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Towards adaptation of OFDM based wireless communication systems

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Material Information

Title:
Towards adaptation of OFDM based wireless communication systems
Physical Description:
Book
Language:
English
Creator:
Billoori, Sharath Reddy
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla.
Publication Date:

Subjects

Subjects / Keywords:
adaptive modulation
orthogonal frequency division multiplexing
noise power estimation
signal-to-noise ratio estimation
modulation detection
Dissertations, Academic -- Electrical Engineering -- Masters -- USF   ( lcsh )
Genre:
government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: OFDM has been recognized as a powerful multi-carrier modulation technique that provides efficient spectral utilization and resilience to frequency selective fading channels. Adaptive modulation is a concept whereby the modulation modes are dynamically changed based on the perceived instantaneous channel conditions. In conjunction with OFDM systems, adaptive modulation is a very powerful technique to combat the frequency selective nature of mobile channels, while simultaneously attempting to fully maximize the time-varying capacity of the channel. This is based on the fact that frequency selective fading affects the sub-carriers unevenly, causing some of them to fade more severely than others. The modulation modes are adaptively selected on the sub-carriers depending on the amount of fading, to maximize throughput and improve the overall BER. Transmission parameter adaptation is the response of the transmitter to the time-varying channel quality. To efficiently react to the dynamic nature of the channel, adaptive OFDM systems rely on efficient algorithms in three key areas namely, channel quality estimation, transmission parameter selection and signaling or blind detection mechanisms of the modified parameters. These are together termed as the enabling techniques that contribute to the effective performance of adaptive OFDM systems. This thesis deals with higher performance and efficient enabling parameter estimation algorithms that further improve the overall performance of adaptive OFDM systems. Traditional estimation of channel quality indicators, such as noise power and SNR, assume that the noise has a flat power spectral density within the transmission band of the OFDM signal. Hence, a single estimate of the noise power is obtained by averaging the instantaneous noise power values across all the sub-carriers. In reality, the noise within the OFDM bandwidth is a combination of white and correlated noise components, and has an uneven affect across the sub-carriers. It is this fact that has motivated the proposal of a windowing approach for noise power estimation. Windowing provides many local estimates of the dynamic noise statistics and allows better noise tracking across the OFDM transmission band. This method is particularly useful for better resource utilization and improved performance in sub-band adaptive modulation, where adaptation is performed on the sub-carriers on a group-by-group basis based on the observed channel conditions. Blind modulation mode detection is another relatively unexplored issue in regard to adaptation of OFDM systems. The receiver has to be informed of the appropriate modulation modes used at the transmitter for proper demodulation. If this can be done without any explicit signaling information embedded within the OFDM symbol, it has the advantage of improved throughput and data capacity. A model selection approach is taken, and a novel statistical blind modulation detection method based on the Kullback-Leibler (K-L) distance is proposed. This algorithm takes into account the distribution of the Euclidian distances from the received noisy samples on the complex plane to the closest legitimate constellation points of all the modulation modes used.
Thesis:
Thesis (M.S.E.E.)--University of South Florida, 2004.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: World Wide Web browser and PDF reader.
System Details:
Mode of access: World Wide Web.
Statement of Responsibility:
by Sharath Reddy Billoori.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 73 pages.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
oclc - 55732247
notis - AJR1187
usfldc doi - E14-SFE0000334
usfldc handle - e14.334
System ID:
SFS0025029:00001


This item is only available as the following downloads:


Full Text
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ABSTRACT: OFDM has been recognized as a powerful multi-carrier modulation technique that provides efficient spectral utilization and resilience to frequency selective fading channels. Adaptive modulation is a concept whereby the modulation modes are dynamically changed based on the perceived instantaneous channel conditions. In conjunction with OFDM systems, adaptive modulation is a very powerful technique to combat the frequency selective nature of mobile channels, while simultaneously attempting to fully maximize the time-varying capacity of the channel. This is based on the fact that frequency selective fading affects the sub-carriers unevenly, causing some of them to fade more severely than others. The modulation modes are adaptively selected on the sub-carriers depending on the amount of fading, to maximize throughput and improve the overall BER. Transmission parameter adaptation is the response of the transmitter to the time-varying channel quality. To efficiently react to the dynamic nature of the channel, adaptive OFDM systems rely on efficient algorithms in three key areas namely, channel quality estimation, transmission parameter selection and signaling or blind detection mechanisms of the modified parameters. These are together termed as the enabling techniques that contribute to the effective performance of adaptive OFDM systems. This thesis deals with higher performance and efficient enabling parameter estimation algorithms that further improve the overall performance of adaptive OFDM systems. Traditional estimation of channel quality indicators, such as noise power and SNR, assume that the noise has a flat power spectral density within the transmission band of the OFDM signal. Hence, a single estimate of the noise power is obtained by averaging the instantaneous noise power values across all the sub-carriers. In reality, the noise within the OFDM bandwidth is a combination of white and correlated noise components, and has an uneven affect across the sub-carriers. It is this fact that has motivated the proposal of a windowing approach for noise power estimation. Windowing provides many local estimates of the dynamic noise statistics and allows better noise tracking across the OFDM transmission band. This method is particularly useful for better resource utilization and improved performance in sub-band adaptive modulation, where adaptation is performed on the sub-carriers on a group-by-group basis based on the observed channel conditions. Blind modulation mode detection is another relatively unexplored issue in regard to adaptation of OFDM systems. The receiver has to be informed of the appropriate modulation modes used at the transmitter for proper demodulation. If this can be done without any explicit signaling information embedded within the OFDM symbol, it has the advantage of improved throughput and data capacity. A model selection approach is taken, and a novel statistical blind modulation detection method based on the Kullback-Leibler (K-L) distance is proposed. This algorithm takes into account the distribution of the Euclidian distances from the received noisy samples on the complex plane to the closest legitimate constellation points of all the modulation modes used.
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0 2 4 6 8 10 12 14 16 -25 -20 -15 -10 -5 0 5 10 Sub-group numberPower (dB) Estimated noise+interferenceActual noise+interferenceConventional noise power estimateDesired signal power sMeWJ@YF‡{„{pQaX%[>-@MTQ†Z)Qa]pQZrFZBMQ†Z>O>ZHum@Q†[§QTCFH)|QgMTCF¦uQ'ˆFU@kTCBMPX>-BMQ†ZROeQ@MBY=X{RDGF>O`M>-BMQZ\Qg]O>ZH\|QaMTCFduQAˆFf@CTQArFf@VBC=SF@A>ZTXMTCTMQ†ZEK>ZHJ{MZBYFU@]Ff@CFZilF"@A>-BMQ)Qg]\HKMT/WSTCFHMZBC=MT^e†WS@CFz2745684BY=JF1>rFU@A>-e†FZJQaMTCF[§QAˆFf@MT‹)HK{RTH9FfTAil@M:FH:F]cQ@CFzBY=JF\iQZrFZBMQZ>OgZSQgMTCF[§QAˆFf@•FfTCBMPX>-BCFXFI>TCWS@CFUTQ†Z?O;>TMZeOFr>OWJFQArFf@BY=JFˆ=QgOF]@CFIbWSFZi;¦:>ZHS{=MTr>OWSFMTNBC=SF>rFU@A>-e†FIHZJQaMTCF[§QAˆFf@Q'rFU@NBY=JFˆ=QgOF:>ZHJ{RTiU>ZE:FdTCFUFZ_zBC=SFiQ†ZrFZBMQZ>OFUTCBMPX>BYFˆQ@C¤TˆFOPOMZXFI>TCWS@MZeBY=JF>rFU@A>-e†FZJQgMTCF[gQ'ˆFU@A{=SF[@Q[§QTCFIHTAi8=JFXFXF>-TCWJ@CFfT:gQBY=OQif>O>ZHeOQ†:>OAZSQgMTCF[§QAˆFU@FUTCBMPX>BYFUTA{=SF¢BQB>OA:>ZHMT/HMrMH9FIHMZBQƒe†@QW[TQg]TCW:J‹:>ZH'T>ZHMZF>i8=TCW:J‹e†@QW[_zBY=JFU@YF>-@CF‡TCW:J‹if>@C@MFf@CTA{=SFMZTCB>ZBA>ZFQWSTZJQaMTCF[§QAˆFU@r>OWJFfT">@CF)>rFf@A>-e†FIHQ'rFU@}FI>†i=TCW:S‹e@QW[{=JFZ_zBC=SFUTCF)>rFf@A>-e†FIHr>OWJFUTQArFU@ FI>†i=TCW:J‹e†@QW[>-@CF]WJ@CBY=JFf@/>rFf@A>-e†FIHQArFf@•…‰/sn%hT;XV:§QgOT/Y>rFf@A>eMZeMZBM`XFHQaX>MZC{=JF^eWJ@YF¦TC=Q'ˆTBY=JF>rFU@>eFHZJQaMTCF[§QAˆFf@FUTCBMPX>BYFUTQArFf@FI>†i=TCW:J‹e†@QW[{sQ@@CF]Ff@CFZijF[WJ@[§QTCFzBY=JF)>†ijBCW?>OaZSQgMTCF[§Q'ˆFU@r>OWSFUTMZFI>†i=TCW:J‹e†@QW[>@YF)>OTQeMrFZ{RT"iU>Z:FdTCFUFZ_zBY=SF[@Q†[§QTCFHE>OeQ@MBC=XFfTCBM`X>-BCFfTvBC=SFOQif>OmZJQaMTCF[gQ'ˆFU@rFU@;LˆFO`O{ZBC=SF^eWJ@CFBY=JFH'FUTM@CFIH)TMeZ>O[gQ'ˆFU@QArFU@/F>i8=TCW:J‹e†@QW[MT3>OTQeMrFZ{s@QgXBY=JFfTCFzOWJFUTQArFf@F>i=)TCW:S‹e@QW[iU>Z:Fif>OilWO>-BCFIHvFI>TMPO;{¢|QBMilF%BY=_>-B¢BY=JFZJQaMTCF[§QAˆFf@¢FUTCBMPX>BYF[FU@]Q@X>ZijFH9F[FZH'TQ†ZBY=SF)OWJFQArFU@F>i8=TCW:S‹e@QW[{¢=JFZBY=JF)OWSFMTrFU@;OQ'ˆzBY=JFFUT‹‚†

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BM`X>-BCFfTvH'FrM>-BCF]@QgXBC=SF3>ilBYW_>OZJQaMTCF[§QAˆFf@r>OWJFdH9WSF/BQMZiQ@C@CFIilBH'FiMTMQ†ZTA{RTvH'FUTAij@M:FIH:F]cQ@CFzBY=JF/FfTCBMPX>-BCFfTvif>Z\:FM`X}[@QArFIH]WS@CBY=JFf@:;WJTMZeH'FiQH'FH\H'FiMTMQ†ZTA{sMea{‡{P‚†{TC=Q'ˆTBY=JFhZijFQa]BY=JF[@Q†[§QTCFH>ZHiQZrFZBMQ†Z>O>OeQ@MBY=XTMZiQaOQ@CFIHZJQaMTCF"HQgXMZ>-BCFIHšFZrM@Q†Z?XFZBYTA{=JFMZBYFU@]FU@YFZilFOPMPXMBYFHšTAijFZ>@MQ>-TXFZBMQZFIH>:gQ'rFMTiQZTMH9Ff@CFIHˆMBC=HM£§Ff@CFZBMZBCFf@]FU@CFZijF[gQ'ˆFf@OFrFOTA{=SFh†ijBCW?>OZJQaMTCF¦>ZHFUTCBM`X>BYFHZJQaMTCFr>OWSFUTMZF>i8=TCW:S‹e†@QW[>@CFif>OilWO>-BCFIH>ZH>rFU@>eFHJ{RT/iU>Z):F 0 1 2 3 4 5 6 7 0 0.2 0.4 0.6 SNR (dB)Mean Squared Error Conventional algorithmProposed algorithm sMeWJ@YF‡{P‚{hFI>ZS‹-@CFIH‹k@Y@Q@/u§Ff@]cQ@X>ZilFQa]pQ†ZrFZBMQZ>O>ZH)u@Q[§QTCFIHROeQ@MBY=XTMZpQaOQ@CFIH\|QgMTCF{TCFUFZBY=JF[@Q[§QTFIH>OeQ@MBY=X[FU@]cQ@XTXW_i=:FfBCBYFU@_BY=?>ZiQ†ZrFZBMQZ>OUZJQaMTCF[§QAˆFf@_FUTCBM`X>-BMQZMZBCFf@XTQg]J^JZHMZeBC=SFOQif>OZSQgMTCF[§QAˆFf@A{sMeWJ@CF‡{‡{ATC=QAˆTGBC=SFhZilFMZˆ=MBYFZJQaMTCF{=MT^eWJ@CFNTC=QAˆTGBC=SF¢@Q:WSTCBZFUTCTQg]BY=JF[@Q[§QTCFIH>OeQ@MBY=Xˆ=SFZBC=SFZJQaMTCFMTZJQB\iQaOQ@CFIHJ{RT1if>Z:F)TCFfFZ?zBC=SF[@Q†[gQTCFIH>OeQ@MBY=XˆQ@C¤T>TˆFOPO>T¦BC=SFiQ†ZrFZBMQ†Z>O>OeQ@MBC=Xˆ=Mi=MT¦T[FiM^iU>OPO;H9FfTMeZFIH]Q@ˆ=MBYFZSQgMTCF>-TCTCWX%[BMQZ{krFZMP]BY=SFZJQaMTCFMTˆ=MBYFzBY=JF[@Q[§QTCFHL>OeQ@MBC=XHQFUTZJQBOQTCF[Ff@]cQ@X>ZilF>-eg>MZTCB3iQZrFZBMQ†Z>OTAi=JFXF{‰ZBC=SFQBY=JFf@=?>ZHz>TFUŠ[_O>MZFIH>:gQ'rFzM`]BC=SFZJQaMTCFMT¦iQaOQ@CFHzBY=JF[@Q†[§QTCFH>OeQ@MBC=XQWSB[FU@]cQ@XT¦iQZrFZBMQ†Z>OgZJQaMTCF[§QAˆFU@%FUTCBM`X>-BMQZ>OeQ@MBY=X{‚

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-2 0 2 4 6 8 10 12 Sub-carrier IndexGain (dB) 1 2 3 4 5 6 7 8 9 10 11 0 0.1 0.2 0.3 0.4 0.5 Window SizeNormalized MSE MSEmin MSEmin MSEmin MSEmin MSEmin sMe†WS@CF‡{{m‰[BMPX>OMZHQAˆZHS{W}$]a^ZŸI3`_fm7f_=JF[Ff@]cQ@X>ZijFN@CFUTCWOBYTŒ>@YFQ:B>MZFIH}BY=J@QWSe†=\iQgX}[WJBYFf@GTMPXWO>BMQ†ZTA{RZ‰/sn•hT;TCBCFXˆMBY=ƒ…„‡TCW:J‹iU>-@C@MFU@CTMT3iQ†ZTMH9FU@YFH>ZH)BY=JFˆMZHQAˆTMfFUT3>@YFr>-@MFH]@QaX„BQš„{sQ@BY=JF\iQaOQ@CFHZSQgMTCFz>iQ†‹i=_>ZJZFOMZBCFf@]FU@YFZilFTQWS@AilFz§ˆ=Mi=MTX%QH'FOFH>T>ZRD[@QilFfTCTQg]r>-@;MZeX%QH'FOQ@AH9Ff@CTzoMTWSTCFHJ{RHSHMBMrFˆ=MBYFZJQgMTCFMTMZiOW_H9FIH>[>@CB]@QaXiQgOQ@CFHZSQgMTCFz>ZH[Ff@]cQ@X>ZijFNFr>OW_>-BMQ†ZTŒ>-@CFX>H9F]cQ@ˆ=MBYF/>ZHiQaOQ@CFIHZJQgMTCF/HQgXMZ>-BCFIHFZrM@Q†Z?XFZBCTzˆ=Mi= >-@CFij@CF>-BCFIH:;r>-@;MZeEBY=JFiQgOQ@YFH‹ZSQgMTCF‹BQ‹ˆ=MBCF‹MZBCFf@]FU@YFZijF@A>-BMQTCp|}DŒC{=SFBY=JFQ@CFfBMif>OilWS@rFUTQ:B>MZFIH]@QaXkb{‡{Pƒ>ZH[@A>†ijBMif>OijWJ@rFUTV>@CF[_OQBCBYFH]cQ@Vp|Dr>OWJFfTQg]‚/HK>ZH‹‚/HK¢z>ZH>@CF]cQWZH%BQdX>Bi=_{RTQ:TCFf@rFIH]@QgXsMeg{‡{`{zBY=JFQ†[BM`X>O9ˆMZHQAˆTMUF]cQ@">iQgXV:_MZ>-BMQ†ZQg]iQgOQ@YFH>ZHˆ=MBCFZSQgMTCF)H9F[FZH9TQZBC=SF\iQ@Y@CFO>BMQ†ZQg]BY=JF[gQ'ˆFf@T[FIilBY@A>OH'FZTMB;]Q@1HM£gFU@CFZBO>eTˆMBC=MZBC=SFˆMZHQAˆQg]BY=JFiQaOQ@CFHZJQaMTCFz>-TˆFO`O>TBC=SFZJQaMTCFr>-@M>ZilFQg]BY=JFˆ=MBYFZJQaMTF¦,C0¢>ZHˆMZHQ'ˆTMfF72{RTVTCFfFZ?zBC=SFh-TCFUTVBMPO`OMBV@CFI>†i=JFfTŒBY=JFQ[BM`X>OˆMZHQAˆTMUFz>ZHBY=JFZiQZBMZWJFfTŒBQMZij@CF>-TCF{‡g„

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200 400 600 800 1000 Sub-carrier IndexGain CINR -3dBCINR 3dB 200 400 600 800 1000 CINR -3dBCINR 3dB 2 8 32 128 512 0.05 0.1 0.15 0.2 0.25 0.3 Window sizeNormalized MSE Simulation CINR=-3dBTheory CINR=-3dBSimulation CINR=3dBTheory CINR=3dB 2 8 32 128 512 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Sim CINR=-3dBTheory CINR=-3dBSim CINR=3dBTheory CINR=3dB Model Order 2 Model Order 4 dfeghji,k0lnmpoqmsrjeptuhwvpxzyre{q|M}k~!h€vy,~1{n‚ƒjƒji,{qƒ„i…e†x‡y,k0ˆ‰e|€ŠQ{…‹Œr„e"kŽm|3‘{v{i!k’Š|„{ne~!k0ŠH{nte|wx‡y!k’Šk"|U“”ei,{q|wtk|Uy,~…•„x‡~y,–„k0t—{”ŠQkŽvr{i…ŠQk"if{y,–jk‘{v{qi!k’Š|„{ne~!k0ŠHk™„|jk’ŠšU›y!–„kL‚9}œƒ„i!{s‘k~!~e|w‘i!k’xz~!k"~…•y!–„kL“Axzi…epx‡y…e{q|{ney!~ƒE{…‹Ÿk"i~!ƒEk’‘y,i!h€t e|y!–„k3¡i!k’¢rh„k|€‘›ŠQ{ntxqe|e~£t{qi!k¤irxzƒ€e†ŠŠHhjk¤y,{y,–we~e|€‘i!k’xz~!k¦e|§‘{qi,i!kŽvpxzyre{q|€m5¨f–€e~e~i,k„kŽ‘y!k’ŠšU›y,–jk3~!kŽvkŽ‘y…e{q|={nx~…txv†vki‹e|wŠH{H‹~…e"ke|x/‘{nv{qi,kŽŠ¦|j{e~!k=ŠQ{te|wxzy,k’ŠMk"|U“sei!{|wt—k"|Uy‹1–€e†‘–‰e~t—{”ŠQk’vk’Šœxz~x‡|‚}œƒ„i!{”‘k"~!~—{Jt—{sŠHkŽvj{qi…ŠHkilxz~‘{nt—ƒ€xzi!k’Š‹ey!–=xt—{”ŠQk’v{qirŠQk"i•f¡{qiy,–jkL~…xt—kL‹1–€ey,kL|j{e~!k“„x‡i…epxz|€‘k’m7¨–we~xqvpv{…‹1~šky,y!k"iy,i…xq‘se|jg{nsy,–jk9|j{ne~!k9~!y…x‡y…e~!yre†‘~e|ŠjeEk"i!k"|Uy—~!hšj‘"xzi!irek"igi!{qh„ƒj~xz|€Šk"|j~!h„i!k~7{ƒjyre†txvt—{”ŠQh€v†x‡y…e{|t—{sŠHk~!k’vk’‘yre{q|‹ey,–we|k’xq‘–~!hšjšxz|€Šjmd{i7‹1–wey,k|j{e~!kŠQ{te|wx‡y!k’Šk|Ž“sei!{|wt—k"|Uyr•sy!–€e~0k~!yreptxzyre{q|t—k"y!–„{sŠi,kŽŠQh€‘k"~0y!{3y!–„k‘{|U“k|Žy…e{q|€xqvEy!k’‘–„|wep¢rh„k{n|j{e~!k0ƒE{…‹Ÿki1k"~!y…eptxzyre{q|€•A‹1–„ki!keye~xz~!~!h€t—kŽŠ9y,–wx‡y1y!–„k7e|Uy,ki…¡k"i…e|jg|j{e~!k7e~‘{t—ƒwvk"y!k’v›‹1–wey!k’mln

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f‰ˆŠ;_"‹c*jŒŽ'Ž‹')(_&*ja'$(H"&ecŠ„e~!y…x‡|w‘ke~Ly,–jk&t—kŽx‡~!hji,k{Šje~…‘i!k"ƒwx‡|w‘›{i3e|w¡{qirtxzyre{q|v{~!~L‹1–„k|M{q|jk—d$e~xzƒƒji,{H”e†tx‡y!k’Š3y,{x‡|j{qy,–„ki#q‡m{”ŠQk’vs~!k’vk’‘yre{q|œxept—~x‡y~!k’vk’‘yre|jgMx;‘x‡|wŠ„e†Š„xzy,k£t—{”ŠQk’v†•*xt—{q|„gtx‡|›•’y!–€xzy—te|weptek"~Ÿy,–we~e|w¡{qi…tx‡yre{|v{q~!~…mw|&¡{qi!y,–w‘{nte|„g3Š„e~…‘hj~!~…e{q|„~…•’y,–jk—dn~Ÿ{šyrxqe|jk’Š¡i!{nty!–„ki!kŽ‘kŽe“qk’Š~…xqt—ƒ€vk"~‹epvpvški!k’ck"i!i!k’Šy!{Mx‡~Lxz|€Šy!–€xzy0{n€y,–jkx‡ƒjƒji,{H”e†tx‡y…e|„gt—{”ŠQk’v†•xU|j{…‹1|8Šje~!y!irešhjyre{|/y,{&‹–wep‘–Le~3xzƒjƒ„i!{…septxzy,kŽŠ;y!{•1x‡~Rm=¨–jkkUƒ„i!k"~!~…e{|5¡{qiLy!–„kŠje~!yrxz|€‘kšk"y‹Ÿkk"|¤y‹Ÿ{Šje~…‘i,ky,kdn~e~…• N’‘LPR;“ ”:•L”v{g L” R” #qmpq‹1–„ki!kJe~Ny!–„ky,{y…xv|Uhwtšk"i*{še|j~—e|y,–jkdfmˆœ–jk"|£tuhwvyreƒ€vkL‘"xz|€ŠjepŠjx‡y!kLt—{sŠHkŽv~—x‡i!kuhj~!k’Šj•y,–jk7t—{”ŠQk’vA‹–wep‘–¦te|€e†te"k~N’‘ LPWR—– e~‘–„{q~!k|¦xz~1y,–jkšk~!yŠjei!k’‘yre{|wxvA™„yšky‹Ÿk"k|¤‹–wxzye~{š~!k"i!“qk’Šx‡|wŠxqvpv„y!–„k‘x‡|wŠ„e†Š„xzy,kt—{sŠHkŽv~9e|€ŠQk"Uk’ŠšU›–m0¨f–„kte|weptuhwtshw‘"v†epŠQk’xz|Šje~!y…x‡|w‘k~šk"y‹Ÿkk"|¦y!–„ki!k’‘k’e“kŽŠ|j{ne~›~…xt—ƒwvk£x‡|wŠ3y,–jk’5‘{q|„~!y!k’v†vpx‡y…e{q|¦ƒn{ne|Uy,~‘{qi,i!k~!ƒn{q|€Šje|jg;y,{;k’xq‘–t—{”ŠQhwvpxzyre{q|¤~…‘–jk’t—k7e~uge“k|Mx‡~…• 8€9U™; š—™ E›—™CFœ9U™ G3iIK5 #qmp‹1–„ki!kšU™e~y,–jki!kŽ‘kŽe“kŽŠ£~…xt—ƒwvk3{|=y,–jk™4Ÿ\ ~hš‘"xzi!irek"i…•E›—™e~y!–„k3k"~!y…eptxzy,kŽŠ/‘–€xz|„|jkŽv¡i!kŽ¢hjk"|w‘›i!k~!ƒn{q|„~!kŽ•nxz|wŠE9U™*e~*y!–„k9‘v{q~!k"~!y*–›ƒE{y!–„k~…ek’Š7‘{q|„~!y!k’vpv†x‡y…e{|ƒn{ne|Uy*{Uy,–jk9t—{”ŠQhvpxzyre{|3~…‘–jk’t—ke|wŠHkŽkŽŠšŽ›Im¨f–„ki!k’¡{qi!k’•s¡i!{txšv{s‘7{ji,kŽ‘kŽe“qk’ŠL|„{ne~›~…xqt—ƒ€vk~…•sx~!ky{n5shw‘"v†epŠQk’xz|&Š„e~!y…x‡|w‘kLŠje~!y!irešhjyre{|j~—‘{i!i!k"~!ƒE{q|€Šje|jgy,{k’xq‘–&t—{sŠHhwvpxzyre{q|7~…‘–„kŽtk9‘x‡|šk{šyrxqe|jk’Šhj~…e|„gN¢Žm#m†!m¤¨f–„kŽei0i!k~!ƒnkŽ‘y…e“k—dn~…•¡uv¢"tp¢…£P£GPXWXXP£)¤£•*x‡i!k‘{nvpvk’‘yre“qk’v›i!k’¡ki!i,kŽŠy,{Mxz~y,–jk¤t—{”ŠQk’vLm—"”y!–„k¤‘x‡|wŠ„e†Š„xzy,k¤t—{sŠHkŽv~c{iŠjeEk"i!k|Žyt—{sŠHhwvpxzyre{q|&~…‘–jk’t—k~xzyŠ„enki,k|Žyrj}~‹Ÿk"i!kLU|„{H‹1|šk’¡{qi!k"–wx‡|wŠ„•ny!–„k¤te|€e†teŽx‡yre{|&{”y!–„k¤Š„e~yrx‡|w‘k"~šk"y‹Ÿkk"|£y!–„k—dn~‘{|j~!yrey,hjyre|„gL•wx‡|wŠy,–jky!–„kŽei9‘{qi!i,k~!ƒE{|wŠ„e|„g—dE~9e|k’xq‘–{Ey,–jk‘x‡|wŠ„e†Š„xzy,kt—{”ŠQkŽv~…•j‹*{qh€v†ŠƒE{ne|Uyy,{;xƒwxzi,y…ep‘h€vpxzit—{”ŠQh€v†x‡y…e{|3~…‘–„kŽt—k’m|jk—~!hw‘–¦‘"xz|wŠ„epŠjxzy,kt{sŠQk’v”e~epvpvh„~!y!irxzy,kŽŠ3e|degm_#m\3m”c{ir„‰t—{sŠHhwvpxzy,kŽŠ9~›tš{v~xzy‘–€xz|j|„kŽvsrj}{c#Š„ml$‡

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0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Magnitude of errorsProbability BPSKQPSK16 QAM64 QAM dfeghji,ky#qmY3qmi,{šxšepvpey›—e~!y,i…ešh„y…e{|¤{nsi!i,{qi!~1‹ey!–Mrj‰x‡yf–wx‡|j|„kŽvr„}{c#Š„mln

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