Wavelet Modulation Performance in Gaussian And Rayleigh Fading Channels Manish J' Manglani And Amy E

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Wavelet Modulation Performance in Gaussian And
Rayleigh Fading ChannelsManish J. Manglani And
Amy E.BellElectrical and Computer Engineering
DapartmentVirginia TechBlacksburg, Virginia

• Chin-Wei Chuang
• 2006-07-13

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Outline

• Introduction
• DWT and Wavelet Modulation
• Methodology
• Results
• Conclusion

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Introduction

• Wavelet Modulation has a novel multirate
  diversity strategy if the message is not
  received at one rate due to channel disturbances,
  it can be received at another rate where the
  channel is clear
• This paper examine the performance of wavelet
  modulation (WM) in time varying channels.

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Introduction

• Results for Rayleigh flat fading channels and
  frequency selective channels are compared to the
  AWGN channel and to the expected performance of
  BPSK in a flat fading channel.
• The results shed light on the suitability of
  wavelet modulation as a technique for signal
  transmission in a mobile environment.

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DWT and Wavelet Modulation

• The discrete wavelet transform (DWT) of a signal
  s(t) is given by

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DWT and Wavelet Modulation

• Mallats fast wavelet transform (FWT)
• It provides computationally efficient,
  practical, discrete time algorithm for computing
  the DWT.
• The scaling and wavelet coefficients at scale m
  can be computed from the scaling coefficient at
  the next finer scale m1 using
• where hn and gn are the lowpass and
  highpass filter in the
• associated 2-channel analysis filter bank.
• Equation(3)(4) represent the FWT for
  computing the DWT

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DWT and Wavelet Modulation

• Conversely, the scaling coefficient can be
  reconstructed by
• Equation(5) represents the IFWT for computing
  the IDWT.
• It corresponds to the 2-channel synthesis
  filter bank.

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DWT and Wavelet Modulation

• The wavelet modulated signal to be transmitted,
  s(t), can be generated via
• where xn is the data that is modulated
  onto the
• wavelet at different scales
• In a practical system xn is modulated onto a
  finite number of contiguous, octave-width
  frequency bands.

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Methodology

• The data to be transmitted takes on one of two
  equally likely values

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Methodology
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Channel models

• Gaussian channel
• Small Scale Fading Channel
• Flat Fading Channel
• Frequency selective Fading Channel

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Gaussian channel

• In the AWGN channel, zero-mean white Gaussian
  noise is added to transmitted signal s(t).
• The received signal r(t) can be represented as
  
• where n(t) is a zero-mean white Gaussian
  noise process with power No/2

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Small Scale Fading Channels

• Small scale fading is comprised of two
  independent mechanism
• the time spreading of the signal and the time
  varying behavior of the channel.
• A doppler shift causes the time varying behavior
  of the channel. In the MW experiments, there are
  two doppler shift are employed.
• military communication frequency(900MHz)?sp
  eed(45mph)?doppler shift(60Hz)
• cellular communication frequency(1800MHz))?
  speed(45mph)?doppler shift(120Hz)

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Flat Fading Channel

• The time dispersion in a multipath environment
  causes the signal to undergo either flat or
  frequency selective fading.
• If the channel has a constant gain and linear
  phase response over a bandwidth that is greater
  then the bandwidth of the transmitted signal,
  then the received signal undergoes flat fading.
• Small scale fading can be modeled as a Rayleigh
  distribution. The received signal is given by

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Frequency Selective Fading Channel

• Frequency Selective Fading is caused by multipath
  delays which approach or exceed the symbol period
  of the transmitted symbol.
• In practice, it will result in a frequency
  selective channel ? the channel introduces
  intersymbol interference (ISI) if
• For the frequency selective fading channel, the
  received signal is given by

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Frequency Selective Fading Channel

• The signal energy in the first term and the power
  of the noise term n(t) determine the SNR of the
  signal.
• The sum of
  is set to unity, so that the channel has an
  average gain of unity.

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Results

• Comparison of N4 and N8 Wavelets
• Performance in a Gaussian Channel
• Performance in Flat Fading Channels
• Frequency Selective Fading Channels
• Channel Performance Comparison

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Comparison of N4 N8 Wavelet

• Fig.1 compares the performance of the Daubechies
  N4 and N8 wavelets in a flat fading channel
  with a doppler spread of 60Hz

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Performance in Gaussian Channel

• Fig.2 compares the performance of wavelet
  modulation with that of theoretical BPSK
  modulation in an AWGN channel.

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Performance in Flat Fading Channels

• Fig.3 depicts a linear BER curve inversely
  proportional to SNR.

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Performance in Flat Fading Channels

• Fig.4 illustrates similar performance of WM at
  scale 13 with the theoretical performance of BPSK
  in a flat fading channel.

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Frequency Selective Fading Channels

• Fig.5 confirm the result that a difference in BER
  performance across scales was expected due to the
  frequency selective nature of the channel.

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Channel Performance Comparison

• Fig.6 compares the BER curve for 3 channel types
  at scales 10 and 13 and fd60Hz.

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Conclusion

• WM offers the unique advantage that if the
  root-mean-square delay spread is known, then the
  signal could be transmitted and demodulated at
  scales for which the ISI is negligible.
• WM performance in an AWGN channel is best at all
  SNRs and the performance in a flat fading channel
  is better than frequency selective channel.