Distributed Power Control and lcoded Power Control

Transcription

1 WiOpt, Paris, France Distributed Power Control and lcoded Power Control S. Lasaulce(*), joint work with [authors] (*) L2S (CNRS CentraleSupelec) May 18, 2017

2 Coded Power Control Introduction 1

3 What is meant by distributed power control Distributed decision-wise and information-wise 2

4 What is meant by distributed power control Distributed decision-wise and information-wise partial control 3

5 What is meant by distributed power control Distributed decision-wise and information-wise partial control partial observation 4

6 Motivation for distributed power control 5

7 Distributed power control algorithms: Typical conclusion Local decision Local information (Affordable complexity) Global inefficiency 6

8 Natural questions Distributedness & global efficiency : Unmarriable features? What is the best we can do with what know? 7

9 Take away messages Power control strategy = code Limiting performance of power control information theory 8

10 Outline Power modulation Limiting performance of coded power control Power control code example 9

11 Distributed Power Control and Coded Power Control Power Modulation 10

12 Global inefficiency: What is the problem? Performance measure: u(p 1,...,p K ;g 11,...,g KK ) = u(p 1,...,p K ;G) 11

13 Considered interference network (Here K = 2, S = 1) 12

14 Global inefficiency: What is the problem? Assumed utility form: u(p 1,p 2 ;g 11,g 12,g 21,g 22 ) = u(p 1,p 2 ;G) Classical example: u sum rate (p 1,p 2 ;G) = 2 log (1+SINR i ) i=1 13

15 Global inefficiency: What is the problem? Complexity issue: maximizing u may be hard Information availability: global CSI G typically not available at the Tx. How to solve this issue? 14

16 The power modulation idea [Varma 2015][Zhang 2017] 15

17 Two main phases coherence time t=1 t=2 exploration exploitation 16

18 How to find p 1 at Tx 2? OK with SINR feedback SINR 2 = g 22p 2 σ 2 +g 12 p 1 OK with RSP feedback ω 2 = σ 2 +g 22 p 2 +g 12 p 1 17

19 Local CSI estimation Training matrix: P = p 1 (1) p 2 (1).. p 1 (N) p 2 (N). Power domain observation equation: ω 1 (1) ( ) g11. = P +σ 2 1 g ω 1 (N) 21 18

20 Numerical analysis: Scenario 19

21 Numerical analysis: Simulations Team BRD with perfect CSI Team BRD with estimated global CSI (LSPD+MEQ) IWFA with estimated local CSI (LSPD) Average sum-rate (bps/hz) Inter site distance (m) 20

22 Take away messages RSP/SINR feedback is sufficient to reconstruct global CSI. Maximal efficiency can be theoretically achieved. Key ingredient: RSP/SINR = communication channel + power modulation. Use interference to manage interference. Other types of (structured) feedbacks, other types of exchange information,... 21

23 Distributed Power Control and Coded Power Control Limiting Performance of Coded Power Control 22

24 Problem statement Available global CSI image: Γ i (s i g 11,...,g KK ), everything discrete Special cases Global CSI: s i = (g 11,g 12,...,g KK ) Individual CSI: s i = g ii Imperfect individual CSI: s i = ĝ ii 23

25 Limiting performance of power control Power control strategy (causal case): f i,t : (s i (1),...,s i (t)) p i (t) Utility: u i (f 1,...,f K ) = lim T + 1 T T E [ u i (p 1 (t),...,p K (t);g(t)) ] t=1 [Larrousse et al ITW 2015] 24

26 Limiting performance of power control Theorem: g i.i.d., Γ i DMC. The average utility u = (u 1,...,u K ) is achievable when T iff it writes as u i = g,p 1,...,p K,s 1,...,s K,v u i (p 1,...,p K ;g) ρ(g)γ(s 1,...,s K g)p V (v) Feasible utility region characterization K P Pi S i,v(p i s i,v) i=1 25

27 Illustration for energy-efficiency 0.4 K=2, S=1, SNR=3 db, SIR=5.2 db, E[g ii ]=1 Card(P)=15 with uniform power, card(g)=15 with MEQ 0.35 EE of user 2 (bits/joule) Centralized solution with perfect knowledge Our technique with perfect g ii Our technique with noisy g ii, ESNR=12 db Our technique with noisy g ii, ESNR=6 db Our technique with noisy g ii, ESNR=3 db EE of user 1 (bits/joule) 26

28 Limiting performance of power control Power control strategy (noncausal case): f i,t : (s i (1),...,s i (T),y i (1),...,y i (t 1)) p i (t) Utility: u i = E Q (u i (p 1,...,p K ;g)) 27

29 Characterization for a special case Theorem [Larrousse et al ITW 2015] Q(g,p 1,p 2 ) implementable iff it is marginal of some Q(p 1,p 2,g,s 1,y 2,v) satisfying = ρ 0 (g)ℸ(s 1 g)p VP1 P 2 S 1 (v,p 1,p 2 s 1 )Γ(y 2 g,p 1 ) I Q (S 1 ;P 2 ) I Q (V;Y 2 P 2 ) I Q (V;S 1 P 2 ) 28

30 Utility region characterization Pareto frontier: use w α = αu 1 +(1 α)u 2 minimize Q(g,p 1,p 2 )w α (g,p 1,p 2 ) g,p 1,p 2 subject to H Q (G)+H Q (P 2 ) H Q (G,P 1,P 2 ) 0 Q(g,p 1,p 2 ) 0 1+ Q(g,p 1,p 2 ) = 0 g,p 1,p 2 ρ 0 (g)+ p 1,p 2 Q(g,p 1,p 2 ) = 0 29

31 Take away messages Finding the limiting performance = solving an OP Open decision/game problems open information theory problems 30

32 Distributed Power Control and Coded Power Control Power control code example 31

33 Long-term utility Scheme 1: g p 1 p Match nature Long-term utility [ 1 E T ] T u(p(t),g(t)) t=1 1 2 = 0.5. for g B ( 1 2 ) 32

34 Long-term utility Scheme 2: g p 1 p 2 Long term utility: E [ 1 T T t=1 u(p(t),g(t)) ] 5 8 =

35 Illustration [Larrousse et al TIT 2017] Setting Multiple access channel, K = 2, binary power control, BSC links, u i = log(1+sinr i ) Expected payoff (a.u.) CCPC CPC length n CPC length n=3 SPC NPC Signal-to-Noise Ratio (db) 34

36 Technical challenges Construct codes (see [Larrousse and Lasaulce ISIT 2013][Larrousse et al TIT 2017]). Joint control-communication problem. Controlled states. Nash equilibrium points. 35

37 Distributed power control and coded power control Thank you for your attention! 36

38 Main references (1/3) Varma et al Eusipco 2015: Vineeth S. Varma, Samson Lasaulce, Chao Zhang, and R. Visoz. Power modulation: Application to inter-cell interference coordination. In EUSIPCO. IEEE, Zhang et al 2017: C. Zhang, V. Varma, S. Lasaulce, and R. Visoz, Implementing Coordination in Interference Networks through Power Domain Channel Estimation, IEEE Transactions on Wireless Communications, Larrousse et al ITW 2015: Larrousse, B., Lasaulce, S. and Wigger, M. (2015, May). Coordination in State-Dependent Distributed Networks. In Information Theory Workshop (ITW). (pp. 1-5). IEEE. Mertikopoulos JSAC 2012: P. Mertikopoulos, E. V. Belmega, A. Moustakas, and S. Lasaulce, Distributed Learning Policies for Power Allocation in Multiple Access Channels, IEEE Journal of Selected Areas in Communications (JSAC), Vol. 30, No. 1, pp , Jan

39 Main references (2/3) C. Zhang, N. Khalfet, S. Lasaulce, and S. Tarbouriech, Utility-oriented quantization and application to power control, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), B. Larrousse, S. Lasaulce, and M. Bloch, Coordination in distributed networks via coded actions with application to power control, IEEE Transactions on Information Theory S. Berri, S. Lasaulce, and M. S. Radjef, Power control with partial observation in wireless ad hoc networks, IEEE Proc. of the EUSIPCO conference, Budapest, Hungary, Aug A. Agrawal, S. Lasaulce, O. Beaude, and R. Visoz, A framework for decentralized power control with partial channel state information, IEEE Proc. of the Fifth International Conference on Communications and Networking (ComNet2015), Hammamet, Tunisia, November 4-7, O. Beaude, A. Agrawal, and S. Lasaulce, A framework for computing power consumption scheduling functions under uncertainty, 6th IEEE International Conference on Smart Grid Communications (SmartGridComm 2015), Miami, Florida, USA, Nov

40 Main references (3/3) A. Agrawal, F. Danard, B. Larrousse, and S. Lasaulce, Implicit coordination in two-agent team problems, European Conference on Control (ECC), Linz, Austria, July B. Larrousse, S. Lasaulce, and M. Wigger, Coordination in state-dependent distributed networks: The two-agent case, IEEE International Symposium on Information Theory (ISIT), Hong Kong, June B. Larrousse, S. Lasaulce, and M. Wigger, Coordination in State-Dependent Distributed Networks, IEEE Proc. of the Information Theory Workshop (ITW), Jerusalem, Israel, Apr.-May B. Larrousse, A. Agrawal, and S. Lasaulce, Implicit coordination in two-agent team problems. Application to distributed power allocation, IEEE 12th Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), Hammamet, Tunisia, May

41 Distributed Power Control and Coded Power Control Backup slides 40

42 The iterative water-filling algorithm (IWFA) At time-slot t, the water-filling solution writes as p i,s (t+1) = [ 1 p ] + i,s(t) λ i SINR i,s (t) References: [Yu et al JSAC 2002] (multi-band); [Scutari et al TSP 2009] (MIMO) 41

43 About IWFA-type algorithms Required knowledge: SINR i,s Complexity: low Convergence: conditional [Scutari et al TSP 2009], sometimes w.p.0. [Mertikopoulos et al JSAC 2012] 42

44 About IWFA-type algorithms. Continued Global efficiency: typically not good for medium/high interference levels w sum (p 1,...,p K ) = K S log (1+SINR i,s ) i=1 s=1 with p i = (p i,1,...,p i,s ) 43

45 Local CSI exchange phase description g i Phase I g i Quant. Q II i ( g i ) Mod. p II i g j i Dequantizer& Demodulator p II i Decoder j, j i ω II j What is not classical in the above operations 44