Document 6589629

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Document 6589629

International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163
Volume 1 Issue 9 (October 2014)
www.ijirae.com
Effect of Cyclic Prefix on OFDM over AWGN Channel
WASIU LAWAL*
ADEWUYI,S.O
OGUNTI,E.O
Electrical/Electronic Department
Rufus Giwa polytechnic owo
Federal University of Technology,Akure Federal University of Technology,Akure
Abstract OFDM has come to stay in communication system design due to its ability to mitigate frequency selective
fading in a multipath channel. Intersymbol interference is a major constraint to transmitted bits after conversion of
data to be transmitted from frequency domain to time domain before transmission through the multipath fading
channel. To overcome this, a cyclic prefix is inserted in between the OFDM symbols to prevent(intersymbol
interference) ISI, making the Symbol period longer. In this paper, the effect of cyclic prefix in an OFDM system over
idea channel AWGN is presented.
Keywords— OFDM, AWGN, Cyclic prefix Intersymbol interference, Fading Channel.
I. INTRODUCTION
A receiver is said to be optimum if it yields the minimum probability of error, Pe. One of the primary performancelimiting factors inherent in wireless channels is multipath fading, which is resulted from the reflection, diffraction or
refraction of the transmitted waveforms through different propagation paths. The superimposed multipath radio waves
could add up either constructively or destructively at the receiver owing to their phase differences, and this will result in
power fluctuation and phase distortion of the received signals, or, multipath fading. Several multicarrier techniques have
been proposed to overcome the fading of which OFDM is found to be the most suitable. OFDM is a modulation
technique especially suitable for wireless communication due to its resistance to intersymbol interference (ISI). Although
the idea of OFDM started back in 1966, it has never been widely utilized until the last decade when it “becomes the
modem of choice in wireless applications” [1].
A. OFDM
An In a single carrier communication system, the symbol period must be much greater than the delay time in order to
avoid intersymbol interference (ISI) [2]. Since data rate is inversely proportional to symbol period, having long symbol
periods means low data rate and communication inefficiency. A multicarrier system, such as FDM (Frequency Division
Multiplexing), divides the total available bandwidth in the spectrum into sub-bands for multiple carriers to transmit in
parallel. An overall high data rate can be achieved by placing carriers closely in the spectrum. However, intercarrier
interference (ICI) will occur due to lack of spacing to separate the carriers. To avoid inter-carrier interference, guard
bands will need to be placed in between any adjacent carriers, which results in lowered data rate. OFDM (Orthogonal
Frequency Division Multiplexing) is a multicarrier digital communication scheme to solve both issues. It combines a
large number of low data rate carriers to construct a composite high data rate communication system. Orthogonality gives
the carriers a valid reason to be closely spaced, even overlapped, without inter-carrier interference. Low data rate of each
carrier implies long symbol periods, which greatly diminishes intersymbol interference [3].
The concept of OFDM in term of parallel transmission was first developed in the 50s and introduced in some papers in
the mid 60s. OFDM signalling was developed back in the [4]and used in some military HF communication systems
[5].It was also considered for use in high-speed modems [6], but did not significantly develop in this field, and
international CCITT standards for high-speed modems are based on single-carrier transmission. It was later proposed for
digital mobile radio systems [7] to alleviate the channel equalization problem, increase robustness against impulse noise,
and possibly make a better use of the available channel bandwidth.
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 or narrowband interference. In a single carrier
system, a single fade or interfere can cause the entire link to fail, but in a multicarrier system, only a small percentage of
the subcarriers will be affected. Error correction coding can then be used to correct for the few erroneous subcarriers. In
digital Communication, modulation can be defined as mapping of the information on changes in the carrier phase,
frequency or amplitude, or combination. Multiplexing is a method of sharing a bandwidth with other independent data
channel. OFDM is a special case of FDM, which combines modulation and multiplexing. Multiplexing generally refers
to independent signals produced by different sources. Hence, in OFDM, the question of multiplexing is applied to
independent signals but these independent signals are a subset of the one main signal. In OFDM, the signal itself is first
split into independent channels, modulated by data and then re-multiplexed to create the OFDM carrier.
B. THE PRINCIPLE OF OFDM TRANSMISSION
Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier transmission technique, which divides the
bandwidth into many carriers; each one is modulated by a low rate data stream. In term of multiple access technique,
OFDM is similar to FDMA in that the multiple user access is achieved by subdividing the available bandwidth into
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multiple channels that are then allocated to users. However, OFDM uses the spectrum much more efficiently by
spacing the channels much closer together. This is achieved by making all the carriers orthogonal to one
another, preventing interference between the closely spaced carriers. Pictorially it can be represented as shown in
the figure 1 .[8]
Fig 1: Concept of OFDM Signal: Orthogonal Multicarrier Technique versus Conventional Multicarrier Technique
The figure shows the difference between the conventional non-overlapping multicarrier technique and
overlapping multicarrier modulation technique. Using the overlapping multicarrier modulation technique, we save
almost 50% of bandwidth. To realize the overlapping multicarrier technique, however we need to reduce crosstalk
between subcarriers, which means that we want orthogonality between the different modulated carriers.
C. Intersymbol and Intercarrier Interference.
In a multipath environment, a transmitted symbol takes different times to reach the receiver through different propagation
paths. From the receiver’s point of view, the channel introduces time dispersion in which the duration of the received
symbol is stretched. Extending the symbol duration causes the current received symbol to overlap previous received
symbols and results in intersymbol interference (ISI) [9]. In OFDM, ISI usually refers as interference of an OFDM
symbol by previous OFDM symbols.
D. Multipath Effects.
In mobile communications, the signal is degraded by terrestrial multipath fading in the lower atmosphere known
as troposphere..[10] This troposphere is between altitude of 0 and 70 km and consists of many objects such as buildings,
mountains, trees, moving cars, sign posts at the ground surface and natural phenomena like temperature, humidity,
rainfall, etc at above the ground surface. These artificial and natural phenomena obstruct the transmitted signal, hindered
the signal to reflect, refract, diffract and scatter, and move in different paths called multipath propagation causing the
received signal to be degraded. The different paths add up constructively when the received signal paths are in phase and
destructively under unfavourable phase conditions. The effects of terrestrial multipath propagation are signal fading,
delay spread which is very dominant in urban environment leading to intersymbol interference (ISI) distortion, and lastly
the doppler spread which occurs when there is relative motion in terrestrial environment. Therefore, these result in signal
fluctuation at the receiver.[11] In wireless channel, the medium is the free space. In this case, there is no specified or
particular path for signal transmission. The transmitted signal may get reflected from many things like hills, trees, etc
before being received at the destined receiver. This can give rise to multiple transmission paths up to the receiver. The
relative phase of the multiple reflected signals causes destructive or constructive interference at the receiver. This is
normally experienced for very short distances (typically at half of the wavelength distances), thus is given the term - fast
fading. These variations can vary from10 to 30dB [12]. over short distances.
E. Fading Statistics in Radio Channel
In communications systems, fading occurs due to the multipath propagation. As a result, signals reaching the
receiver from several different paths that may have different lengths corresponding to different time delays and gains.
Time delay causes additional phase shifts to the main signal component. Therefore, the signal reaching the receiver is the
sum of some copies of the original signal with different delays and gains. With this explanation, the channel impulse
response can be modelled as described in [13] with the equation given below:
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Where:
Complex path gain
Number of paths
Path delay
Fading can be classified into two different scales:
Small Scale fading: small-scale fading happens in very short time duration, is caused by reflectors, and scatters that
change the amplitude, phase and angle of the arriving signal. Rayleigh distribution and Rician distribution are often used
to define small scale fading.
Large Scale fading: Large-scale fading is due to shadowing and the mobile station should move over a large distance to
overcome the effects of shadowing. Log-normal distribution is often used to define large-scale fading.
Fast Fading
In a fast fading channel, the rate of change of the channel is higher than the signal symbol period and hence the channel
changes over one period. In other words, the channel coherence time , is smaller than the symbol period .
is
related to the Doppler spread, , as:
=0.423/
2
From this relation it is clear that a high Doppler spread results in a smaller channel
coherence time. The coherence time of 0.423ms corresponding to a
of 1 kHz is clear.
Slow Fading
As the name suggests, in a slow fading channel, the channel coherence time is larger than the symbol period and
hence the channel remains approximately static over a symbol or multiple symbols. From the above equation it is clear
that slow fading is usually expected with low Doppler spread values; i.e. with slower moving obstacles and
receiver/transmitter. Multipath delay spread based and Doppler spread based fades are completely independent of each
other and hence is quite possible to have a flat, fast fading channel or a flat, slow fading channel; and so on.
F. Additive White Gaussian Noise
Zero-mean white Gaussian Noise (WGN) has the same power spectral density AWGN (f) for all frequencies.
The adjective ‘white’ is used in the sense that white light contains equal amounts of all frequencies within the visible
band of electromagnetic radiation. The autocorrelation function of WGN is given by the inverse Fourier transform of the
noise power spectral density GWGN (f): The autocorrelation function RaWGN (t) is zero for t 0. This means that any
two different samples of WGN, no matter how close together in time they are taken, are uncorrelated. The noise signal
WGN (t) is totally decorrelated from its time-shifted version for any t 0.
Fig 2:Signal with AWGN Noise
The amplitude of ‘integrated’ (bandwidth) WGN has a Gaussian probability density distribution P
(WGNi).Noise exists in all communications systems operating over an analog physical channel, such as radio. The main
sources are thermal background noise, electrical noise in the receiver amplifiers, & inter-cellular interference. In addition,
this noise can also be generated internally to the communications system because of Intersymbol Interference,
Intercarrier Interference & Intermodulation Distortion. These sources of noise decrease the Signal to Noise Ratio (SNR)
& thus limiting the spectral efficiency of the system. Noise is the main detrimental effect in most radio communication
systems. Most types of noise present in radio communication systems can be modelled accurately using Additive White
Gaussian Noise (AWGN). This noise has a uniform spectral density & a Gaussian distribution in amplitude. Thermal &
electrical noise from amplification, primarily have white Gaussian noise properties, allowing them to be modelled
accurately with AWGN. In addition, most other noise sources have AWGN properties due to the transmission being
OFDM. OFDM signals have a flat spectral density & a Gaussian amplitude distribution if the number of carriers is large,
because of this the inter-cellular interference from other OFDM systems have AWGN properties. For the same reason
ICI, and ISI also have AWGN properties for OFDM signals.
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G. Rayleigh Fading Distribution
Rayleigh distributions are defined for fading of a channel when all the received signals are reflected signals and
there is no dominant component. The Rayleigh distribution has a Probability Density Functions (PDF) given as:[13]
Where is the Root Mean Square (RMS) value of voltage in a received signal and
is the time-average
power of the received signal. The Cumulative Distribution Function (CDF) is defined to specify the probability that the
received signal does not exceed a specific threshold [16] gives the CDF
The Rayleigh distribution is commonly used to describe the statistical time varying nature of the received signal
power. It describes the probability of the signal level being received due to fading. The probability of the signal level for
the Rayleigh distribution is shown in this following table 1:
TABLE 1:CUMMULATIVE DISTRIBUTION FOR RAYLEIGH DISTRIBUTION [14]
Signal Level (dB about median)
10
0
-10
-20
-30
% Probability of signal level being
less than the value given
99
50
5
0.5
0.05
When information is transmitted in an environment with obstacles (Non Line-of-sight - NLOS)
more than one transmission paths will appear as result of the reflection(s). The receiver will then have to process a
signal, which is a super-position of several different transmission paths. If there exists a large number of transmission
paths may be modelled as statistically independent; the central limit theorem will give the channel the statistical
characteristics of a Rayleigh Distribution.
Fig. 3: Rayleigh distribution
II
RESULT AND SIMULATION
To analyse the effect of cyclic prefix on an OFDM system over AWGN channel, simulations were performed using
Simulink Matlab Software and the results are been discussed in the plots of BER against SNR below:
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0
10
-1
10
-2
BER
10
-3
10
-4
10
0
5
10
15
20
EbNo [dB]
25
30
35
40
Fig 4: Single Carrier Modulation Schemes over Multipath Rayleigh Fading.
0
10
OFDM-BPSK
OFDM-QPSK
OFDM-4QAM
OFDM-16QAM
-1
10
-2
BER
10
-3
10
-4
10
0
5
10
15
20
EbNo [dB]
25
30
35
40
Fig 5: BER versus SNR for OFDM over Multipath Rayleigh fading Channel with different modulation Schemes
0
10
BPSK
QPSK
4QAM
16QAM
-1
10
-2
BER
10
-3
10
-4
10
0
5
10
15
20
EbNo [dB]
25
30
35
40
Fig 6: BER versus SNR for Single Carrier over AWGN with different modulation Schemes
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0
10
OFDM-BPSK
OFDM-QPSK
OFDM-4QAM
OFDM-16QAM
-1
10
-2
BER
10
-3
10
-4
10
0
5
10
15
20
EbNo [dB]
25
30
35
40
Fig 7: BER versus SNR for OFDM with Cyclic Prefix over AWGN with different modulation Schemes
0
10
OFDM-BPSK
OFDM-QPSK
OFDM-4QAM
OFDM-16QAM
-1
10
-2
BER
10
-3
10
-4
10
0
5
10
15
20
EbNo [dB]
25
30
35
40
Fig 8: BER versus SNR for OFDM without Cyclic Prefix over AWGN with different modulation Schemes.
It can be seen from figure 3 and 4 above, that OFDM is employed to mitigate multipath interference over a
fading channel and not an idea AWGN channel. Error in a Single Carrier is enormous making the graph not to converge
as shown in fig 3, while OFDM Optimum receiver was with minimum error with convergence over Rayleigh multipath
fading as in fig 4.
From figure 5, the performance of different modulation schemes in a Single Carrier Modulation System is
analyzed such that BPSK requires a SNR of at least 6 dB, QPSK modulation scheme needs an SNR of 12 dB, 4-QAM
uses 11 dB and 16-QAM requires 14 dB.
It can also be analyzed from figures 6 and 7 above that since OFDM technique is not intended to overcome the
effect of AWGN, hence the performance of OFDM is almost similar to a BPSK, QPSK, 4-QAM and 16-QAM standard
Single Carrier digital transmission. OFDM has worse performance in an AWGN because of the Cyclic Prefix has made
the symbol period longer than in a Single Carrier. When Cyclic Prefix is removed from OFDM, it has almost the same
performance with Single Carrier. An equalizer is not needed when using AWGN.
So it can be seen from the graph that in an OFDM without Cyclic Prefix over AWGN i.e. fig. 7, modulation
scheme when compared with Single Carrier over AWGN i.e. fig 5, BPSK will need SNR of 4 dB as against 16 dB when
with Cyclic Prefix in fig 6. This when compared with Single Carrier has just 2 dB difference. In addition, with QPSK
modulation scheme, an SNR of 12 dB will be needed as against 35 dB when with Cyclic Prefix and of the same SNR
with the Single Carrier. For 4-QAM modulation Scheme, OFDM over AWGN without Cyclic Prefix will make use of 7
dB as against 30 dB when with Cyclic Prefix and a difference of 4 dB when compared with a Single Carrier.
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An SNR of 17 dB will be required of the OFDM system with 16-QAM modulation Scheme when the system is
without Cyclic Prefix as against 40 dB it will use when with Cyclic Prefix. This gives a difference of about 3 dB between
OFDM without Cyclic Prefix and a Single Carrier.
III
CONCLUSION
Hence, from this research work, it has been shown that OFDM has worst performance over AWGN Channel
because of the cyclic Prefix inclusion that makes the symbol period longer. It can then be concluded that OFDM is
crucial in multipath fading environment because it has the ability to counter and resolve Frequency Selective fading
environment due to its ability to resolve selective fading channel into flat fading by one tap equalizer. This implies that,
the OFDM has an ability to overcome the effect of burst error due to sudden noise such as lightning by using parallel data
transmission, so that instead of several adjacent bits being completely error, many symbols are only slightly distorted,
and they can be fixed using a simple Forward Error Correction (FEC) method.
REFERENCES.
1
Lui, Hui and Li, Guoqing (2005). OFDM-Based Broadband Wireless Networks Design and Optimization WileyInterscience.
2 Schulze, Henrik and Christian Luders, (2005). “Theory and Applications of OFDM and CDMA” John Wiley & Sons,
Ltd.
3 Acosta, Guillermo. (2000). “OFDM Simulation Using MATLAB”
4 Saltzberg,B.R. (1967). Performance of an efficient parallel data transmission system” IEE Trans. Commu. Technol.
Vol COM-15, NO 6. pp 805-811.
5 Zimmerman,M.S. and Kirsh,A.L. (1967). The AN/GSC-10 (KATHRYN) variable rate data modem for HF radio,
IEEE Trans. Commun. Technol. Vol. COM-15, April 1967, pp 197- 205.
6 Hirosaki, B. (1981). An orthogonally multiplexed QAM system using the discrete Fourier transform, IEEE Trans.
Commun. Tchn., vol.COM-29, no 7, pp. 982- 989.
7 Cimini, L.J Jr (1985). Analysis and simulation of a digital mobile channel using orthogonal frequency division
multiplexing, IEEE Transaction on Communication., vol. COM-33, no. 7, pp. 665-675.
8 Anibal Luis Intini (2000). Orthogonal Frequency Division Multiplexing for Wireless Networks, University Of
California, Santa Barbara.
9 Proakis, J.G.( 1995). Digital Communications, (3rd ed)., NY: Mcgraw-Hill.pp 67-78
10 Pornchai, S., Wannaree, W., and Sawasd, T. (2009).Performance of M-PSK in mobile satellite communication over
combined Ionospheric scintillation and Flat Fading channels with MRC Diversity, IEEE Transactions on wireless
communications, vol. 8, no.7, pp.3360-3364
11 Raji T. I. and Adeyemo Z. K. (2009). Performance of Binary Phase Shift keying(BPSK) and Quartenary Phase Shift
Keying (QPSK) Signalling Schemes in Fast and Frequency Non- Selective Rayleigh fading channel with Decision
Feedback Equalizer (DFE) at the Receiver’ Advanced Materials Research, Trans Tech Publications,
Switzerland,vols.62- 64, pp.99-104.
12 Molisch, A.F (2005). Wireless Communications. John Wiley and Sons.(1st ed.) pp23-37
13 Rappaport, T.S (1996). Wireless Communications: Principle and Practice. NJ:Prentice-Hall.”
14 Louis Litwin (2000). An introduction to multicarrier modulation, IEEE Potential vol 19, no 20”
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