Background of OFDM and WLANs

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Background of OFDM and WLANs

• Wei-Hsuan Chang

Aug. 9, 2005
Wei-Hsuan Chang
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Outline

• What is OFDM
• Stochastic Processes and Random Variables
• Discrete-Time Signal Processing
• Discrete Fourier Transform

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What is OFDM(1/5)

• Orthogonal Frequency Division Multiplexing
• Avoid frequency selective fading
• Bandwidth efficiency
• Using cyclic prefix (CP) to eliminate ISI
• To simplify the equalizer
• Easy to implement by FFT/IFFT

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What is OFDM(2/5)

• Subcarriers of OFDM

Freq(HZ)
Freq(HZ)
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What is OFDM(3/5)

• OFDM modulation system

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What is OFDM(4/5)

• OFDM demodulation system

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What is OFDM(5/5)

• Digital implement of OFDM system
• Transmitter IFFT D/A conversion
• Receiver A/D conversion FFT
• Sensitive to frequency synchronization
• Mathematical backgrounds
• Stochastic and random process
• Discrete-time signals
• Discrete Fourier Transform(DFT)

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Stochastic Processes and Random Variables(1/5)

• Distribution function (c.d.f)
• Probability density function (p.d.f)
• Ensemble averages (mean)

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Stochastic Processes and Random Variables(2/5)

• Variance
• Mean square value

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Stochastic Processes and Random Variables(3/5)

• Correlation of two random variables
• Covariance of two random variables
• Autocorrelation and autocovariance

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Stochastic Processes and Random Variables(4/5)

• Statistically independent
• Uncorrelated

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Stochastic Processes and Random Variables(5/5)

• WSS (Wide-sense stationary)
• Properties of WSS

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Discrete-Time Signal Processing(1/2)

• Delta function and unit step function
• Discrete-time system
• LSI (linear shift-invariant)
• Causal
• Stable ?BIBO (bounded input bounded output)

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Discrete-Time Signal Processing(2/2)

• FIR
• Finite length impulse response
• The output only depends on the input
• IIR
• Infinite length impulse response

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Filtering Random Process

• System

x(t)
y(t)
h(t)
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Discrete Fourier Transform

• Discrete-time Fourier transform
• Discrete Fourier transform
• Sample version of DTFT (N points)
• Fast Fourier transform