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

Loen June 4-6

**on****on** Correlated Rayleigh

Channels

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

Department of Telecommunicati**on**s

**NTNU**

NORWAY

1 ola jetlund.com

**NTNU**

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Overview Loen June 4-6

• Motivati**on**

• Channel model

• **on**

• Predicti**on**

• Simulati**on**s

• C**on**clusi**on**s

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Motivati**on** Loen June 4-6

• Wireless communicati**on**: channel signal-to-noise ratio

(CSNR) varies in time and space

• **on** (ACM)

− Uses codecs with high spectral efficiency (SE) when

CSNR is high (and vice versa)

• Rate of channel variati**on** depends **on** mobility of receiver

and transmitter

• Existing theoretical performance measures are based **on**

idealized assumpti**on**s

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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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**on** 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 regi**on**s

• Thresholds determined for

each codec such that

BER < BER 0 (under idealized

assumpti**on**s)

✲◮ Transmitter

✻

✲◮ Channel

✲ ◮ Receiver

✲ ◮

• Receiver predicts CSNR, ̂γ

• Select codec n when

γ n ≤ ̂γ < γ n+1

Channel state informati**on**, n

• CSI (n) is transmitted back

to transmitter

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**on** 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

• Comp**on**ent Codecs

−

− Multilevel signal c**on**stellati**on**s

− Block length after modulati**on** is M

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Predicti**on** I Loen June 4-6

SOURCE

informati**on**

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

informati**on**

bits

✛◭

❄

DECODER

✛◭

✛◭

❄

PILOT-

SOFT-

DEMAP

✛◭ DEPILOT ✛ ◭ DETECT ✛ ◭

❄

EXTRACT

✛◭

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Predicti**on** II Loen June 4-6

**on** (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

• Positi**on**s and values of the pilots are known to both

transmitter and receiver

• PSAM can be used as an aid for both channel estimati**on**

(detecti**on**) and channel predicti**on**

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Predicti**on** III Loen June 4-6

For the pilot symbols we assume

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

and informati**on** symbols: |a p | = √ P

• Equal number of pilot symbols in each transmitted block

(block length after pilot inserti**on** is M ′ )

ASE after pilot inserti**on**:

ASE = M M ′

N ∑

n=1

R n · P n

[bits/s/Hz]

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Predicti**on** IV Loen June 4-6

• Predicti**on** of z(k + j), ẑ:

− From buffered estimates ˜z based **on** received pilot symbols

− j is the predicti**on** 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 combinati**on** of estimates ˜z

− Correlati**on** between predicted and actual CSNR:

ρ = r ≤ 1

(Biased)

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Simulati**on**s I Loen June 4-6

• Assumpti**on**s:

− Perfect channel estimati**on** (coherent detecti**on**)

− Predicti**on** uses a filter of order K = 1000

− Jakes spectrum

− Predict CSNR of first symbol in a block (approximately

c**on**stant fading during transmissi**on** of **on**e block)

•

M ′ = 220

• Predicti**on** lags j ∈ {0, M ′ , 2M ′ , . . .}

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

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Simulati**on**s II Loen June 4-6

• Codecs:

Codec Code C**on**stellati**on** 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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Simulati**on**s III Loen June 4-6

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

varying velocities and predicti**on** lags.

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Simulati**on**s IV Loen June 4-6

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

CSNR for varying velocities and predicti**on** lags.

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Simulati**on**s V Loen June 4-6

The correlati**on** coefficient as a

functi**on** of velocity v and expected

CSNR γ for j = M ′

The correlati**on** coefficient as a

functi**on** of predicti**on** lag j and

expected CSNR γ for v = 1 m/s.

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Simulati**on**s VI Loen June 4-6

BER plotted against expected

CSNR and varying velocities, and

j = M ′ .

BER plotted against expected

CSNR and varying predicti**on** lags,

and v = 1 m/s.

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Simulati**on**s 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 predicti**on**

lags, and v = 1 m/s.

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Simulati**on**s VII Loen June 4-6

BER, after thresholds are increased

by 1.0 dB, plotted against

expected CSNR and varying predicti**on**

lags, and v = 1 m/s.

Theoretical ASE, simulated ASE

for the system using the original

and modified thresholds.

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C**on**clusi**on**s Loen June 4-6

• Predictor performance is quite satisfying (with a negative

bias)

• Assumpti**on** of approximately c**on**stant fading during

transmissi**on** of **on**e block is quite good

• System performance is satisfying for low velocities and

small predicti**on** lags

• Increasing thresholds yields an improvement in BER performance

and reducti**on** 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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