Pilot-Aided Adaptive Gallager Coded Modulation on ... - NTNU

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Pilot-Aided Adaptive Gallager Coded Modulation on ... - NTNU

Loen June 4-6

ong>Pilotong>-ong>Aidedong> ong>Adaptiveong> ong>Gallagerong> ong>Codedong>

ong>Modulationong> on Correlated Rayleigh

Channels

Ola Jetlund 1 , Geir E. Øien, Bengt Holter, and Kjell J. Hole

Department of Telecommunications

NTNU

NORWAY

1 ola jetlund.com

NTNU

1


Overview Loen June 4-6

• Motivation

• Channel model

ong>Adaptiveong> ong>Gallagerong> coded modulation

• Prediction

• Simulations

• Conclusions

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Motivation Loen June 4-6

• Wireless communication: channel signal-to-noise ratio

(CSNR) varies in time and space

ong>Adaptiveong> coding and modulation (ACM)

− Uses codecs with high spectral efficiency (SE) when

CSNR is high (and vice versa)

• Rate of channel variation depends on mobility of receiver

and transmitter

• Existing theoretical performance measures are based on

idealized assumptions

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Channel model Loen June 4-6

• Frequency-flat time-selective multipath fading channel

• Rayleigh distributed envelope

y(t) = z(t) · x(t) + n(t)

• CSNR:

γ(t) = |α(t)|2·P

N 0 B

¯γ = ΩP

N 0 B

z(t) = α(t) exp(θ(t))

Ω = E[|α(t)| 2 ]

P − Average transmit power

N 0 − Noise spectral dens.

B − Transmit bandwidth

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ong>Adaptiveong> ong>Gallagerong> coded modulation I Loen June 4-6


BER[bits/s/Hz]

• Employ N codecs

BER 0

0

γ 1

1

γ 2

2

γ 3

γ N−1

N−1

γ N

N

CSNR[dB]

✲◮

γ N+1 = ∞

• Spectral efficiency of codec

n is R n :

R 1 < R 2 < · · · < R N

• Divide the CSNR range in

N + 1 regions

• Thresholds determined for

each codec such that

BER < BER 0 (under idealized

assumptions)

✲◮ Transmitter


✲◮ Channel

✲ ◮ Receiver

✲ ◮

• Receiver predicts CSNR, ̂γ

• Select codec n when

γ n ≤ ̂γ < γ n+1

Channel state information, n

• CSI (n) is transmitted back

to transmitter

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ong>Adaptiveong> ong>Gallagerong> coded modulation II Loen June 4-6

• Average spectral efficiency:

ASE =

N∑

n=1

R n · P n

[bits/s/Hz]

− R n : SE of code n

− P n : probability of codec n being selected

• Component Codecs

ong>Gallagerong> (block) codes (LDPC codes) with different SE

− Multilevel signal constellations

− Block length after modulation is M

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Prediction I Loen June 4-6

SOURCE

information

bits

✲ ◮

ENCODE

✲ ◮ MAPPING

✲ ◮ PILOTING

x(k)








RETURN

FADING

CHANNEL




CHANNEL



CSI, n

CHANNEL-

PREDICTOR

✛◭ ˜z k

BUFFER

✛◭

ML-

CSI, n

ESTIMATE

✛◭

ESTIMATE


y(k)

decoded

information

bits

✛◭


DECODER

✛◭

✛◭


PILOT-

SOFT-

DEMAP

✛◭ DEPILOT ✛ ◭ DETECT ✛ ◭


EXTRACT

✛◭

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Prediction II Loen June 4-6

ong>Pilotong> symbol assisted modulation (PSAM)

• An aid used to provide knowledge about the fading at

the receiver

• Introduce pilots periodically into the stream of channel

symbols: Every Lth channel symbol x(lL) is a pilot symbol

• Positions and values of the pilots are known to both

transmitter and receiver

• PSAM can be used as an aid for both channel estimation

(detection) and channel prediction

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Prediction III Loen June 4-6

For the pilot symbols we assume

• Equal value x(lL) = a p and equal power for pilot symbols

and information symbols: |a p | = √ P

• Equal number of pilot symbols in each transmitted block

(block length after pilot insertion is M ′ )

ASE after pilot insertion:

ASE = M M ′

N ∑

n=1

R n · P n

[bits/s/Hz]

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Prediction IV Loen June 4-6

• Prediction of z(k + j), ẑ:

− From buffered estimates ˜z based on received pilot symbols

− j is the prediction lag: Time lag between last pilot and

the time instant of the predicted fading

− Expected CSNR: E[̂γ] = E[|ẑ|2 ]P

N 0 B

= r · γ

• Maximum a posteriori optimal predictor:

− Linear combination of estimates ˜z

− Correlation between predicted and actual CSNR:

ρ = r ≤ 1

(Biased)

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Simulations I Loen June 4-6

• Assumptions:

− Perfect channel estimation (coherent detection)

− Prediction uses a filter of order K = 1000

− Jakes spectrum

− Predict CSNR of first symbol in a block (approximately

constant fading during transmission of one block)

ong>Pilotong> spacing L = 11 and block length M = 200:

M ′ = 220

• Prediction lags j ∈ {0, M ′ , 2M ′ , . . .}

• Target bit error rate BER 0 = 10 −3 NTNU

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Simulations II Loen June 4-6

• Codecs:

Codec Code Constellation R n Threshold

n rate size and type [bits/s/Hz] γ n [dB]

1 1/2 4QAM 1 2.72

2 2/3 8PSK 2 8.03

3 3/4 16QAM 3 11.21

4 4/5 32QAM 4 14.91

5 5/6 64QAM 5 17.89

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Simulations III Loen June 4-6

̂γ(k) versus γ(k): Scatter plots of predicted CSNR versus actual CSNR for

varying velocities and prediction lags.

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Simulations IV Loen June 4-6

̂γ(k) versus γ M ′(k): Scatter plots of predicted CSNR versus averaged actual

CSNR for varying velocities and prediction lags.

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Simulations V Loen June 4-6

The correlation coefficient as a

function of velocity v and expected

CSNR γ for j = M ′

The correlation coefficient as a

function of prediction lag j and

expected CSNR γ for v = 1 m/s.

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Simulations VI Loen June 4-6

BER plotted against expected

CSNR and varying velocities, and

j = M ′ .

BER plotted against expected

CSNR and varying prediction lags,

and v = 1 m/s.

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Simulations VII Loen June 4-6

BER, after thresholds are increased

by 0.5 dB, plotted against

expected CSNR and varying velocities,

and j = M ′ .

BER, after thresholds are increased

by 0.5 dB, plotted against

expected CSNR and varying prediction

lags, and v = 1 m/s.

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Simulations VII Loen June 4-6

BER, after thresholds are increased

by 1.0 dB, plotted against

expected CSNR and varying prediction

lags, and v = 1 m/s.

Theoretical ASE, simulated ASE

for the system using the original

and modified thresholds.

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Conclusions Loen June 4-6

• Predictor performance is quite satisfying (with a negative

bias)

• Assumption of approximately constant fading during

transmission of one block is quite good

• System performance is satisfying for low velocities and

small prediction lags

• Increasing thresholds yields an improvement in BER performance

and reduction in ASE performance

• A more sophisticated threshold design is desirable

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Acknowledgements Loen June 4-6

This work is supported in part by the joint Telenor-NTNU

project TURBAN and in part by the project BEATS 1 founded

by the Research Council of Norway.

1 http://www.tele.ntnu.no/projects/beats

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