ccu wireless access tech. lab. ofdm transmission over gaussian channel gwo-ruey lee
TRANSCRIPT
CCU Wireless Access Tech. Lab.
OFDM Transmission over Gaussian Channel
Gwo-Ruey Lee
Wireless Access Tech. Lab.
CCU 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
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
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
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
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
2/2
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
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
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
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
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
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
1/6
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
OFDM System Performance over AWGN Channel
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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Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
OFDM System Performance over AWGN Channel
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
3/6
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
OFDM System Performance over AWGN Channel
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
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
OFDM System Performance over AWGN Channel
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
5/6
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
OFDM System Performance over AWGN Channel
QAM
3
2 1sE
aM
2
2
0
2| 1
ap c Q
N
2 2
0 0
2 2| 1 2 1
a ap c Q Q
N N
2
2
0
2| 1 2
ap c Q
N
6/6
2
,2
1 11 4 | 4 2 | 2 |
loge M QAMp p c M p c M p cM M
3aa- a- 3a
a
3a
- a
- 3a
na
nb
: I part
: II part
: III part
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
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
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
The Signal Constellation of Different Modulation over AWGN Channel
(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
2/6
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
The Signal Constellation of Different Modulation over AWGN Channel
(c) QPSK, SNR=10, (d) QPSK, SNR=20; (c) (d)
3/6
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
The Signal Constellation of Different Modulation over AWGN Channel
(e) 8PSK, SNR=10, (f) 8PSK, SNR=20; (e) (f)
4/6
Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
The Signal Constellation of Different Modulation over AWGN Channel
(g) 16PSK, SNR=10, (h) 16PSK, SNR=20;
(g) (h)
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Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
The Signal Constellation of Different Modulation over AWGN Channel
(i) 16QAM, SNR=10, (j) 16QAM, SNR=20
(i) (j)
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Wireless Access Tech. Lab.
CCU Wireless Access Tech. Lab.
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.