OFDM can be seen as either a modulation technique or
a multiplexing technique. One of the main reasons to use OFDM is to increase
the robustness against frequency selective fading and narrowband interference.
It has been accepted for the wireless local area network standards IEEE
802.11a, High Performance LAN type 2 (HIPERLAN/2) and Mobile Multimedia
Access Communication (MMAC) Systems (Zhao et al., 1998). Also,
it is expected to be used for wireless broadband multimedia communications
In OFDM Multipath interference, was handled in a better
way compared to the single carrier modulation systems. The property of
spectral overlapping makes the system very sensitive to the frequency
offset, which is usually introduced by the mismatch of oscillators at
the transmitter and the receiver or the Doppler Effect under the mobile
environments. Once the orthogonality of the subcarriers is lost then the
ICI occurs which might degrade the system performance significantly.
Without performing frequency offset compensation at the
receiver, the conventional ICI self-cancellation schemes (Speth et
al., 1999; Zhao and Haggman, 2001) is used to mitigate ICI, at the
expense of spectral efficiency. Without halving the spectral efficiency
the ICI can be suppressed using the Correlative coding scheme (Zhao et
al., 1998). The performance of the correlative scheme can be increased
by using a higher order correlative polynomial (Zhao, 2000).
The ICI on each subcarrier is a function of the channel
frequency offset (Cimini, 1985).Windowing can be used to reduce the ICI
created as a result of frequency offset (Chin et al., 2006). As
compared to the existing correlative coding scheme, the proposed windowing
technique achieves a better ICI suppression performance. The carrier to
interference ratio is improved and a better BER is achieved in this proposed
scheme compared to the correlative coding.
ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING
In an OFDM system, the whole available bandwidth is divided
into N small parts and a block of N data symbols are modulated on N corresponding
subcarriers which are orthogonal to each other. The spectra of the subcarriers
are overlapping; therefore, accurate frequency recovering is needed (Speth
et al., 1999).
An efficient use of bandwidth can be obtained with a
parallel system if the spectra of the individual subchannels are permitted
to overlap. The spectra of the individual subchannels are zero at the
other subcarrier frequencies The N serial data elements are spaced by
Δt = 1/fs where fs is the symbol rate modulates
N subcarrier frequencies, which are then frequency division multiplexed.
The signaling interval T has been increased to NΔt, which makes the
system less susceptible to delay spread impairments (Seyedi and Saulnier,
M-ary digital modulation schemes using OFDM can achieve
a bandwidth efficiency, defined as bit rate per unit bandwidth, of log2
M bits s-1 Hz-1. The subcarriers are spaced by Δf
= 1/NΔt satisfying the orthogonality constraint. The bandwidth efficiency
in strictly bandlimited spectra β = log2 M bits/s/Hz.
To obtain the highest bandwidth efficiency in an OFDM system, N must be
large (Seyedi and Saulnier, 2005).
Consider the block diagram shown in the Fig.
1 , the serial to parallel converter groups the stream of input bits
into group of log2 M bits, where M is the word size of the
digital modulation employed. An IFFT is used to determine the corresponding
time domain waveform for the modulated data. The multipath delay spread
can be improved by the addition of a guard period between transmitted
The cyclic prefix is a copy of the last n samples from
the IFFT, which are placed at the beginning of the OFDM symbol (Moose,
1994) serves as the guard period. The pilot carriers are included along
with the data sub carriers for synchronization. Thus the base band signal
for the OFDM transmission is obtained.
Additive White Gaussian Noise (AWGN) channel is introduced
between the transmitter and receiver. The receiver does the reverse operation
to the transmitter. The guard period is removed from the received signal.
The FFT of each symbol is then performed to retrieve the original transmitted
spectrum (Cimini, 1985). The demodulation is then performed to retrieve
the transmitted input data bits. The equipment complexity can be greatly
reduced by eliminating any pulse shaping and by using the IFFT to implement
the modulation process. An OFDM signal offers an advantage in a channel
that has a frequency selective fading response. Instead of losing the
whole symbol, only a small subset of the (1/N) bits is lost in OFDM, which
can be recovered with proper coding.
|| OFDM system block diagram
ICI SUPPRESSION TECHNIQUES
There are three different approaches for reducing ICI
have been developed including frequency-domain equalization, time-domain
equalization and the self-cancellation scheme. In the frequency domain
equalization technique, the frequency independent sub channels are multiplied
by a complex number. In time domain equalization technique, the time domain
signals are multiplied by window function. In self cancellation, a symbol
is modulated on two different sub carriers with a 180° phase shift
In this study, correlative coding is used in frequency
domain equalization scheme for ICI compression, without halving the spectral
efficiency. In the proposed scheme, time domain window function is defined
in equivalent to the correlation polynomial used in the frequency domain
equalization technique. Better ICI suppression performance is achieved
in time domain compared to frequency domain scheme.
FREQUENCY DOMAIN EQUALIZATION
Frequency domain correlative coding is a simple solution
to IC1 problems and makes OFDM systems less sensitive to frequency errors,
thus it reduces the system complexity and increasing bandwidth efficiency
(Zhao et al., 1998). The correlative coding between signals modulated
on subsequent subcarriers is used to compress ICI in OFDM system and the
IC1 is measured using subcarrier frequency offset response.
The (1-D) type of correlative coding was chosen and the
subcarrier frequency offset response was introduced in terms of Doppler
shifts in the channel. For better ICI suppression performance, a higher
order correlation polynomial can be used for correlative coding however,
the error propagation will come out in the decoding process and degrade
the BER performance (Zhao, 2000).
The structure of an OFDM system with correlation coding
can be derived from conventional single carrier systems (Fig.
2). By using BPSK modulator, the serial modulated signal, ak
is coded using correlative coding where k is the sub carrier index with
k = 0, 1. . .N-1 and N is the total number of subcarriers. Denoting D
as the unit delay of the subcarrier index k, the proposed coding with
correlation polynomial F(D) = 1-D is performed as:
Then the coded symbol bk, are modulated on
N subcarriers. The symbol bk takes three possible values (-2,
0, 2). Equation 1 introduces the correlation between
the adjacent symbols (bk, bk-1). To avoid the error
propagation in the decoding procedure due to correlative coding, precoding
is performed before the BPSK modulation.
||Simplified block diagram of correlative coding scheme
In OFDM systems, the ICI signal on each subcarrier is
a function of the channel frequency offset and the signal values modulated
on all subcarriers (Cimini, 1985). For the OFDM, the main sources affecting
its BER performances are Additive White Gaussian Noise and Intercarrier
Interference. When the frequency error exists, then without considering
AWGN, the received signal on each subcarrier can be recognized as a sum
of the expected signal and the interference signal.
For an OFDM system with N subcarriers, if the channel
frequency offset normalized to the subcarrier separation is denoted by
ε, then the received signal on subcarrier k can be derived as:
The received signal rk can be expressed as
a sum of the desired signal Ck and the undesired ICI signal
The desired signal value Ck depends only on the signal
transmitted on subcarrier k, while Ik depends on the signals
transmitted on all the other subcarriers. The Carrier to Interference
Ratio (CIR) of an OFDM system with (1-D) type correlative coding can be
obtained from the following equation:
To analyze ICI level with respect to the frequency error,
it is necessary to have a corresponding basic ICI function with respect
to the system frequency error. At the transmission side of OFDM systems,
signals ak when k = 0, ... N-1 are modulated onto N subcarriers.
It can be done by performing Inverse Fast Fourier Transform to the signal
If the frequency error is sufficiently large, it is possible
that Ik>Ck occurs. In such a case, a data decision
error can be made even in the absence of AWGN. The BER of an OFDM systems
increases rapidly when frequency error increases. The condition ε<0.05
is necessary to maintain acceptable system performance.
In Time domain equalization technique, a window function
is applied to the data in time domain obtained after performing IFFT operation.
For the correlative polynomial (1-D) used in the section 4, the window
function proposed to use for ICI suppression is (1-exp (j2πn/N))
(Chin et al., 2006). Time domain equalization technique offers
a better performance compared to the frequency.
The application of the windowing function tapers the
start and ends of waveform reducing the transients and consequently the
spectral spreading. The application can be divided into two groups.
In the first group, windowing is used to reduce the sensitivity
to linear distortions. In the second group, windowing is used to reduce
the sensitivity to frequency errors. In this study, the second approach
is performed. In this case, the window function improves the spectral
efficiency and reduces the BER of the OFDM system.
According to the circular convolution property, we can
realize the frequency domain circular convolution process by taking an
equivalent time-domain windowing operation. For the correlative polynomial
used in frequency domain scheme, the window function is proposed in this
paper to improve the performance of the OFDM system. For the correlative
polynomial (1-D) used in section 4, the window function proposed in this
study is expressed as (1-exp (j2πn/N)).
If ICI can be suppressed well by applying the proposed
window function, then the remaining task that will affect the BER performance
would be decided by the demodulation technique. In the proposed method
the decoding process does not need prior information of the transmitted
data. For convenience, the proposed window
||The equivalent realization form of the proposed correlative
coding scheme in time domain
function is applied at the transmitter. The subcarrier
spectrum can be observed for the various order of the windowing function.
The Fig. 3 shows that the proposed
correlative coding scheme can be realized in the time domain by using
a window function. When the time domain window function (1-exp (j2πn/N))
is applied, the data samples transmitted on the kth subcarrier
can be expressed as:
bk = ak (1-exp(j2πn/N))
The window function used is optimized to obtain a maximized
Carrier to Interference Ratio (CIR). So, the order of the window function
is optimized to be 1, assuming the modulation system to be BPSK.
The theoretical CIR for the order 1 of the window function
is given by:
The correlative pairs would in average contribute to
the smallest ICI only when the weighting magnitudes of
|| OFDM simulation parameters
|| BER performance analysis for Eb/No = 3 dB
the elements of each pair are equal or symmetric, this
also agrees with the observation that the distributions of ICI coefficients
are circularly symmetric.
When a higher-order correlative polynomial is selected,
better ICI suppression performance can be obtained (Zhao, 2000) in equivalent
to that if the order of the window function is varied in the proposed
window function a stronger main lobe and smaller side lobes in each subcarrier
spectrum can be achieved.
In this section, the MATLAB simulations results are provided
to evaluate the performance of the proposed ICI suppression scheme. The
CIR performance of the proposed scheme is independent of the modulation
used, so BPSK modulation is used for convenience. The simulation is performed
for various values of ε, in the simulated results performance is
shown for the values ε = 0.15, 0.16, 0.17. Other simulation parameters
used are shown in Table 1. The same parameters can be
used for other modulation techniques such as QPSK, 16 QAM, 64 QAM.
The simulated results for BER performance are shown in
Fig. 4-6 and Table 2
for the proposed time domain windowing technique and the correlative coding.
In Fig. 4 BER performance curve for the time domain
scheme and correlative coding method shows that the BER is reduced considerably
compared to the correlative coding scheme. Comparison of the BER performance
in the Fig. 4-6 implies that with
the increase in the frequency offset value the BER increases and the time
domain windowing technique offers a better performance compared to the
correlative coding method.
Figure 7 shows the CIR versus normalized
frequency offset for the correlative coding and proposed scheme.
||BER performance of time domain windowing and correlative
coding scheme for ε = 0.15
||BER performance of time domain windowing and correlative
coding scheme ε = 0.16
||BER performance of time domain windowing and correlative
coding scheme ε = 0.17
||CIR performance of time domain windowing and correlative
|| CIR performance analysis
From the simulated curves, it can be observed that, when
the normalized frequency offset is zero the time domain equalization technique
behaves same as the standard OFDM without any equalization technique.
The effect of the time domain windowing can be explicitly seen from the
Table 3, when the frequency offset value increases above
0.1. Thus the proposed scheme outperforms the correlative coding scheme,
due to its better capabilities in suppressing ICI and preventing error
propagation through OFDM symbols.
This proposed ICI suppression scheme using time-domain
windowing for OFDM systems, provides a better BER performance compared
to the correlative coding. The window function used also avoids the propagation
of errors in the demodulation performed. From the Fig. 7
it is inferred that there is a 3dB improvement in CIR in the proposed
scheme compared to the existing correlative coding scheme. Further work
can be done to improve the BER performance by applying the Maximum Likelihood
Sequence Detection (MLSD) and by increasing the order of the window function
the CIR can be improved.