Signal Quality Pricing - cs.cmu.edu
Transcript of Signal Quality Pricing - cs.cmu.edu
Background Decomposition System Design Experiments
Signal Quality PricingDecomposition for Spectrum Scheduling and System Configuration
Eric Anderson†? Caleb Phillips? Douglas Sicker?
Dirk Grunwald?
†Carnegie Mellon UniversityElectrical and Computer Engineering
?University of ColoradoComputer Science
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1 8 7 6
LET YOUR
LIGHT
SHINE
DySPAN 20116 May 2011
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
Background: Separate Scheduling and Configuration
Scheduling
Which transmissions occur when?
Partition transmissions into compatible groups.
Assign groups to times,
Or frequencies.
Configuration
How does each transmission (and reception) occur?
Transmission power,
Modulation / rate,
Antenna steering / selection,
Frequency (sometimes).
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
Scheduling Example
3
D
2
1
C
4
5
6
BA
(S)TDMA schedule
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
Scheduling Example
3
D
2
1
C
4
5
6
BA
(S)TDMA schedule
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
Scheduling Example
3
D
2
1
C
4
5
6
BA
(S)TDMA schedule
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
Scheduling Example
3
D
2
1
C
4
5
6
BA
(S)TDMA schedule
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
Scheduling Example
3
D
2
1
C
4
5
6
BA
(S)TDMA schedule
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
Scheduling Example
3
D
2
1
C
4
5
6
BA
(S)TDMA schedule
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Constraints:Link SINR,Half-duplex,...
B
D
A
C
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Intended signal:D→A
B
D
A
C
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Intended signal:B→C
B
D
A
C
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Interference:B→AD→C(If both links were in use)
B
D
A
C
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Signal betweentransmitters:Not an issue(Would matter for CSMA)
B
D
A
C
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Trivial Schedule:Each link gets oneslot (TDMA).
B
D
A
C
Slot 1
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Trivial Schedule:Each link gets oneslot (TDMA).
B
D
A
C
Slot 2
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Faster Schedule:Concurrent links,Interference
B
D
A
C
Slot 1
Slot 1
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Per-link best(maximum SNR)antenna choices:Boosts interferingsignals, too.
C
A B
D
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Definitions Scheduling Example Limitations of Separate Scheduling & Configuration
“Chicken and Egg” Example
Link demand:B→C: 1 slotD→A: 1 slot
Scheduling-awareantenna selection:Low gain for inter-ference.
C
A B
D
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Integration and decomposition
Configuration and scheduling can be expressed as a combined problem— but the state space is huge: Θ(n22m) variables
Key Idea
Transform problem into many coupled subproblems.
Individually simple to solve
Naturally parallel
Iterate and update (not too many times)
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Decomposition Process (Idealized)
Goal: Optimize complete schedule
Given:Subject to: Complete constraints (PHY, MAC, Network, user, . . . )
Goal: Marginally improving concurrent group
Given: Current scheduleSubject to: Link (set) compatibility (PHY, MAC constraints)
Goal: Best set of active links
Given: Estimated configurationsSubj. to: PHY, MAC constraints
Goal: Best configurations
Given: Estimated active link setSubj. to: PHY constraints
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Decomposition Process (Idealized)
Goal: Optimize complete schedule
Given:Subject to: Complete constraints (PHY, MAC, Network, user, . . . )
Goal: Marginally improving concurrent group
Given: Current scheduleSubject to: Link (set) compatibility (PHY, MAC constraints)
Goal: Best set of active links
Given: Estimated configurationsSubj. to: PHY, MAC constraints
Goal: Best configurations
Given: Estimated active link setSubj. to: PHY constraints
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Decomposition Process (Idealized)
Goal: Optimize complete schedule
Given:Subject to: Complete constraints (PHY, MAC, Network, user, . . . )
Goal: Marginally improving concurrent group
Given: Current scheduleSubject to: Link (set) compatibility (PHY, MAC constraints)
Goal: Best set of active links
Given: Estimated configurationsSubj. to: PHY, MAC constraints
Goal: Best configurations
Given: Estimated active link setSubj. to: PHY constraints
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Decomposition Process
. . .
Goal: Marginally improving concurrent group
Given: Current scheduleSubject to: Link (set) compatibility (PHY, MAC constraints)
Lagrangian dual problem: Price PHY & MAC constraintse.g.
Signal to Interference and Noise Ratio (SINR) threshold
Half-duplex requirement
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Decomposition Process
. . .
Goal: Marginally improving concurrent group
Given: Current scheduleSubject to: Link (set) compatibility (PHY, MAC constraints)
Lagrangian dual problem: Price PHY & MAC constraintse.g.
Signal to Interference and Noise Ratio (SINR) threshold
Half-duplex requirement
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
What do Constraint Prices Mean?(Lagrangian relaxation in 60 seconds)
Original problem: Minimize objective subject to constraints.
minx
f (x)
s.t. gi (x) ≤ ci
Lagrangian: Minimize (objective + penalty) w/o constraints.
minx
f (x) + λi (gi (x)− ci )
Price (λi ): For each constraint i , marginal cost per unit of violation.
Dual: Find the lowest prices such that the degree of violation ≈ 0.
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Look up, this is important!
Scheduling ConfigurationAvoid using link ijor interfering with ij
Increase gain for ijattenuate interference
High SINRij price
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Subgradient / Relaxed Primal Problem method
Solution of dual problem:
Link Activation Problem
Choose (estimate) link sets.
Given:
Estimated antennaconfigurationEstimated prices (dualmultipliers)
Antenna ReconfigurationProblem
Choose (estimate) antennaconfiguration.
Given:
Estimated link selectionEstimated prices (dualmultipliers)
Combined estimates may not satisfy complicating constraints.Non-compliance determines subgradient. Update price estimates.
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Subgradient / Relaxed Primal Problem method
Solution of dual problem:
Link Activation Problem
Choose (estimate) link sets.
Given:
Estimated antennaconfigurationEstimated prices (dualmultipliers)
Antenna ReconfigurationProblem
Choose (estimate) antennaconfiguration.
Given:
Estimated link selectionEstimated prices (dualmultipliers)
Combined estimates may not satisfy complicating constraints.Non-compliance determines subgradient. Update price estimates.
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Subgradient / Relaxed Primal Problem method
Solution of dual problem:
Link Activation Problem
Choose (estimate) link sets.
Given:
Estimated antennaconfigurationEstimated prices (dualmultipliers)
Antenna ReconfigurationProblem
Choose (estimate) antennaconfiguration.
Given:
Estimated link selectionEstimated prices (dualmultipliers)
Combined estimates may not satisfy complicating constraints.Non-compliance determines subgradient. Update price estimates.
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Subgradient / Relaxed Primal Problem method
Solution of dual problem:
Link Activation Problem
Choose (estimate) link sets.
Given:
Estimated antennaconfigurationEstimated prices (dualmultipliers)
Antenna ReconfigurationProblem
Choose (estimate) antennaconfiguration.
Given:
Estimated link selectionEstimated prices (dualmultipliers)
Combined estimates may not satisfy complicating constraints.
Non-compliance determines subgradient. Update price estimates.
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Subgradient / Relaxed Primal Problem method
Solution of dual problem:
Link Activation Problem
Choose (estimate) link sets.
Given:
Estimated antennaconfigurationEstimated prices (dualmultipliers)
Antenna ReconfigurationProblem
Choose (estimate) antennaconfiguration.
Given:
Estimated link selectionEstimated prices (dualmultipliers)
Combined estimates may not satisfy complicating constraints.Non-compliance determines subgradient. Update price estimates.
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 1
node valueB 0C 0D 0
node valueA 0B 0C 0
node valueA 0C 0D 0
node valueA 0B 0D 0
off, SINRprice
=0, SINR=
off, 0,
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 2
node valueB 0C 0D 0
node valueA 0B 0C 0
node valueA 0C 0D 0
node valueA 0B 0D 0
on, 0, 10
off, 0,
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 3
node valueB 0C 0D 0
node valueA 0B 0C 0
node valueA 0C 0D 0
node valueA 0B 0D 0
on, 0, 0.7
on, 0, 0.7
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 4
node valueB 0C 0D 5
node valueA 5B 0C 0
node valueA -5C 0D 0
node valueA 0B 0D 0
on, 5, 0.7
on, 0∗ , 0.7
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 5
node valueB 0C 0D 8
node valueA 8B 0C -5
node valueA -8C 5D 0
node valueA 0B 5D 0
off, 8,
off, 5,
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 6
node valueB 0C 0D 7.2
node valueA 7.2B 0C -4.5
node valueA -7.2C 4.5D 0
node valueA 0B 4.5D 0
off, 7.2,
off, 4.5,
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 15
node valueB 0C 0D 1.6
node valueA 1.6B 0C -0.9
node valueA -1.6C 0.9D 0
node valueA 0B 0.9D 0
off, 1.6,
off, 0.9,
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 16
node valueB 0C 0D 1.4
node valueA 1.4B 0C -0.8
node valueA -1.4C 0.8D 0
node valueA 0B 0.8D -0.8
on, 1.4, 10
off, 0.8,
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 17
node valueB 0C 0D 1.3
node valueA 1.3B 0C -0.7
node valueA -1.3C 0.7D 0
node valueA 0B 0.7D -0.7
on, 1.3, 10
off, 0.7,
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 20
node valueB -0.9C 0D 0.9
node valueA 0.9B 0C -0.5
node valueA -0.9C 0.5D 0
node valueA 0B 0.5D -0.5
on, 0.9, 5
on, 0.5, 7
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Idealized Lagrangian/RPP Example
Example (simplified)
C
A B
DT = 21 (done)
node valueB -0.8C 0D 0.8
node valueA 0.8B 0C -0.5
node valueA -0.8C 0.5D 0
node valueA 0B 0.5D -0.5
on, 0.9, 7
on, 0.5, 7
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments
Proof-of-Concept System
Dual problem: Node-local price and configuration estimates, distributedconsensus algorithm.
Asynchronous
Delay- and loss-tolerant
Eventually consistent
Global “restricted master” problem, flooding updates.
Passively observes dual problem results.
Recomputes (global) schedule when possible.
Local computation, but requires global data.
Implemented on top of 802.11 PHY with STDMA MAC usingswitched-beam phased array antennas.
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Testbed Execution Numerical Results
Experimental Test Bed
Phase array antennasinstalled around C.U.campus
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Testbed Execution Numerical Results
Test Load
TDMA: 2 slots
Best case:1 slot
Incompatiblewhen using“obvious”antennas
Algorithmachieves bestcase A
B
C
D
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Testbed Execution Numerical Results
Test Load
TDMA: 2 slots
Best case:1 slot
Incompatiblewhen using“obvious”antennas
Algorithmachieves bestcase A
B
C
D
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Testbed Execution Numerical Results
Test Load
TDMA: 2 slots
Best case:1 slot
Incompatiblewhen using“obvious”antennas
Algorithmachieves bestcase A
B
C
D
Anderson et al. Signal Quality Pricing
Execution Trace at Node Cpr
ice
acti
vati
onga
in
Execution Trace at Node Cpr
ice
acti
vati
onga
in
Execution Trace at Node Cpr
ice
acti
vati
onga
in
Execution Trace at Node Cpr
ice
acti
vati
onga
in
Execution Trace at Node Cpr
ice
acti
vati
onga
in
Execution Trace at Node Cpr
ice
acti
vati
onga
in
Background Decomposition System Design Experiments Testbed Execution Numerical Results
Numerical Results
Numerical experiments: 1400 varying scenarios
Number of nodes (2 - 48)
Link density (1/2 - 3 per node)
Size of simulated area (1 - 16 sq. km)
Random seed
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Testbed Execution Numerical Results
Improvement
Acheived Speedup in Numerical Simulations
Speedup
Fra
ctio
n o
f E
xp
eri
me
nts
0.0
0.2
0.4
0.6
0.8
1.0
1 2 3 4 5 6
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Testbed Execution Numerical Results
Running Time 1
Iterations to Specified Fraction of Optimality
Number of Minor Iterations
Fra
ctio
n o
f E
xp
eri
me
nts
0.0
0.2
0.4
0.6
0.8
1.0
0 500 1000 1500
optimal95%90%80%
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Testbed Execution Numerical Results
Running Time 2
Time to Optimal Solution vs. Problem Size
Number of Nodes
Ite
ratio
ns
0
500
1000
1500
10 20 30 40 50
Anderson et al. Signal Quality Pricing
Background Decomposition System Design Experiments Testbed Execution Numerical Results
Conclusions
Tractable solution to optimal joint beam steering and scheduling
Mean 234% speedup over simple TDMA
Mean 150 iterations to optimality (90th %ile: 500)
Dual-decomposition based scheduling works in practice
More responsive on-line MAC in progress
Anderson et al. Signal Quality Pricing
Thank you!
References Formulation Long Motivation Related Work Extra Results
Backup Slides
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra Results
References I
Erdal Arikan.
Some Complexity Results about Packet Radio Networks.IEEE Transactions on Information Theory, vol. 30, no. 4, pages 681 – 685, July 1984.
Patrick Bjorklund, Peter Varbrand & Di Yuan.
Resource optimization of spatial TDMA in ad hoc radio networks: a column generation approach.In INFOCOM 2003. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies,volume 2, pages 818– 824. IEEE, March 2003.
Gurashish Brar, Douglas M. Blough & Paolo Santi.
Computationally efficient scheduling with the physical interference model for throughput improvement in wireless meshnetworks.In MobiCom ’06: Proceedings of the 12th annual international conference on Mobile computing and networking, pages2–13, New York, NY, USA, 2006. ACM.
J. Bibb Cain, Tom Billhartz, Larry Foore, Edwin Althouse & John Schlorff.
A link scheduling and ad hoc networking approach using directional antennas.In Military Communications Conference, 2003, volume 1, pages 643– 648. IEEE, Oct 2003.
Lijun Chen, Steven H. Low, Mung Chiang & John C. Doyle.
Optimal Cross-layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks.In Proceedings of IEEE INFOCOM 2006, 2006.
Imrich Chlamtac & Anat Lerner.
Fair Algorithms for Maximal Link Activation in Multihop Radio Networks.Communications, IEEE Transactions on, vol. 35, no. 7, pages 739–746, Jul 1987.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra Results
References II
Ashish Deopura & Aura Ganz.
Provisioning link layer proportional service differentiation in wireless networks with smart antennas.Wirel. Netw., vol. 13, no. 3, pages 371–378, 2007.
K. Dyberg, F. Farman L.and Eklof, J. Gronkvist, U. Sterner & J. Rantakokko.
On the performance of antenna arrays in spatial reuse TDMA ad hoc networks.In MILCOM 2002, volume 1, pages 270– 275, Oct 2002.
Anthony Ephremides & Thuan V. Truong.
Scheduling broadcasts in multihop radio networks.Communications, IEEE Transactions on, vol. 38, no. 4, pages 456–460, Apr 1990.
Jimmi Gronkvist.
Assignment methods for spatial reuse TDMA.In MobiHoc ’00: Proceedings of the 1st ACM international symposium on Mobile ad hoc networking & computing, pages119–124, Piscataway, NJ, USA, 2000. IEEE Press.
Bruce Hajek & Galen Sasaki.
Link scheduling in polynomial time.Information Theory, IEEE Transactions on, vol. 34, no. 5, pages 910–917, Sep 1988.
M. Johansson & L. Xiao.
Cross-layer optimization of wireless networks using nonlinear column generation.Wireless Communications, IEEE Transactions on, vol. 5, no. 2, pages 435–445, 2006.
Tzu-Ming Lin & Juin-Jia Dai.
A Collision Free MAC Protocol using Smart Antenna in Ad Hoc Networks.In CCNC 2004, Jan 2004.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra Results
References III
Xi Liu, Anmol Sheth, Michael Kaminski, Konstantina Papagiannaki, Srinivasan Seshan & Peter Steenkiste.
DIRC: Increasing Indoor Wireless Capacity Using Directional Antennas.In Proc. SIGCOMM 2009, pages 171 – 182, Barcelona, Spain, August 2009. ACM.
Randolph Nelson & Leonard Kleinrock.
Spatial TDMA: A Collision-Free Multihop Channel Access Protocol.Communications, IEEE Transactions on, vol. 33, no. 9, pages 934– 944, Sep 1985.
B. Radunovic & J.-Y. Le Boudec.
Optimal power control, scheduling, and routing in UWB networks.Selected Areas in Communications, IEEE Journal on, vol. 22, no. 7, pages 1252–1270, Sept. 2004.
Marvin Sanchez & Jens Zander.
Adaptive Antennas in Spatial TDMA Multihop Packet Radio Networks.In RadioVetenskap och Kommunikation (RVK), Karlskrona, Sweden, June 1999.
Karthikeyan Sundaresan, Weizhao Wang & Stephan Eidenbenz.
Algorithmic aspects of communication in ad-hoc networks with smart antennas.In MobiHoc ’06: Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing,pages 298–309, New York, NY, USA, 2006. ACM.
Karthikeyan Sundaresan & Raghupathy Sivakumar.
A unified MAC layer framework for ad-hoc networks with smart antennas.IEEE/ACM Trans. Netw., vol. 15, no. 3, pages 546–559, 2007.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Master Problem (JBSS-MP)
Minimize total time
Allocate sufficient time to eachlink
Half-duplex unicast operation
SINR on active links
Antenna selection convexity
Gain-antenna coupling
min
∑l∈LA
xl
s.t.
∑l∈LA
Sijl xl ≥ qij ∀i,j
∑j :(i,j)∈A
Sijl +∑
j :(j,i)∈A
Sjil ≤ 1 ∀i,l
Pil Dijl Djil
Lb(i, j)NrSijl +
γ1(1 + Mijl )(1− Sijl ) ≥
γ1
1 +∑
k∈N\{i,j}
Pkl Dkjl Djkl
Lb(k, j)NrVkl
∀i,j,l
Sijl ≤ Vil ∀i,j,l∑p∈P
Bjpl = 1 ∀j,l
Dik =∑p∈P
Gikp Bipl ∀i,k,l
xl ≥ 0 ∀l∈LA
Sijl , Bjpl ∈ {0, 1}
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Master Problem (JBSS-MP)
Minimize total time
Allocate sufficient time to eachlink
Half-duplex unicast operation
SINR on active links
Antenna selection convexity
Gain-antenna coupling
min
∑l∈LA
xl
s.t.
∑l∈LA
Sijl xl ≥ qij ∀i,j
∑j :(i,j)∈A
Sijl +∑
j :(j,i)∈A
Sjil ≤ 1 ∀i,l
Pil Dijl Djil
Lb(i, j)NrSijl +
γ1(1 + Mijl )(1− Sijl ) ≥
γ1
1 +∑
k∈N\{i,j}
Pkl Dkjl Djkl
Lb(k, j)NrVkl
∀i,j,l
Sijl ≤ Vil ∀i,j,l∑p∈P
Bjpl = 1 ∀j,l
Dik =∑p∈P
Gikp Bipl ∀i,k,l
xl ≥ 0 ∀l∈LA
Sijl , Bjpl ∈ {0, 1}
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Master Problem (JBSS-MP)
Minimize total time
Allocate sufficient time to eachlink
Half-duplex unicast operation
SINR on active links
Antenna selection convexity
Gain-antenna coupling
min
∑l∈LA
xl
s.t.
∑l∈LA
Sijl xl ≥ qij ∀i,j
∑j :(i,j)∈A
Sijl +∑
j :(j,i)∈A
Sjil ≤ 1 ∀i,l
Pil Dijl Djil
Lb(i, j)NrSijl +
γ1(1 + Mijl )(1− Sijl ) ≥
γ1
1 +∑
k∈N\{i,j}
Pkl Dkjl Djkl
Lb(k, j)NrVkl
∀i,j,l
Sijl ≤ Vil ∀i,j,l∑p∈P
Bjpl = 1 ∀j,l
Dik =∑p∈P
Gikp Bipl ∀i,k,l
xl ≥ 0 ∀l∈LA
Sijl , Bjpl ∈ {0, 1}
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Master Problem (JBSS-MP)
Minimize total time
Allocate sufficient time to eachlink
Half-duplex unicast operation
SINR on active links
Antenna selection convexity
Gain-antenna coupling
min
∑l∈LA
xl
s.t.
∑l∈LA
Sijl xl ≥ qij ∀i,j
∑j :(i,j)∈A
Sijl +∑
j :(j,i)∈A
Sjil ≤ 1 ∀i,l
Pil Dijl Djil
Lb(i, j)NrSijl +
γ1(1 + Mijl )(1− Sijl ) ≥
γ1
1 +∑
k∈N\{i,j}
Pkl Dkjl Djkl
Lb(k, j)NrVkl
∀i,j,l
Sijl ≤ Vil ∀i,j,l∑p∈P
Bjpl = 1 ∀j,l
Dik =∑p∈P
Gikp Bipl ∀i,k,l
xl ≥ 0 ∀l∈LA
Sijl , Bjpl ∈ {0, 1}
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Master Problem (JBSS-MP)
Minimize total time
Allocate sufficient time to eachlink
Half-duplex unicast operation
SINR on active links
Antenna selection convexity
Gain-antenna coupling
min
∑l∈LA
xl
s.t.
∑l∈LA
Sijl xl ≥ qij ∀i,j
∑j :(i,j)∈A
Sijl +∑
j :(j,i)∈A
Sjil ≤ 1 ∀i,l
Pil Dijl Djil
Lb(i, j)NrSijl +
γ1(1 + Mijl )(1− Sijl ) ≥
γ1
1 +∑
k∈N\{i,j}
Pkl Dkjl Djkl
Lb(k, j)NrVkl
∀i,j,l
Sijl ≤ Vil ∀i,j,l∑p∈P
Bjpl = 1 ∀j,l
Dik =∑p∈P
Gikp Bipl ∀i,k,l
xl ≥ 0 ∀l∈LA
Sijl , Bjpl ∈ {0, 1}
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Master Problem (JBSS-MP)
Minimize total time
Allocate sufficient time to eachlink
Half-duplex unicast operation
SINR on active links
Antenna selection convexity
Gain-antenna coupling
min
∑l∈LA
xl
s.t.
∑l∈LA
Sijl xl ≥ qij ∀i,j
∑j :(i,j)∈A
Sijl +∑
j :(j,i)∈A
Sjil ≤ 1 ∀i,l
Pil Dijl Djil
Lb(i, j)NrSijl +
γ1(1 + Mijl )(1− Sijl ) ≥
γ1
1 +∑
k∈N\{i,j}
Pkl Dkjl Djkl
Lb(k, j)NrVkl
∀i,j,l
Sijl ≤ Vil ∀i,j,l∑p∈P
Bjpl = 1 ∀j,l
Dik =∑p∈P
Gikp Bipl ∀i,k,l
xl ≥ 0 ∀l∈LA
Sijl , Bjpl ∈ {0, 1}
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Master Problem (JBSS-MP)
Minimize total time
Allocate sufficient time to eachlink
Half-duplex unicast operation
SINR on active links
Antenna selection convexity
Gain-antenna coupling
min
∑l∈LA
xl
s.t.
∑l∈LA
Sijl xl ≥ qij ∀i,j
∑j :(i,j)∈A
Sijl +∑
j :(j,i)∈A
Sjil ≤ 1 ∀i,l
Pil Dijl Djil
Lb(i, j)NrSijl +
γ1(1 + Mijl )(1− Sijl ) ≥
γ1
1 +∑
k∈N\{i,j}
Pkl Dkjl Djkl
Lb(k, j)NrVkl
∀i,j,l
Sijl ≤ Vil ∀i,j,l∑p∈P
Bjpl = 1 ∀j,l
Dik =∑p∈P
Gikp Bipl ∀i,k,l
xl ≥ 0 ∀l∈LA
Sijl , Bjpl ∈ {0, 1}
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Master Problem (JBSS-MP)
Symbol InterpretationSij Activation of
link ij
Vi Node i is active(in current linkset)
Dij Directivity ofnode i toward j
Bjp Indicator: beamp used at node j
Table: Key Notation
full notation
min
∑l∈LA
xl
s.t.
∑l∈LA
Sijl xl ≥ qij ∀i,j
∑j :(i,j)∈A
Sijl +∑
j :(j,i)∈A
Sjil ≤ 1 ∀i,l
Pil Dijl Djil
Lb(i, j)NrSijl +
γ1(1 + Mijl )(1− Sijl ) ≥
γ1
1 +∑
k∈N\{i,j}
Pkl Dkjl Djkl
Lb(k, j)NrVkl
∀i,j,l
Sijl ≤ Vil ∀i,j,l∑p∈P
Bjpl = 1 ∀j,l
Dik =∑p∈P
Gikp Bipl ∀i,k,l
xl ≥ 0 ∀l∈LA
Sijl , Bjpl ∈ {0, 1}
Anderson et al. Signal Quality Pricing
Decomposition Approach – Detailed
JBSS-MP
RMP CLAP
CLAP-dual-1
CLAP-dual-2FLAP
FARPRP-FLAP
SNRP-FLAP_0 SNRP-FLAP_1... SNARP_0 SNARP_1...
SDQ-FLAP_0 SDQ-FLAP_1...
Master problem
Dantzig-Wolfedecomposition
LagrangianRelaxation on
SINR constraint
LagrangianRelaxation on
duplex constraint
Block separation
Block separation
Quadraticapproximation
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Dantzig-Wolfe Decomposition
Restricted Master Problem (RMP)Given feasible link sets, allocates time toeach.Produces capacity constraint dual values(β).
SubproblemGiven β, finds improving link set.
Subproblem ComplexityVariables
Functional Degree S V D B
Objective: Reduced-Cost Column 1 X
Constraint:
Duplex 1 XCoupling 1 X X
SINR 3 X X XAntenna coupling 1 X X
Antenna uniqueness 1 X
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Dantzig-Wolfe Decomposition
Restricted Master Problem (RMP)Given feasible link sets, allocates time toeach.Produces capacity constraint dual values(β).
SubproblemGiven β, finds improving link set.
Subproblem ComplexityVariables
Functional Degree S V D B
Objective: Reduced-Cost Column 1 X
Constraint:
Duplex 1 XCoupling 1 X X
SINR 3 X X XAntenna coupling 1 X X
Antenna uniqueness 1 X
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Dantzig-Wolfe Decomposition
Restricted Master Problem (RMP)Given feasible link sets, allocates time toeach.Produces capacity constraint dual values(β).
SubproblemGiven β, finds improving link set.
Subproblem ComplexityVariables
Functional Degree S V D B
Objective: Reduced-Cost Column 1 X
Constraint:
Duplex 1 XCoupling 1 X X
SINR 3 X X XAntenna coupling 1 X X
Antenna uniqueness 1 X
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Dantzig-Wolfe Decomposition
Restricted Master Problem (RMP)Given feasible link sets, allocates time toeach.Produces capacity constraint dual values(β).
SubproblemGiven β, finds improving link set.
Subproblem ComplexityVariables
Functional Degree S V D B
Objective: Reduced-Cost Column 1 X
Constraint:
Duplex 1 XCoupling 1 X X
SINR 3 X X XAntenna coupling 1 X X
Antenna uniqueness 1 X
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Lagrangian Dual Problem
SINR and duplex constraints relaxed; multipliers are λ, µ. Constraintfunctionals are d s() and dd ().
L′(S ,D,V , λ, µ) = βTS − λTd s(S ,D,V )− µTdd (S)
φ′(λ, µ) = maxS,D,V
L′(S ,D,V , λ, µ)
[CLAP-dual-2]
minλ,µ
φ′(λ, µ)
s.t. Sij ≤ Vi ∀i
Dik =∑p∈P
GikpBip ∀i ,k∑p∈P
Bjp = 1 ∀j
Anderson et al. Signal Quality Pricing
Decomposition Approach – Detailed
JBSS-MP
RMP CLAP
CLAP-dual-1
CLAP-dual-2FLAP
FARPRP-FLAP
SNRP-FLAP_0 SNRP-FLAP_1... SNARP_0 SNARP_1...
SDQ-FLAP_0 SDQ-FLAP_1...
Master problem
Dantzig-Wolfedecomposition
LagrangianRelaxation on
SINR constraint
LagrangianRelaxation on
duplex constraint
Block separation
Block separation
Quadraticapproximation
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Block Separation
minx
f (x1, x2)
s.t. g1(x) ≤ c1
g2(x) ≤ c2
↔
minx1
f1(x1)
s.t. g1(x1) ≤ c1
minx2
f2(x2)
s.t. g2(x2) ≤ c2
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Relaxed Primal Fixed-antenna Link Assignment Problem(RP-FLAP)
[RP-FLAP]
maxS ,V
βTS + λTd ′s(S ,V )− µTdd (S)
s.t. Sij ≤ Vi ∀ij
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Fixed-Link Antenna Reconfiguration Problem (FARP)
[FARP]
maxD,B
βT S −∑
ij
λij
(PiDijDji
Lb(i , j)NrSij +
γ1(1 + Mij )(1− Sij ) −
γ1
(1 +
∑k∈N\{i ,j}
PkDkjDkj
Lb(k, j)NrVk
))s.t. Dik −
∑p∈P
GikpBip = 0 ∀i ,k∑p∈P
Bip = 1 ∀i
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Single-Node Antenna Reconfiguration Problem (SNARP) I
Let x denote the vector of all antenna gains D. Now let i partition x as:xi = ∪k 6=iDik .
gi (x) =
∑j
(1
2λij Sij
Pi
Lb(i, j)NrDij Dji
)+
k
|N|
if i is a transmitter∑j
(1
2λji Sji
Pj
Lb(j, i)NrDji Dij
)+
k
|N|
if i is a receiver
hi (x) =
∑j
( ∑k,l∈N\{i,j}
(1
2γ1Sij λkl
Pi
Lb(i, l)NrDil Dli
))if i is a transmitter∑
j
( ∑k,l∈N\{i,j}
(1
2γ1Sji λji
Pk
Lb(k, i)NrDki Dik
))if i is a receiver
fi (x) = gi (xi )− hi (x)
f (x) =∑
i
fi (x) given∑
j
Sij ≤ Vi ∀i
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Single-Node Antenna Reconfiguration Problem (SNARP) II
[SNARPi ]
maxD,B
1− fi (D)
s.t. Dik −∑p∈P
GikpBip = 0 ∀k∑p∈P
Bip = 1
Bip ≤ 1 ∀p∈P
Bip ≥ 0 ∀p∈P
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsMaster Problem Decomp. Tree Dantzig-Wolfe Lagrangian Dual Block Separation Sub-problems Mathematical Components
Mathematical Components
Per-node:
Link activation problem
Antenna configuration problem
Incremental subgradient calculation
Primal estimate sequence
Inter-node exchange of:
Primal and dual estimates
Distributed, asynchronous, incremental optimization process
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Interference-Limited Wireless Networks
Shannon capacity of a narrowband Gaussian channel is given by:
C = B log2 (1 +P
N) (1)
B is a fixed resource.
P has practical and regulatory limits.
Your P may be someone else’s N.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Interference-Limited Wireless Networks
Shannon capacity of a narrowband Gaussian channel is given by:
C = B log2 (1 +P
N) (1)
B is a fixed resource.
P has practical and regulatory limits.
Your P may be someone else’s N.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Interference-Limited Wireless Networks
Shannon capacity of a narrowband Gaussian channel is given by:
C = B log2 (1 +P
N) (1)
B is a fixed resource.
P has practical and regulatory limits.
Your P may be someone else’s N.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Interference-Limited Wireless Networks
Shannon capacity of a narrowband Gaussian channel is given by:
C = B log2 (1 +P
N) (1)
B is a fixed resource.
P has practical and regulatory limits.
Your P may be someone else’s N.
Anderson et al. Signal Quality Pricing
Interference-Limited Wireless Networks
Aggregate capacity of n interacting interference−limited Gaussian channels
Number of channels (links)
Info
rma
tio
n c
ap
acity,
bits p
er
tra
nsm
issio
n
1
2
3
4
5
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Interference power relative to signal power
0.05 * P0.1 * P0.2 * P0.4 * P0.8 * P
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Interference-Limited Wireless Networks
Absent some other bottleneck, Signal-to-Interference and Noise Ratio(SINR) limits throughput.
Concurrent links increase totalcapacity,
If the links don’t undulyinterfere with each other.
Identify or create lowmutual-interference link sets.
Aggregate capacity of n interacting interference−limited Gaussian channels
Number of channels (links)
Info
rma
tio
n c
ap
acity,
bits p
er
tra
nsm
issio
n
1
2
3
4
5
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Interference power relative to signal power
0.05 * P0.1 * P0.2 * P0.4 * P0.8 * P
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Interference-Limited Wireless Networks
Absent some other bottleneck, Signal-to-Interference and Noise Ratio(SINR) limits throughput.
Concurrent links increase totalcapacity,
If the links don’t undulyinterfere with each other.
Identify or create lowmutual-interference link sets.
Aggregate capacity of n interacting interference−limited Gaussian channels
Number of channels (links)
Info
rma
tio
n c
ap
acity,
bits p
er
tra
nsm
issio
n
1
2
3
4
5
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Interference power relative to signal power
0.05 * P0.1 * P0.2 * P0.4 * P0.8 * P
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Interference-Limited Wireless Networks
Absent some other bottleneck, Signal-to-Interference and Noise Ratio(SINR) limits throughput.
Concurrent links increase totalcapacity,
If the links don’t undulyinterfere with each other.
Identify or create lowmutual-interference link sets.
Aggregate capacity of n interacting interference−limited Gaussian channels
Number of channels (links)
Info
rma
tio
n c
ap
acity,
bits p
er
tra
nsm
issio
n
1
2
3
4
5
6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Interference power relative to signal power
0.05 * P0.1 * P0.2 * P0.4 * P0.8 * P
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Spatial-Reuse TDMA (STDMA)
Goal: Select sets of links or broadcasts such that spatial separationminimizes interference.
Old idea: (goes back to [Nelson 85]).
Which sets?
How much time for each?
What configuration?
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Spatial-Reuse TDMA (STDMA)
Goal: Select sets of links or broadcasts such that spatial separationminimizes interference.
Old idea: (goes back to [Nelson 85]).
Which sets?
How much time for each?
What configuration?
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Spatial-Reuse TDMA (STDMA)
Goal: Select sets of links or broadcasts such that spatial separationminimizes interference.
Old idea: (goes back to [Nelson 85]).
Which sets?
How much time for each?
What configuration?
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Spatial-Reuse TDMA (STDMA)
Goal: Select sets of links or broadcasts such that spatial separationminimizes interference.
Old idea: (goes back to [Nelson 85]).
Which sets?
How much time for each?
What configuration?
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
STDMA Scheduling
Optimal scheduling is NP-Hard.
Responses:
Relax objective X
Relax constraints X
Tighten constraints X
Measuredsignal strengths?
Assumedpairwiseconflict
no
Boolean SINRrequirement?
yes
Conflictmodel
yes
Continuouslink quality
no
Pairwiselink conflict
Cumulativeset conflict
Low HighRealism and complexity
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
STDMA Scheduling
Optimal scheduling is NP-Hard.
Responses:
Relax objective X
Relax constraints X
Tighten constraints X
Measuredsignal strengths?
Assumedpairwiseconflict
no
Boolean SINRrequirement?
yes
Conflictmodel
yes
Continuouslink quality
no
Pairwiselink conflict
Cumulativeset conflict
Low HighRealism and complexity
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Steerable, Switchable and Smart Antennas
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Complication
If each node has p patterns, each set of m links has p2m configurations.Hairier than other adaptations:
Power change affects signal and interference equally.
Modulation change affects only the link in question.
Antenna change affects everyone arbitrarily.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Complication
If each node has p patterns, each set of m links has p2m configurations.Hairier than other adaptations:
Power change affects signal and interference equally.
Modulation change affects only the link in question.
Antenna change affects everyone arbitrarily.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsInterference Spatial-Reuse TDMA Antennas
Complication
If each node has p patterns, each set of m links has p2m configurations.Hairier than other adaptations:
Power change affects signal and interference equally.
Modulation change affects only the link in question.
Antenna change affects everyone arbitrarily.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsSTDMA Scheduling Antennas Smart Antenna STDMA
STDMA Scheduling
Goal: Partition links into concurrently-feasible sets to achieve desiredthroughput (delay, jitter, BER, etc.)
Ignoring RF interference: Nodes can only participate in one link ata time. → Graph coloring-like algorithms (polynomial), e.g.[Hajek 88].
Pair-wise RF interference: Link pairs are either compatible or not;any combination of links not including a forbidden pair is OK. →Polynomial graph algorithms, e.g.[Chlamtac 87, Ephremides 90, Chen 06, Liu 09].
Cumulative RF interference: Combined interference from all otherlinks must be acceptable for every link. Optimality is NP-hard[Arikan 84]. Greedy algorithms by, e.g. [Gronkvist 00, Brar 06].Optimization algorithms by e.g. [Bjorklund 03, Johansson 06]. *
Continuous Interference Effect: Link capacity as a function ofSINR, not a threshold, e.g. [Radunovic 04].
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsSTDMA Scheduling Antennas Smart Antenna STDMA
Antenna Capabilities
Omnidirectional & Fixed Directional.
Switched Beam
Sectorized antennas or arrays with pre-computed patterns.Control consists of selecting among available patterns.
Adaptive Array
Synthesizes beam patterns using on-line techniques.Generally involves active measurement e.g. pilot tones.
NO wedges, cones, pencil beams, etc.
... and the environment would distort them if there were.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsSTDMA Scheduling Antennas Smart Antenna STDMA
Antenna Capabilities
Omnidirectional & Fixed Directional.
Switched Beam
Sectorized antennas or arrays with pre-computed patterns.Control consists of selecting among available patterns.
Adaptive Array
Synthesizes beam patterns using on-line techniques.Generally involves active measurement e.g. pilot tones.
NO wedges, cones, pencil beams, etc.
... and the environment would distort them if there were.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsSTDMA Scheduling Antennas Smart Antenna STDMA
Antenna Capabilities
Omnidirectional & Fixed Directional.
Switched Beam
Sectorized antennas or arrays with pre-computed patterns.Control consists of selecting among available patterns.
Adaptive Array
Synthesizes beam patterns using on-line techniques.Generally involves active measurement e.g. pilot tones.
NO wedges, cones, pencil beams, etc.
... and the environment would distort them if there were.
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsSTDMA Scheduling Antennas Smart Antenna STDMA
Controllable Antennas in Wireless Networks
CSMA Protocols (not going to talk about)
“Deafness” problem, mixed directional/omni RTS-CTS, directionalNAV, etc..
Cellular (telephone or data)
One smart base station with many dumb clients.≈ No client-client interference.Linear problem size, information & control all at BS.(Some limited inter-cell interference mitigation exists.)
STDMA
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsSTDMA Scheduling Antennas Smart Antenna STDMA
Controllable Antennas in STDMA
Schedule then configure
[Lin 04]
Configure then schedule
[Sanchez 99, Dyberg 02] and others. Special case: [Sundaresan 07]
Schedule with assumed capabilities
Infinitesimal beam width [Cain 03]Geometric rules e.g. significant signal propagates only in a wedge[Deopura 07].Arbitrary k nulls [Sundaresan 06].
Joint Scheduling and Configuration *
Pairwise configuration considered in scheduling [Sundaresan 07], DIRC[Liu 09].
Anderson et al. Signal Quality Pricing
References Formulation Long Motivation Related Work Extra ResultsBad Neighbor Incidence Speedup by density Time to Termination
“Bad Neighbor” links
Bad Neighbor SIR at Receiver
SIR (dB)
Pro
po
rtio
n o
f lin
k p
airs
0.0
0.2
0.4
0.6
0.8
1.0
−20 0 20 40
Anderson et al. Signal Quality Pricing
Speedup by Node Density
Acheived Speedup in Numerical Simulations
Speedup
No
de
De
nsity (
no
de
s/m
^2)
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.012
0.014
0.016
0.018
0.024
1 2 3 4 5 6
patty
References Formulation Long Motivation Related Work Extra ResultsBad Neighbor Incidence Speedup by density Time to Termination
Time to Algorithm Termination
Running Time vs. Problem Size
Number of Nodes
Ite
ratio
ns
0
20000
40000
60000
80000
100000
10 20 30 40 50
terminationoptimal value
Anderson et al. Signal Quality Pricing