OFDM Transmission over Gaussian Channel

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OFDM Transmission over Gaussian Channel

• Gwo-Ruey Lee

2
Outlines

• OFDM Transmission over Gaussian Channel
• Gaussian Distribution
• The AWGN Channel Model
• OFDM System Performance over AWGN Channel
• The Signal Constellations of Different Modulation
  over AWGN Channel

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Gaussian Distribution
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• The PDF of a Gaussian or normally distributed
  random variable is

The PDF of a Gaussian-distributed random variable
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Gaussian Distribution
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• The CDF of a Gaussian or normally distributed
  random variable is
• where

The CDF of a Gaussian-distributed random variable
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The AWGN Channel Model
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• The received signal in the interval
  may be expressed as
• where denotes the sample function
  of the additive white Gaussian noise (AWGN)
  process.

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The AWGN Channel Model
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• 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
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OFDM System Performance over AWGN Channel
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Serial-to-Parallel Converter
Random Data Generator
Parallel-to-Serial Converter
Guard Interval Insertion
Signal Mapper
S(t)
IFFT
OFDM Transmitter
AWGN
Channel Model
Serial Data Output
Guard Interval Removal
Parallel-to-Serial Converter
Serial-to-Parallel Converter
Signal Dema-pper
FFT
OFDM Receiver
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OFDM System Performance over AWGN Channel
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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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OFDM System Performance over AWGN Channel
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• BER versus SNR curves for the OFDM system in AWGN
  channel using BPSK, QPSK, 8PSK,16-PSK .

Simulation parameter Value
Channel AWGN
FFT size 1024
Subcarrier 1024
Modulation BPSK, QPSK, 8PSK, 16PSK
Guard Type Cyclic Prefix
SNR 0 - 30 dB
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OFDM System Performance over AWGN Channel
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• PSK
• BPSK
• QPSK with Gray code
• M-ary PSK
• where

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OFDM System Performance over AWGN Channel
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• 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
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OFDM System Performance over AWGN Channel
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• QAM

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The Signal Constellation of Different Modulation
over AWGN Channel
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Signal-space diagram for 16-QAM
Signal-space diagram for 8-PSK
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The Signal Constellation of Different Modulation
over AWGN Channel
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• (a) BPSK, SNR10, (b) BPSK, SNR20

(a)
(b)
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The Signal Constellation of Different Modulation
over AWGN Channel
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• (c) QPSK, SNR10, (d) QPSK, SNR20

(c)
(d)
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The Signal Constellation of Different Modulation
over AWGN Channel
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• (e) 8PSK, SNR10, (f) 8PSK, SNR20

(e)
(f)
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The Signal Constellation of Different Modulation
over AWGN Channel
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• (g) 16PSK, SNR10, (h) 16PSK, SNR20

(g)
(h)
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The Signal Constellation of Different Modulation
over AWGN Channel
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• (i) 16QAM, SNR10, (j) 16QAM, SNR20

(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
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  Editions, 1995.