Rate Constrained Power Control in Space-Time Coded Fading Ad-Hoc Networks

Transcription

1 Rate Constraned Power Control n Space-Tme Coded Fadng Ad-Hoc Networks Homayoun Yousef zadeh Lynn Zheng Hamd Jafarkhan Department of EECS, UCI [hyousef, llzheng,hamdj]@uc.edu

2 Outlne Problem Descrpton Lterature Revew Contrbuton System Model Constraned Power Optmzaton Smulaton Results Conclusons

3 Descrpton and Contrbutons Mnmze power consumpton of wreless ad-hoc networks wth multple antenna nodes under throughput and QoS provsonng constrants Modelng the MIMO fadng channel. Integratng a fntesate MC model nto power mnmzaton problem of ad-hoc networks wthout ncurrng prohbtve overhead. Solvng the problem wth low complexty Investgatng moblty effects.

4 SINR Model Instantaneous SINR for an M N lnk wth transmsson power s defned as SINR t P P () t M N ( mn, ) G() t M () F 1 1 t m= n= () = Pj () t M j N ( mn, ) j j M j m= 1 n= 1 j + G () t F () t Nn () t Gj () t captures factors such as path loss, ( mn, shadowng, and antenna gan. F ) j () t s the fadng factor between transmttng antenna m of lnk j and recevng antenna n of lnk.

5 Assumptons Tme shft correlatons of fadng factors over the same lnks are temporally correlated Tme shft correlatons of fadng factors over dfferent lnks are..d Dstrbuton of the whte Gaussan nose s ndependent from the fadng dstrbutons F s have unt means so long as G j j s are approprately scaled Wreless channel vares slowly wth respect to the symbol nterval.

6 Dgtal Channel Descrpton Prevously, we modeled the analog fadng channel wth a fnte state MC. Glbert-Ellott Error Model Transton probabltes from Raylegh stats SER s a functon of SINR, M, and N P G SER = γ, P = β, G B << SER B

7 Recepton Probabltes What s the prob. of recevng exactly k UOIs from n transmtted UOIs? Pnk (, ) = PnkG (,, ) + PnkB (,, ), n k > 0 PnkG (,, ) = ε [ γ Pn (, 1 kg, ) + (1 β) Pn (, 1 kb, )] G + (1 ε )[ γ Pn (, 1 k, 1 G) + (1 β) Pn (, 1 k, 1 B)] G PnkB (,, ) = ε [(1 γ) Pn ( 1, kg, ) + βpn (, 1 kb, )] B + (1 ε )[(1 γ) Pn (, 1 k, 1 G) + βpn (, 1 k, 1 B)] B 1 β 1 γ P(0, 0, G) = gss =, P(0, 0, B) = bss =, 2 γ β 2 γ β P(10,, G) = ε [ γ g + (1 β) b ], P(10,, B) = ε [(1 γ) g + βb ] G ss ss B ss ss

8 MIMO Codng Effects We show that SER of 1xN MRC wth M-PSK s N 1 M 1 1 ϑ π 2 j 1 1 ε ( SINR, M, N) = {( + tan ξ) M π 1+ ϑ 2 j= 0 j [4(1 + ϑ)] σ + sn(tan ) [cos(tan )] } where 2 sn ( ) cot M 1+ ϑ M N 1 j 1 j 1 2( j ) + 1 ξ ξ j j= 1 = 1 (1 + ϑ) π ϑ π ϑ= SINR ξ = σ = 2 j j 2( j ) j 4[2( j ) + 1] For an even N and consderng the codng gan, the SER of 2 x N/2 STBC wth M-PSK s calculated by replacng proper SINR for the SER of 1xN MRC j j

9 Channel Codng Utlze Reed-Solomon Codes Apply per state MIMO codng results, e.g., the 2x2 case w/ BPSK yelds ε SNR 2j = j [4(1+SNR )] 1 1 GB, 3 1 GB, j=0 SNR GB, j G,B Probablty of Block Loss Conservatve Estmate Ψ ( nt,, ε, ε, γ, β) = 1 Pn (, ) c G B n n k = = n t c t c 2

10 Optmzaton Problem Problem mn PM, P Total = 1 = 1 Subject To : Ψ Ψ = n n R P ub, R lb P P P lb, ub, 1,...,n 1,...,n where usng adaptve modulaton, R 1 = log2 T M

11 Optmzaton Soluton Soluton: SQP and KKT Equatons n n LG = P + µ ( Ψ Ψ ) + λ( R R ) + θ ( P P ) P ub, lb = 1 ub, = 1 P( ) 0 LG Ω = µ λ θ * ( Ψ Ψ ub, ) = 0 * n * Rlb R = 1 ( ) = 0 ( P P ) = 0 * * ub, µ, λ, θ 0 * * Complexty OId ( log d)

12 Moble Topology

13 Parameter Settngs Power Bounds: Gan Matrx a functon of x: G= G G = G = Power: 1 [ j],, d j Baseband: 4 4 dj P = 1 W En [ ] = 10 µ W Same Parttonng Thresholds: 1 1: { γ, β} = {0{ , 0875}. } Throughput Bound: P = 1 W P = W ub 1 = 100 KHz RS(3115), T η Rlb lb = 2Mbps

14 Global (Centralzed) Results

15 Global vs Local (per lnk) Results

16 Concluson Summary: MIMO Raylegh fadng modelng wth fnte-state MC Provdng an ntegrated system framework relatng temporally correlated loss, modulaton, channel codng, and antenna characterstcs Formulatng and effcently solvng a QoS constraned power optmzaton problem Numercally valdatng the results under moblty Future work: Investgaton of the problem for transmttng rch content More Sophstcated QoS Metrcs

17 References [1] S.M. Alamout, A Smple Transmtter Dversty Scheme for Wreless Communcatons, IEEE JSAC, November [2] M. Andersn, Z. Rosberg, J. Zander, Gradual Removals n Cellular PCS wth Constraned Power Control and Nose, IEEE/ACM Trans. Networkng, Aprl [3] N. Bambos, S. Chen, G. Potte, Rado Lnk Admsson Algorthms for Wreless Networks wth Power Control and Actve Lnk Qualty Protecton, In Proc. IEEE INFOCOM, [4] D.P. Bertsekas, Nonlnear Programmng, 2nd Edton, Athena Scentfc Publshng, ISBN , [5] M. Chang, D. O Nel, D. Julan, S. Boyd, Resource Allocaton for QoS Provsonng n Wreless Ad Hoc Networks, In Proc. IEEE GLOBECOM, [6] S.T. Chung, A. J. Goldsmth, Degrees of Freedom n Adaptve Modulaton: A Unfed Vew, IEEE Trans. on Communcatons, September [7] E.O. Ellott, Estmates on Error Rates for Codes on Burst-Nose Channels, Bell Syst. Tech. J., September [8] M. Hayajneh, C.T. Abdallah Performance of Game Theoretc Power Control Algorthms for Wreless Data n Fadng Channels, In Proc. IEEE GLOBECOM, [9] S. Kandukur, S. Boyd, Optmal Power Control n Interference Lmted Fadng Wreless Channels wth Outage Probablty Specfcatons, IEEE JSAC, [10] X. Qu, K. Chawla, On the Performance of Adaptve Modulaton n Cellular Systems, IEEE Trans. on Communcatons, June [11] R. Ramanathan, R. Rosales-Han, Topology Control of Multhop Wreless Networks Usng Transmt Power Adjustment, In Proc. IEEE INFOCOM, [12] M.J. Shah, P.G. Flkkema, Power-Based Leader Selecton n Ad-Hoc Wreless Networks, IEEE Int. Performance, Computng and Communcatons Conf., [13] M.K. Smon, M.S. Aloun, Dgtal Communcaton over Fadng Channels: A Unfed Approach to Performance Analyss, John Wley, ISBN , [14] V. Tarokh, H. Jafarkhan, A.R. Calderbank, Space-Tme Block Codng for Wreless Communcatons: Performance Results, IEEE JSAC, March [15] V. Tarokh, H. Jafarkhan, A.R. Calderbank, Space-Tme Block Codng from Orthogonal Desgns, IEEE Trans. on Informaton Theory, July [16] S. Ulukus, R. Yates, Adaptve Power Control and MMSE Interference Suppresson, ACM/Baltzer Wreless Networks, [17] H. Yousef zadeh, H. Jafarkhan, M. Moshfegh Power Optmzaton of Wreless Meda Systems wth Space- Tme Block Codes, IEEE Trans. on Image Processng, July [18] L. Zheng, H. Yousef zadeh, H. Jafarkhan, Resource Allocaton n Fadng Wreless Ad-Hoc Networks wth Temporally Correlated Loss, In Proc. IEEE WCNC, 2004.