EE360: Lecture 9 Outlne Resource Allocaton n Ad Hoc Nets Announcements Paper summares due next Wednesday Overvew of resource allocaton n ad-hoc networks Cross-layer adaptaton Dstrbuted power control Jont schedulng and power control for wreless ad hoc networks (Haleh Tabrz) Adaptaton and nterference (wdeband CDMA) Adaptaton va game theory (Manas Deb)
Adaptve Technques for Wreless Ad-Hoc Networks Network s dynamc (lnks change, nodes move around) Adaptve technques can adjust to and explot varatons Adaptvty can take place at all levels of the protocol stack Negatve nteractons between layer adaptaton can occur
What to adapt, and to what? QoS Adapts to applcaton needs, network/lnk condtons, energy/power constrants, Routng Adapts to topology changes, lnk changes, user demands, congeston, Transmsson scheme (power, rate, codng, ) Adapts to channel, nterference, applcaton requrements, throughput/delay constrants, Adaptng requres nformaton exchange across layers and should happen on dfferent tme scales
Bottom-Up Vew: Lnk Layer Impact Connectvty determnes everythng (MAC, routng, etc.) Lnk SINR and the transmt/receve strategy determne connectvty Can change connectvty va lnk adaptaton Lnk layer technques (MUD, SIC, smart antennas) can mprove MAC and overall capacty by reducng nterference Lnk layer technques enable new throughput/delay tradeoffs Herarchcal codng removes the effect of burstness on throughput Power control can be used to meet delay constrants
Power Control Adaptaton P G G P j j G Each node generates ndependent data. Source-destnaton pars are chosen at random. Topology s dynamc (lnk gan G j s tme-varyng) Dfferent lnk SIRs based on channel gans G j Power control used to mantan a target R value R j P G j P j
Power Control for Fxed Channels Semnal work by Foschn/Mljanc [1993] Assume each node has an SIR constrant Wrte the set of constrants n matrx form F R j G 0, G G j j, P G j P j j j Scaled Interferer Gan I FP u 0, P 0 u γ1η G 1 11 γ Nη,, G N NN T Scaled Nose
Optmalty and Stablty Then f r F <1 then a unque soluton to P * P * s the global optmal soluton I -1 F u Iteratve power control algorthms PP * Centralze d : Dstrbuted : P(k 1) P (k 1) FP(k) R γ ( k) u P (k)
What f the Channel s Random? Can defne performance based on dstrbuton of R : Average SIR Outage Probablty Average BER The standard F-M algorthm overshoots on average E[log R ] log γ ER γ How to defne optmalty f network s tme-varyng?
Can Consder A New SIR Constrant Orgnal constrant j j j γ P G η P G R 0 P G η γ P G E j j j Multply out and take expectatons 0 u P F I Matrx form j, E G E G γ j 0, F j j T u ] E[G η γ,, ] E[G η γ NN N N 11 1 1 Same form as SIR constrant n F-M for fxed channels
New Crteron for Optmalty If r F <1 then exsts a global optmal soluton * P I F-1 u For the SIR constrant Eη E G j P G j P Can fnd P* n a dstrbuted manner usng stochastc approxmaton (Robbns-Monro) j γ
Robbns-Monro algorthm P(k 1) P(k)-a Where e k s a nose term k g P(k) a ε k k ε k Step sze: F F(k) P(k) u u(k) a k n1 Under approprate condtons on 0 k a k * P(k) P ε k k n1 a 2 k
Admsson Control What happens when a new user powers up? More nterference added to the system The optmal power vector wll move System may become nfeasble Admsson control objectves Protect current user s wth a protecton margn Reject the new user f the system s unstable Mantan dstrbuted nature of the algorthm Trackng problem, not an equlbrum problem
Fxed Step Sze Algorthm Propertes Have non-statonary equlbra So cannot allow a k 0 Step sze:a k a k n1 a k k n1 a 2 k A fxed step sze algorthm wll not converge to the optmal power allocaton P(k) ~ P where ~ P* P O(a) E Ths error s cost of trackng a movng target
Example:..d. Fadng Channel Suppose the network conssts of 3 nodes Each lnk n the network s an ndependent exponental random varable 1 E[G].0375.02.0375 1.04.02.04 1 γ 5 η 1 Note that r F =.33 so we should expect ths network to be farly stable
Power Control + Power control mpacts multple layers of the protocol stack Power control affects nterference/sinr, whch other users react to Useful to combne power control wth other adaptve protocols Adaptve routng and/or schedulng (Haleh) Adaptve modulaton and codng Adaptve retransmssons End-to-end QoS
Multuser Adaptaton Recever Channel Traffc Generator Data Buffer Source Coder Channel Coder Modulator (Power) Cross-Layer Adaptaton Channel nterference s responsve to the crosslayer adaptaton of each user
Multuser Problem Formulaton Optmze cross-layer adaptaton n a multuser settng Users nteract through nterference Creates a Chcken and Egg control problem Want an optmal and stable equlbrum state and adaptaton for the system of users The key s to fnd a tractable stochastc process to descrbe the nterference
Lnear Mult-User Recever Assume each of K mobles s assgned a N-length random spreadng sequence The recever c takes dfferent values for dfferent structures (MMSE, de-correlator, etc.) j j j j T T T K N t z t a S c c c t z t a S c t SIR V V N S ) ( ) ( ) ( ) ( ) ( ) ( ) ( ), (,, 1 2 2 2 1 Interference term
Interference Models Jontly model the state space of every moble n the system Problem: State space grows exponentally Assume unresponsve nterference Avods the Chcken and Egg control ssue Problem: Unresponsve nterference models provde msleadng results Approxmatons use mean-feld approach Model aggregate behavor as an average Can prove ths s optmal n some cases
Power CDMA Wdeband Lmt K= number of users, N=spreadng gan K K Let K, N and the system load N Prevous research has proved convergence of the SIR n the wdeband lmt [Tse and Hanly 1999,2001] Can apply a wdeband approxmaton to the stochastc process descrbng a CDMA system and the correspondng optmal control problem 3 2 1 Hz
Optmzaton n the Wdeband Lmt Want to fnd optmal mult-user cross-layer adaptaton for a gven performance metrc, subject to QoS constrants Approxmate the network dynamcs wth wdeband lmt Optmze the control n the wdeband lmt Check convergence and unqueness to ensure the soluton s a good approxmaton to a fnte bandwdth system Specal case of usng mean feld theorems
Equlbrum n the Wdeband Lmt For any K, N, the system state vector fracton of users n each state K (t) s the Defne matrx P K ( t), g as the sngle user transton In the wdeband lmt we have determnstc nonlnear dynamcs for the system state ( t) lm K, N K ( t) and ( t 1) ( t) P ( t), g Furthermore P, g has a unque fxed pont
Wdeband Optmal Control Problem subject to: ( g) P mn g ( g) r( g) g, ( g) ( g), ( g) 1, f ( ) T Very smlar to the sngle user optmzaton The non-lnear constrant can ntroduce sgnfcant theoretcal and computatonal complcatons The non-lnear program s not convex Can show that t can be solved by a sequence of lnear programs
Example: Power Adaptaton Wth Deadlne Constraned Traffc Assume deadlne senstve data (100ms) 50 km/h Mcrocell (same channel as before) Mnmze average transmsson power subject to a deadlne constrant Assume we have a matched flter recever What happens as system load ncreases? Let number of users per Hz vary between 0 and 1
Average Power Power vs. System Load vs. Deadlne Constrant Infeasble Regon Users/Hz
Crosslayer Desgn n Ad-Hoc Wreless Networks Applcaton Network Access Lnk Hardware Substantal gans n throughput, effcency, and end-to-end performance from cross-layer desgn
Crosslayer Desgn Hardware Lnk Access Network Delay Constrants Rate Requrements Energy Constrants Moblty Applcaton Optmze and adapt across desgn layers Provde robustness to uncertanty
Crosslayer Adaptaton Applcaton Layer Desgn optmzaton crteron Data prortzaton Adaptve QoS Network Layer Adaptve routng MAC Layer Access control MUD/nterference cancellaton/smart antennas Lnk Layer Adaptve rate, codng, power, framng, etc. Adaptve retransmsson/herarchcal codng Lnk, MAC, and network have the most obvous synerges, but the applcaton layer dctates the optmzaton crteron
Why a crosslayer desgn? The techncal challenges of future moble networks cannot be met wth a layered desgn approach. QoS cannot be provded unless t s supported across all layers of the network. The applcaton must adapt to the underlyng channel and network characterstcs. The network and lnk must adapt to the applcaton requrements Interactons across network layers must be understood and exploted.
Adaptve Routng Source Destnaton Routng establshes the mechansm by whch a packet traverses the network As the network changes, the routes should be updated to reflect network dynamcs Updatng the route can ental sgnfcant overhead.
Route dessemnaton Route computed at centralzed node Most effcent route computaton. Can t adapt to fast topology changes. BW requred to collect and dessemnate nformaton Dstrbuted route computaton Nodes send connectvty nformaton to local nodes. Nodes determne routes based on ths local nformaton. Adapts locally but not globally. Nodes exchange local routng tables Node determnes next hop based on some metrc. Deals well wth connectvty dynamcs. Routng loops common.
Relablty Packet acknowledgements needed May be lost on reverse lnk Should negatve ACKs be used. Combned ARQ and codng Retransmssons cause delay Codng may reduce data rate Balance may be adaptve Hop-by-hop acknowledgements Explct acknowledgements Echo acknowledgements Transmtter lstens for forwarded packet More lkely to experence collsons than a short acknowledgement. Hop-by-hop or end-to-end or both.
MIMO n Ad-Hoc Networks Antennas can be used for multplexng, dversty, or nterference cancellaton Cancel M-1 nterferers wth M antennas What metrc should be optmzed? Cross-Layer Desgn
How to use Feedback n Wreless Networks Output feedback CSI Acknowledgements Network/traffc nformaton Somethng else Nosy/Compressed
Dversty-Multplexng-Delay Tradeoffs for MIMO Multhop Networks wth ARQ ARQ ARQ Multplexng Beamformng H1 H2 Error Prone Low P e MIMO used to ncrease data rate or robustness Multhop relays used for coverage extenson ARQ protocol: Can be vewed as 1 bt feedback, or tme dversty, Retransmsson causes delay (can desgn ARQ to control delay) Dversty multplexng (delay) tradeoff - DMT/DMDT Tradeoff between robustness, throughput, and delay
Multhop ARQ Protocols Fxed ARQ: fxed wndow sze Maxmum allowed ARQ round for th hop satsfes Adaptve ARQ: adaptve wndow sze Fxed Block Length (FBL) (block-based feedback, easy synchronzaton) L N 1 L L Block 1 ARQ round 1 Block 1 ARQ round 2 Block 1 ARQ round 3 Block 2 ARQ round 1 Block 2 ARQ round 2 Recever has enough Informaton to decode Varable Block Length (VBL) (real tme feedback) Block 1 ARQ round 1 Block 1 ARQ round 2 Block 1 round 3 Block 2 ARQ round 1 Block 2 ARQ round 2 Recever has enough Informaton to decode
Asymptotc DMDT Optmalty Theorem: VBL ARQ acheves optmal DMDT n MIMO multhop relay networks n long-term and short-term statc channels. Proved by cut-set bound An ntutve explanaton by stoppng tmes: VBL ARQ has the smaller outage regons among multhop ARQ protocols Accumlated Informaton (FBL) Short-Term Statc Channel re 0 4 t 1 8 12 t 2 Channel Use 39
Delay/Throughput/Robustness across Multple Layers A B Multple routes through the network can be used for multplexng or reduced delay/loss Applcaton can use sngle-descrpton or multple descrpton codes Can optmze optmal operatng pont for these tradeoffs to mnmze dstorton
Cross-layer protocol desgn for real-tme meda Loss-reslent source codng and packetzaton Congeston-dstorton optmzed schedulng Rate-dstorton preamble Applcaton layer Transport layer Traffc flows Lnk state nformaton Jont wth T. Yoo, E. Setton, X. Zhu, and B. Grod Congeston-dstorton optmzed routng Capacty assgnment for multple servce classes Adaptve lnk layer technques Lnk capactes Network layer MAC layer Lnk layer
Vdeo streamng performance s 5 db 3-fold ncrease 100 1000 (logarthmc scale)
Approaches to Cross-Layer Resource Allocaton* Network Optmzaton Dynamc Programmng Network Utlty Maxmzaton Dstrbuted Optmzaton Game Theory State Space Reducton Wreless NUM Multperod NUM Dstrbuted Algorthms Mechansm Desgn Stackelberg Games Nash Equlbrum *Much pror work s for wred/statc networks
Network Utlty Maxmzaton Maxmzes a network utlty functon max s. t. Ar U flow k k ( r R k ) routng Assumes Steady state Relable lnks Fxed lnk capactes Fxed lnk capacty Dynamcs are only n the queues U 2 (r 2 ) U n (r n ) U 1 (r 1 ) R R j
Wreless NUM Extends NUM to random envronments user vdeo Network operaton as stochastc optmzaton algorthm Upper Layers Upper Layers Physcal Layer Upper Layers Physcal Layer max st E[ U ( r m ( G))] Physcal Layer Upper Layers Physcal Layer Upper Layers Physcal Layer E[ r( G)] E[ R( S( G), G)] E[ S( G)] S Stolyar, Neely, et. al.
WNUM Polces Control network resources Inputs: Random network channel nformaton G k Network parameters Other polces Outputs: Control parameters Optmzed performance, that Meet constrants Channel sample drven polces
Example: NUM and Adaptve Modulaton Polces Informaton rate r() Tx power S() Tx Rate R() Tx code rate Polcy adapts to Changng channel condtons (G) Packet backlog Hstorcal power usage U 1 ( r 1 ) Data U 2 ( r 2 ) Data Upper Layers Buffer Physcal Layer U 3 ( r 3 ) Data Upper Layers Buffer Physcal Layer Block codes used
Rate-Delay-Relablty Polcy Results
Game theory Coordnatng user actons n a large ad-hoc network can be nfeasble Dstrbuted control dffcult to derve and computatonally complex Game theory provdes a new paradgm Users act to wn game or reach an equlbrum Users heterogeneous and non-cooperatve Local competton can yeld optmal outcomes Dynamcs mpact equlbrum and outcome Adaptaton va game theory
Network Metrcs Fundamental Lmts of Wreless Systems Network Fundamental Lmts Capacty Delay (DARPA Challenge Program) A C B Outage D Research Areas - Fundamental performance lmts and tradeoffs - Node cooperaton and cognton - Adaptve technques - Layerng and Cross-layer desgn - Network/applcaton nterface - End-to-end performance optmzaton and guarantees Capacty Cross-layer Desgn and End-to-end Performance (C*,D*,R*) Applcaton Metrcs Delay Robustness
Summary The dynamc nature of ad-hoc networks ndcate that adaptaton technques are necessary and powerful Adaptaton can transcend all layers of the protocol stack Approaches to optmzaton nclude dynamc programmng, utlty maxmzaton, and game theory Network dynamcs make centralzed/dstrbuted control challengng Game theory provdes a smple paradgm that can yeld near-optmal solutons