CCU Wireless Access Tech. Lab. OFDM Transmission over Gaussian Channel Gwo-Ruey Lee.

CCU Wireless Access Tech. Lab.

OFDM Transmission over Gaussian Channel

Gwo-Ruey Lee

Wireless Access Tech. Lab.


Outlines

OFDM Transmission over Gaussian ChannelGaussian DistributionThe AWGN Channel ModelOFDM System Performance over AWGN

ChannelThe Signal Constellations of Different

Modulation over AWGN Channel



Gaussian Distribution

The PDF of a Gaussian or normally distributed random variable is

2

2

1

22x

X

x mp x e

The PDF of a Gaussian-distributed random variable

( )Xp x

x

2

1

1

xm0

1/2



Gaussian Distribution

The CDF of a Gaussian or normally distributed random variable is

where

2

2

2exp( )

21 exp( )

x

x

erf x z dz

erfc x erf x z dz

1 1 11

2 2 22 2x x

X

x m x mF x erf erfc

xm0

2

1

( )XF x

xThe CDF of a Gaussian-distributed random variable

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The AWGN Channel Model

The received signal in the interval may be expressed as

where denotes the sample function of the additive white Gaussian noise (AWGN) process.

0 t T

, 0mr t s t n t t T

2/2

n t



The AWGN Channel Model

The channel is assumed to corrupt the signal by the addition of white Gaussian noise as shown below

Transmission model for received signal passed through an AWGN channel

2/2

(t)Sm

+

AWGN

Received Signal Transmitted Signal Channel

)(tn

n(t)(t) Sr(t) m



OFDM System Performance over AWGN Channel

Serial Data Output

OFDM Receiver

Channel Model

OFDM Transmitter

AWGN

S(t)Guard

Interval Insertion

Parallel-to-Serial

Converter IFFT

Signal Mapper

Serial-to-Parallel

Converter

Random Data

Generator

Serial-to-Parallel

Converter FFT

Signal Dema-pper

Parallel-to-Serial

Converter

Guard Interval Removal

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Modulation of OFDM subcarrier is analogous to the modulation in conventional serial systems.

The modulation schemes of the subcarriers are generally QAM or PSK in conjunction with both coherent and non-coherent detection.

As the additive white Gaussian noise (AWGN) in the time domain channel corresponds to AWGN of the same average power in the frequency domain, an OFDM system performance in an AWGN channel is identical to that of a serial system.

Analogously to a serial system, the bit error rate (BER) verses signal-to-noise rate (SNR) characteristics are determined by the modulation scheme used.

It can be seen from the figures that the experimental BER performance of the OFDM system is in very good accordance with the theoretical BER curves of conventional serial systems in AWGN channels.

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Simulation parameter Value

Channel AWGN

FFT size 1024

Subcarrier # 1024

Modulation BPSK, QPSK,8PSK, 16PSK

Guard Type Cyclic Prefix

SNR 0 - 30 dB

BER versus SNR curves for the OFDM system in AWGN channel using BPSK, QPSK, 8PSK,16-PSK .

0 5 10 15 20 25 3010

-6

10-5

10-4

10-3

10-2

10-1

100

BER vs. SNR

SNR

BE

R

BPSK theoretical result BPSK simulation QPSK theoretical result QPSK simulation 8PSK approximate result 8PSK simulation 16PSK approximate result 16PSK simulation

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PSK BPSK

QPSK with Gray code

M-ary PSK

where

,

1

2e BPSKp erfc

,

1

2e QPSKp erfc

22exp( )

xerfc x z dz

sE

2m

3m

4m

5m

6m

7m

8m

Decision boundary

2

message point

sE

sE

d

d

MM 1m

Decision region

1sE

MN

Eerfcp s

MPSKe

sin

0,

0

bESNR

N

4/6




BER versus SNR curves for the OFDM system in AWGN channel using BPSK/QPSK, 16QAM, 64QAM, 256QAM.

Simulation parameter Value

Channel AWGN

FFT size 1024

Subcarrier # 1024

Modulation BPSK, QPSK, 16QAM, 64QAM, 256QAM

Guard Type Cyclic Prefix

SNR 0 - 30 dB

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

10-5

10-4

10-3

10-2

10-1

100

BER vs.Eb/N0

Eb/N0

BE

R

BPSK/QPSK theorem BPSK/QPSK simulation16QAM theorem 16 QAM simulation 64 QAM simulation 64 QAM theorem 256 QAM simulation 256 QAM theorem

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The Signal Constellation of Different Modulation over AWGN Channel

Signal-space diagram for 16-QAMSignal-space diagram for 8-PSK

sE

2m

3m

4m

5m

6m

7m

8m

Decision boundary

2

message point

sE

sE

d

d

MM 1m

Decision region

1sE

1/6




(a) BPSK, SNR=10, (b) BPSK, SNR=20

-2 -1 0 1 2-2

-1

0

1

2BPSK signal constellation with SNR=10

Real part

Imag

e pa

rt

(a) (b)

-2 -1 0 1 2-2

-1

0

1

2BPSK signal constellation with SNR=20

Real part

Imag

e pa

rt

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(c) QPSK, SNR=10, (d) QPSK, SNR=20; (c) (d)

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(e) 8PSK, SNR=10, (f) 8PSK, SNR=20; (e) (f)

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(g) 16PSK, SNR=10, (h) 16PSK, SNR=20;

(g) (h)

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(i) 16QAM, SNR=10, (j) 16QAM, SNR=20

(i) (j)

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References

[1] Richard van Nee, Ramjee Prasad, OFDM wireless multimedia communication, Artech House Boston London, 2000.

[2] Ahmad R. S. Bahai and Burton R. Saltzberg, Multi-carrier digital communications - Theory and applications of OFDM, Kluwer Academic / Plenum Publishers New York, Boston, Dordrecht, London, Moscow 1999.

[3] L. Hanzo, W. Webb and T. Keller, Single- and multi-carrier quadrature amplitude modulation – Principles and applications for personal communications, WLANs and broadcasting, John Wiley & Sons, Ltd, 2000.

[4] Zou, W.Y.; Yiyan Wu, “ COFDM: An overview ” Broadcasting, IEEE Transactions on, Vol. 41, Issue 1, pp. 1 –8, Mar. 1995.

[5] Simon Haykin, Communication Systems, John Wiley & Sons, Inc., 3rd edition, 1994.

[6] Roger L. Peterson, Rodger E. Ziemer, David E. Borth, Introduction to spread spectrum communications, Prentice Hall International Editions, 1995.

CCU Wireless Access Tech. Lab. OFDM Transmission over Gaussian Channel Gwo-Ruey Lee.

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Transcript of CCU Wireless Access Tech. Lab. OFDM Transmission over Gaussian Channel Gwo-Ruey Lee.