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Fundamental Tradeoffs between Probing and Channel-aware Scheduling in Stochastic Wireless

Networks

Junshan Zhang

Ohio State University, March 5, 2010

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Example Wireless Applications

The Coming Mobile Meltdown

“Broadband's take-up has repeatedly been jumpstarted by must-have applications. Napster drove the shift from dialup to wired broadband. Now Apple's iPhone is playing the same role in triggering explosive growth in the wireless Web. Unless we miss our guess, this dynamic is about to rudely change the subject from net neutrality to a shortage of wireless capacity to meet enthusiastic consumer demand …”

[10/14/2009, Wall Street Journal]

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Connected Anywhere Anytime

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Wireless Data Traffic

• Many signs of explosive growth: web browsing, audio/video streaming

• Start from small base (1% of wireline); already comparable to wireless voice in volume; overall growth rate 100+% (500+% in some cases)

• “Metrics” in space of wireless communications:

• Throughput (how much data): 4G requires 10~50Mps 100Mbps

• Latency (how long does it take to get): 4G requires 10ms RTT

• Cost (technology <--> economics)

• Ubiquitous coverage (reachability)

• Significant gap between demand and wireless capacity

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A Roadmap of Technology Evolution

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802.11n802.16m

Major Advances in Wireless Communications

MIMO (multi-antenna tech) OFDM and OFDMA Turbo coding, LDPC Cooperative relaying Interference alignment Channel-aware scheduling (in 4G) Wireless network coding Cognitive radio networks …

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(in 3G/4G)

Technology trend: towards a holistic view of wireless networks; towards exploiting interplay across technology & economics, …

Cooperative Relaying and Concurrent Transmissions in 4G Networks

Our initial steps started in 2001/2002 and studied 1) Capacity bounds of MIMO relay channel; 2) Power allocation in wireless relay networks; 3) Scaling laws of Wideband sensory relay networks

Three of our IT papers received about 600 citations: B. Wang, JZ & Host Madsen (IT 05); Host-Madsen & JZ (IT 05); B. Wang, JZ & L. Zheng (IT 06)

• High traffic volume • Need “smart” adaptive scheduling

Focus of This Talk

Channel-aware distributed scheduling Centralized version has been implemented in 3G

(Qualcomm’s HDR, EXDO) Also called “Channel dependent scheduling” in 4G. One outstanding example of cross-layer optimization Cross-layer optimization:

Q) Which layers should respond to wireless channel variations? What layers should be “jointly” optimized?

Does not mean to get rid of protocol layer architecture

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Consummation of Information Theory and Network Theory: The Wireless Case

• Bridging information theory and network research [Hajek-Ephremides 98]• Far from consummation, particularly multi-scale network dynamics in wireless communciations are not well understood.

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Multi-scale Stochastic Dynamics

Unique challenges in wireless networks: Channel fading occurs on multi-timescales; Time varying topology due to mobility; Co-channel interference occurs on multi-

timescales. Network dynamics: Session-level, packet-level,

channel-level, and topology-level, …

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Timescales of Interference Variation (at MAC)

Measurement data [Aguayo-Bicket-Biswas-Judd-Morris 04] [Cao-Raghunagthan-Kumar 06]

White Space Dynamics and Cognitive Radio

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Q: How to increase wireless capacity in order tomeet enthusiastic consumer demand?

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Channel-aware Data Transmission:Tradeoff between Probing and Scheduling

Challenge: How should we design robust and opportunistic data transmission in multi-scale dynamics?

Network/channel states are changing continuously; Probing is needed to estimate/track states for state-

aware data transmission.Our study: I) Tradeoff between probing and channel-aware

scheduling in contention-based networks II) Tradeoff between probing and state-aware

scheduling in cognitive radio networks

Tradeoffs between Probing and Channel-aware Distributed Scheduling

This talk

Focus on distributed scheduling with probing: in an interference environment, who can talk, at what rate, in each time slot?

Distributed opportunistic scheduling for throughput maximization

Distributed opportunistic scheduling under delay constraints

Opportunistic channel-aware DOS: Distributed opportunistic scheduling

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System Model: Practice-Theory Dichotomy

Simple ones used, analysis can be very challenging: • Aloha, CSMA/CD • CSMA/CA, 802.11 with RTS/CTS Sophisticated algorithms based on information theory,

graph theory, optimization, game theory, control theory

Our philosophy: combining practical relevance and rigorModel: CSMA-type networks with two phases of channel probing:

1) Phase I: contention 2) Phase II: channel estimation (noiseless/noisy cases)

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Distributed Opportunistic Scheduling: Unified PHY/MAC Optimization

Traditional wisdom attempts to separate link losses due to fading from those incurred by interference;

MAC layer: scheduling used to resolve interference PHY layer: coding/modulation, diversity schemes

However, fading can often adversely affect MAC layer -- time scales of channel variation and MAC variation are coupled ! This calls for channel-aware (opportunistic)

scheduling!

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Centralized Opportunistic Scheduling and Channel-Aware Aloha

Downlink scheduling: [Tse00], [Liu-Chong-Shroff01],… Channel-aware Aloha: [Qin-Berry03] [Adireddy-Tong03]

Multiuser diversity: riding the channel peak across users

Distributed Scheduling in Ad-hoc Networks

Model: consider contention-based ad-hoc networks

Challenges in devising channel-aware scheduling for ad-hoc communications:

Links have no knowledge of others’ channel conditions; even their own channel conditions are unknown before probing.

Q) which link to schedule, and how?

A

BC

DE

F

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Noiseless Probing: Probing with Perfect Rate Estimation

Suppose after one successful contention, link condition is poor. Two options:

Continue data transmission; Or, alternatively, let this link give up

this opportunity, and all links re-contend.

Intuition: At additional cost, further channel probing can lead to data transmission with better channel conditions.

In this way, multiuser diversity and time diversity can be exploited in a distributed and opportunistic manner.

A

BC

D

E

F

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Tradeoff between Probing and Throughput Gain

s(n) denote the successful link in n-th round of channel probing.

Clearly, there is a tradeoff between throughput gain from better channel conditions and the cost for further channel probing.

Using optimal stopping theory, we characterize this tradeoff for distributed scheduling.

Probing time

Channel coherence time

Technical Conditions

Throughout Maximization via Maximizing Rate of Return

Characterizing N* and X*: Optimality Equation

Characterizing N* and X* (Cont’d)

(Based on joint work with D. Zheng and W. Ge [IT 2009])

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Threshold Structure of Optimal Scheduling Policy

Joint PHY/MAC Design

The optimal distributed scheduling is simple to implement:

if the current rate is larger than the threshold, then transmit data; otherwise, continue probing.

Tra

nsm

itte

rs Rece

ivers

Link 1

Link 2

Link 3

Link 4

RTS

RTS NCTS

RTS

R < x*

R >= x*CTSDATA

RTS

RTS

RTS

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Noisy Probing: Probing with Imperfect Rate Estimation

• In the above, channel state information (CSI) is assumed to be perfectly known at receiver/transmitter after probing.

• In practical scenarios, channel conditions are often estimated using

noisy observations, and CSI is imperfect.• Consider channel-aware distributed scheduling with noisy

rate estimation.

MMSE Estimation of the channel rate:

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Noisy Probing Major differences between noisy/perfect probing:

The “observed” rate, Rn, is now a r.v., and is not perfectly known.

The stopping rule in noisy case is defined over the filtration generated by noisy observations

Can show that structure of optimal scheduling remains same, except that random “reward” is replaced with its conditional expectation.

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Reactive Strategy: Linear Rate Backoff

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Proactive Strategy with Noisy Probing

Further probing may be helpful to improve the quality of rate estimation and hence the throughput.

Particularly interested in the wideband low SNR regime, i.e., and Potential significant improvement of rate estimation due to further probing in wideband regime. [Verdu’ IT2002]

Trade-off between enhanced rate gain due to improved estimate and further probing cost.Proactive approach: DOS with two-Level probing;

Underlying theory: optimal stopping theory with incomplete information [Stadje’ 97].

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Proactive Strategy: DOS with Two-Level Probing

Q: Is it worthwhile for the successful link to perform further channel estimation, with an additional cost? How much can we bargain?

In noisy case, back-off factor is proportional to estimation error Lower estimation error ---- > higher transmission rate

Channel condition is bad

refinement is not helpful, defer and re-contend

Channel condition is good

refinement is relatively meager, transmit immediately at the current rate

?

The answer is yes or no; there is a grey area where additional probing will help.

- Gain: better rate estimate; - Cost: time overhead

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Refined Rate Estimate with 2nd-Level

Probing

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Contention successful ! Estimated

What are the options ?

2nd-level: Estimated at cost .

C I S(n)

C I S(n)

Continue transmissionReward: bits.

C I S(n)

C I S(n) C I Give up and re-contend.Reward: bits.

Two optionsTransmit for Reward:

S(n)

Give up and re-contend

C IS(n)

Scheduling Options and Rewards: Illustration

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Scheduling Options and Rewards

After n-th round of probing, with first-level rate estimate ,the successful link has the following options :

1. Transmit at rate for time T;

2. Defer transmission and let all nodes re-contend;

3. Perform second-level probing to obtain new rate at the cost of additional probing, and then

a. Transmit at the rate for ; b. Defer and let all nodes re-contend.

Rewards

Lagrange multiplier, “ cost per unit time ”

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DOS with Two-Level Probing:Structural results

Optimality Conditions:

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Possibilities

R(2)

Give up and re-contend Transmit at R(2)

1st level probing

Rate R(1)

C I

Give up and re-contend

?C I S(n)

Possibilities

R(1)

Transmit at R(1)

T

2nd Level Probing Refined rate R(2)

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DOS with Two-Level Probing:Strategy A

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DOS with Two-Level Probing:Strategy B

1-st level probing

Rate R(1)

?C I S(n)

Possibilities

Give up and re-contend

Transmit at R(1)

T

Details [Infocom’09]

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Numerical Example

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Numerical Results

- performance gap is significant in the low-SNR regime.- As increases, the performance gap narrows down - In mitigating estimation errors, the overhead due to additional probing offsets its gain. - the “gray area” collapses. As a result, Strategy A degenerates to Strategy B

Delay Performance

Performance metrics in space of wireless communications:

• Throughput

• latency (coming next …)

• Cost

• Coverage

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Distributed Opportunistic Scheduling with Delay Constraints

Many wireless applications, e.g., multimedia traffic, have stringent delay requirements.

A VOIP application typically requires an average delay less than 200ms to maintain a normal conversation.

Network-wide average delay constraint: applicable to applications such as event monitoring by sensor networks where a group of sensor nodes observe the same phenomenon and try to deliver the messages to the fusion center.

DOS under Network-wide Delay Constraint

Relaxation and Duality

From Primal to Dual to Dual’s Dual

Main Result for Continuous Rate Case

Remarks

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Conclusions

Distributed opportunistic scheduling will play a critical role in handling high-volume data traffic in 4G and beyond.

Study distributed opportunistic scheduling for exploiting PHY/MAC diversities in dynamics of channel/interference variations

Noiseless probing: probing with perfect rate estimation Noisy probing: reactive strategy and proactive strategy (two-

level probing). Explore distributed opportunistic scheduling with delay

constraints. (Delay analysis of distributed scheduling using diffusion/fluid

approximation).

Thank you !!