OFDMA Cross Layer Resource Control

Transcription

1 OFDA Cross Layer Resource Control Gwanmo Ku Adaptive Signal Processing and Information Theory Research Group Jan. 25, 2013

2 Outline 2/20 OFDA Cross Layer Resource Control Objective Functions - System Throughput (L1), Total Transmit Power (L1) Constraints - Transmit Power Constraint (L1) - Quality of Service (User Demand, Fairness), Buffer Status (L2-3) - Stability (L2-3) Generalized Cross Layer Control (GCLC) Stochastic Network Optimization (SNO) Network Utility aximization (NU)

3 OFDA Cross Layer Resource Control 3/20 System odel ( users, K subcarriers) obile (UE) u 1 OFDA Base Station (enb) u Higher Layer r m GCLC Higher Layer Buffer Buffer PHY Ian Wong & Brian Evans PHY

4 OFDA Resource Control 4/20 Objective Functions System Throughput aximization Transmit Power inimization Constraints Transmit Power Constraint Quality of Service User Demands : Each User Required Data Rate Fairness : inimum User Data Rate Stability based on Buffer Status

5 OFDA Resource Allocation 5/20 Notations m {1,, } User Index k {1,, K} Subcarrier Index p m,k : Power Control Coefficient γ m,k : SINR for user index m and subcarrier index k P T Total Transmit Power Constraint r m Required Each User Data Rate r 0 Required inimum User Data Rate b m Buffer Service Rate R m Overall Coding Rate for User m

6 OFDA Resource Allocation 6/20 System Throughput aximization Power Control System Throughput K p m,k = argmax E w m log(1 + p m,k γ m,k ) s.t m=1 k=1 K E p m,k P T m=1 k=1 max (β m R m r 0, β m R m r m ) w m log(1 + p m,k γ m,k ) K k=1 Stability

7 OFDA Resource Allocation 7/20 Work by Ian Wong and Brian Evans System Throughput aximization with Tx. Power Constraint p m,k = argmax E w m m=1 K k=1 log(1 + p m,k γ m,k ) s.t K E p m,k P T m=1 k=1 w m = 1 m=1

8 OFDA Resource Allocation 8/20 Optimization Framework L p, λ = E w m m=1 K k=1 log(1 + p m,k γ m,k ) Dual Optimization g = min λ 0 Θ(λ) +λ P T E( p m,k ) K m=1 k=1 Θ λ = max p P T L(p, λ)

9 OFDA Resource Allocation 9/20 Dual Θ λ = max p P T L(p, λ) K = λp T + max E w m log 1 + p m,k γ m,k λp m,k p P T K k=1 m=1 = λp T + max E w m log 1 + p m,k γ m,k λp m,k p k P k k=1 K m=1 = λp T + E max w m log 1 + p m,k γ m,k λp m,k p k P k k=1 m=1 max dual user selection = λp T + KE γk max m {1,,} max (w m log 1 + p m,k γ m,k λp m,k ) p m,k 0 multilevel water filling

10 OFDA Resource Allocation 10/20 A Simple Closed Form p m,k (λ) = 1 γ 0,m λ 1 γ m,k + x + = max(0, x) γ 0,m λ = λ ln 2 w m Cutoff value g = min λ 0 [λp T + K E γk g k γ k, λ ] g k γ k, λ = max m {1,,} {g m,k γ m,k, λ } g m,k γ m,k, λ = w m log 1 + p m,k λ λ p m,k λ

11 OFDA Resource Allocation 11/20 g m,k γ m,k, λ = w m log 1 + p m,k λ λ p m,k λ = w m ln 2 ln Optimal Solution γ m,k γ 0,m λ w m ln 2 + p m,k = p m,k λ 1(m = m k ) p m,k (λ ) = m k = argmax m {1,,} 1 γ 0,m λ 1 γ m,k λ γ m,k u(γ m,k γ 0,m λ ) + u x = 0 x < 0 1 x 0 λ = argmin [λp + K g kf gk g k dg k ] λ 0 0 w m log 1 + p m,k λ γ m,k λ p m,k (λ )

12 Cross Layer Control 12/20 Generalized Cross Layer Control (GCLC) Proposed by Georgiadis, Neely, and Tassiulas Focus on Stability based on Queuing Statistics Stochastic Network Optimization Network Utility aximization Network Stability Differential Equation of Queuing Statistics Lyapunov Stability

13 Cross Layer Control 13/20 Stochastic Network Optimization Buffer for user m Arrival Rate λ m Service Rate μ m Backlog Queue Q m (t) Network State Variable S(t) Control Action I t I S(t) feasible control region under S(t) Q t S t,i(t) Q(t + 1)

14 Cross Layer Control 14/20 Stochastic Network Optimization Q m t + 1 max Q m t R m out I t, S t, 0 + R m in (I t, S t ) Outgoing Queue Entering Queue Stability Issue t 1 lim t sup 1 t τ=0 E{Q m τ } <

15 Lyapunov Stability 15/20 If there exist B > 0 and ε > 0, such that for all times slot t we have : E t Q t B ε Q m (t) Then network is strongly stable, and m=1 lim t sup 1 t t 1 τ=0 E{Q τ } < B ε

16 Cross Layer Control 16/20 Find I(t) I t = argmax I t I S(t) W ab ab W ab t μ ab (t) t = max Q a t Q b t + μ ab maximum queue backlog differential Find Λ by Lyapunov Drift Drift Definition t = L t + 1 L(t) L t = 1 2 m=1 Q m 2 (t)

17 Lyapunov Drift 17/20 t = L t + 1 L(t) = 1 2 [Q m 2 t + 1 Q 2 m (t)] m=1 After applying Q m 2 (t + 1) Find Lyapunov Bound with Conditional Expectation t Q t t 1 lim t sup 1 t τ=0 E{Q m τ } <

18 Network Utility aximization (NU) 18/20 Rate r Λ with aximum Utility r = argmax r λ g r r Λ g(r) : Utility Function inimize Cost

19 Generalized Cross Layer Control 19/20 General Form of GCLC min r λ f x g(y) q x Q, h y H, r Λ Cost Variable Vector x : aximum cost constraints Q Utility Variable Vector y :inimum utility constraints H Stable Region r Λ Arrival Rate Vector λ inimize net cost Natural cost function f(x) and Concave Utility function g(y)

20 OFDA Resource Control via GCLC 20/20 OFDA via GCLC min r λ f x g(y) q x Q, h y H, r Λ Cost Variable Vector x : power coefficients Q = P T : Total Power Constraint Utility Variable Vector y : user data rate y = r H : Quality of Service (User demands, Fairness) Stable Region based on Queuing Statistics inimize net cost : aximize System Throughput