Automatic Rate Adaptation

Aditya Gudipati & Sachin KattiStanford University

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Wireless channel varies rapidly

• To maximize throughput, we have to estimate channel and adjust bit rate continuously.

Motivation

0

5

10

15

20

25

30

0 2000 4000 6000 8000 10000

Time (Milliseconds)

SN

R (

dB

)

10 s

Source: VJB’09

2

Passive Adaptation• Infer channel from

packet loss rate• Coarse estimate ;

wasted transmissions

Passive Adaptation

P1

P2

P3

P1

ACK1

4

Active Adaptation

P1

P2

P3

P1

ACK1+ SNR1NACK2+ SNR2NACK3+ SNR3

SNR1

SNR2

SNR3

5

Passive Adaptation• Infer channel from

packet loss rate• Coarse estimate ;

wasted transmissions

Active Adaptation• Receiver feedback on

channel conditions• Higher overhead;

inaccurate for mobile wireless channels

• Redundancy to correct bit errors• ‘b’ data bits mapped to ‘c’ coded bits (c>b) then

code rate = (b/c)• Ideally this code can correct (c-b)/2 bit errors• Typical convolutional code rates : 1/3, 1/2, 2/3

• Higher code rate implies• Smaller redundancy• Lesser resilience to errors

Channel Coding

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• Map channel coded bits to constellation points

Modulation

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-b

(0,0)

-a

(0,1)

a=√(P/5) ; b=3√(P/5)[ (-b)2 + (-a)2 + a2 +b2]/4 =P

a

(1,1)

b

(1,0)

• Attenuation and additive noise from channel• To demodulate, map to closest constellation point

Demodulation

WirelessChannel

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-b

(0,0)

-a

(0,1)

a=√(P/5) ; b=3√(P/5)[ (-b)2 + (-a)2 + a2 +b2]/4 =P

a b-b -a

N N

a

(1,1)

b

(1,0)

• 4-PAM to BPSK reduces errors for the same noise

Sparser Constellation Lesser Bit Errors

WirelessChannel

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a-a

a=√P[ (-a)2 + a2]/2 =P

a-a

Minimum Distance between constellation points determines error rate

N

• Throughput α Coding rate α Constellation density

• Estimate highest coding rate and densest

constellation that can be supported.

Rate Adaptation

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Automatic Rate Adaptation (ARA):• Uses fixed code rate• Automatically adjusts minimum distance of the

constellation without channel state feedback• Achieves throughput almost as good as omniscient

scheme with perfect advance channel knowledge

This Talk …

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Can we achieve the best rate without doing any estimation or requiring channel feedback?

• Take 2 BPSK coded symbols• Keep sending random linear combinations of

coded symbols

An Example

-1

-1 1

1

-c-d(B1 = -1B2 = -1)

B1

B2

c = 0.89 ; d = 0.45c2 + d2=1

P1

P2

-c+d(B1 = -1B2 = 1)

c-d(B1 = 1B2 = -1)

c+d(B1 = 1B2 = 1)

-c-d(B1 = -1B2 = -1)

-c+d(B1 = 1B2 = -1)

c-d(B1 = -1B2 = 1)

c+d(B1 = 1B2 = 1)

2(c-d)

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2d2d

P1 : cB1 + dB2

P2 : dB1 + cB2

• Take 2 BPSK coded symbols• Keep sending random linear combinations of

coded symbols

An Example

-1

-1 1

1B1

B2P1

P2

(-c-d, -c-d)(B1 = -1 , B2 = -1)

(-c+d, c-d)(B1 = -1 , B2 = 1)

(c-d, -c+d)(B1 = 1 , B2 = -1)

(c+d, c+d)(B1 = 1 , B2 = 1)

√2(2 (c-d))

Minimum Distance Transformer24

c = 0.89 ; d = 0.45c2 + d2=1

P1 : cB1 + dB2

P2 : dB1 + cB2

Formally,

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cd

d

c

B1

B2

=P1

P2

P3e f

An Example

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c11

c21

c12

c22

B1

B2

=P1

P2

…… …cM1 cM2 PM

• 2 dimensional point mapped to M dimensional space • Minimum distance α √M

An Example

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B1

B2

=P1

P2

…PM

G

• 2 dimensional point mapped to M dimensional space • Minimum distance α √M

How does the receiver decode?

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B1

B2

P1

P2

PM

…Transmitter

Receiver

ChannelP1+n1

P2+n2

PM+nM

…B1

B2

How does the receiver decode?

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=

n1

n2

nM

…+B1

B2

G

y1

y2

yM

…=

P1+n1

P2+n2

PM+nM

…

How does receiver decode• Receiver : y = Gx +n

• x = [B1 B2]T є 2- dimensional space ( the coded symbols we wished to transmit)

• y = [y1 y2 … yM]T є M - dimensional space ( each entry being a different received symbol)

• Find possible values of ‘x’ given ‘y’ and known G• Sphere Decoding

– Outputs probability of each bit in x• Probabilities fed into channel decoder

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Characteristics• Existing coding and modulation techniques need not

be changed.• G is fixed and known at the transmitter and receiver.• Keep transmitting until minimum distance sufficient to

decode and receiver sends ACK• Achieved Rate = (2/M) bits per transmitted symbol

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MATLAB Evaluation• ARA uses

– QPSK and fixed 2/3 convolutional code– 8 packets linearly combined

• Compared with omniscient scheme– Knows exact channel SNR in advance– Chooses best possible modulation and code rate among:

• (QPSK, 8-PSK, 16-QAM, 64-QAM) and (1/4,1/3,1/2,2/3) rates

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Evaluation

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4 6 8 10 12 14 16 18 200.5

1

1.5

2

2.5

3

3.5

4

Automatic Rate Adaptation

Omniscient Scheme

SNR

Thro

ughp

ut(b

its/t

rans

mitt

ed s

ymbo

l)

ARA’s throughput is almost as good as omniscient scheme without advance channel SNR knowledge

64 - QAM16 - QAM8 - PSKQPSK

2/31/21/31/4

Conclusion• ARA adapts the minimum distance without

estimation or channel feedback• Automatically adapts rate and simplifies PHY design• Future Work

– Reducing complexity of decoder– Extend ARA to work in the presence of collisions– Prototype implementation on USRP2

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