Table Of ContentMIMO Wireless
Networks
To my wife, family and friends
Bruno Clerckx
MIMO Wireless
Networks
Channels, Techniques and
Standards for Multi-Antenna,
Multi-User and Multi-Cell
Systems
Second edition
Bruno Clerckx and Claude Oestges
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13 14 15 16 10 9 8 7 6 5 4 3 2 1
List of Figures
Figure 1.1 TypicalreceivedsignalstrengthinaRayleighfadingchannel. 5
Figure 1.2 DiversitygaininRayleighfadingchannels. 8
Figure 1.3 DiversityandarraygainsinRayleighfadingchannels. 9
Figure 1.4 PerformanceoftransmitMRCandAlamoutischemeswithtwotransmit
antennasini.i.d.Rayleighfadingchannels(forBPSKmodulation). 19
Figure 1.5 PerformanceofdominanteigenmodeandAlamoutitransmissionsina
2×2i.i.d.Rayleighfadingchannel(withQPSKmodulation). 24
Figure 2.1 Atypicalmultipathscenario. 31
Figure 2.2 ExtensionofBello’sfunctionstothespatialandangulardomains. 34
Figure 2.3 TypicalDopplerspectraformobileandfixedscenarios. 39
Figure 2.4 Transmitcorrelationasafunctionofrelativeantennaspacingd /λand
t
azimuthspread(thelargerκ,thelowerthespread). 48
Figure 2.5 Mutual dipole impedance (real and imaginary parts) as a function of
antennaspacingrelativetothewavelength. 52
Figure 2.6 Field-radiation pattern (in magnitude) of the right-hand side antenna
forseveralinter-elementspacings. 53
Figure 2.7 Copolar (solid) and cross-polar (dahsed) field-radiation patterns (in
magnitude)ofaplanemonopolarantennaat2.4GHz. 55
Figure 3.1 EffectivediversitymeasureinseveralRiceanMIMOchannels. 66
Figure 3.2 PathconfigurationforscenarioA. 67
Figure 3.3 PathconfigurationforscenarioB. 67
Figure 3.4 Correlationmatrixdistancefordifferentscenarios. 68
Figure 3.5 XPDmodeling:separationbetweenspaceandpolarization. 80
Figure 3.6 Effectivediversitymeasureina2×2Kronecker-structuredsystemas
afunctionoftransmitandreceivecorrelations. 86
Figure 3.7 Virtualchannelrepresentationofa2×4channel. 87
Figure 3.8 ImagingofthescatteringenvironmentforscenarioAvia(cid:2)v,A(cid:2)(cid:2)v,A
(indBscale). 95
Figure 3.9 ImagingofthescatteringenvironmentforscenarioBvia(cid:2)v,B(cid:2)(cid:2)v,B
(indBscale). 95
xviii List of Figures
Figure 3.10 Mutualinformationvs.SNRfordifferentmodelsintwo8×8scattering
scenarios. 98
Figure 4.1 One-ringmodel. 104
Figure 4.2 Two-ringmodel(symmetric). 106
Figure 4.3 Combinedelliptical-ringmodelforthreeellipsesandalocalscatterer
ring(thesizeofthediscandthecirclehavebeenincreasedforbetter
legibility). 108
Figure 4.4 Channelcorrelations(includingtheKroneckerapproximationofs and
1
s asequaltort)vs.receiveantennaspacingd/λ. 112
2
Figure 4.5 Illustration of exponential decay of mean cluster amplitude and ray
amplitudewithinclusters. 114
Figure 4.6 GeneralstructureofCOST273model,withlocal,single-bounceand
twinclusters. 119
Figure 4.7 WINNERmodelphilosophy. 120
Figure 4.8 WINNERmodel:segmentsimulation. 121
Figure 4.9 Extendedclustermodelingthedensemultipaths. 122
Figure 4.10 ExampleofacommonclusterinascenariowithoneMTandtwoBSs
+
[PTH ss]. 123
Figure 4.11 WINNERIImulti-linkmodel. 123
Figure 5.1 Principleofwater-fillingalgorithm. 129
Figure 5.2 Capacityofvariousi.i.d.channelsat20dBSNR. 139
Figure 5.3 Ergodiccapacityofvariousn ×n i.i.d.Rayleighchannelswithfull
r t
(CSIT)andpartial(CDIT)channelknowledgeatthetransmitter. 141
Figure 5.4 Average mutual information of various correlated channels at 20 dB
SNRasafunctionofone/bothcross-channelcorrelation(s). 147
Figure 5.5 Averagemutualinformationofdiagonalchannelsat15dBSNRasa
functionofthenumberofantennasateachside. 148
Figure 5.6 Averagemutualinformationoftwofinitescattererchannelsat20dB
SNRasafunctionofthenumberofantennasateachside. 150
Figure 5.7 Mutualinformationofvariousstrategiesat0dBSNRasafunctionof
thetransmitcorrelation|t|. 152
Figure 5.8 Optimalfractionofpowertononbeamformingmodeasafunctionof
|t|andρ forn =2. 153
r
Figure 5.9 Mutual information of Ricean 2×2 channels for different K-factors
(H˜ =Hw,so K =0correspondstoaRayleighi.i.d.channel). 155
Figure 5.10 MutualinformationofRicean2×2uni-anddual-polarizedchannels. 156
Figure 5.11 Asymptoticdiversity-multiplexingtrade-offg(cid:5)(g ,∞)ini.i.d.Rayleigh
d s
fadingchannels. 161
List of Figures xix
Figure 5.12 OutageprobabilityP (R)asafunctionofthetransmissionrateRfor
out
bothfixedandvariableratescalingas R =g log (ρ)in2×2MIMO
s 2
i.i.d.Rayleighfadingchannels(courtesyofH.Yao[YW03]). 162
Figure 5.13 Diversity-multiplexing trade-off g(cid:5)(g ,ρ) at realistic SNR (5 and 10
d s
dB) of a 2×2 MIMO i.i.d. Rayleigh fading channel (courtesy of R.
Narasimhan[Nar05]). 167
Figure 5.14 Normalizedmaximumdiversitygaingˆ(cid:5)(0,ρ)/(n n )asafunctionof
d t r
SNRini.i.d.Rayleighfadingchannels. 168
Figure 5.15 Diversity-multiplexing trade-off g(cid:5)(g ,ρ) at realistic SNR (5 and 10
d s
dB)in2×2MIMOtransmitcorrelatedRayleighfadingchannels(cour-
tesyofR.Narasimhan[Nar06a]). 169
Figure 5.16 Diversity-multiplexingtrade-offg(cid:5)(g ,ρ)atrealisticSNR(10dB)in
d s
2×2MIMOtransmitcorrelatedRayleighandRicean(K =5and10
dB)fadingchannels(courtesyofR.Narasimhan[Nar06a]). 170
Figure 6.1 Generaloverviewofaspace-timeencoderofaMIMOsystem. 174
Figure 6.2 Bit error rate (BER) of Spatial Multiplexing with various receivers
(ML, (ordered) ZF SIC, ZF) in i.i.d. slow Rayleigh fading channels
withn =2andn =2for4bits/s/Hz. 205
t r
Figure 6.3 Block error rate of the Alamouti code in i.i.d. slow Rayleigh fading
channelswithn =2inR =2log (M)=4,8,12,16bits/s/Hztrans-
r 2
missions using M2-QAM constellations of sizes M = 4,16,64,256
(courtesyofH.Yao[YW03]). 213
Figure 6.4 Bit error rate (BER) of several LDC in i.i.d. slow Rayleigh fading
channelswithn =2andn =2for4bits/s/Hz. 217
t r
Figure 6.5 Block error rate of the tilted-QAM code in i.i.d. slow Rayleigh fad-
ing channels with n = 2 in a R = 2n log (M) = 4,8,...,32-
r t 2
bit/s/Hz transmissions using M2-QAM constellations of sizes M =
2,4,8,...,256(courtesyofH.Yao[YW03]). 220
Figure 6.6 Biterrorrate(BER)ofDayalandAlamouticodesini.i.d.slowRayleigh
fadingchannelswithn =1andn =2ina4-bit/s/Hztransmission. 221
r r
Figure 6.7 Asymptotic diversity-multiplexing trade-off g (g ,∞) achieved by
d s
severalspace-timecodesina2×2i.i.d.RayleighfadingMIMOchannel. 223
Figure 6.8 Biterrorrate(BER)ofseveralalgebraicspace-timeblockcodesini.i.d.
slowRayleighfadingchannelswithn =2andn =2ina4-bit/s/Hz
t r
transmission. 224
Figure 6.9 Bit error rate (BER) of SM, Dayal and Alamouti codes in i.i.d. slow
Rayleighfadingchannelswithn =2,3,4ina4-bit/s/Hztransmission. 225
r
Figure 6.10 LabelingoftheQPSKconstellation. 226
Figure 6.11 STTCencoderfortwotransmitantennas. 227
xx List of Figures
Figure 6.12 Trellis representation of QPSK 4-state 2 bits/s/Hz space-time trellis
codesfortwotransmitantennas:(a)“TSC”code(delay-diversitycode)
[Wit93,SW94,TSC98]; (b) “BBH” code [BBH00]; (c) “CYV” code
[CYV01];(d)“FVY”code[FVY01]. 228
Figure 6.13 TrellisrepresentationofaQPSK8-state2-transmitantennaspace-time
trelliscodewhosegeneratormatrixisgivenby(6.201). 229
Figure 6.14 Frameerrorrateofseveral4-stateSTTCini.i.d.slowRayleighfading
channelswithn =2andn =2,4. 233
t r
Figure 6.15 Frameerrorrateof4-stateand8-state“CYV”and“TSC”codesini.i.d.
slowRayleighfadingchannelswithn =2andn =4. 234
t r
Figure 6.16 Frameerrorrateofseveral4-stateSTTCini.i.d.fastfadingchannels
withn =2andn =1. 235
t r
Figure 7.1 Biterrorrate(BER)ofSpatialMultiplexingwiththreereceiversini.i.d.
Rayleighslowfadingchannelswithn =n =4andQPSK. 242
t r
Figure 7.2 (a)Thesphereiscenteredatthereceivedvectorandcontainsthelattice
pointstobeenumerated.(b)Thesphereistransformedintoanellipsoid
intheT coordinatesystem. 245
Figure 7.3 Illustrationofspheredecodingtree. 247
Figure 7.4 Illustrationofbreadth-firstsearchtreefor K =1. 251
Figure 7.5 Principleofslowestdescentdetection:theellipsoidsrepresenttheequi-
probable regions of logp(y|s), and e is chosen as the direction of
SD
slowestdecent. 254
Figure 7.6 BERperformanceofslowestdescentdetectionini.i.d.Rayleighslow
fadingchannelswithn =n =4andQPSK. 256
t r
Figure 7.7 BICMiterativereceiver. 258
Figure 7.8 Kalmanfilter-basedestimationcombinedwithMMSE-DFEreceiver. 261
Figure 8.1 Visualizationoftheimpactofthescatteringrichnessandinter-element
spacingonMIMOsystemperformance. 266
Figure 8.2 G (θ |c ) (θ varying over 360◦) for the four possible phase shifts
t t k t
betweentwotransmittedQPSKsymbolsandMTinterelementspacing
d /λ=0.1. 268
t
Figure 8.3 G (θ |c ) (θ varying over 360◦) for the four possible phase shifts
t t k t
betweentwotransmittedQPSKsymbolsandMTinterelementspacing
d /λ=0.5. 269
t
Figure 8.4 Symbolerrorrateasafunctionofthephaseshift(inradians)between
thetransmittedQPSKsymbols. 270
Figure 8.5 Performance of full rank LDCs in i.i.d. and correlated channels with
n =2andn =2. 280
t r
Figure 8.6 Performance of rank-deficient LDCs in i.i.d. and spatially correlated
channelswithn =2andn =2. 288
t r
List of Figures xxi
Figure 8.7 PerformanceofSTTCsini.i.d.andspatiallycorrelatedchannelswith
n =2andn =4. 290
t r
Figure 8.8 Performance ofSTTCsini.i.d.andspatiallycorrelatedfastRayleigh
fadingchannelswithn =2andn =1. 291
t r
Figure 8.9 Performanceofrank-deficientSpatialMultiplexingschemeson2×2
Riceanfadingchannelswith K =4and K =10. 292
Figure 8.10 Performanceofapproximatelyuniversalcodeson2×2Riceanfading
channelswith K =4and K =10. 293
Figure 9.1 Repetitioncodingfor L =2withrate R =4bits/s/Hz. 302
Figure 9.2 Permutationcodingfor L =2withrate R =4bits/s/Hz. 302
Figure 9.3 MutualcouplingeffectsontheG (θ |C,a (θ ))ofaSMschemewith
sum t t t
QPSK. 312
Figure 9.4 MutualcouplingeffectsontheSERofaSMschemewithQPSK. 313
Figure 9.5 G (θ |C,a (θ ))ofseveralSMschemesasafunctionoftheangleof
sum t t t
departureθ [rad]. 321
t
Figure 9.6 SERasafunctionofthephaseoft for|t| = 0.95(up)andSERasa
functionof|t|withthephaseoftequalto0(down). 322
Figure 9.7 Biterrorrateofseveral2×2SMschemesini.i.d.andspatiallycorre-
latedRayleighfadingchannels(withtwoantennaorientationsθ = 0
t
andθ =0.63). 323
t
Figure 9.8 G (θ |C,a (θ ))ofseveralLDCasafunctionoftheangleofdepar-
sum t t t
tureθ [rad]. 324
t
Figure 9.9 G (θ |C,a (θ ))ofseveralLDCsasafunctionoftheangleofdepar-
sum t t t
tureθ [rad]. 325
t
Figure 9.10 G (θ |C,a (θ ))ofseveralfull-ratealgebraiccodesasafunctionof
sum t t t
theangleofdepartureθ [rad]. 326
t
Figure 9.11 G (θ |C,a (θ ))ofseveral4-and8-stateSTTCsasafunctionofthe
sum t t t
angleofdepartureθ . 327
t
Figure 9.12 Frameerrorrateofseveral4-stateSTTCsini.i.d.andspatiallycorre-
latedRayleighfadingchannelswithn =2andn =4. 328
t r
Figure 9.13 Frameerrorrateofseveral8-stateSTTCsini.i.d.andspatiallycorre-
latedRayleighfadingchannelswithn =2andn =4. 329
t r
Figure 9.14 G (θ |C,a (θ ))ofseveral4-stateSTTCsasafunctionoftheangle
sum t t t
ofdepartureθ . 331
t
Figure 9.15 G (θ |C,a (θ )) of several 4-states STTCs as a function of the
product t t t
angleofdepartureθ . 332
t
Figure 9.16 Frameerrorrateofseveral4-statesSTTCsini.i.d.andspatiallycorre-
latedRayleighfastfadingchannelswithn =2andn =1. 333
t r
xxii List of Figures
(cid:5)(cid:5)
Figure 10.1 OverviewofprecoderP:Wactsasamulti-modebeamformer,C is
thecodewordbeingshapedbyS1/2. 337
Figure 10.2 PerformanceofatransmitcorrelationbasedprecodedAlamoutischeme
in2×2transmitcorrelated(t =0.7)Rayleighchannels. 343
Figure 10.3 PerformanceofatransmitcorrelationbasedprecodedAlamoutischeme
in2×2transmitcorrelated(t =0.95)Rayleighchannels. 344
Figure 10.4 Performanceofa4-stateSTTC“CYV”inacorrelatedRayleighfading
channel (n = n = 2, n = 4), with a high transmit correlation
e t r
usingtwoprecodingschemes:UE˜· =Int andE˜· =argminE˜(cid:6)=0det(E˜)
(proposedin[SP02]). 350
Figure 10.5 Bit error rate of Spatial Multiplexing as a function of the transmit
correlationcoefficientt in2×2correlatedMIMOchannelswithand
withoutprecoding(SNR=15dB). 356
Figure 10.6 BiterrorrateofSpatialMultiplexingincorrelatedchannelswithand
without precoding: precoders I, II and III exploit the knowledge of
t, while the robust precoder has been designed following the G
sum
criterioninChapter9. 357
Figure 10.7 IllustrationofGrassmannian,adaptiveanddifferentialcodebooks. 362
Figure 10.8 Symbolerrorrate(SER)ofa3×3MIMOsystemusing2-bitand6-bit
quantized BPSK-based dominant eigenmode transmissions (courtesy
ofD.Love[LHS03]). 365
Figure 10.9 Symbol error rate (SER) of a 8×1 MISO system using 6-bit quan-
tizedi.i.d.androtateddominanteigenmodetransmissionsinspatially
correlatedRayleighchannels(courtesyofD.Love[LH06]). 368
Figure 10.10 Normalized average distortion (SNR loss) df,n as a function of the
codebooksizen =2B andthetransmitcorrelationcoefficientt with
p
n =4. 370
t
Figure 10.11 Symbolerrorrate(SER)of3-bitand6-bitprecodedAlamoutischemes
in2×4i.i.d.Rayleighfadingchannels(courtesyofD.Love[LH05a]). 378
Figure 10.12 Symbolvectorerrorrate(SVER)ofa6-bitprecodedBPSK-basedSM
scheme in i.i.d. Rayleigh fading channels with n = 4 and n = 2
t r
(courtesyofD.Love[LH05b]). 381
Figure 11.1 OFDMmodulatoranddemodulator. 386
Figure 11.2 BlockdiagramofaMIMO-OFDMsystem. 389
Figure 11.3 FER of the 16-state “FVY” code for L = 2, 3 and 4 in uniformly
distributedi.i.d.Rayleighchannelswithandwithoutinterleaver. 406
Figure 11.4 CyclicdelaydiversityinMIMO-OFDM. 409
Figure 12.1 MIMOBroadcastChannel(BC)andMultipleAccessChannel(MAC). 420