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**OFDM Transmission over Gaussian Channel**

Gwo-Ruey Lee

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**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**

1/2 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**

2/2 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 2/2**

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 2/2**

The channel is assumed to corrupt the signal by the addition of white Gaussian noise as shown below + AWGN Received Signal Transmitted Signal Channel Transmission model for received signal passed through an AWGN channel

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**OFDM System Performance over AWGN Channel**

1/6 Random Data Generator Serial-to-Parallel Converter Signal Mapper Parallel-to-Serial Converter Guard Interval Insertion S(t) IFFT OFDM Transmitter AWGN Channel Model Serial Data Output Guard Interval Removal Serial-to-Parallel Converter Signal Dema-pper Parallel-to-Serial Converter FFT OFDM Receiver

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**OFDM System Performance over AWGN Channel**

2/6 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**

3/6 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 # Modulation BPSK, QPSK, 8PSK, 16PSK Guard Type Cyclic Prefix SNR dB

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**OFDM System Performance over AWGN Channel**

4/6 PSK BPSK QPSK with Gray code M-ary PSK where

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**OFDM System Performance over AWGN Channel**

5/6 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 # Modulation BPSK, QPSK, 16QAM, 64QAM, 256QAM Guard Type Cyclic Prefix SNR dB

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**OFDM System Performance over AWGN Channel**

6/6 QAM

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**The Signal Constellation of Different Modulation over AWGN Channel**

1/6 Signal-space diagram for 8-PSK Signal-space diagram for 16-QAM

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**The Signal Constellation of Different Modulation over AWGN Channel**

2/6 (a) BPSK, SNR=10, (b) BPSK, SNR=20 (a) (b)

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**The Signal Constellation of Different Modulation over AWGN Channel**

3/6 (c) QPSK, SNR=10, (d) QPSK, SNR=20; (c) (d)

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**The Signal Constellation of Different Modulation over AWGN Channel**

4/6 (e) 8PSK, SNR=10, (f) 8PSK, SNR=20; (e) (f)

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**The Signal Constellation of Different Modulation over AWGN Channel**

5/6 (g) 16PSK, SNR=10, (h) 16PSK, SNR=20; (g) (h)

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**The Signal Constellation of Different Modulation over AWGN Channel**

6/6 (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 [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.

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