CDS 270-2: Lecture 6-3 Optimum Receiver Design for Estimation over Wireless Links

Transcription

1 CDS 70-: Lecture 6-3 Otimum Receiver Desig for stimatio over Wireless Lis Goals: Yasami Mostofi May 5, 006 To uderstad imact of wireless commuicatio imairmets o estimatio over wireless To lear o-traditioal desigs for estimatio over wireless alicatios Otimizatio of acet dro Use of cross-layer iformatio aths May 5, 006 Yasami Mostofi 1

2 System Model review # #1 Dyamical System x y Observer Trasmitter Wireless Chael Receiver xˆ stimator ode#1 ode# May 5, 006 Yasami Mostofi

3 System Model review Dyamical System x y Observer Trasmitter Wireless Chael Receiver xˆ stimator To focus o commuicatio oise, assume scalar quatities Liear dyamical system: x 1 x w Observatio: y Cx v w v : : Zero mea oise with variace of Zero mea oise with variace of xˆ : Kalma filter estimate of x Q R May 5, 006 Yasami Mostofi 3

4 Wireless Trasmissio review receiver oise y quatizatio chael codig/ rocessig D/ & modulatio wireless chael demodu latio yˆ dequatizatio decodig/ rocessig No acet dro error detectio /D y ˆ y is commuicatio oise with variace of Yes May 5, 006 Yasami Mostofi 4

5 ast Lectures receiver oise y quatizatio chael codig/ rocessig D/ & modulatio wireless chael demodu latio yˆ dequatizatio decodig/ rocessig No acet dro error detectio /D Yes Last wee s lectures: Oly allow oise-free samles Last lecture: We looed at a receiver that ees all the acets ad uses a cross-layer iformatio ath We derived aalytical exressio to evaluate erformace We showed that the desig is always stable May 5, 006 Yasami Mostofi 5

6 Today: Otimum Desig What is the otimum acet dro for estimatio ad cotrol over wireless lis? What are the beefits of usig chael owledge i the estimator? Stability & erformace Cosider geeral cases: geeral ad ad system arameters Ideal oise rofile: eeig oly oise-free samles Suitable for o delay-sesitive alicatios May 5, 006 Yasami Mostofi 6

7 bstractio i the Higher Layer dro quatizatio oise 1 & dro : Distributio of : Fuctio of TX/RX techologies lie quatizatio, oise figure, modulatio, chael codig,.. Fuctio of eviromet May 5, 006 Yasami Mostofi 7

8 bstractio i the Higher Layer quatizatio oise 1 dro roximate & dro : Distributio of : Fuctio of TX/RX techologies lie quatizatio, oise figure, modulatio, chael codig,.. Fuctio of eviromet May 5, 006 Yasami Mostofi 8

9 New Desig aradigms Tae imact of oisy samles ito accout Oly ee oise-free samles dro No-ideal oise rofile cross-layer o cross-layer Sceario#3? Sceario#? Ideal oise-rofile Sceario#1 Siooli et al. & Liu et al. ee all?? Sceario#1: Siooli et al. TC 04, to maitai stability: for o -mobile odes : dro, sceario#1 May 5, 006 Yasami Mostofi 9 <

10 Sceario#: No Chael Ifo vailable 1 dro What is the otimum acet dro desig? If is too high, may acets are droed > iformatio loss If is too low, estimatio will be too oisy Ituitively, there should be a otimum May 5, 006 Yasami Mostofi 10

11 Sceario# I Sceaior#, KF does ot ow aythig about the quality of the commuicatio li From the oit of view of the Kalma filter, the li was erfect To focus o commuicatio oise, we assume that observatio oise is egligible i the derivatios of sceario# May 5, 006 Yasami Mostofi 11

12 Sceario# The xˆ xˆ 1 C 1 if yˆ th if samle is droed th samle is et We will have the followig recursio for estimatio error variace: C 1 Q S where S 1 else May 5, 006 Yasami Mostofi 1

13 May 5, 006 Yasami Mostofi 13 Sceario# veragig over Sigal to Noise Ratio distributio,,will result i the followig: d f d f Q C N dro L N L 1 0 where f

14 Stability Coditio for Sceario# To ee average estimatio error variace bouded : dro f d < 0 Remar: Defie stability rage as the rage of average Sigal to Noise Ratios or matrices for which estimatio is stable. Havig lower will icrease the stability rage. May 5, 006 Yasami Mostofi 14

15 Sceario#: Otimum erformace Theorem1: Balace of Iformatio Loss & Commuicatio Noise Cosider asymtotic average estimatio error variace: C N Q for L < 1 L Otimum that miimizes asymtotic average estimatio error variace will be as follows:, ot 0 else 0 May 5, 006 Yasami Mostofi 15

16 Sceario#: Otimum erformace Where balaces iformatio loss ad commuicatio oise as follows: L N, ormalized C Q Iformatio loss Commuicatio oise q. #1 where N, ormalized N May 5, 006 Yasami Mostofi 16

17 roof of Theorem 1 Let rereset ay solutio to q#1. c Let rereset the critical stability c old: 1 L 0 c We have < It is easy to verify that 0 at We have to rove that q#1 has a uique solutio May 5, 006 Yasami Mostofi 17

18 May 5, 006 Yasami Mostofi 18 roof of Theorem 1 cot.,,1,,1,,1,1,,,,,1,1,,1,1,, ,,,,1,1, ormalized N L ormalized N L Q C d f d f d f Q C Q C < > Therefore have we will is a o -icreasig fuctio of Sice ad q#1has two solutios : ssume that

19 Remars o Otimum erformace Theorem 1 shows that as log as q#1 has a ositive solutio, the the otimum way of droig acets is the oe that balaces loss of iformatio ad the amout of commuicatio oise that eters the estimatio rocess If rocess oise is the domiat factor comared to the commuicatio oise, q#1 may ot have a ositive solutio. The eeig all the acets is otimum May 5, 006 Yasami Mostofi 19

20 xamle: Otimum acet Dro for Sceario# SNR 5dB SNR 10dB SNR : ex.dist. SNR 15dB SNR 30dB SNR 0dB SNR 5dB Kee more Dro more May 5, 006 Yasami Mostofi 0

21 May 5, 006 Yasami Mostofi 1 Sceario#3: Kowledge of chael available for KF else where z z R C C Q 1

22 Sceario#3: Stability Coditio Lemma 1: Stability regio of sceario#1 icludes that of sceario#3 roof: cosider a secial case of sceario#1 with R0. Let g ad rereset estimatio error variaces of sceario#1 with R0 ad sceario#3 resectively. We will have, g 1 L g Q May 5, 006 Yasami Mostofi

23 May 5, 006 Yasami Mostofi 3 Sceario#3: Stability Coditio g g Q S S C C Q L if The, have will We else where

24 Sceario#3: Stability Coditio Lemma : Stability regio of sceario#3 icludes that of sceario# roof: Let q rereset estimatio error variace of sceario# with R 0, where o owledge of R is available at the KF. We will have, q 1 where N, R L q N Q 1 L R C N, R May 5, 006 Yasami Mostofi 4

25 May 5, 006 Yasami Mostofi 5 Sceario#3: Stability Coditio, 1. 1, 1, z z L L C C Q > > < > s Iequality, Jese' The usig coditioal is a cocave fuctio of

26 May 5, 006 Yasami Mostofi 6 Sceario#3: Stability Coditio , > > > q q C C Q C C Q L R N z z L z L if Notig that s Iequality, yig Jese' had side is a cocave fuctio of The third term o the right The,

27 Sceario#3: Cross-layer Desig Theorem : Cross-layer ath o chael quality does NOT imact stability regio roof: Lemma 1 ad Lemma roved that stability regio of sceario#1 icludes that of sceario#3 ad stability regio of sceario#3 icludes that of sceario#. We roved that stability regio of sceario# is the same as sceario#1. Therefore, sceario#3 will have the same stability coditio. Keeig all acets miimizes average estimatio error variace asy to rove: see CDC05 i the referece list Cross-layer available > ee all acets for stability & erformace May 5, 006 Yasami Mostofi 7

28 ffect of Cross-Layer Desig Solid: o cross-layer Dashed: cross-layer May 5, 006 Yasami Mostofi 8

29 stimatio Over Wireless: Summary We studied otimum acet dro mechaism We roved that stability coditio is the SM ideedet of cross-layer or shae of commuicatio oise variace Cross-layer o chael owledge available: ee acets for both stability & erformace Cross-layer o chael owledge ot available: Stability rage mai factor: ee acets stimatio error mai factor: acet dro to balace iformatio loss ad comm. oise May 5, 006 Yasami Mostofi 9

30 ossible rojects: Study Imact of Commuicatio Imairmets o stimatio ad Cotrol over Wireless Have a ode estimate/cotrol a dyamical system over a wireless li study the imact of chael variatios, chael correlatio exlore redesigig the commuicatio side: eeig acets, usig cross-layer desig, cotrol acet dro, use of SNR ifo i estimatio/cotrol Try other commuicatio rotocols lie aalog commuicatio, sesor etwor rotocols lie ZigBee, Comare differet rotocols ZigBee, 80.11b, Bluetooth, alog, Survey of suitable etworig rotocols for these alicatios May 5, 006 Yasami Mostofi 30