ofdma cross layer resource controlofdma cross layer resource control 3/20 system model (๐ด users,...
TRANSCRIPT
OFDMA Cross Layer
Resource Control
Gwanmo Ku
Adaptive Signal Processing and Information Theory Research Group
Jan. 25, 2013
Outline
OFDMA 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 Maximization (NUM)
2/20
OFDMA Cross Layer Resource Control
3/20
System Model (๐ด users, ๐ฒ subcarriers)
Base Station (eNB)
Mobile (UE)
๐๐
๐๐ด
โฆ
Higher Layer
Buffer
PHY
Higher Layer
Buffer
PHY
OFDMA
Ian Wong & Brian Evans
GCLC
๐๐
OFDMA Resource Control
4/20
Objective Functions
System Throughput Maximization
Transmit Power Minimization
Constraints
Transmit Power Constraint
Quality of Service
User Demands : Each User Required Data Rate
Fairness : Minimum User Data Rate
Stability based on Buffer Status
OFDMA Resource Allocation
5/20
Notations
๐ โ {๐,โฆ ,๐ด} User Index
๐ โ {๐,โฆ ,๐ฒ} Subcarrier Index
๐๐,๐ : Power Control Coefficient
๐ธ๐,๐ : SINR for user index ๐ and subcarrier index ๐
๐ท๐ป Total Transmit Power Constraint
๐๐ Required Each User Data Rate
๐๐ Required Minimum User Data Rate
๐๐ Buffer Service Rate
๐น๐ Overall Coding Rate for User ๐
OFDMA Resource Allocation
6/20
System Throughput Maximization
Power Control
๐๐,๐ = argmaxE ๐ค๐
๐
๐=1
log(1 + ๐๐,๐๐พ๐,๐)
๐พ
๐=1
๐๐ฒ๐ฌ๐ญ๐๐ฆ ๐๐ก๐ซ๐จ๐ฎ๐ ๐ก๐ฉ๐ฎ๐ญ
๐ธ ๐๐,๐
๐พ
๐=1
๐
๐=1
โค ๐๐
s.t
max (๐ฝ๐๐ ๐๐0, ๐ฝ๐๐ ๐๐๐) โค ๐ค๐ log(1 + ๐๐,๐๐พ๐,๐)
๐พ
๐=1
Stability
OFDMA Resource Allocation
7/20
Work by Ian Wong and Brian Evans
System Throughput Maximization with Tx. Power Constraint
๐๐,๐ = argmax ๐ ๐ค๐
๐
๐=1
log(1 + ๐๐,๐๐พ๐,๐)
๐พ
๐=1
๐ ๐๐,๐
๐พ
๐=1
๐
๐=1
โค ๐๐
๐ค๐
๐
๐=1
= 1
s.t
OFDMA Resource Allocation
8/20
Optimization Framework
Dual Optimization
๐ฟ ๐ โ , ๐ = ๐ ๐ค๐
๐
๐=1
log(1 + ๐๐,๐๐พ๐,๐)
๐พ
๐=1
+๐ ๐๐ โ ๐( ๐๐,๐
๐พ
๐=1
)
๐
๐=1
๐โ = min๐โฅ0
ฮ(๐)
ฮ ๐ = max๐ โ โ๐๐
๐ฟ(๐ โ , ๐)
OFDMA Resource Allocation
9/20
Dual
ฮ ๐ = max๐ โ โ๐๐
๐ฟ(๐ โ , ๐)
= ๐๐๐ + max๐ โ โ๐๐
๐ ๐ค๐ log 1 + ๐๐,๐๐พ๐,๐ โ ๐๐๐,๐
๐
๐=1
๐พ
๐=1
= ๐๐๐ + max๐๐ โ โ๐๐
๐ ๐ค๐ log 1 + ๐๐,๐๐พ๐,๐ โ ๐๐๐,๐
๐
๐=1
๐พ
๐=1
= ๐๐๐ + ๐ธ max๐๐ โ โ๐๐
๐ค๐ log 1 + ๐๐,๐๐พ๐,๐ โ ๐๐๐,๐
๐
๐=1
๐พ
๐=1
= ๐๐๐ + ๐พ๐ธ๐พ๐max
๐โ{1,โฆ,๐}max
๐๐,๐โฅ0(๐ค๐ log 1 + ๐๐,๐๐พ๐,๐ โ ๐๐๐,๐)
multilevel water filling
๐๐๐ฅ ๐๐ข๐๐ ๐ข๐ ๐๐ ๐ ๐๐๐๐๐ก๐๐๐
OFDMA Resource Allocation
10/20
A Simple Closed Form
๐ ๐,๐(๐) =1
๐พ0,๐ ๐โ
1
๐พ๐,๐
+
๐ฅ + = max(0, ๐ฅ)
๐พ0,๐ ๐ =๐ ln 2
๐ค๐ Cutoff value
๐โ = min๐โฅ0
[๐๐๐ + ๐พ ๐๐พ๐๐๐ ๐พ๐ , ๐ ]
๐๐ ๐พ๐ , ๐ = max๐โ{1,โฆ,๐}
{๐๐,๐ ๐พ๐,๐ , ๐ }
๐๐,๐ ๐พ๐,๐ , ๐ = ๐ค๐ log 1 + ๐ ๐,๐ ๐ โ ๐ ๐ ๐,๐ ๐
OFDMA Resource Allocation
11/20
Optimal Solution
๐๐,๐ ๐พ๐,๐ , ๐ = ๐ค๐ log 1 + ๐ ๐,๐ ๐ โ ๐ ๐ ๐,๐ ๐
=๐ค๐
ln 2ln
๐พ๐,๐
๐พ0,๐ ๐โ
๐ค๐
ln 2+
๐
๐พ๐,๐๐ข(๐พ๐,๐ โ ๐พ0,๐ ๐ )
๐ข ๐ฅ = 0 ๐ฅ < 01 ๐ฅ โฅ 0
๐โ = ๐๐๐min๐โฅ0
[๐๐ + ๐พ ๐๐๐๐๐๐๐ ๐๐๐
โ
0
]
๐ ๐,๐(๐โ) =
1
๐พ0,๐ ๐โโ
1
๐พ๐,๐
+
๐๐,๐โ = ๐ ๐,๐ ๐โ 1(๐ = ๐๐
โ )
๐๐โ = argmax
๐โ{1,โฆ,๐}๐ค๐ log 1 + ๐ ๐,๐ ๐โ ๐พ๐,๐ โ ๐โ๐ ๐,๐ (๐โ)
Cross Layer Control
12/20
Generalized Cross Layer Control (GCLC)
Proposed by Georgiadis, Neely, and Tassiulas
Focus on Stability based on Queuing Statistics
โข Stochastic Network Optimization
โข Network Utility Maximization
Network Stability
โข Differential Equation of Queuing Statistics
โข Lyapunov Stability
Cross Layer Control
13/20
Stochastic Network Optimization
Buffer for user ๐
Arrival Rate ๐๐ Service Rate ๐๐
Backlog Queue ๐ธ๐ (๐)
Network State Variable ๐บ(๐)
Control Action ๐ฐ ๐ โ ๐ฐ๐บ(๐) feasible control region under ๐บ(๐)
๐ ๐ก๐ ๐ก ,๐ผ(๐ก)
๐(๐ก + 1)
Cross Layer Control
14/20
Stochastic Network Optimization
Stability Issue
๐๐ ๐ก + 1 โค max ๐๐ ๐ก โ ๐ ๐๐๐ข๐ก ๐ผ ๐ก , ๐ ๐ก , 0 + ๐ ๐
๐๐(๐ผ ๐ก , ๐ ๐ก )
๐ถ๐๐๐๐๐๐๐ ๐ธ๐๐๐๐ ๐ฌ๐๐๐๐๐๐๐ ๐ธ๐๐๐๐
lim๐กโ โ
sup1
๐ก ๐{๐๐ ๐ }
๐กโ1
๐=0
< โ
Lyapunov Stability
If there exist ๐ฉ > ๐ and ๐ > ๐, such that for all
times slot ๐ we have :
Then network is strongly stable, and
๐ โ ๐ก Q ๐ก โค ๐ต โ ๐ ๐๐(๐ก)
๐
๐=1
lim๐กโ โ
sup1
๐ก ๐{Q ๐ }
๐กโ1
๐=0
<๐ต
๐
15/20
Cross Layer Control
16/20
Find ๐ฐ(๐)
Find ๐ฒ by Lyapunov Drift
Drift Definition
๐ผโ ๐ก = argmax๐ผ ๐ก โ๐๐(๐ก)
๐๐๐โ ๐ก ๐๐๐
โ (๐ก)
๐๐
๐๐๐โ ๐ก = max
๐๐๐
๐๐ ๐ก โ ๐๐ ๐ก +
maximum queue backlog differential
โ ๐ก = ๐ฟ ๐ก + 1 โ ๐ฟ(๐ก)
๐ฟ ๐ก =1
2 ๐๐
2 (๐ก)
๐
๐=1
Lyapunov Drift
17/20
โ ๐ก = ๐ฟ ๐ก + 1 โ ๐ฟ(๐ก)
=1
2 [๐๐
2 ๐ก + 1 โ
๐
๐=1
๐๐2 (๐ก)]
After applying ๐๐2 (๐ก + 1)
Find Lyapunov Bound with Conditional Expectation
โ ๐ก ๐ ๐ก โค โฆ
lim๐กโ โ
sup1
๐ก ๐{๐๐ ๐ }
๐กโ1
๐=0
< โ
Network Utility Maximization (NUM)
18/20
Rate ๐ซ โ ๐ฒ with Maximum Utility
๐ซโ = argmax๐ซโค๐
๐ ๐ซ |๐ซ โ ๐ฒ
๐(๐ซ) : Utility Function
Minimize Cost
Generalized Cross Layer Control
19/20
General Form of GCLC
Cost Variable Vector ๐ฑ : Maximum cost constraints ๐
Utility Variable Vector ๐ฒ :Minimum utility constraints ๐
Stable Region ๐ซ โ ๐ฒ
โข Arrival Rate Vector ๐
Minimize net cost
โข Natural cost function ๐(๐) and Concave Utility function ๐(๐)
min๐ซโค๐
๐ ๐ฑ โ ๐(๐ฒ)|๐ช ๐ฑ โค ๐, ๐ก ๐ฒ โฅ ๐, ๐ซ โ ๐ฒ
OFDMA Resource Control via GCLC
20/20
OFDMA via GCLC
Cost Variable Vector ๐ฑ : power coefficients
โข ๐ = ๐๐ : Total Power Constraint
Utility Variable Vector ๐ฒ : user data rate ๐ฒ = ๐ซ
โข ๐ : Quality of Service (User demands, Fairness)
Stable Region based on Queuing Statistics
Minimize net cost : Maximize System Throughput
min๐ซโค๐
๐ ๐ฑ โ ๐(๐ฒ)|๐ช ๐ฑ โค ๐, ๐ก ๐ฒ โฅ ๐, ๐ซ โ ๐ฒ