seminar code
08-08-2014, 10:40 AM
WAVELET OFDM
[attachment=66729]
INTRODUCTION
As the need for high speed communication grows, we turn to broadband communication.
Normally for a channel with small width, the frequency response is fairly flat throughout
the channel. Also, the noise in the channel is AWGN (Additive White Gaussian Noise).
As the channel width grows, it is difficult to model the channel. Therefore we split the
channel into smaller sub-channels.
Data transmission over a difficult channel is transformed through the use of advanced
signal processing techniques into the parallel transmission of the given data stream over a
large number of sub-channels such that each sub-channel may be viewed effectively as an
AWGN channel. Orthogonal Frequency division multiplexing offers an effective way to
handle high data rate. The OFDM requires a cyclic prefix to remove ISI. This causes
overhead and this overhead may be sometimes much large for the system to be effective.
In OWPDM the modulation and demodulation are implemented by wavelets rather than
OFDM
Most of the modulation technique uses the advantage of flat channel. But with larger
channel width, this assumption is not valid. OFDM uses the policy of divide and rule. It
breaks down the problem of transmission over a large difficult channel into transmission
over smaller flat sub channels. The total incoming bit stream is divided over a large
number of sub channels. These bits are then modulated on each sub channel using
modulation technique like PSK, QAM etc. The sum of these composite sub carriers is
then sent over the channel. If the sub carriers are orthogonal then the different spectra
may overlap giving a larger spectral efficiency. In OFDM the transformation is
performed in discrete time as well as discrete frequency. The generation of the sub
carriers is done by using the Fourier transform. Let the number of sub carrier be Nc and m
be the number of bits that form a symbol for a sub carrier then OFDM input can be
considered as a block of Nc x m bits. The channel has a finite impulse response h(t)
confined to finite interval [0,Tb]. Let the sequence h1 h2 h3… hv denote the base band
equivalent impulse response of the channel sampled at rate 1/ TS, where Tb = (1+ v)TS.
The sampling rate is chosen to be greater than twice the higher frequency component of
interest.
Wavelet Transform and Wavelet PACKET Transform
The wavelet transform is usually represented as MRA. The wavelet transform
decomposes the signal using a set of basis function into different resolution subspaces
…..V-2< V-1 < V0 < V1 <……
The decomposition is done using a basis function and a wavelet function and there
translation and dilation. The dilated and translated scaling function forms the basis of the
various subspaces. i.e. { ø (t)} forms a basis for V0 . The wavelet functions forms a
subspace orthogonal to the basis formed by the scaling function. The scaling and the
wavelet function both satisfy some dilation equation
Wavelet-OFDM or OPDWM
The OFDM implemented by using IFFT’s and FFT’s have some problems. The OFDM
suffers from
• ISI (intersymbol interference) –This is usually taken care of by using a adding a
cyclic prefix greater than the channel length but this may not always be possible.
This occurs due to loss of orthogonality due to channel effects. • Time and Frequency Synchronization- The OFDM requires time and frequency
synchronization to get a low bit error rate.
• Carrier Frequency Offset- The offset between the carrier frequency and the
frequency of the local oscillator also causes a large bit error rate.
Due to these problems we need to look at other type of modulation to generate the carrier.
One of these is the wavelet transform. The wavelet transform is proposed by many
authors, it has a higher degree of side lobe suppression and the loss of orthogonality leads
to lesser ISI and ICI. In Wavelet OFDM the FFT and IFFT is replace by DWT and IDWT
respectively. For the Wavelet transform we see that from the time-frequency plot that the
basic Wavelet transform offers lesser flexibility than the wavelet packet transform. For
the wavelet packet transform we can construct an algorithm to do the decomposition such
that the effect due to the noise (assuming that we know the frequency that is affected
most by the noise and the time when it affected most).
Channel Model
For an AWGN channel the parameters used are 4 subcarriers, BPSK
modulation and bi-orthogonal wavelets. In [4] it is shown that some of the
wavelets perform worse than the single carrier case while ideally it should
perform the same. This can be explained as follows: the basis function for
a biorthogonal wavelet are not orthogonal to each other. This causes the
AWGN to become correlated within a subcarrier and thus an AWGN
channel doesn’t remain an AWGN channel. Thus the non-orthogonality
has now become a problem, but some wavelets are still useful.
For the Haar wavelet case [5] the performance of a DWT-OFDM is much
better than the DFT-OFDM.case when no timing, frequency
synchronization is done.
Conclusion
We see that DWT-OFDM performs much better than the DFT-OFDM over AWGN and
Rayleigh channel with low SNR. Also we find that use of Wavelet’s reduces the
overhead thus giving a larger bandwidth. The wavelet packet is much better than the
implementing just the wavelet transform as it is more flexible. The bi-orthogonal
wavelets though may provide some advantage and better flexibility doesn’t perform well
for some wavelets considered to the theoretical case.
[attachment=66729]
INTRODUCTION
As the need for high speed communication grows, we turn to broadband communication.
Normally for a channel with small width, the frequency response is fairly flat throughout
the channel. Also, the noise in the channel is AWGN (Additive White Gaussian Noise).
As the channel width grows, it is difficult to model the channel. Therefore we split the
channel into smaller sub-channels.
Data transmission over a difficult channel is transformed through the use of advanced
signal processing techniques into the parallel transmission of the given data stream over a
large number of sub-channels such that each sub-channel may be viewed effectively as an
AWGN channel. Orthogonal Frequency division multiplexing offers an effective way to
handle high data rate. The OFDM requires a cyclic prefix to remove ISI. This causes
overhead and this overhead may be sometimes much large for the system to be effective.
In OWPDM the modulation and demodulation are implemented by wavelets rather than
OFDM
Most of the modulation technique uses the advantage of flat channel. But with larger
channel width, this assumption is not valid. OFDM uses the policy of divide and rule. It
breaks down the problem of transmission over a large difficult channel into transmission
over smaller flat sub channels. The total incoming bit stream is divided over a large
number of sub channels. These bits are then modulated on each sub channel using
modulation technique like PSK, QAM etc. The sum of these composite sub carriers is
then sent over the channel. If the sub carriers are orthogonal then the different spectra
may overlap giving a larger spectral efficiency. In OFDM the transformation is
performed in discrete time as well as discrete frequency. The generation of the sub
carriers is done by using the Fourier transform. Let the number of sub carrier be Nc and m
be the number of bits that form a symbol for a sub carrier then OFDM input can be
considered as a block of Nc x m bits. The channel has a finite impulse response h(t)
confined to finite interval [0,Tb]. Let the sequence h1 h2 h3… hv denote the base band
equivalent impulse response of the channel sampled at rate 1/ TS, where Tb = (1+ v)TS.
The sampling rate is chosen to be greater than twice the higher frequency component of
interest.
Wavelet Transform and Wavelet PACKET Transform
The wavelet transform is usually represented as MRA. The wavelet transform
decomposes the signal using a set of basis function into different resolution subspaces
…..V-2< V-1 < V0 < V1 <……
The decomposition is done using a basis function and a wavelet function and there
translation and dilation. The dilated and translated scaling function forms the basis of the
various subspaces. i.e. { ø (t)} forms a basis for V0 . The wavelet functions forms a
subspace orthogonal to the basis formed by the scaling function. The scaling and the
wavelet function both satisfy some dilation equation
Wavelet-OFDM or OPDWM
The OFDM implemented by using IFFT’s and FFT’s have some problems. The OFDM
suffers from
• ISI (intersymbol interference) –This is usually taken care of by using a adding a
cyclic prefix greater than the channel length but this may not always be possible.
This occurs due to loss of orthogonality due to channel effects. • Time and Frequency Synchronization- The OFDM requires time and frequency
synchronization to get a low bit error rate.
• Carrier Frequency Offset- The offset between the carrier frequency and the
frequency of the local oscillator also causes a large bit error rate.
Due to these problems we need to look at other type of modulation to generate the carrier.
One of these is the wavelet transform. The wavelet transform is proposed by many
authors, it has a higher degree of side lobe suppression and the loss of orthogonality leads
to lesser ISI and ICI. In Wavelet OFDM the FFT and IFFT is replace by DWT and IDWT
respectively. For the Wavelet transform we see that from the time-frequency plot that the
basic Wavelet transform offers lesser flexibility than the wavelet packet transform. For
the wavelet packet transform we can construct an algorithm to do the decomposition such
that the effect due to the noise (assuming that we know the frequency that is affected
most by the noise and the time when it affected most).
Channel Model
For an AWGN channel the parameters used are 4 subcarriers, BPSK
modulation and bi-orthogonal wavelets. In [4] it is shown that some of the
wavelets perform worse than the single carrier case while ideally it should
perform the same. This can be explained as follows: the basis function for
a biorthogonal wavelet are not orthogonal to each other. This causes the
AWGN to become correlated within a subcarrier and thus an AWGN
channel doesn’t remain an AWGN channel. Thus the non-orthogonality
has now become a problem, but some wavelets are still useful.
For the Haar wavelet case [5] the performance of a DWT-OFDM is much
better than the DFT-OFDM.case when no timing, frequency
synchronization is done.
Conclusion
We see that DWT-OFDM performs much better than the DFT-OFDM over AWGN and
Rayleigh channel with low SNR. Also we find that use of Wavelet’s reduces the
overhead thus giving a larger bandwidth. The wavelet packet is much better than the
implementing just the wavelet transform as it is more flexible. The bi-orthogonal
wavelets though may provide some advantage and better flexibility doesn’t perform well
for some wavelets considered to the theoretical case.