OFDM Precoder for Minimizing BER Upper Bound of MLD under Imperfect CSI

Transcription

1 MIMO-OFDM OFDM Precoder for Miimizig BER Upper Boud of MLD uder Imperfect CSI MCRG Joit Semiar Jue the th 008 Previously preseted at ICC 008 Beijig o May the st 008 Boosar Pitakdumrogkija Kazuhiko Fukawa ad iroshi Suzuki Suzuki-Fukawa Laboratory

2 Itroductio Research backgroud Presetatio Outlie Literature Review Precoder for miimizig BER upper boud uder perfect CSI Problem idetificatio uder imperfect CSI ad research objective Proposed Precodig Method uder Imperfect CSI Criterio formulatio ad optimizatio Computer simulatio results Coclusios Summary ad suggestios for future work

3 Research Backgroud Demads for future mobile commuicatios igh Speed + igh Reliability Framework: MIMO-OFDM system with feedback chael Iput b Chael Maximum b Liear State Likelihood Precoder Iformatio Detector F CSI: MLD b M Output b M Liear precodig criteria Maximum Capacity Adaptive Modulatio Codig AMC Waterfillig-based power allocatio No-Capacity Based Fixed modulatio ad codig Phase ad power optimizatio: - Satisfy QoS - Miimize trasmit power - Miimize bit error rate MBER Icrease reliability BER performace: Focus of this research 3

4 Detectio Error ad MBER Precodig Trasmitted sigal replica of MIMO with QPSK ad M= data streams Received sigal c is detected rather tha b: Detectio error c b b is really trasmitted Detectio error: Received sigal closer to aother sigal tha trasmitted oe MBER precodig: Miimize detectio error Icrease reliability 4

5 MBER Precoder uder Perfect CSI Trasmitter ad receiver: Same CSI Procedures at trasmitter No precoder Trasmitted sigal replica of MIMO with QPSK ad two data streams With MBER precoder Trasmitted sigal replica of MIMO with QPSK ad two data streams. Calculate BER upper boud J e F. Optimize F to miimize J e F Sigificat BER improvemet over spatial multiplexig oprecoded system B. Pitakdumrogkija K. Fukawa. Suzuki ad T. agiwara Liear precodig with miimum BER criterio for MIMO-OFDM systems employig ML detectio IEEE ICC 007 pp Jue

6 Ucoded BER uder Perfect CSI 6 db 6

7 System Model uder Imperfect CSI # # 5. MBER Precodig... Preamble Sigal 4. Quatized Estimated CSI #N T #N R 6. Precoded Data... Chael Estimatio 3. CSI Quatizatio 7. Sigal Detectio Trasmitter Receiver CSI model - Receiver: Chael Estimatio Error - Trasmitter: Chael Estimatio Error + Quatizatio Error Trasmitter ad receiver: Differet CSI 7

8 Problem ad Proposed Solutio Problem with covetioal MBER precoder desiged by assumig perfect CSI BER Boud 0 Covetioal cost fuctio CSI error F o Covetioal optimal J e F Large Degradatio F Calculated value CSI error Large degradatio Proposed solutio New BER cost fuctio: Robust to imperfect CSI CSI error F o New optimal New cost fuctio J e F F Calculated value Small Degradatio Precodig Matrix CSI error Small degradatio 8

9 Itroductio Research backgroud Presetatio Outlie Literature Review Precoder for miimizig BER upper boud uder perfect CSI Problem idetificatio uder imperfect CSI ad research objective Proposed Precodig Method uder Imperfect CSI Criterio formulatio ad optimizatio Computer simulatio results Coclusios Summary ad suggestios for future work 9

10 MIMO-OFDM OFDM Trasmitter System with N T trasmit ad N R receive ateas M mi{n T N R } data streams N subcarriers Modulatio sigal vector bi Basebad trasmitted sigal vector si = Fbi k-th atea trasmitted sigal x k p = IDFT{s k i} 0

11 MIMO-OFDM OFDM Receiver l - th atea r p l N = T D k = d = 0 received sigal : h lk x p d + p d k l Basebad received sigal vector : y i = F b i + z i d-th path impulse respose betwee l-th ad k-th ateas AWGN zero mea ad variace σ N R -by-n T chael frequecy respose matrix N R -by- oise vector

12 CSI at receiver: CSI at trasmitter: CSI Error Model ~ MMSE chael estimatio OFDM Packet Preamble Data.... x p x p p ~ hl = arg mi hl p= p = h l + ψ l λ p p Uiform quatizatio Quatizatio level 4S υ 3S υ S υ S υ 0 Re{ h lk d } h lk d = hlk d +ψ lk d h ˆ lk d = hlk d +ψ lk d + υlk d r p h l l x p L 0 3 L D d Estimatio error ψ = 0 l ψ ψ l l Quatizatio error - Estimatio error statistics: υ lk υ * l k d = 0 υ σ I - Quatizatio error statistics: Re{ } [ ] h lk = σ δ d l k d υ l l k k d d - If the d B = log / S υ δ υ δ σ / = S υ / No. of quatizig bit per path

13 Detectio error coditio whe σ υ is small Pairwise Pairwise Error Probability PEP Error Probability PEP ˆ ˆ i i i i c F y b F y > d lk d lk d lk lk lk lk lk h ˆ υ +ψ + + Υ + Ψ = B C C = B ε PEP averaged with respect to CSI errors ~ ~ erfc d ˆ ~ ~ 0 c b p c b P = = γ ε ε 4 / ] [ ˆ ~ ~ i i c b e F c b F σ γ = Joit p.d.f. betwee AWGN ad CSI errors [ ] [ ] i i N e b F b F F + = σ σ Υ Υ Ψ Ψ + = Error variace: Covetioal Proposed additioal term CSI errors: 3 Estimatio error Quatizatio error

14 BER Upper Boud Miimizatio BER upper boud cost fuctio J e F = All pairs of bi ad ci ~ ~ b b c~ Solutio for optimal precodig matrix ~ F o = arg mi J F N = 0 N e ~ ~ b c~ P b c~ ˆ No. of error bit whe ci rather tha bi is detected ~ e F Optimizatio by the steepest descet algorithm subjected to q q F = F µ Iteratio idex Real positive costat = N = 0 J e F * F F Gradiet of J e F Mathematically Utraceable q { F F } = 0 F b i tr P Total average trasmit power 4

15 Modulatio Simulatio Coditios QPSK Tx Rx atea N T x N R x Data stream M OFDM packet format Total subcarrier 64 Effective subcarrier GI legth Chael model Maximum Doppler freq. CSI at Rx IEEE80.a Preamble: symbols Data: 0 symbols 5 Pilot:4 Data:48 6 poits 7 path expoetial decay Rayleigh fadig 0 z MMSE chael estimatio λ=.0 CSI at Tx CSI from Rx + Quatizatio error σ υ = Sigal detectio MLD 5

16 Average BER Performace 3 bits/path 6 db db 6

17 Robustess to Quatizatio Error 0.06 bits/path 7

18 Coclusios ad Future Works Coclusios: Proposed MBER precodig techique uder imperfect CSI Cosider chael estimatio ad quatizatio errors as CSI imperfectio Average PEP with respect to CSI errors Employ steepest descet algorithm for optimizatio Improve BER robustess to imperfect CSI Future Works: Improvemet of optimizatio ad reductio of CSI amout Precodig techique for time-varyig chael 8