OFDM SIGNAL IN FADING TRANSMISSION CHANNELS OF COMMUNICATION SYSTEM.pdf

OFDM SIGNAL IN FADING TRANSMISSION CHANNELS OF COMMUNICATION SYSTEM

OSMAN PASHA SHAIK M.Tech-Digital Electronics & Communication Systems,

Sri Indu College of Engg & Technology, (Affiliated to JNTU-Hyderabad),

Ibrahimpatnam, Hyderabad, Andhra Pradesh, India – 501 510.

Prof. K. ASHOK BABU Professor & HOD,

Sri Indu College of Engg & Technology, (Affiliated to JNTU-Hyderabad),

Ibrahimpatnam, Hyderabad, Andhra Pradesh, India – 501 510.

Abstract-Orthogonal Frequency Division Multiplexing is a

technique for increasing the amount of information that can be

carried over a wireless network. In this paper, a OFDM model is

designed which improves bit error rate (BER) and reduces the

Inter Symbol Interference(ISI) by using the Binary Cyclic

Encoder/Decoder and Cyclic Prefix respectively. In frequency-

division multiplexing, multiple signals or carriers are sent

simultaneously over different frequencies between two points.

Wireless signals can travel multiple paths from transmitter to

receiver; receiver can have all trouble sorting all the resulting

data out. Digital base band parts of an OFDM transmitter

consists of four basic blocks. Cyclic Encoder, Mapper, IFFT and

Cyclic Prefix. Orthogonal FDM deals with these multipath

problems by splitting carriers into smaller sub carriers, and then

broadcasting those simultaneously. Using the QAM modulation,

the encoded data is mapped onto sub carriers; an N-point IFFT,

which transforms the data into the time domain. Finally, an n

sample long cyclic prefix (CP) is added to reduce the inter symbol

interference. The proposed OFDM model reduces multipath

distortion and reduces RF interference, allowing for greater

throughput. The performance of OFDM model under multipath

channel are simulated and analyzed respectively.

Keywords-OFDM, Encoder, Mapper, IFFT, Cyclic Prefix &

Multipath Channel.

I. INTRODUCTION The name „OFDM‟ is derived from the fact that the digital

data is sent using several carriers, each of a different frequencies (Frequency Division Multiplexing) and these carriers are orthogonal to each other, hence Orthogonal Frequency Division Multiplexing.

OFDM is a technique for transmitting data in parallel by using a large number of modulated sub-carriers. These sub-carriers (or sub-channels) divide the available bandwidth and sufficiently separated in frequency (frequency spacing) so that they are orthogonal.

OFDM is the concept of MC where the different carriers are orthogonal to each other. Orthogonal in this respect means that the signals are totally independent. It is achieved by ensuring that the carriers are placed exactly at the nulls in the modulation spectra of each other. Source for OFDM spectral efficiency is the fact that the drop off of the signal at the band is primarily due to a single carrier which is carrying a low data

rate. OFDM allows for sharp rectangular shape of the spectral power density of the signal.

In this paper, a OFDM model is designed which improves bit error rate (BER) and reduces the Inter Symbol Interference by using the Binary Cyclic Encoder and Cyclic Prefix in the transmitter block with multipath channel. On simulation in MATLAB 7.6 (R2008a), we can clearly observe by using cyclic encoder we are getting the better power density and BER compare to normal OFDM signal.

II. PRICIPLE OF OFDM The main features of a practical OFDM system are as

follows: Some processing is done on the source data, such as

coding for correcting errors, interleaving and mapping of bits onto symbols. An example of mapping used is QAM.

The symbols are modulated onto orthogonal sub-carriers. This is done by using IFFT.

Orthogonality is maintained during channel transmission. This is achieved by adding a cyclic prefix to the OFDM frame to be sent. The cyclic prefix consists of the L last samples of the frame, which are copied and placed in the beginning of the frame. It must be longer than the channel impulse response.

Synchronization: the introduced cyclic prefix can be used to detect the start of each frame. This is done by using the fact that the L first and last samples are the same and therefore correlated. This works under the assumption that one OFDM frame can be considered to be stationary.

Demodulation of the received signal by using FFT. Channel equalization: the channel can be estimated

either by using a training sequence or sending known so-called pilot symbols at predefined sub-carriers.

Decoding and de-interleaving.

OFDM is generated by firstly choosing the spectrum required, based on the input data, and modulation scheme used. Each carrier to be produced is assigned some data to transmit. The required amplitude and phase of the carrier is

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OSMAN PASHA SHAIK* et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 10, Issue No. 2, 185 - 192

ISSN: 2230-7818 @ 2011 http://www.ijaest.iserp.org. All rights Reserved. 85

then calculated based on the modulation scheme (typically differential BPSK, QPSK, or QAM). Then, the IFFT converts this spectrum into a time domain signal.

Figure 1. The System of OFDM

A. Binary Cyclic Encoder An (n, k) linear code C is called a cyclic code. If every

cyclic shift of a code vector in C is also a code vector in C. The Binary Cyclic Encoder block creates a systematic cyclic code with message length K and codeword length N. The number N must have the form 2M-1, where M is an integer greater than or equal to 3. The input must contain exactly K elements. If it is frame-based, then it must be a column vector. The output is a vector of length N. Codeword length N=7; Message length K=4. ( ) For binary codes, only repetition codes and single-parity check codes reach this upper bound. A class of non binary codes that doesn‟t reach the above bound are the Reed-Solomon codes. Because of their good distance properties and the availability of efficient coding and decoding algorithms, Reed-Solomon codes are the most popularly used block codes. Reed-Solomon codes are defined for block symbols with M bits per symbol, where the code length n is related to M by: For Binary cyclic encoder it is in the form of .

B. Serial to Parallel conversion The serial input data is formatted into the word size

required for transmission, e.g. 6 bits/word for 64QAM, and shifted in parallel format. Then the data will be transmitted in parallel by adding each data word to one carrier in the transmission.

C. QAM Modulation is a mapping of the information on changes in

the carrier phase, frequency or amplitude or combination. Quadrature Amplitude Modulation (QAM) is an encoding scheme where digital data is mapped to an analog signal consisting of two signals. One signal is reference signal for the receiver and the other is quadrature component A continuous data stream can be encoded and represented on a 3-bit table and therefore and 8-point signal constellation. For example: QAM, PAM. The sub-carrier frequencies are chosen so that the modulated data streams are orthogonal to each other, meaning that cross talk between the sub-channels is eliminated.

An OFDM signal is a sum of subcarriers that are individually modulated by using phase shift keying (PSK) or

quadrature amplitude modulation (QAM). The symbol can be written as:

( ) {∑ ⁄ ( (

) ( ))

},

≤ t ≤ (1) ( ) Where: Ns is the number of subcarriers T is the symbol duration fc is the carrier frequency

The equivalent complex baseband notation is given by:

( )

{

∑ ⁄ (

( ))

}

(2) ( )

D. IFFT In the OFDM system, Inverse Fast Fourier Transform/Fast

Fourier Transform (IFFT /FFT) algorithms are used in the modulation and demodulation of the signal. The length of the IFFT/FFT vector determines the resistance of the system to errors caused by the transmission channel. ( ) ∑ ⁄ (

( ))

(3) s(t)=0, t < ts Λ t < ts +T In this case, the real and imaginary parts corresponds to the in-phase and quadrature parts of the OFDM signal. They have to be multiplied by a sine and cosine of the desired frequency to produce the final OFDM signal. figure shows the block diagram for the OFDM modulator. ( ( ) )

OFDM

Input signal ( ( )( )

OFDM Modulator

Serial to Parallel

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E. Cyclic Prefix for elimination of ISI Inter symbol interference (ISI) is a form of distortion of

signal in which one symbol interferes with subsequent symbol of other. One key principle of OFDM is that since low symbol rate modulation schemes (i.e., where the symbols are relatively long compared to the channel time characteristics) suffer less from inter symbol interference caused by channel propagation, it is advantageous to transmit a number of low-rate streams in parallel instead of a single high-rate stream. Since the duration of each symbol is long, it is feasible to insert a guard interval between the OFDM symbols, thus eliminating the inter symbol interference. The guard interval also eliminates the need for a pulse-shaping filter, and it reduces the sensitivity to time synchronization problems.

For example: If one sends a million symbols per second using conventional single-carrier modulation over a wireless channel, then the duration of each symbol would be one microsecond or less. This imposes severe constraints on synchronization and necessitates the removal of multipath interference. If the same million symbols per second are spread among one thousand sub-channels, the duration of each symbol can be longer by a factor of a thousand (i.e., one millisecond) for orthogonality with approximately the same bandwidth. Assume that a guard interval of 1/8 of the symbol length is inserted between each symbol. Inter symbol interference can be avoided if the multipath time-spreading (the time between the reception of the first and the last echo) is shorter than the guard interval (i.e., 125 microseconds). This corresponds to a maximum difference of 37.5 kilometres between the lengths of the paths.

The cyclic prefix, which is transmitted during the guard interval, consists of the end of the OFDM symbol copied into the guard interval, and the guard interval is transmitted followed by the OFDM symbol. The reason that the guard interval consists of a copy of the end of the OFDM symbol is so that the receiver will integrate over an integer number of sinusoid cycles for each of the multipath when it performs OFDM demodulation with the FFT.

Figure 2. Cyclic prefix is this superfluous bit of signal we add to the front of

our precious cargo, the symbol.

F. Communication Channel A channel model is then applied to the transmitted signal.

The model allows for the signal to noise ratio, multipath, and peak power clipping to be controlled. The signal to noise ratio is set by adding a known amount of white noise to the transmitted signal. while the coefficient amplitude represents the reflected signal magnitude.

Channel, in communications (sometimes called communications channel), refers to the medium through which information is transmitted from a sender (or transmitter) to a receiver. In practice, this can mean many different methods of facilitating communication, including: 1. A connection between initiating and terminating nodes of a circuit. 2. A path for conveying electrical or electromagnetic signals, usually distinguished from other parallel paths. 3. The portion of a storage medium, such as a track or a band, that is accessible to a given reading or writing station or head. 4. In a communications system, the part that connects a data source to a data sink.

a. Multipath In wireless communications, multipath is the propagation

phenomenon that results on radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric reflection and refraction from terrestrial object such as mountains and buildings.

The effects of multipath include constructive and destructive interference and phase shifting of the signal. This causes Rayleigh Fading named after Lord Rayleigh. Rayleigh fading with a strong line of sight is said to have a Rician distribution or to be Rician fading.

In digital radio communications such as GSM Multipath can cause errors and affect the quality of communications. The errors are due to Inter symbol Interference (ISI). Equalizers are often used to correct the ISI. Alternatively, techniques such as orthogonal frequency division modulation and Rake receivers may be used.

b. Fading If the path from the transmitter to the receiver either has

reflections or obstructions, we can get fading effects. In this case, the signal reaches the receiver from many different routes, each a copy of the original. Each of these rays has a slightly different delay and slightly different gains. The time delays result in phase shifts which added to main signal component (assuming there is one.) causes the signal to be degraded.

Fading is about the phenomenon of loss of signal in telecommunications. Fading or fading channels refers to mathematical models for the distortion that a carrier modulated telecommunication signal experiences over certain propagation media. Short team fading also known as multipath induced fading is due to multipath propagation. Fading results from the superposition of transmitted signals that have experienced differences in attenuation, delay and phase shift

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http://en.wikipedia.org/wiki/Channel_(communications)

http://en.wikipedia.org/wiki/Intersymbol_interference

http://en.wikipedia.org/wiki/Multipath_propagation

http://en.wikipedia.org/wiki/Multipath_propagation

http://en.wikipedia.org/wiki/Guard_interval

http://en.wikipedia.org/wiki/Pulse-shaping_filter

http://en.wikipedia.org/wiki/Cyclic_prefix

while travelling from the source to the receiver. It may be caused by attenuation of a single signal.

The most common types of fading known as “slow fading” and “fast fading” as they apply to a mobile radio environment. Fading refers to the time variation of the received signal power caused by changes in the transmission medium or path. Slow fading: Shadowing or Large Scale Fading is a kind of fading caused by larger movements of a mobile or obstructions within the propagation environment. Fast fading also known as Multipath fading or small scale fading is a kind of fading occurring with small movements of a mobile.

The best way to combat fading is to ensure that multiple versions of the same signal are transmitted, received and coherently combined. This is usually termed diversity and is sometimes acquired through multiple antennas. Mathematically, the simplest model for the fading phenomenon is multiplication of the signal waveform with a time dependent coefficient which is often modeled as a random variable, making the received signal to noise ratio a random quantity.

Fading channel models are often used to model electromagnetic transmission of information over wireless media such as with cellular phones and in broadcast communication. Small scale fading is usually divided into fading based on multipath time delay spread and that based on Doppler spread. There are two types of fading based on multipath time delay spread:

Flat fading: The bandwidth of the signal is less than the coherence bandwidth of the channel or the delay spread is less than the symbol period.

Frequency selective fading: The bandwidth of the signal is greater than the coherence bandwidth of the channel or the delay spread is greater than the symbol period.

There are two types of fading based on Doppler spread:

Fast Fading: has a high Doppler spread and the coherence time is less than the symbol time and the channel variations are faster than baseband signal variation.

Slow Fading: has a low Doppler spread. The coherence time is greater than the symbol period and the channel variations are slower than the baseband signal variation.

c. Multipath Fading

Multipath Fading is simply a term used to describe the multiple paths a radio wave may follow between transmitter and receiver. Such propagation paths include the ground wave, ionospheric refraction, and radiation by the ionospheric layers, reflection from the earth‟s surface or from more than one ionospheric layer, and so on.

Multipath fading occurs when a transmitted signal divides and takes more than one path to a receiver and some of the

signals arrive out of phase, resulting in a weak or fading signal. Some transmission losses that effect radio wave propagation are ionospheric absorption, ground reflection and free space losses. Electromagnetic interference (EMI) both natural and manmade, interfere with radio communications. The maximum useable frequency (MUF) is the highest frequency that can be used for communications between two locations at a given angle of incidence and time of day. The lowest usable frequency (LUF) is the lowest frequency that can be used for communications between two locations.

d. Multipath Channel Characteristics Because, there are obstacles and reflectors in the wireless

propagation channel, the transmitted signal arrivals at the receiver from various directions over a multiplicity of paths. Such a phenomenon is called multipath. It is an unpredictable set of reflections and/or direct waves each with its own degree of attenuation and delay.

Multipath is usually described by: Line-of-sight (LOS): the direct connection between the transmitter (TX) and the receiver (RX). Non-line-of-sight (NLOS): the path arriving after reflection from reflectors. The illustration of LOS and NLOS is shown in Figure 3.

Figure 3. Effect of multipath on a mobile station

Characteristics of a Multipath Channel are:

Delay spread – this is the interval for which a symbol remains inside a multipath channel

Channel can be modeled as a FIR filter with one line of sight (LOS) path & several multipaths, the signals from the multipath being delayed and attenuated version of the signal from the LOS path

Multipath will cause amplitude and phase fluctuations, and time delay in the received signals.

e. Diversity Schemes A diversity scheme is a method that is used to

develop information from several signals transmitted over independent fading paths. This means that the diversity method requires that a number of transmission paths be available, all carrying the same message but having independent fading statistics. The mean signal strengths of the paths should also be approximately the same. The basic

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requirement of the independent fading is received signals are uncorrelated. Therefore, the success of diversity schemes depends on the degree to which the signals on the different diversity branches are uncorrelated. Multipath fading may be minimized by practices called spaced diversity and frequency diversity. In space diversity, two or more receiving antennas are spaced some distance apart. Fading does not occur at both antennas. Therefore, enough output is almost always available from one of the antennas to provide a useful signal. In frequency diversity, two transmitter and two receivers are used, each pair tuned to a different frequency, with the same information being transmitted simultaneously over both frequencies. One of the two receivers will almost always produce a useful signal.

Proper combining the multiple signals will greatly reduce severity of fading and improve reliability of transmission. Because deep fades seldom occur simultaneously during the same time intervals on two or more paths. The simplest combining scheme is selection combining, which is based on the principle of selecting the best signal (the largest energy or SNR) among all of the signals received from different branches.

f. Rayleigh Fading Channel Rayleigh fading is a statistical model for the effect of a

propagation environment on a radio signal such as that used by wireless devices. It assumes that the power of a signal that has passed through such a transmission medium (also called a communications channels will vary randomly or fade according to a Rayleigh distribution – the radial component of the sum of two uncorrelated Gaussian random variables. It is reasonable model for tropospheric and ionospheric signal propagation as well as the effect of heavily built up urban environment on radio signals. Rayleigh fading is most applicable when there is no line of sight between the transmitter and receiver.

Figure 4. Principle of multipath channel

As shown in the model above, the path between base station and mobile stations of terrestrial mobile

communications is characterized by various obstacles and reflections. The radio wave transmitted from the base station radiates in all directions. These radio waves, including reflected waves that are reflected off of various objects, diffracted waves, scattering waves, and the direct wave from the base station to the mobile station. Therefore the path lengths of the direct, reflected, diffracted, and scattering waves are different, the time each takes to reach the mobile station is different. The phase of the incoming wave also varies because of the reflection. As a result, the receiver receives a superposition consisting of several waves having different phase and time of arrival. The generic name of a radio wave in which the time of arrival is retarded in comparison with this direct wave is called a delayed wave. Then, the reception environment characterized by a superposition of delayed waves is called multipath propagation environment.

In a multipath propagation environment, the received signal is sometimes weakened or intensified. The signal level of the received wave changes from moment to moment. Multipath fading raises the error rate of the received data.

The delayed wave with incident angle is given by the following equation (4) and corresponding to Figure 4, when a continuous wave of single frequency (Hz) is transmitted from the base station.

[ ( ) ( )] (4) where Re[ ] indicates the real part of a complex number that gives the complex envelope of the incoming wave from the direction of the number n. θ n

Mobile station

Delayed wave with an incident angle θ

Moreover, j is a complex number. En(t) is given in (5) by using propagation path length from the base station of the incoming waves: ( ), the speed of the mobile station, v (m/s), and the wavelength, λ (m). ( ) (

( )

) (5)

= ( ) ( )

where and are the envelope and phase of the nth incoming wave. ( )and ( )are the in-phase and quadrature phase factors of ( ), respectively. The incoming nth wave shifts the carrier frequency as (hz) by the Doppler effect (Hz). This is called the Doppler shift, which

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described as , has a maximum value of , when the incoming wave comes from the running direction of the mobile station in = 1 . Then this maximum is the largest Doppler shift. The delayed wave that comes from the rear of the mobile station also has a frequency shift of - Hz). It is shown by (4), since received wave r(t) received in the mobile station is the synthesis of the above-mentioned incoming waves, when the incoming wave number is made to be N.

( ) ∑ ( )

= [(∑ ( )

) ( )]

= [( ( ) ( ))( )] (6) ( ) ( )

where x(t) and y(t) are given by ( ) ∑ ( )

( ) ∑ ( )

(7)

and x(t) and y(t) are normalized random processes, having an average value of 0 and dispersion of σ , when N is large enough. The combination probability density p(x, y) is then given by (8), where x=x(t), y=y(t) ( )

(

) (8)

In addition, it can be expressed as r (t) using the amplitude and phase of the received wave. ( ) ( ) ( ( )) (9)

R(t) and θ(t) are given by ( ) √

( ) [ ⁄ ] (10) By using a transformation of variables, p(x, y) can be converted into p(R, θ) ( )

(

) (11)

By integrating p(R, θ) over θ from 0 to 2, the probability density function p(R) is obtained (12). ( )

(

) (12)

By integrating p(R, θ) over R from 0 to infinity, the probability density function p(θ) is obtained (13). ( )

(13)

From these equations, the envelope fluctuation follows a Rayleigh distribution, and the phase fluctuation follows a uniform distribution on the fading in the propagation path.

g. Receiver The receiver basically does the reverse operation to the

transmitter. The guard period is removed. The FFT of each symbol is then taken to find the original transmitted spectrum. The phase angle of each transmission carrier is then evaluated and converted back to the data word by demodulating the received phase. The data words are then combined back to the same word size as the original data.

III. SIMULATION AND RESULT The simulation is based upon the multipath channel.

QAM modulation mode is used in the OFDM system. Here, I compared with the 4, 16, &64 QAM modulations with 48, 64, &128 subcarriers. On simulation in MATLAB 7.6 (R2008a), we can clearly observe by using cyclic encoder we are getting the better power density and BER compare to normal ofdm signal. Figure shows the transmitter & received signals of OFDM.

Figure 5. Transmitted OFDM signal IJA

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Figure 6. Received OFDM signal

Here, the power spectral density will be varying. Figure 7 & 8 shows the normal & encoded power density.

Figure 7. Power density without encoding

Figure 8. Power density with Encoding

It was found that the SNR performance of OFDM is similar to a standard single carrier digital transmission. This is to be expected, as the transmitted signal is similar to a standard Frequency Division Multiplexing (FDM) system. The results

show that using 64QAM with Encoding technique, the BER is improved compare to normal signal.

Figure 8. Comparison between normal & encoded BER

IV. CONCLUSION The BER performance of Orthogonal Frequency Division

Multiplexing (OFDM) under multipath fading channels in wireless communications. In order to achieve more efficient data transmission (by adding cyclic encoder) using cyclic prefix and reduce the Inter Symbol Interference (ISI). The encoded signal improves the bit error rate as shown from the above figures. This may provide the basis for further study of OFDM diversity systems. In the future, more experiments can be done, in order to provide more bases for improving the data transmission. Especially compared with the traditional OFDM technology. This advantage will attract people to pay more particular attention to this new technology.

ACKNOWLEDGMENT My sincere thanks goes to my supervisor, Prof. K. Ashok Babu, for his guidance in the execution of the project. I am especially grateful for all the help he provided and resources he made available without which the project would not have reached its current stage. I am also indebted to thank Mr. Sharma sir, for being most efficient in coordinating the project. Many thanks also goes out to the project presentation assessor, Mr. Suresh Balla sir, who have given me much advice and guidance during the project.

REFERENCES [1] Eric Philip Lawrey, „„Adaptive Techniques for Multi-users OFDM‟‟, James cooks University, December 2001. [2] www.skydsp.com/publications/4thyrthesis/index.htm. [3] OFDM Simulation using MATLAB. Retrieved May 9, 2003from http://users.ece.gatech.edu/~mai/tutorial/OFDM/Tutorial_web.pdf. [4] Moose P H, “A technique for orthogonal frequency division multiplexing Frequency offset correction,” Communications, IEEE Trans, 1994, 42(10) : 2908 22914. [5] www.csee.wvu.edu/wcrl/public/jianofdm.pdf

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http://www.skydsp.com/publications/4thyrthesis/index.htm

http://users.ece.gatech.edu/~mai/tutorial/OFDM/Tutorial_web.pdf

http://users.ece.gatech.edu/~mai/tutorial/OFDM/Tutorial_web.pdf

http://www.csee.wvu.edu/wcrl/public/jianofdm.pdf

[6] Hiroshima Harada, Ramjee Prasad, Simulation and Software Radio for Mobile Communication, Artech House, 165-226, 2002. [7] www.complextoreal.com [8] Guillermo Acosta, “OFDM Simulation Using Matlab,” Faculty Advisor: Dr. Mary Ann Ingram, August. 2000. [9] Richard Van Nee, Ramjee Prasad, OFDM for Wireless Multimedia Communications, Norwood, MA:Artech House, 2000 [10] Leon W.Couch II, Digital and Analog Communication Systems, 6 th Edition, Prentice Hall, 2001 [11]http://en.wikipedia.org/wiki/Orthogonal_frequency- division_multiplexing

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http://www.complextoreal.com/

http://en.wikipedia.org/wiki/Orthogonal_frequency-

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