08-08-2014, 02:20 PM
DWT based FFT in Practical OFDM Systems
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Abstract
OFDM is a multi-carrier technique based on a very
simple modulation scheme that uses IFFT and FFT at
its core for transmission and reception respectively.
The performance of the OFDM receiver is significantly
affected in the presence of noise in the wireless
channel. In this work a receiver that has built-in
denoising capacity with little additional computation is
proposed.It is based on a DWT based FFT algorithm.
Experiments using MATLAB are conducted to verify
the feasibility of this denoising algorithm on OFDM
signals. The result shows noise suppression thus
supports our claim.
Introduction
The basic principle of OFDM is to split high rate
data stream into a number of lower rate streams and
transmit them simultaneously over a number of
subcarriers. This way, inter-symbol interference (ISI)
may be mitigated without equalization. The subcarriers
are generated using IFFT [1] and they are used to
modulate BPSK, QPSK or QAM symbols. At the
receiver, the signal is demodulated using FFT.
In a practical OFDM system, not all subcarriers are
mapped with data. One OFDM symbol consists of data
subcarriers, for data transmission, pilot subcarriers, for
various estimation purposes and null subcarriers that
are left empty as guard bands. The purpose of the guard
bands is to enable the signal to naturally decay and
create the FFT “brick Wall” shaping. [2] Figure 1 is an
example of a practical OFDM symbol with QPSK
modulated data.
The FFT and its approximation using DWT
The FFT was introduced in [4] as an efficient
method to compute the DFT. Many variants of the
algorithm are known i.e. Decimation in Time,
Decimation in Frequency, Prime Factor, Split-Radix,
but the basic premise is the same. Computations are
reduced through divide and conquer approach by
introducing a reordering and recombination operation.
The recombination operation is simply multiplication
and addition performed in pairs on all intermediate
samples and is commonly known as butterfly operation.
Equation (1) shows decimation in time FFT in
matrix form, where IN/2 and TN/2 are size N/2 identity
and twiddle factor matrices respectively, which make
up the recombination operation. FN/2 is a size N/2
matrix of complex exponentials to be convolved with
smaller chunks of the input sample, X. SN is the
reordering (bit-reversal) operation.
Wavelet domain denoising
Conventional wavelet domain denoising [6] method
applies thresholding whereby wavelet domain
coefficients are pruned based on certain threshold or
cutoff value. This method is very effective for the
DWT of primarily low pass signals such as voice and
image but not for signals that occupies the entire
bandwidth such as OFDM. Since noise also occupies
the entire bandwidth, it is rather difficult to separate
noise from signal the conventional way.
In our denoising algorithm, we propose a new
strategy that exploits a “feature” in practical OFDM
symbol – the guard bands. Since they are left empty
during transmission, and noise occurs at all bands, we
could always identify the bands that correspond to the
empty guard bands in the wavelet domain and set them
to some constant value. After that, by recombining the
coefficients, we could achieve an overall SNR
improvement through the contribution of our
correction.
Signal denoising analysis
For a 256-point OFDM symbol, 55 coefficients are
set to zero as guard bands during mapping. We perform
IFFT followed by DWT and DFT without butterfly
operation on a clean signal to obtain the graph shown
in figure 3. The ramps in the figure have constant
values regardless of the data and those bands
correspond to the guard bands that were set to zero
previously.
Results and discussion
The objective of the experiment is to achieve some
minimal SNR improvement. The algorithm is simulated
in MATLAB over 1000 random data for every varied
input SNR value. The output SNR is then captured to
obtain the noise figure (ratio of input over output SNR)
Conclusion
A novel FAFT algorithm using wavelet transform is
proposed for implementation in OFDM application.
The algorithm has integrated denoising capability
which has the potential to reduce Gaussian noise from
corrupted OFDM signals, thus significantly improves
the recognition accuracy, reliability and consistency of
OFDM reception with little additional computation.
The MATLAB simulation result showed that there is
marginal SNR improvement in the implementation of
the FAFT, thus the objective is achieved.