RMEMENT Une Nouvelle Direction La DGA Prend

DE L ’A RMEMENTReliability of radio-mobile systems consideringfading and shadowing channelsDGA/Comm - 01 - 10.2009 - Photos : DGA/CD IRECTION G ÉNÉRALE7-9 rue des Mathurins - 92 221 Bagneux cedexTéléphone : 33 (0)1 46 19 50 00 - Fax : 33 (0)1 46 19 50 01Philippe MaryIETR UMR 6164 CNRS, INSA de Rennes, France2/12/2010Philippe Mary2/12/20101 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsGeneral ContextCellular mobile communications (GSM, UMTS, WLAN)Philippe Mary2/12/20102 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsMotivationsTo increase the quality of services (QoS) of cellular networks :Considering both short and long term effect (multipath andaverage power variation)In the literatureSignal processing community multipath cancellation(equalization, channel coding, smart antennas.)”Network” community fight again the QoS variations dueto the variation of the average powerMinimal research effort has been allocated to the study ofboth effectsOur workStudy of a QoS criterium considering both short and longterm effectsPhilippe Mary2/12/20103 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsPurposes of the workAnalytical performance of radio-mobile systems in fading channelsand shadowing environment Allows to point out quickly the behavior of a system Allows to predict behaviorx x Difficult for high complexe environmentCoverage prediction over QoS constraint, best effort resourceallocation.Philippe Mary2/12/20104 / 32

IntroModelsApprox el models and assumption2Quick overview of SEP approximation3Outage considering fading and shadowing4Outage considering interference5Conclusion and further workPhilippe Mary2/12/20105 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsShort term effect/long term effectPhilippe Mary2/12/20106 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsDealing with shadowingWork with ”outage” [Conti03] :Symbol error outage (SEO) (non-ergodic channel)Ps (O) Pr (SEP Ps )The important network design criterium is the packet error outage(PEO)Philippe Mary2/12/20107 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsFading channels modelFlat fading channelsThe received power is :2Pr αshad · αfading· Ptαfading : Short term effect (fast fading)Nakagami-m or Rice distributedInstantaneous SNR variation2γs αfadingEs /N0αshad : Long term effect (change after one or several packets)log-normally distributedAverage SNR variationγ s αshad Es /N0 ,2αshad E αfading Average SNR log-normally distributedMean : µdB E (10 log10 γ s )Standard deviation : σdBPhilippe Mary2/12/20108 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsError modelisation in fading channelsAverage error probability (w.r.t. short term effects) :Classic form of the average SEP :Z Ps (E γ s ) Ps (E γs , γ s ) pγs γ s (γs ) dγs{z} 0 f (Q ( γs ))Craig91 alternative form for Gaussian function QAllowed to derive closed-form SEP expressions in an unifiedway thanks to the moment generating function (MGF) of theSNR [Alouini04] :Ps (E γ s ) 1πPhilippe MaryZ(M 1)π/M Mγs0 gpsksin2 θ dθ2/12/20109 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsPerformance with shadowingSymbol error outage (SEO) :Ps (O µ ) P (Ps (E γ s ) Ps (E γ s ) µ ) Pγ s (O µ ) P (γ s γ th µ )Need of the SNR threshold : γ th f (Ps (E )) oùf (Ps (E )) Ps (E γ s ) 1The SEO is hence :„«Z γ th (Ps (E )) 1µdB 10 log10 γ s (Ps (E ))pγ s (γ s µ) dγ s QPs (O µ) σdB0StepsFind an accurate and simple expression for SEPInverting this expression w.r.t. the SNREstimate the SEOPhilippe Mary2/12/201010 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsInvertible approximation of the SEPAsymptotic analysis [Giannakis03] :Behavior of the SEP for high SNRPs (E ) (Gc γ s ) GdGc Coding gain horizontal shift compared to a referenceGd Diversity gain error probability slop in high SNR regimex x Not accurate at low SNRBounds of Conti et al. [Conti03] Tight bounds of the average SEP thanks to bounds on theMGF of the SNRx x One kind of channel (Nakagami-m)x x No channel codingx x No interferencesPhilippe Mary2/12/201011 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsLaplace methodCan be used for Nakagami-m and Rice channelsIntegral approximation :ZI h(y )e λg (y ) dyλ R, D Ry DThe Laplace approximation of I is :s 2πĨ h(y0 )e λg (y0 ) and I Ĩ 1 O λ 1 , λ λ g 00 (y0 ) y0 {z}min g (y )yPhilippe Mary2/12/201012 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsScenarioA simple point-to-point SISO systemGoal : Estimated the probability that the SEP exceeds thethresholdPhilippe Mary2/12/201013 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSEP approximation in Nakagami-m channels (1/3)The exact average SEP (M-PSK, M-QAM) can be written as[Shin04] :«„««1113; m 1; x (γ s ) k2 · F1, m, m; ; y (γ s ) , 1 gpsk2222„„««13 x2 (γ s ) 1,Psqam (E γ s ) x1 (γ s )m k3 ·2 F1 m, ; m 1; x1 (γ s ) x2 (γ s )m k4 ·F1 1, m, 1; m ;22 x1 (γ s ) 2Pspsk (E γ s ) x (γ s )m„„k1 · 2 F1m,Philippe Mary2/12/201014 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSEP approximation in Nakagami-m channels (2/3)The Gauss hypergeometric function can be expressed as Z 11 1Fm,;m 1;x B(m,1)t m 1 (1 tx) 1/2 dt,2 120Laplace approximation by choosing [Wood03] :h(t) B (m, 1) 1 t 1 , 1g (t) m ln t ln(1 xt)2Philippe Mary2/12/201015 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSEP approximation in Nakagami-m channels (3/3)Theorem (SEP approximation)In a flat Nakagami-m fading channel, the average SEP ofM-PSK/M-QAM signals is well approached by :Ps (E γ s ) kmod xm1 x t̃; γ swith t̃ m/(m 1), x 1/ (1 gmod γ s /m), gmod and kmod aremodulation dependent constants.Philippe Mary2/12/201016 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsAccuracy of the approximationPhilippe Mary2/12/201017 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSEP inversionTheorem (SEP inversion)Under the same conditions as previously, the average SNR is : 1111 m2m m m kmodγ s (Ps (E )) c0 Ps (E )1 c1 Ps (E )Sketch of proof.Solving in [0, 1] : (kmod )2 x 2m (Ps (E ))2 t̃x (Ps (E ))2 0Constructing the series :8 x0 : xn 1 0,«1„ 1Ps (E ) m 1 t̃xn 2mkmodWe can show that {xn }n N is converging towards xsPhilippe Mary2/12/201018 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSEO with shadowingPhilippe Mary2/12/201019 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSEP approximation in Rice channelPropagation with a specular componentNo closed-form solutions :(M 1)π/M gpskMγs 2dθ(E γ s ) sin θ0ZZ g g 4g π/24g 2 π/4qamqamPsqam (E γ s ) Mγs 2 dθ Mγs 2 dθπ 0sin θπ 0sin θ gmod K γ s)sin2 (θ)gmodwith Mγs sin (1 K(1 K2θ)sin2 (θ) gmod γ exp (1 K )sin2 (θ) gmod γPspsk1πZ sPhilippe Marys2/12/201020 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSEO EstimationWe can show that : γ s (Ps (E )) 2K Kgmod W0 ( πPs (E )Ke K ) 1 KgmodPs 10 2Philippe Mary2/12/201021 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSystems with channel codingGoal : Considering the PEO PEP inversion w.r.t. SNRAssumptions : Hard decision decodingPhilippe Mary2/12/201022 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsBlock codesHamming and Golay codesPhilippe Mary2/12/201023 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsPEO estimationNakagami-m fadingPackets 4600 bits, 8-PSK signal1 t 1 PER target of 10 1 ; Pb Pm(E )(t 1)B(t 1,J t)„«J t 11 (E )(t 1)B(t 1,J t)] t 1 ỹ1 [Pm N/kand Pp (E ) 1 (1 Pm (E ))Philippe Mary2/12/201024 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSTBC MIMO systemsThe output SNR is :γSTBC H 2Fγnt R sγ s E0 /N0The MGF of SNR can be shown to be (without correlation) :MγSTBC (Mγs )nt nrPhilippe Mary2/12/201025 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsV-BLAST MIMO systemsZF linear receiver. The substream SNR is [Gore02] :γk Hγ s 1[H H]kkIn Rayleigh channel : Z HH H , CW nt (nr , 0, Σnt )nr nt 1We can shown that : Mγk (Mγs )Philippe Mary2/12/201026 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsSEP approximation with one co-channel interferenceThe exact SEP is obtainedR by averaging the conditional SEPw.r.t. the INR Ps (E ) 0 Ps (E γi ) pγi (γi ) dγiThe average SEP (M-PSK, M-QAM) with one co-channelinterference in Rayleigh channel is bounded by :s1 gmod γ d1 γiPs (E γ d , γ i ) 2kmodgmod γ d γ i 2 (1 gmod γ d )Philippe Mary2/12/201027 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsAccuracy of the approximationQPSKPhilippe Mary2/12/201028 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsOutage probability with shadowing and co-channelinterferenceShadowing both SNR γ d and INR γ i are random variablesWe can show the following result :Theoremγ d et γ i are two random variables i.i.d. and log-normally distributed. The SEO of thedesired signal with one co-channel interference is :P (Ps (E ) Ps ) Z 010/ log (10) eσi 2πγ i(10 log10 γ i µi )22σ 2i„Qµd 10 log10 γ th (Ps , γ i )σd«dγ iwhere γ th (Ps , γ i ) is the needed average SNR to reach the QoS target Ps knowing theaverage INR γ i .Philippe Mary2/12/201029 / 32

IntroModelsApprox ols to study the performance of wireless communications ina realistic environment (Fading Shadowing)When shadowing is considered the channel is non-ergodicThe PEO is a measure of the reliability that a wireless networkcan offer under constraint of QoS (average PEP)ApplicationsCoverage prediction (4G Cellular networks, · · · )Resource allocation considering an average target PEP with acertain outage probabilityPhilippe Mary2/12/201030 / 32

IntroModelsApprox SEPSEO,PEOMIMOInterferenceConclusionsFurther worksWith codingHow do we deal with capacity approaching codes (LDPC,Turbo, · · · ) ?Quantify the tradeoff Energy consumption/PEO reductionConnectivity study in access networkActive links : average PEP PEP targetDefined the connectivity in function of the PEP targetExtension to multi-hop and cooperative networksPhilippe Mary2/12/201031 / 32

IntroModelsApprox 1] P. Mary, M. Dohler, J.-M. Gorce, G. Villemaud, M. Arndt, ”BPSKBit Error Outage over Nakagami-m Fading Channels in LognormalShadowing Environments”, IEEE Commun. Letters, 2007[2] P. Mary, M. Dohler, J.-M. Gorce, G. Villemaud, M. Arndt, ”M-arySymbol Error Outage over Nakagami-m Fading Channels inShadowing Environments”, IEEE Trans. on Commun., 2009[3] P. Mary, M. Dohler, J.-M. Gorce, G. Villemaud, ”Symbol ErrorOutage Analysis of MIMO OSTBC Systems over Rice FadingChannels in Shadowing Environments”, Minor Revisions for IEEETrans. on Wireless Commun.[4] P. Mary, M. Dohler, J.-M. Gorce, G. Villemaud, ”Symbol ErrorOutage for Spatial Multiplexing Systems in Rayleigh FadingChannel and Lognormal Shadowing”, In Proc. of IEEE Spawc 2009,Italy, 2009[5] P. Mary, M. Dohler, J.-M. Gorce, G. Villemaud, ”Packet ErrorOutage for Coded Systems Experiencing Fading Channels andInterference in Shadowing Environment”, In preparationPhilippe Mary2/12/201032 / 32

D IRECTION G N RALE DE LÕA RMEMENT La DGA prend une nouvelle direction D IRECTION G N RALE DE LÕA RMEMENT 7-9 rue des Mathurins - 92 221 Bagneux cedex T l phone : 33 (0)1 46 19 50 00 - Fax : 33 (0)1 46 19 50 01 Site institutionnel DGA : www.defense.gouv.fr Portail industrie : www.ixarm.com DGA/Comm - 01 - 10.2009 - Photos : DGA/Comm - F .