Rethinking MIMO for Wireless Networks: Linear Throughput Increases with Multiple Receive Antennas

Transcription

1 Retnng MIMO for Wreless etwors: Lnear Trougput Increases wt Multple Receve Antennas ar Jndal Unversty of Mnnesota Unverstat Pompeu Fabra Jont wor wt Jeff Andrews & Steven Weber

2 MIMO n Pont-to-Pont Cannels y Hx z Foscn-Gans '98: Capacty of a pont-to-pont MIMO cannel scales lnearly wt mn( t, r ) C mn(, )log t r SR Transmt mn( t, r ) data streams, eac at rate ~ log (SR) o ncrease n power or bandwdt MIMO an ntegral part of every contemporary g-rate wreless systems (LTE, 80.n, WMax)

3 MIMO n Ad-Hoc etwors Many TX-RX pars smultaneously communcatng, mutually nterferng If eac node as antennas, use pont-to-pont MIMO tecnques to ncrease per-ln rate lnearly wt Interference power does not ncrease wt Spatal color of nterference ncreases rates Lnear ncrease n system trougput: transport capacty & area spectral effcency (ASE) Is ts te only way?

4 Multple RX Antennas n Ad-Hoc etwors Eac TX as antenna, eac RX as antennas Man Result: System trougput scales lnearly wt Use RX antennas to smultaneously: Cancel nearby nterferers Increase receved sgnal power (array gan) Mantan a constant per-ln rate (SIR) & ncrease spatal densty of smultaneous transmssons lnearly wt Lnear ncrease n densty, constant per-ln rate -> lnear ncrease n system trougput

5 etwor Model Decentralzed networ wt randomly located TX-RX pars (sngle-op) TX s randomly located accordng to -D Posson process Densty λ, nfnte # of TX's on nfnte -D plane Eac TX assocated wt a RX a dstance d meters away Models networ usng ALOHA

6 etwor Model () Consder reference par TX0-RX0 Interferers stll form a -D Posson process (densty λ) TX-RX dstance: d meters : pat-loss exponent X :dstance to -t nearest nterferer :vector cannel to -t nterferer d complex Gaussan components Receved sgnal (-dm vector): y d u 0 0 X u SIR after RX flter v z SIR TX 0 TX 3 TX d meters H ρ v η ρ v 0 H X X 3 d TX X RX 0 X X 4 TX 4

7 Performance Metrcs Outage probablty relatve to SIR tresold β: P out ( λ,, β ) P[ SIR β ] Increasng n λ, decreasng n (good RX flter) Correspondng spectral effcency: log (β) bpshz Transmsson Capacty [Weber, Andrews, et. al '05]: maxmum densty λ suc tat outage no larger tan ε λ ε (, β ) P out ( ε ) Objectve: Sow λ ε (,β) ncreases lnearly wt

8 RX Flter Desgn Maxmum-rato combnng (MRC): [Hunter-Andrews-Weber] max sgnal power by coosng flter n drecton of desred cannel Full Zero-Forcng (ZF): [Huang-Andrews-Heat-Guo-Berry] mnmze nt. power by coosng flter ortogonal to cannels of nearest - nterferers MMSE: maxmzes SIR,..., v ( ) 0 0 v 0 X I v H η 0 H H X v d v SIR ρ η ρ

9 Pror Wor [Hunter-Andrews-Weber '07]: Maxmum rato combnng allows densty to ncrease wt as: λ O ( ) [Huang-Andrews-Heat-Guo-Berry '08]: Full zero-forcng allows densty to ncrease wt as λ O ( ) [Govndasamy-Blss-Staeln '07]: For fxed densty, wt MMSE expected SIR scales wt as E [ SIR] O ( )

10 Partal Zero Forcng Coose flter ortogonal to ( -) nearest nterferers Sgnal term Interference terms ( ) v v,...,,..., 0 on ullspace of Projecton ) ( 0 ~ H v χ,...,..., 0 v v H H ~ χ ) ( ~ a X d SIR χ ρ η χ ρ

11 Expected Interference Power Expected nterference power: Ordered squared-dstances ~ -D PPP(πλ) Dstance-squared to -t nearest nterferer ~ ) ( ~ X d SR SIR χ χ [ ] [ ] [ ] ( ) ) ( ) ( λ π πλ χ χ < Γ Γ X E X E E X E ( ) χ πλ η ρ SR d

12 Outage Probablty Upper Bound For fxed densty and : Proof: Use Marov nequalty & ndependence of S, I ( ) ( ) ) ( ] [ SR SIR P β νλ β ( ) ( ) ] [ < SR S E I E S I E S I P I S P β νλ β β β β

13 Densty Lower Bound Invert outage probablty upper bound to get max-densty lower bound: λ ε ε β ( ) ε πd β SR ( ) Array Gan Int. Cancellaton eed to coose suc tat bound s lnear n

14 Acevng Lnear Densty Scalng Use a strct fracton of RX degrees of freedom to cancel nterference: θ for any 0 < θ < Max-densty lower bound: λ ε ε β ( ) πd ( θ ) Lower bound scales lnearly wt ε βsr θ θ ( θ )

15 Intuton Expected sgnal power Expected nt power (cancel ) Fxed outage requres constant rato between sgnal power & nt power MRC (0) [H-A-W Sgnal ~ O Full ZF (-) [H-A-H-G-B] Sgnal ~, Partal ZF (θ for θ<) Sgnal ~, Int ~ λ λ Int ~ λ d ( ) π ~ λ ( ) λ O ( ) ( θ ) λ O( ) ( θ ), Int ~ λ

16 Optmzaton of Partal ZF Densty lower bound converges to: ε ( ) β Maxmze wt respect to θ: πd * θ ( ) θ θ Small PL exponent: far nterferers powerful, so no pont n cancelng nearby ones Large PL exponent: nearby nterferers muc more powerful, so get beneft by cancelng

17 umercal Results Maxmum densty vs. (ε0.) β,d m, 3 (left), 4 (rgt) Very large densty gans even for small

18 umercal Results () Maxmum densty vs. # cancelled, 0, 3, ε0. Consstent wt θ * 3

19 Rate vs. Densty Increase [Govndasamy-Blss-Staeln] consdered almost dentcal model for fxed densty, optmal MMSE recever Expected SIR scales superlnearly: Expected spectral effcency scales logartmcally: () log() If densty ept constant and RX antennas used to ncrease per-ln rate: trougput ~ log() Increasng densty sub-lnearly (wt ) leads to sublnear trougput scalng Implcaton of ncreasng densty: In ALOHA networ, can ncrease contenton probablty wt In general, can be more aggressve wt smultaneous transmssons

20 Concluson RX cancellaton allows transmtter densty to grow lnearly wt # of RX antennas, wtout requrng multple TX antennas Constant per-ln rate, lnearly ncreasng densty Results suggest MIMO can be very powerful n ad-oc networs Spatal nterference cancellaton canges perspectve on mult-user nterference: s careful transmsson scedulng needed? Extensons: Evaluate beneft n mult-op settng MMSE recever Imperfect CSI