Transcript Opportunistic Scheduling with Reliability Guarantees in Cognitive Radio Networks Rahul Urgaonkar, Michael J.

Opportunistic Scheduling with
Reliability Guarantees in
Cognitive Radio Networks
Rahul Urgaonkar, Michael J. Neely
University of Southern California
http://www-rcf.usc.edu/~urgaonka/
*Sponsored in part by the DARPA IT-MANET Program, NSF OCE-0520324
Cognitive Radio Networks
• Radio spectrum: a precious commodity
- recent FCC auction of 700MHz band ~$20 billion
• Existing static allocation of spectrum considered
inefficient
- “white spaces” observed
• Motivation: Improve spectrum usage by dynamic
spectrum access
• Key enabler: Cognitive Radio
- here, cognitive radio ~ dynamic operating frequency
Design Issues and Challenges
• Primary (licensed) and Secondary (unlicensed)
users
• Basic requirement: To ensure secondary users
take advantage of the unused spectrum without
adversely affecting primary users
• Challenges:
– potentially oblivious primary users
– imperfect “channel state information” may cause
collisions
– network dynamics (mobility, traffic)
– distributed solutions desirable
Our Contributions
• Develop a throughput optimal control algorithm for
cognitive radio networks
– general mobility and interference models
• Notion of collision queues
– inspired by the virtual power queue technique of [1]
– worst case deterministic bound on maximum number of collisions
• prior works give probabilistic guarantees
• Consider full effects of queueing
– yields bounds on average delay
• Constant factor distributed approximation
- in a special case
[1] M. J. Neely, Energy Optimal Control for Time Varying Wireless Networks, IEEE Transactions
on Information Theory, July 2006
Network Model
• M primary, N secondary users
• Primary users static, each has a unique channel
– channels orthogonal in frequency or space
• Secondary users mobile, no licensed channel
– set of channels they can access time-varying
– H(t) : 0/1 channel accessibility matrix
• Mobility model
– time-slotted
– resulting channel accessibility matrix H(t) Markovian
Example Network
hij(t) = 1 if SU i can access
channel j in slot t
H(t) evolves according to a finite state ergodic
Markov Chain, transition probabilities unknown
Network Model (contd.)
• Interference model
–
–
–
–
Sm(t) : actual state for channel m (busy, idle)
at most one transmission per channel per slot
additionally, interference sets Inm
conditions for successful SU transmission
I21 = {1, 2}
Important special case
Inm = {m} for all n,m
Network Model (contd.)
• Channel State Information model
– probability Pm(t) = E{Sm(t)|S(t-1)}
– known at slot t
– obtained by sensing the channels or knowledge of PU
traffic statistics or combination etc.
– models imperfect channel state information
2 state Markov chain example. Assume know ε, δ
E{S(t)|S(t-1) = ON} = 1- ε
E{S(t)|S(t-1) = OFF} = δ
Queueing Dynamics
• Secondary user queues Un(t)
• Flow control decision Rn(t)
– how many new packets to admit
• Transmission decisions μnm(t)
– subject to network model constraints
Setting up the problem
Goal: Maximize secondary user throughput utility
subject to maximum time average rate of collisions
ρm with any primary user m
Rn(t) = admitted data for SU n in slot t
Cm(t) = collision variable for PU m in slot t
Let
can solve if know all
parameters
challenge: unknowns
mobility, Λ, dynamics
Our Approach
• Lyapunov Optimization technique [2]
– generalization of backpressure technique
– [2] also covers related work
• Unifies stability and utility optimization
• Main idea: Convert time average constraints into
queueing stability problems
– notion of virtual queues
• Then, use Lyapunov Stability argument to design
an optimal control algorithm
[2] Resource Allocation and Cross-Layer Control in Wireless Networks, Georgiadis, Neely,
Tassiulas, NOW Foundations and Trends in Networking, 2006
Collision queue
• Define a collision queue Xm(t) for channel m
Observation: If this queue is stable, then the
constraint on the maximum time average rate of
collisions is met
This is exactly the collision constraint in our optimization problem
Algorithm Design and Proof
sketch
• Define our state as Q(t) = (U(t), X(t))
• Define Lyapunov function
• Compute Lyapunov drift
• Every slot, take control actions to minimize (V≥0)
• Compare with a stationary, randomized policy
• Delayed drift analysis for Markovian dynamics
Cognitive Network Control Algorithm
“cross-layer” algorithm decoupled into 2 components. (V≥0)
1. Flow control: Each secondary user chooses the number of
packets to admit
as the solution to:
- simple threshold policy, implemented separately at each SU
2. Scheduling transmissions of secondary users: Choose a
resource allocation
that maximizes:
subject to network constraints
- a generalized Maximum Weight Match problem
CNC Performance Theorem
1. Strong reliability bound: The worst case number of
collisions suffered by any primary user m is no more than
ρmT + Xmax over any finite interval T (where Xmax is a
constant)
- deterministic performance guarantee
2. Bounded worst case queue backlog: The worst case queue
backlog is upper bounded by a finite constant Umax for all
secondary users
- Umax linear in V
3. Utility-Delay tradeoff: The average secondary user
throughput achieved by CNC is within O(1/V) of the
optimal value
Distributed Implementation
• Focus on the case with Imn = {m}
• The resource allocation problem becomes the
Maximum Weight Match problem on a Bipartite graph
– NxM Bipartite graph, N secondary users, M channels
• Constant factor (1/2) distributed approximation
using Greedy Maximal Match Scheduling
• Reliability guarantees stay the same
Simulation example
• Cell partitioned network with 9 static
primary users, 8 mobile secondary users,
moving according to a Random Walk
7
2
4
1
8
• One channel per primary user
3
5
6
• Here, greedy maximal match = MWM
Total average congestion vs.
input rate for different V
(also no flow control case)
Simulation example
7
2
4
Throughput
vs. Input rate
for different V
1
8
3
5
6
• All collision constraints met
• The achieved throughput is very close to the input rate for
small values of the input rate
• The achieved throughput saturates at a value depending on V,
being very close to the network capacity for large V