion (TCM), in which he modulaion and coding ae uniied, exhiis signiican coding gains wihou equiing moe andwidh. Souce daa is convoluionally encoded o geneae he code symols o e ansmied diecly ove he channel. The eceived daa is hen decoded using he Viei algoihm. q-lyk+, Viei Decode Figue 5 1 SPSK TCM Model Alhough his sysem is he mos complex o he hee lised hee, i is sill elaively simple. Convoluional encoding is a simple opeaion while he 4-sae Viei pocesso is no vey much moe complicaed han he wo 2-sae Viei pocessos pesen in he QPSK-PRS sysem. The small incease in complexiy poduces a signiican incease in peomance (Figue 6). Fo channel andwidhs a o elow 1.5.Rs, he sysem exhiis a peomance gain ove ideal uncoded QPSK. Alhough he sysem peomance degadaion is close o 4.5d o a andwidh equal o he symol ae a an eo ae o x~o-~, hee is less han 2.5d o degadaion compaed o ideal uncoded QPSK Auhoized licensed use limied o: Souhen llinois Univesiy Caondale. Downloaded on May 29, 29 a 22:37 om EEE Xploe. Resicions apply.

5 + QPSKPRS _ P a E-l E-2.j...,," ~".. " ;."....; ,.... _ ' E-2 - ~ -. ~ -- _ i..,.. E-3 E _ , ! - -. C -- E-3 ' E-4 +- E l E O 12 J - QPSK Theoy * OPSK EMo (d) QPSK PRS SPSK TCM Figue 7 / Peomance Compaison, W = 1.5-Rs Peomance Compaison Up o his poin, each sysem has een judged individually y is peomance ove a ange o andwidhs. The peomance o he dieen sysems in a common channel andwidh has no ye een compaed. This secion will make diec compaisons eween he sysems in he wo mos andlimied channels sudied. The i eo ae o each sysem, ove a ange o signal o noise aios, o a channel andwidh o 1 S.Rs is shown in Figue 7 elow. This se o cuves is epesenaive o all o he daa pesened o channel andwidhs a o elow 1.5.R~. Fo he wide andwidhs sudied -- no andlimiing, 3.Rs and 1.5.R~ - hee is clealy no advanage o choosing he QPSK PRS sysem ove uncoded QPSK in such siuaions. Such a decision would esul in oh inceased complexiy and peomance degadaion. Howeve, he use o 8PSK TCM insead o uncoded QPSK will esul in a gain o almos 2d in sysem peomance a an eo ae o l~lo-~. The gain is also inceasing wih smalle eo aes. Figue 8 compaes each o he sysem's peomances in he seveely andlimied channel in which he andwidh is equal o he symol ae. Hee, he PRS sysem egins o show a sligh advanage ove uncoded QPSK. Howeve, he gain is no moe han 1d a l~lo-~ i eo ae. The gain does seem o e inceasing wih deceasing eo aes, u only slighly. Again, he peomance o he TCM sysem is supeio o ha o he ohe wo sysems. Even in he mos seveely andlimied channel sudied, he 8PSK TCM peomance exhiis aound 2d o gain a an eo ae o p ' h E 1 E-2 E-3 E O 12 QPSK Theoy QPSK EMo (d) ' RPSKTCM Figue 8 / Peomance Compaison, W = Rs Auhoized licensed use limied o: Souhen llinois Univesiy Caondale. Downloaded on May 29, 29 a 22:37 om EEE Xploe. Resicions apply.

6 Conclusion Fo he simple u pacical sysems sudied, i appeas ha 8PSK TCM does povide he peomance gain pomised - i will povide coding gain ove uncoded QPSK in he same channel andwidh. On he ohe hand, he duoinay PRS scheme does no appea o delive on is pomise o mainaining ideal QPSK peomance levels in a naowand channel. n ac, o any channel andwidh geae hen Rs, uncoded QPSK acually oupeoms duoinay. This demonsaes ha one mus e vey caeul in dawing conclusions aou he likely peomance o signaling schemes in naow channels ased upon he powe specum o he ansmied signal. also aises many quesions aou he peomance, o he many andwidh eicien schemes eing oued in he lieaue oday, in ealisic communicaions channels - channeis wih andwidhs limis, phase disoion and nonlineaiies. Reeences [] P. Kaal and S. Pasupahy, Paial-Response Signaling, EEE Tans. Comm. vol. COM-23, No. 9, pp , Sepeme 1975 [2] G.D. Foney. J., Maximum-Likelihood Sequence Esimaion o Digiial Sequences in he Pesence o nesymol neeence, EEE Tans. nom. Theoy, vol. T-81, pp , May [3] A. Lende, The Duoinay Technique o High-speed Daa Tansmission, EEE Tans. Commun. Elecan., vol. 82, pp , May 1963 [4] G. Ungeoeck, Channel Coding wih Mulilevel/Phase Signals, EEE Tans. nom. Theoy, Vol. T-28, No. 1, pp , Januay [5] R. D. Gilin, J. F. Hayes & S.. Weinsein, Daa Communicaions Pinciples, New ok: Plenum Pess, Auhoized licensed use limied o: Souhen llinois Univesiy Caondale. Downloaded on May 29, 29 a 22:37 om EEE Xploe. Resicions apply.