Introduction and Scope of the Thesis Power Optimal Scheduling Summary and Future Scope Stochastic Control for Energy Efficient Resource Allocation in Wireless Networks Abhijeet Bhorkar (01D07014) under the guidance of Prof. A. Karandikar Indian Institute of Technology Bombay, Powai, Mumbai-76 July 05, 2006 Abhijeet Bhorkar Resource Allocation in Wireless Networks
Introduction and Scope of the Thesis Power Optimal Scheduling Summary and Future Scope Outline Introduction and Scope of the Thesis 1 Power Optimal Scheduling 2 Minimum Rate Guarantee Fairness Guarantee Average Delay Guarantee- point To point Link Learning Algorithms: Overview Problem Formulation Energy Efficient Video Transmis- sion Summary and Future Scope 3 Abhijeet Bhorkar Resource Allocation in Wireless Networks
Introduction and Scope of the Thesis Power Optimal Scheduling Summary and Future Scope Motivation Wireless LANs, ad-Hoc networks, sensor networks limited battery life, bandwidth Maintain acceptable QoS metric rate, delay, fairness Efficient utilization of limited resources Time varying wireless channel conditions Exploit channel variations opportunistic scheduling : Schedule user with the best channel condition Can we perform power control to exploit channel variations? Joint opportunistic and energy efficient control Abhijeet Bhorkar Resource Allocation in Wireless Networks
Introduction and Scope of the Thesis Power Optimal Scheduling Summary and Future Scope Motivation Wireless LANs, ad-Hoc networks, sensor networks limited battery life, bandwidth Maintain acceptable QoS metric rate, delay, fairness Efficient utilization of limited resources Time varying wireless channel conditions Exploit channel variations opportunistic scheduling : Schedule user with the best channel condition Can we perform power control to exploit channel variations? Joint opportunistic and energy efficient control Abhijeet Bhorkar Resource Allocation in Wireless Networks
Introduction and Scope of the Thesis Power Optimal Scheduling Summary and Future Scope Motivation Wireless LANs, ad-Hoc networks, sensor networks limited battery life, bandwidth Maintain acceptable QoS metric rate, delay, fairness Efficient utilization of limited resources Time varying wireless channel conditions Exploit channel variations opportunistic scheduling : Schedule user with the best channel condition Can we perform power control to exploit channel variations? Joint opportunistic and energy efficient control Abhijeet Bhorkar Resource Allocation in Wireless Networks
✆ ✄ ✝ ✝ ✝ ✝ ✆ ✞ ☎ ☎ ✄ ✄ ✄ ✂ ✝ ✂ ✂ ✂ �✁ � ✞ ✞ ✞ ✞ ✞ ✝ Minimum Rate Guarantee Introduction and Scope of the Thesis Fairness Guarantee Power Optimal Scheduling Average Delay Guarantee- point To point Link Summary and Future Scope Energy Efficient Video Transmission Scenario Power optimal scheduling Minimum rate guarantee (Multi-user) Fairness guarantee (Multi-user) Average delay guarantee with finite buffer (point to point link) Abhijeet Bhorkar Resource Allocation in Wireless Networks
Minimum Rate Guarantee Introduction and Scope of the Thesis Fairness Guarantee Power Optimal Scheduling Average Delay Guarantee- point To point Link Summary and Future Scope Energy Efficient Video Transmission Preliminaries(1) Shannon’s capacity : P = N 0 W � � e u / W − 1 , x N 0 : Spectral density of AWGN channel W : Spectrum bandwidth u : Transmission rate Stochastic approximation: λ ( n + 1 ) = λ ( n )+ α ( n )( H ( λ ( n ))+ M ( n + 1 )) (1) E [ h ( λ , x )] = H ( λ ) Martingale M ( n + 1 ) = h ( λ ( n ) , x ( n )) − H ( λ ( n )) ∞ ∞ ∑ ∑ α ( n ) 2 < ∞ α ( n ) = ∞ , If step sizes satisfy , n = 0 n = 0 then (1) tracks the Ordinary Differential equation (ODE), ˙ λ ( t ) = H ( λ ( t )) (2) Abhijeet Bhorkar Resource Allocation in Wireless Networks
✧ ✒ ✒ ✁ ✞ ✩ ★ ✄ ◆ ✧ ✁ ✒ ✁ ✞ ✩ ◆ ✖ ✦ ✦ ✧ ✁ ◆ Minimum Rate Guarantee Introduction and Scope of the Thesis Fairness Guarantee Power Optimal Scheduling Average Delay Guarantee- point To point Link Summary and Future Scope Energy Efficient Video Transmission System Model ✲✳✫✵✴✔✶✯✶ ✘✷✰ ✲✹✸✺✶ ✭✼✻✾✽✙✻ ✸✿✶ �✂✁☎✄✝✆✟✞ ✕✗✖✙✘☎✚✜✛ ✄✝✆✟✞ ✄✝✆✟✞ �✓✒✔✄✝✆✟✞ ✕✗✖✙✘☎✚✣✢ ✄❁❀ ✸❃❂ ✘✷✚✣❄✣✘ ✻❅✖❆✻ ✸✺✶ ✒❖✄✝✆✟✞ ✄❑❏ ✄✝✆✟✞❉❈▲❏ ✄❑✆▼✞✷❈✔❋❍❋❍❋✔❈▲❏ ✄✝✆✟✞■✞ ✄✝✆✟✞ ★✪✩✬✫ ✘☎✭✯✮✯✰✱✘☎✚ ✕✗✖✬✘✷✚ ✘❉✰✱✘ ✽✙✻ ✸✺✶ ✄✝❇ ✄✝✆✟✞❉❈❊❇ ✄✝✆✟✞❉❈●❋❍❋●❋●❈❊❇ ✄✝✆✟✞■✞ ✠☛✡✌☞✎✍✑✏ ✕✗✖✙✘☎✚✥✤ ✄❑✆▼✞ ✄✝✆✟✞ ✦✑✧ Figure: Single hop system model Slotted single-hop TDMA system Uplink scheduling Perfect channel state information Channel process ergodic (i.i.d. or Markovian) Abhijeet Bhorkar Resource Allocation in Wireless Networks
Minimum Rate Guarantee Introduction and Scope of the Thesis Fairness Guarantee Power Optimal Scheduling Average Delay Guarantee- point To point Link Summary and Future Scope Energy Efficient Video Transmission Problem Formulation Minimize average power M 1 ∑ min limsup q ( n ) , M M → ∞ n = 1 Subject to average rate constraints C i M 1 ∑ limsup U i ( q i ( n ) , x i ( n ))) ≥ C i ∀ i , M M → ∞ n = 1 q ( n ) ≥ 0 , N ∑ y i ( n ) ≤ ∀ n (3) 1 i = 1 U is information theoretic rate and is concave differentiable function of x i , q i U = log ( 1 + x i q i ) x = ( x 1 , x 2 , ··· , x N ) y = ( y 1 , y 2 , ··· , y N ) Abhijeet Bhorkar Resource Allocation in Wireless Networks
Minimum Rate Guarantee Introduction and Scope of the Thesis Fairness Guarantee Power Optimal Scheduling Average Delay Guarantee- point To point Link Summary and Future Scope Energy Efficient Video Transmission Problem Formulation Minimize average power M 1 ∑ min limsup q ( n ) , M M → ∞ n = 1 Subject to average rate constraints C i M 1 ∑ limsup U i ( q i ( n ) , x i ( n ))) ≥ C i ∀ i , M M → ∞ n = 1 q ( n ) ≥ 0 , N ∑ y i ( n ) ≤ ∀ n (3) 1 i = 1 U is information theoretic rate and is concave differentiable function of x i , q i U = log ( 1 + x i q i ) x = ( x 1 , x 2 , ··· , x N ) y = ( y 1 , y 2 , ··· , y N ) Abhijeet Bhorkar Resource Allocation in Wireless Networks
Minimum Rate Guarantee Introduction and Scope of the Thesis Fairness Guarantee Power Optimal Scheduling Average Delay Guarantee- point To point Link Summary and Future Scope Energy Efficient Video Transmission Multiuser Optimal Solution Proposition Optimal Policy for multiple users is to select k th user and transmit with power q ∗ Sketch of Proof Use ergodicity to convert optimization problem (3) in continuous domain Minimize Lagrangian of (3) w.r.t. q first, then w.r.t. y Optimal power for single user, � � + q ∗ λ i − 1 i = , where λ i is the Lagrange multiplier x i Minimizing w.r.t. y , we get, i ( q ∗ i − λ i [ log ( 1 + q ∗ k = argmin i x i ) − C i ]) Details Abhijeet Bhorkar Resource Allocation in Wireless Networks
Minimum Rate Guarantee Introduction and Scope of the Thesis Fairness Guarantee Power Optimal Scheduling Average Delay Guarantee- point To point Link Summary and Future Scope Energy Efficient Video Transmission Online Algorithm (1) After minimizing over the primal variables, optimal value of Lagrangian is, i ( q ∗ i − λ i log ( 1 + q ∗ F ( λ ) = [ E ( min i x i ( n )) − C i )] F ( λ ) strictly concave → unique maximum Need to find saddle point Consider for example f ( x ) is continuous differentiable Gradient ascent scheme for maximizing f is, x n + 1 = x n + α n ˙ f ( x n ) It tracks the differential equation, x ( t ) = d f dx = ˙ ˙ f Abhijeet Bhorkar Resource Allocation in Wireless Networks
Minimum Rate Guarantee Introduction and Scope of the Thesis Fairness Guarantee Power Optimal Scheduling Average Delay Guarantee- point To point Link Summary and Future Scope Energy Efficient Video Transmission Online Algorithm (2) Estimate λ i online Channel Find the Transmit Optimal power, with Measurement optimal power user Update Parameter Figure: Block diagram for on-line policy Update Equation � � � � + 1 } + λ i ( n + 1 ) = { λ i ( n ) − α ( n )[ y i ( n ) log 1 + λ i ( n ) − x i ( n ) ] − C i ∀ i , (4) x i ( n ) � �� � h i ( λ ) Abhijeet Bhorkar Resource Allocation in Wireless Networks
Minimum Rate Guarantee Introduction and Scope of the Thesis Fairness Guarantee Power Optimal Scheduling Average Delay Guarantee- point To point Link Summary and Future Scope Energy Efficient Video Transmission Optimality and Stability of Update Equation Iterations converge to differential inclusion almost surely to , ˙ λ ( t ) = h ( λ ( t )) and thus to a supergradient ascent scheme ˙ λ ( t ) ∈ ∂ F ( λ ( t )) ∂ F supergradient of F Stability Boundedness of λ i using projection method or linear stochastic approximation method Abhijeet Bhorkar Resource Allocation in Wireless Networks
Recommend
More recommend
