Wireless Transmission Using Orthogonal Frequency Division Multiplexing

8/2/2019 Wireless Transmission Using Orthogonal Frequency Division Multiplexing

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Wireless Communication usingOrthogonal Frequency DivisionMultiplexing

------------------------------------------------------MATLAB Simulation of the Transmitter, Communication

Channel and Receiver of an OFDM System

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Wireless Communication usingOrthogonal Frequency Division

Multiplexing----------------------------------------------------------------------------------------------MATLAB Simulation of the Transmitter, Communication

Channel and Receiver of an OFDM System----------------------------------------------------------------------------------------------

There are presently many well known multiplexing techniques in

wireless communications FDM, TDM, and CDM. But these have various limitations

such as low bit rate capacity, less spectral efficiency, multi-path fading and inter-

symbol interference (ISI). ISI occurs when a transmission interferes with itself due to

reflection of the signal from large objects such as mountains or buildings and thus the

receiver sees more than one copy of the signal and cannot decode the transmission

correctly. Since the indirect paths take more time to travel to the receiver, the

delayed and attenuated copies of the signal interfere with the primary signal; causing

ISI. The use of Orthogonal Frequency Division Multiplexing provides better solutions

to the above mentioned problems. OFDM is a multi-carrier modulation technique

which distributes the data over large number of carriers that are mathematically

orthogonal. The orthogonality of the carriers prevents the demodulator from seeing

frequencies other than their own.

In this paper, we have simulated the transmitter, communication

channel and the receiver using the OFDM principle through MATLAB. It clearlyshows that OFDM greatly reduces the bit-error rate as compared to other

conventional modulation techniques. We have used BPSK and QPSK modulation

schemes and demonstrated that OFDM system with BPSK scheme is suitable for low

capacity, short distance applications while OFDM with QPSK for large capacity and

long distance applications. With the rapid growth of digital communication in recent

years, the need for high-speed data transmission has increased. OFDM is especially

suitable for high-speed communication as it sends many low speed transmissions

simultaneously. The benefits of OFDM are high spectral efficiency, resiliency to RF

interference and low multi-path distortion. The use of FFT technique to implement

modulation and demodulation function makes it computationally more efficient. Theprocessing power of modern digital signal processors has increased to a point where

OFDM has become feasible and economical. Examining the patents, journal articles,

and books available on OFDM, it is clear that this technique will have an impact on

the future of communication.

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Orthogonal Frequency Division Multiplexing

Orthogonal Frequency Division Multiplexing is a special case of

Frequency Division Multiplexing where we use multi-carrier modulation and thecarriers taken are orthogonal. OFDM allows the transmission of high data rates over

extremely hostile channels. OFDM distributes the available bandwidth among a large

number of narrow band sub-carriers that are mathematically orthogonal. This

orthogonality property ensures compact spectral utilization and at the same time

prevents inter-channel interference (ICI). Frequency selective fading occurs when

particular frequencies are either enhanced or attenuated due to the channel frequency

response. In conventional single carrier modulation the whole symbol is affected but

in OFDM which is a multi-carrier modulation technique only particular sub-carrier

symbols are lost.

Another advantageous feature of an OFDM system relates to its ease of

implementation. This refers to the fact that modulation can be performed digitally by

IDFT which can be implemented very efficiently as an Inverse Fast Fourier

Transform (IFFT). So, the entire modulation is done by the IFFT Block and this

reduces the need of multiple carrier generators. Obviously, the FFT Block fills in for

the corresponding demodulator at the receiver end.

Significance of Orthogonality

The concept of orthogonality allows the carriers to be distinguished

from each other at the receiver. The sub-carriers are chosen in such a way that the

sidebands of the individual carriers can overlap as long as there is no cross-talk from

the other sub-channels at the critical frequency of each sub-carrier. By using an IFFT

for modulation we implicitly choose the spacing of the sub-carriers in such a way that

at the frequency where we evaluate the received signal, all other signals are zero.

There are many advantages of the orthogonal selection of the sub-carriers:

Proper utilization of the spectrum and thus reduced bandwidth requirement.

Reduction in inter-channel interference (ICI). The IFFT/FFT implementation can be done in hardware at affordable rates.

Hence it reduces the overall cost.


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OFDM Signal Generation

Transmitter

Random Data Generator It accepts any source of data and outputs bits in theform of 1s and -1s. The source could be a text file, a sound file or a stream of

random numbers.

Serial to Parallel Converter It takes in the serial stream of bipolar bits andoutputs the data distributing it among a number of channels.

IFFT BlockThis block generates the time domain signal as per the spectrumsupplied to its input. This block performs the necessary modulation and

ensures that the sub-carriers are orthogonal.

Parallel to Serial Converter It produces a serial stream of the OFDM signalfrom the parallel chunks.

Guard Interval Addition BlockThis block adds a guard space between eachsymbol. The first half of the guard interval is zero-padded and the other half is

the cyclic extension of the end part of the corresponding symbol. Thus the

output is the OFDM signal which is ready to be transmitted.

Communication Channel

Noise We have assumed an AWGN channel. Multipath We have considered the effects of frequency selective fading and

inter-symbol interference (ISI). Clipping Due to high PAPR, we clip the amplitude to simulate the problem

of amplifier saturation.

Receiver

Guard Interval Removal Block - This removes the guard space betweenadjacent symbols from the received OFDM signal.

Serial to Parallel Converter This block again distributes the signal intoparallel streams to be inputted to the FFT Block.

FFT BlockThis block acts as the demodulator in the receiver end. It takes inthe parallel chunks of the received signal and generates the spectrum

accordingly, which in turn was the input we had supplied to the IFFT block.

Parallel to Serial Converter This block takes in the parallel chunks of theoutput of the FFT block and outputs the serial stream of bipolar bits.

Source File Interpreter - This block interprets the serially received bits andrecovers the source file.


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Working Model

OFDM Signal Generation Simulation Parameters

Parameters/

Specifications

Values/

Types

Modulation Schemes used BPSK and QPSK

Number of Carriers used 32

IFFT/FFT Size 128

Guard Interval Size 32

Guard Interval

Type

The first half of the guard interval is zero-padded

and the other half is the cyclic extension of the end

part of the corresponding symbol

OFDM Frame Size 128

Channel Noise AWGN

Other Channel Attributes

Considered in

Simulation

InterSymbol Interference,

Frequency Selective Fading,

Clipping Effects


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Significance of IFFT/FFT Implementation

The transmitter first converts the input data from a serial stream to parallel sets. Each

set of data contains one symbol, S i, for each sub-carrier. For example, a set of four data

would be [S0

S1

S2

S3

]. Before performing the Inverse Fast Fourier Transform (IFFT),this example data set is arranged on the horizontal axis in the frequency domain as

shown in following figure:

Frequency domain distribution of symbols

This symmetrical arrangement about the vertical axis is necessary for

using the IFFT to manipulate this data. An inverse Fourier transform converts the

frequency domain data set into samples of the corresponding time domain

representation of this data. Specifically, the IFFT is useful for OFDM because it

generates samples of a waveform with frequency components satisfying orthogonality

conditions. Then, the parallel to serial block creates the OFDM signal by sequentially

outputting the time domain samples.

Since OFDM is a multi-carrier modulation (MCM) technique, we need

to have a mechanism to economically generate a large number of sub-carriers and at

the same time we have to maintain the condition that they must be orthogonal. Using

conventional methods, we would need a bank of sinusoidal generators of precise

orthogonal frequencies. At the same time, at the receiver end, we would need amechanism for coherent carrier generation for each sub-channel. Since the number of

carriers is large, this would be quite expensive.

The IFFT/FFT block pairs remove this difficulty as they ensure that

only orthogonal carriers are used in modulation. In our design, the essence of OFDM

being purely orthogonal relies on an environment of digital manipulation. Through

IFFT, our digital sequence is converted to analog transmission, and the spacing


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between carriers equals the inverse of the time duration of the transmitted symbols,

causing the carriers to be orthogonal. Similar is the case with FFT; the only difference

is that it will give us back the original digital sequence from the analog received

signal.

Guard Interval Addition

The addition of an extra guard interval greatly reduces the effects due

to inter-symbol interference (ISI). The guard interval is added in such a way that the

starting part of the symbol is well protected from the delay spread zone produced due

to ISI. So we start the symbol from a new point so that actual symbol will be safe from

this zone. But this occurs at the expense of increase in the increased bandwidth

requirement.

Generally, we take the guard interval duration as about 25% of the

original symbol duration. So, after the addition of guard interval, the new length ofthe symbol becomes 5/4 times the original.

Channel Characteristics

Noise

The noise present in the channel is assumed to be white and having a Gaussian

distribution. Hence, we use the AWGN (Additive White Gaussian Noise) channel.

Multipath

Due to the signals getting reflected by obstructions, the receiver sees delayed andattenuated signals along with the original signal. Hence, it is not able to correctly

decode the message properly. We have considered two delayed versions of the

signal of different path gains.

Clipping

Clipping simulates the problem of amplifier saturation in the channel. In OFDM

signal there is a high Peak-to-Average Power Ratio (PAPR). Due to the sudden rise in


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amplitude at the peak value of the OFDM signal, there is an increase in the in -band

noise and this increases the BER when the signal has to go through amplifier non-

linearity. Thus, the signal is clipped to a fixed clip value if it exceeds the threshold.

Comparison of the efficiencies of BPSK and QPSK

In our simulation, we have used two modulation schemesBPSK and

QPSK. We have chosen Phase Shift Keying because it produces constant amplitude

signals and we face fewer problems with amplitude fluctuations caused by fading.

Plots of BER vs SNR for QPSK and BPSKThe plot shows higher BER for QPSK than BPSK at any value of SNR

Thus, we see that at any value of SNR, the bit-error rate for QPSK modulation

scheme is higher than that of BPSK scheme. But at the same time we should

remember that BPSK modulates 1-bit at a time, while QPSK 2-bits at a time. So QPSK

has higher data carrying capacity than BPSK. Hence we conclude that:

The OFDM system with BPSK scheme is suitable for low capacity and shortdistance applications.

The OFDM system with QPSK scheme is useful for large capacity and longdistance applications at the cost of slight increase in the bit-error rate.

Spectrum of OFDM Signal


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Now let us view the spectrum of an OFDM signal by taking Fast

Fourier Transform. We can clearly see the 32 sub-carriers central frequencies. At

each frequencys peak, we see that there is no cross-talk from the other sub-carriers.

Thus we observe that the carriers produced by the IFFT block are indeed orthogonal.

Spectrum of the OFDM signalThe peaks represent the central frequencies of the 32 carriers used


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Practical Applications of OFDM

OFDM is used in:

Digital Audio & Video Broadcasting [DAB and DVB] in Europe.

Asymmetric Digital Subscriber Line [ADSL] modems. HDTV Broadcasting. Cellular Radio. Wireless Networking Standard IEEE 802.11a.

Conclusion

In this paper, we have simulated all the necessary parts of an OFDM system.We have used BPSK and QPSK modulation schemes and compared their

working efficiencies. We have also shown how OFDM is more effective than

other contemporary techniques such as 16-QAM in channels where multi-path and noise prevail.

Examining the patents, journal articles, and books available on OFDM, it isclear that this technique will have an impact on the future of communication.

References

OFDM and MC-CDMA for Broadband Multi-User CommunicationsL Hanzo, M Munster, BJ Choi, T Keller.

IETE Technical Review

Volume 23

No. 3, 2006SB Pokle and KD Kulat

Digital CommunicationsSimon Haykin

Digital Signal Processing: A Computer-Based ApproachSanjit K Mitra

Contemporary Communication Systems Using MatlabJohn G Proakis and M Salehi

Wireless CommunicationsTheodore Rappaport

OFDM versus Single Carrier with Cyclic Prefix: A System-Based comparisonJan Tubbax, Boris Come, Liesbet Van der Perre, Luc Deneire, Marc Engels

MATLAB 6.5 Software Modeling tool for CommunicationM/s Mathworks Inc., USA.


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MATLAB Code------------------------------------------------------------------------------------------------------------%Developed by AMIT KUMAR and SRIRAM BHATTARU%under the guidance of Prof. G.Panda%Head of Department of ECE%NIT Rourkela

% setupdisp(' '), disp('------------------------------------------------------------')disp('Simulation Setup')

fft_size = 128 % should be a power of 2 for fast computation% more points = more time domain samples (smoother & more cycles)

num_carriers = 32 % should be it does not get copied over y-axisspaced_chunks(i,fft_size:-1:fft_size/2+2) = conj(spaced_chunks(i,2:fft_size/2));

end

% perform ifft to create time domain waveform representing datatd_sets = zeros(num_chunks,fft_size);for i = 1:num_chunks

td_sets(i,1:fft_size) = real(ifft(spaced_chunks(i,1:fft_size)));end

% Construct signal to transmit by placing time domain sets in seriesxmit = zeros(1,num_chunks*fft_size);


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for i = 1:num_chunksfor k = 1:fft_size

xmit(k + (i-1)*fft_size) = td_sets(i,k);end

end

% simulating channel-----------------------------ch%completed---------------------------------------

disp('Receiving')

% rx_chunk

% break received signal into parellel sets for demodulationrecv_td_sets = zeros(num_chunks,fft_size);for i = 1:num_chunks

for k = 1:fft_sizerecv_td_sets(i,k) = recv(k + (i-1)*fft_size);

endend

% perform fft to recover original data from time domain setsrecv_spaced_chunks = zeros(num_chunks,fft_size);for i = 1:num_chunks

recv_spaced_chunks(i,1:fft_size) = fft(recv_td_sets(i,1:fft_size));end

% rx_dechunk

% take out zeros_between from recv_spaced_chunks --> recv_chunksrecv_chunks = zeros(num_chunks, num_carriers);i = 1;for k = zeros_between +1:zeros_between +1:fft_size/2

recv_chunks(1:num_chunks,i) = recv_spaced_chunks(1:num_chunks,k);i = i+1;

end

% Recover bit stream by placing reconstructed frequency domain data in seriesrecv_dechunked = zeros(1, num_chunks*num_carriers);for i = 1:num_chunks

for k = 1:num_carriersrecv_dechunked(k + (i-1)*num_carriers*2) = real(recv_chunks(i,k));recv_dechunked(k + (i-1)*num_carriers*2 + num_carriers) = imag(recv_chunks(i,k));

endend

% take out trailing zeros from output --> outputoutput_analog = recv_dechunked(1:data_length);output = sign(output_analog);output = pol2bin(output);

output_samples_big = zeros(1,floor(length(output)/8)); %extra zeros are not original datafor i = 1:length(output_samples_big)

output_samples_big(i) = bin2eight(output(1 + (i-1)*8:(i-1)*8 + 8));end%convert dynamic range from 0:255 to -1:1output_samples = (output_samples_big-127)/128;%sound file outputwavwrite(output_samples, 11025, 8, 'OFDM_out.wav')

% Analysis

disp(' '), disp('------------------------------------------------------------')disp('Preparing Analysis')

figure(1), clfsubplot(221), plot(data_samples), title('OFDM Symbol Input Data');subplot(223), plot(output_samples), title('OFDM Recovered Symbols');

subplot(222), plot(xmit), title('Transmitted OFDM');subplot(224), plot(recv), title('Received OFDM');

dig_x_axis = (1:length(xmit))/length(xmit);figure(2), clf


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num = [1, zeros(1, d1-1), a1, zeros(1, d2-d1-1), a2];den = [1];[H, W] = freqz(num, den, 512);mag = 20*log10(abs(H));phase = angle(H) * 180/pi;

subplot(313)freq_data = abs(fft(recv));L = length(freq_data)/2;plot(dig_x_axis(1:L), freq_data(1:L))xlabel('FFT of Received OFDM')axis_temp = axis;

subplot(311),freq_data = abs(fft(xmit));plot(dig_x_axis(1:L), freq_data(1:L)), axis(axis_temp)title('FFT of Transmitted OFDM')

subplot(312)plot(W/(2*pi),mag),ylabel('Channel Magnitude Response')

figure(3), clfsubplot(211);

plot(W/(2*pi),mag);title('Channel Magnitude Response');

xlabel('Digital Frequency');ylabel('Magnitude in dB');

subplot(212);

plot(W/(2*pi),phase);title('Channel Phase Response');

xlabel('Digital Frequency');ylabel('Phase in Degrees');

binary_err_bits_OFDM = 0;for i = 1:length(data_in)

err = abs(data_in(i)-output(i));if err > 0

binary_err_bits_OFDM = binary_err_bits_OFDM +1;end

endBER_OFDM = 100 * binary_err_bits_OFDM/data_length;

disp(strcat('OFDM: BER=', num2str(BER_OFDM,3), ' %'))

disp(strcat(' Number of error bits=', num2str(binary_err_bits_OFDM)))

% Listen to soundsdo_again = '1';while ( ~(isempty(do_again)) )

disp(' ')disp('Press any key to hear the original sound'), pausesound(data_samples,11025)disp('Press any key to hear the sound after OFDM transmission'), pausesound(output_samples,11025)do_again = '';do_again = input('Enter "1" to hear the sounds again or press "Return" to end ',

's');end

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ch.m

disp('Simulating Channel'),disp('--------------------------------------------------------------')recv = xmit; % channel is applied to recv, don't modify transmitted data

norm_factor = max(abs(recv)); % Normalize all data before applyingrecv = (1/norm_factor) * recv; % channel for a fair comparison

% ch_clippingclip_level = 1;for i = 1:length(recv)


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if recv(i) > clip_levelrecv(i) = clip_level;

endif recv(i) < -clip_level

recv(i) = -clip_level;end

end

% ch_multipatha1 = 0.3;a2 = 0.25;d1 = 6;d2 = 10;copy1=zeros(size(recv));for i=1+d1:length(recv)

copy1(i)=a1*recv(i-d1);end

copy2=zeros(size(recv));for i=1+d2:length(recv)

copy2(i)=a2*recv(i-d2);end

recv=recv+copy1+copy2;

% channel noise

% noise_level = 0.1;% noise = (rand(1,length(recv))-0.5)*2*noise_level;

% recv = recv + noise;

recv = awgn(recv,300);

recv = norm_factor * recv;

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bin2pol.m

function y = bin2pol(x)

% bin2pol%% Converts binary numbers (0,1) to polar numbers (-1,1)% Accepts a 1-D array of binary numbers

y = ones(1,length(x));for i = 1:length(x)

if x(i) == 0y(i) = -1;

endend

pol2bin.m

function y = pol2bin(x)

% pol2bin%% Converts polar numbers (-1,1) to binary numbers (0,1)% Accepts a 1-D array of polar numbers% Removes trailing zeros, since they are not valid data

% % Remove zeros - not needed with intelligent decoding% last_data=length(x);% while x(last_data) == 0

% last_data = last_data - 1;% end

y = ones(1,length(x));for i = 1:length(x)

if x(i) == -1y(i) = 0;

endend

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Wireless Transmission Using Orthogonal Frequency Division Multiplexing

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