Wireless Networks with Wireless Networks with Limited Limited

FeedbackFeedback: PHY and MAC Layer : PHY and MAC Layer

AnalysisAnalysis

PhD Proposal

Ahmad Khoshnevis

Rice University

Wireless Networks

• Higher throughput

• TAP: 400 Mbps

• WiMax

• 4G

Network of Unknowns

Queue

TopologyInterference

Channel

Battery

Why Unknowns Matter?

• Physical layer example– Channel varies with time

– If current condition known• Adapt and achieve higher throughput

• Catch– We don’t care about the channel (unknown)

• Only care about sending data

– Time varying in nature• Periodic measurements • Spend resources for non-data

• Should you measure unknowns ? If yes, how accurately ?

In This Thesis

• Unknowns in channel and source

• Channel

• Source

1

2q1

q2 S1

S2

D

h

Outline

• Analysis of Physical Layer with Feedback– Background and related works

– Feedback design

– Throughput-reliability tradeoff

• Proposed work: Managing Unknowns at Medium Access Layer– Background and related works

– Road-map

• Contribution summary

PHY: System Model

H(t) +X(t) W(t)

Y(t)

PHY Objective

• Maximize throughput– Ergodic capacity

• Minimize packet loss– Outage probability

• Intuitively– Two metrics are against each other

PHY Unknown: Channel (H)

• No one measures – Out of fashion

• Receiver (Rx) measures

• Transmitter and Receiver measures (Tx+Rx)

H(t)Tx Rx

PHY: Limiting PerformanceShannon, Goldsmith & Varaiya. Telatar, Jayaweera & Poor, Caire et. al.

• Outage– Large gain with Tx knowledge

– Greater rate of decay (slope)

• Ergodic capacity– Some gain

– Same rate of increase (slope)

PHY: Div-Mux Tradeoff

• Rx only knows the channel

• Finite block length

– Multiplexing gain » throughput

– Diversity order » reliability

• Reliability and Throughput can not be improved at the same time

[Zheng and Tse 03]

0 1 2 3 40

5

10

15

20

25

30

r

d

Summary and Question

System Tx+Rx outperforms Rx only

Perfect channel knowledge requires infinite capacity in feedback

If only few bits were available for feedback, then

What would be the impact on performance?

How would the mux-div be affected?

Related Work: Finite Feedback

• Beamforming– Narula et. al., 99, quantized beamforming

– Mukkavilli et. al., Love and Heath, 03

• Power Control– Bhashyam et. al. 02, One bit feedback design, outage

– Ligdas and Farvardin 00, Lloyd-Max quantizer, bit error rate

– Yates et. al. 03, Lloyd-Max, power and rate, ergodic capacity

• My work– Design and analysis of a low complexity channel quantizer

• Multiple antenna system• Outage as metric

– Analysis of diversity-multiplexing tradeoff

Outline

• Analysis of Physical Layer with Feedback– Background and related works

– Feedback design

– Throughput-reliability tradeoff

• Proposed work: Collision Channel with Feedback– Background and related works

– Road-map

• Contribution summary

Limited Feedback Design

• B bits of feedback– L= 2B

– For a multiple antenna system

• In Tap: m=4, n=4• H is in 2*4*4 = 32 dimensional space

H +X W

Y

Q(H)

Quantized Parameter

• Equal power on transmit antennas

– i ,

• eigenvalues of HHy

• are enough to know for outage

– There are only m of them

– Even more simplify, use only one

• Assume ordered eigenvalues

– 1>2>>m

TransmitterX

ReceiverY

H

Feedback and Power Allocation

• Allocate Power level s. t.– No outage

– Average power constraint

• But the first interval– For i<0, we are in outage

H +X W

Y

Q(i)0 1 2 43

1 2 53 4

Sketch of Optimum Mapping, Q

nonlinearequations

Local behaviorof Fi

(x) at x!0

linear equationsrecursive solution

Approximation

Quantizer, Q

Throughput-Reliabilitycurve0 1 2 43

Mux-Div Tradeoff

0 1 2 3 40

50

100

150

200

250

Multiplexing Gain (r)

Div

ersi

ty O

rder

(d)

Quantizer of 1

Quantizer of 2

Quantizer of 3

Diversity-Multipleding w/ FeedbackDiversity-Multiplexing w/o Feedback

Quantized Power and Rate Control

• Threshold L

• For i>L

– Variable Codebook

• Gives mux gain

• For i<L

– Constant Codebook

• Gives div order

• Decouple mux and div

Mux-Div: Quantized Power/Rate Control

nonzero

Rx only

Outline

• Analysis of Physical Layer with Feedback– Unknown: Channel

– Even a ‘little’ knowledge has a ‘lot’ of gain

• Proposed work: Collision Channel with Feedback– Background and related works

– Road-map

• Contribution summary

Network of Users

• So far– Only one user

– Knowledge used in power/rate control

• More than one user

• The resources need to be divided

1

2q1

q2 S1

S2

D

Unknowns: Managing Queue State

• Queues have time-varying state– Might be empty sometimes

• In effect, # of active nodes is time varying

• Design for Max # of user is conservative– Underutilized network for many traffic

• “Active” management of queue states = Medium Access Protocols

Class of MAC Protocols

• CDMA

• TDMA– Round-Robin

– Adaptive Scheduling

• Random Access– Abramson 70, ‘The ALOHA System’, only random access w/o CA

– Tobagi and Kleinrock 75, CSMA/CA, out-of-band busy tone

– Karn 90, MACA, control handshake (RTS/CTS)

• All of the above consume resources– Price paid for managing unknowns

Major Question

What is the minimum price for unknown queue-state information ?

• NOTE– Unknowns themselves not of interest, data is

– How much overhead you HAVE to pay to send on this channel with unknowns (queue states) ?

Proposed Approach

• Considered queuing theoretic [ISIT 2005]– Abandon it

• Not scalable for more then 2 users

• Does not provide intuition

• Inspired by information theory– Rate of information in unknowns

– In a finite delay system, transmitted packet conveys two information• Information contained in the packet

• Timing information

– Quantify timing information as a function of delay (=distortion)

– Rate-distortion over collision channel

Summary

• Managing unknowns– Physical layer

– MAC layer

• There is a lot of gain in knowing even a ‘little’– Showed at PHY

– Under investigation at MAC layer

Which Eigenvalue Though?

• Take i to be quantized

– Power guarantees channel 1,…,i

– Let ri = , 2[0,1]

– rj>ri 8 j<i

• Total mux gain– r > i

• r 2 [0 , i ]

• Can be done reverse– For given r, choose i=dre

m m

X Y

i,Ri

Quantized Parameter

TransmitterX

ReceiverY

NtNr m m

X Y

• Equivalent channel

– m parallel channel

m

• Equal power on transmit antennas

– i are enough to know

– There are only m of them

• Assume ordered eigenvalues

– 1>2>>m

H