# Overview Of Orthogonal Frequency Division Multiplexing Computer Science Essay

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## ABSTRACT

Orthogonal Frequency Division Multiplexing (OFDM) is one of the methods where multiple signals are transmitted simultaneously dividing the total bandwidth into a number of frequency bands or sub-channels which are equally distributed. Thus it can be considered as a multi carrier modulation technique which splits a high-rate data stream into a low-rate data stream. Here subcarriers are used to transmit the data to each one of the frequency bands such that each one of the subcarrier is orthogonal to each other. Here the subcarriers are independent to each other.

Even though OFDM is considered as one of the best modulation schema for high speed transmission links, one major problem is with the peak to average power ratio (PAPR). This is due to the adding of multiple subcarriers for the signal transmission. As a result of these subcarriers the OFDM signal contains large peaks which cannot be controlled by a power amplifier. This results in the degradation of the system. Thus the main aim of the project is to reduce those large peaks of the OFDM signals; reducing the peak to average power ratio. Many methods have been implemented for reduction of PAPR, but efficient techniques among them are Clipping method, Tone Reservation Method, Selective Mapping method and Partial Transmission method.

The project is based on Clipping and Filtering method.

In clipping technique, sub-carriers do not affect the amplifier's efficiency. The main reason behind the implementation of this method is that the implementation is simple when compared to other methods. In this method once clipping has been done, it results in the leakage of spectrum into adjacent channels, causing out-of-band distortion among the signals. This distortion leads to adjacent channel interference which is caused due to the spectral leakage. It can be reduced by implementing filtering technique, where almost all of the out-of-band distortions get eliminated. By the whole PAPR gets reduced which can be shown by calculation and plotting the curves of Complementary Cumulative Distribution Function (CCDF) represented in amplitude and Peak to Average Power Ratio (PAPR) represented in power gain 'dB'. These CCDF vs. PAPR curves are plotted for the original OFDM signal, clipped signal and filtering signal. Finally these three signals are compared and the amount of reduction of PAPR is noted.

## INTRODUCTION

## What is OFDM:

OFDM is one of the frequency division multiplexing (FDM) schemes employed as a digital multicarrier modulation method. Here a large number of orthogonal sub-carriers are used to transmit the data. The transmitted data is evenly divided into parallel data streams, one for each one of the subcarriers. Then modulation is carried out for each subcarrier using a conventional modulation scheme such as phase-shift keying or quadrature amplitude modulation. Here the modulation is done at a very low symbol rate similar to single-carrier modulation techniques.

## History of OFDM:

The concept of OFDM was dated back to 1960's and 1970's where the multiple propagation of carriers are responsible for inter symbol interference. Thus OFDM was used for the reduction of the inter symbol interference. For a parallel data system the total frequency bands are divided into N non-overlapping frequency sub bands or sub channels. For the reception of the signals they must be orthogonal to each other. Orthogonality can be achieved by transmitting different signals using different carriers. This method of separating signals from each other is known as Frequency Division Multiplexing (FDM) which has been used from the days of radio and telecommunications. However the main drawback of FDM is insufficient use of the available frequency spectrum. This can be sorted out by using both FDM and parallel data using overlapping of sub-channels. But there arise some problemssuch as inter symbol interference (ISI) and inter channel interference (ICI).

OFDM being a modern way of modulation technique has been widely used in today's radio communications. Also it is used in Wi-Fi along with 802.11a standard. It is also used for digital terrestrial television transmission and also in DAB digital radio. Digital Radio Mondi ale which is a recent form of broadcasting adopted COFDM (Coded OFDM), which is one of the variants of OFDM where the signal has been incorporated with error correction coding.

## Variants of OFDM:

OFDM consists in several forms which are known as variants. All these variants exhibit the same basic format of OFDM with some added features. Some of them are listed below.

COFDM: It is one of the variants of OFDM which is known as coded OFDM which incorporates error detection coding into the signals.

Flash OFDM: This is one of the fastest variants of OFDM developed by Flarion which spreads signals over a given spectrum band using multiple tones.

VOFDM: It is also known as vector OFDM. It uses MIMO (multiple input multiple output) technology; developed by CISCO. MIMO makes use of multiple antennas for the signal transmission and reception such that the multi-path effects are utilized for the enhancement of signal reception and improving transmission speeds.

WOFDM: It is known as wideband OFDM. The main function of it is to make sure that transmitter and receiver won't be affected by the frequency errors, mainly the system performance. WOFDM is mainly used in Wi-Fi systems.

Telecommunications industry has been facing problem providing telephonic services to the rural areas where there is a less customer base. This is because the cost of installation of a phone network with wired connection is very high. In such a case wireless network can be used but the problem in using such a network is that for urban and rural areas, for maintaining the required coverage very large cell sizes are required leading to longer delay times and signal path losses. Now-a-days GSM technology is implemented for wireless telephone systems in rural areas. But the problem is that this technology makes use of TDMA which causes inter symbol interference (ISI) due to its high symbol rate. In order to reduce these effects digital telephone systems are introduced with the aim of improving the capacity of cells, flexibility and multipath immunity. To achieve these aims techniques such as code division multiple access (CDMA) and Coded OFDM (COFDM) have been introduced. These systems are implemented to provide wireless system in rural areas. Some of the new radio broadcast systems like Digital Video Broadcasting (DVB) and Digital Audio Broadcasting (DAB) makes use of the COFDM technology.

In code division multiple access (CDMA) all the users are given same frequency band to transmit using special set of codes. The information transmitted is bandwidth spread by multiplying with pseudo random sequence codes. Both mobile station and base station will be aware of the codes that are used for transmitting and receiving the signal.

While in OFDM/COFDM many users are allocated a frequency band to transmit the signal, subdividing the given bandwidth into many bandwidth carriers. Thus several carriers will be assigned to each user for transmitting the data. Here the transmission is done such that there is orthogonality between the carriers, where the carriers are closely packed to each other which is quite opposite to FDM. Thus higher spectral efficiency is achieved in OFDM. OFDM exhibits high data rates and applicable to wireless and mobile communications like digital audio broadcasting (DAB), digital video broadcasting (DVB) and mobile phones etc. The purpose of OFDM is to eliminate the errors pertaining to inter symbol interference (ISI).

## Multiple Access Techniques:

Multiple Access techniques are used where more users are allocated with a given bandwidth radio spectrum. Generally limited bandwidth is allocated to any radio spectrum. The total bandwidth of a mobile phone is usually in the range of 50MHz, which is divided into half for covering the forward and reverse links of a system. Sharing of such a frequency spectrum results in increase of capacity and efficiency of any network. Some of the methods which share their frequency spectrum among multiple users in a wireless system are FDMA, TDMA and CDMA.

## Frequency Division Multiple Access (FDMA)

In is a method in which the available bandwidth is sub-divided into a number of frequency channels equally spaced to each other. Here every user is assigned with a specific frequency range for transmitting and receiving the data. When in a call no two users can use the same frequency channel. Further every user is provided with a forward link channel (from base station to mobile) and a backward/reverse channel (towards the base station). The signal transmitted on each of the channel is continuous which allows the transmissions that are analog. FDMA exhibits a low channel bandwidth typically of 30 KHz as every user is supported with only a single channel. Thus FDMA is primarily used for the subdivision of large frequency spectrum of bands. Figure (fig number) below shows the users being allocated with bandwidth in different channels.

Figure ( ) Shows that each user is allotted to each channel

Figure ( ) Bandwidth divided into frequency channels

## Time Division Multiple Access (TDMA)

TDMA is a technique in which the available bandwidth is divided into a number of time slots, where every user is assigned with a specific time slot for transmitting and receiving the data. The allocation of time slots per frame to each user is shown in the figure ( ).

http://www.skydsp.com/publications/4thyrthesis/Image14.gif

Figure ( ) shows that each user has been allotted a time slot per frame

The process of signal transmission is quite different in TDMA where the data to be transmitted is kept in a buffer and then burst transmitted preventing the continuous transmission of the channel. First the data to be transmitted is buffered along the previous frame and then burst transmitted at a very high data rate for the time slot duration of a channel. TDMA is vulnerable to errors such as multipath effects due to very high data transfer rate which leads to inter symbol interference (ISI).

Generally TDMA is used in association with FDMA for subdividing the allocated bandwidth into several channels. The main reason in doing this is to minimize the number of users per channel using a lower data rate. The association of TDMA with FDMA is shown in the below figure ( ).

http://www.skydsp.com/publications/4thyrthesis/FDMA_TDMA.jpg

Figure ( ) showing the bandwidth is divided into both frequency channels and time slots

Here the channels that are divided using FDMA are further sub-divided using TDMA so that more users use a single channle to transmit the data. TDMA technique is mostly used by second generation digital mobile phones.

## Code Division Multiple Access(CDMA)

CDMA technology is quite different compared to both FDMA and TDMA because in CDMA neither uses frequency channels nor time slots. The message gets multiplied with a large bandwidth signal called pseudo random noise code (PN code). All the users transmit data using the same frequency simultaneously. The transmitted signals are received by the receiver making use of the PN code used by the transmitter .

Figure ( ) shows the spectrum of CDMA.

http://www.skydsp.com/publications/4thyrthesis/CDMA.jpg

Figure ( ) showing the spectrum of CDMA

## Clipping and Filtering

In general OFDM signal consists of a lot of subcarriers which results in the large peaks of the signal. All these peaks are reduced by using clipping technique which reduces the PAPR.

In clipping method all those peaks of the signal exceeding the threshold level are cut-off, thus resulting in the reduction of PAPR.

Clipped signal Ac(t) can be expressed by followings relationship:

Ac(t) = C.ejα(t) ; |A(t)| > C

= A(t) ; |A(t)| ≤ C

Where: Ac(t) stands for the clipped signal

A(t) stands for the original signal

C stands for the clipping level

α(t) stands for the phase of Ac(t)

Thus the large peaks of the signal are removed by the limitation of threshold which results in the PAPR reduction. During the process of clipping, there happens to be a decrease in the power of input band, effecting the operation of the system and power leakage in out-of-band.

These affect the other users by creating some distortions and inter channel interference (ISI).

Thus signal distortions occur due to this clipping which results in the adjacent channel interference. Filtering of the clipped signal has to be done in order to reduce these effects which further results in the increase of PAPR. For the smooth operation of the system filtering is introduced after the clipping. By the introduction of filtering block unwanted spectrum is eliminated up to some level. Thus filtering reduces the effects caused by the clipping method.

## Advantages of clipping:

Tends to cut-off large peaks up to a threshold level.

Helps in the reduction of PAPR of the OFDM systems.

It is one of the cheapest and easy method to implement

## Disadvantages of clipping:

In-band power reduces due to clipping, resulting in the degradation of the system.

Leads to out-of-band power leakage thus affecting the other users and the system causing adjacent channel interference (ISI).

## PEAK TO AVERAGE POWER RATIO (PAPR)

In OFDM systems one of the main limitations is with the Peak to Average Power Ratio (PAPR). In OFDM systems subcarriers are used in large number which results in the rise of the PAPR. As long as the subcarriers tends do increase, the maximum peak power of the signal goes higher than that of the average power which cannot be controlled by the power amplifier (PA). Those signals having large peaks need an extensive liner region of the power amplifier for avoiding signal distortions. In a linear region the amplifier allows only some part of the OFDM signals having large peaks due to its limitation, beyond that limit is a region called the saturation region in which even though the input power increases the output remains the same without increasing. Thus saturation is caused in the power amplifier leading to the inter-modulation among the subcarriers, which results in interference among the band of signals and delivers the out-of-band energy which is unwanted. OFDM symbols exhibits some of the non-linear effects such as spectral spreading, inter-modulation (crosstalk among the carriers) and change in the signal constellation. Thus signals face in-band and out-of-band interference or noise due to the non-linear distortion. A high PAPR is undesirable due to the requirements of the system such as high dynamic range of both analog to digital and digital to analog converters.

An example of OFDM signal having large PAPR can be shown in the figure ( ).

Figure ( ) PAPR signal

PAPR is defined as

PAPR = 10 log {( A k)2}max / E{( A k)2}

Where {( A k)2}max is the peak amplitude of the signal and

E{( A k)2} is the average value of the signal

Some of the methods are proposed to reduce these peaks which help in the reduction of PAPR. Some of them are Clipping and Filtering method, Selective Mapping (SLM), Partial Transmit Sequence (PTS) and Tone Reservation method (TR).

## Partial Transmit Sequence Technique:

Partial Transmit Sequence is one of the techniques that are used for the reduction of PAPR in OFDM. The block diagram of the PTS system is shown in the below figure.

<b>Figure 3:</b> Block diagram for the PTS technique.

In PTS technique an input data block of 'N' symbols are partitioned into sub-blocks. After the symbols got partitioned and are converted from serial to parallel these parallel data blocks 'X' are again divided into 'M' sub-blocks. It is done for making the 'M' component signals to get passed through IFFT which is linear region. All these components are combined known as partial transmit sequence (PTS). During the process of adding up of all the components the PAPR of the OFDM signal raises which is a problem. Thus to reduce the high PAPR in OFDM signal, additional blocks have to be introduced to the 'M' blocks which is the weighting factor 'bm' after every individual block of IFFT before it sums up for getting the final result. For 1<m<M, the signal of the mth component of weighting factor is normally the phase rotation, bm = ejαm whose factor is the unit amplitude and which has to hold the output signal with same power like that of the original OFDM signal. The values of the 'm' factor {b1, b2, b3,..., bM} = {ejα1 , ejα2 , ejα3 ,..., ejαM } are chosen in such a way that the signal having large peaks is kept to be minimal. By making an exclusive search of all possible values of 'M' weighting phase factor, the CCDF for PAPR will have maximum values. The selection of phase factor usually is limited within finite number of elements which has,

αm € {µ| µ = (q/w) * 2π, for 1 ≤ q ≤ W} used for the reduction of complexity of search.

## Selective Mapping method (SLM):

SLM is one of the techniques used for reducing the PAPR in OFDM systems. Here each one of the information or data signal is mapped into 'Z' candidate blocks and chooses the better candidate having less PAPR. Now the candidate with less PAPR is then sent to the transmitter. The figure below shows the block for the implementation of SLM method.

Here the actual data to be sent to the transmitter is partitioned into blocks and converted from serial to parallel. After when it is converted to parallel the data 'X' is further divided into many candidate blocks. Here X1 is obtained by multiplying 'X' with B1, X2 by multiplying 'X' with B2 and likewise XZ by multiplying 'X' with BZ. The sequence is given by , B(z) = [b z,0 ,b z,1 ,...b z ,N − 1] T ,z=1, 2, ...,Z, resulting in Z modified data blocks. Here B1,B2,......Bz are statically independent vectors. The modified data block for the uth phase sequence X (u) is given by X (u) = [X 0 b z,0 ,X 1 b z,1 ,...,X N − 1 b z , N-1 ] T , z = 1, 2, ...,Z. The block having less PAPR is selected for transmission among the modified set of blocks X(z), z = 1,2,3,...,Z. This block information is thus sent to the receiver as the side information. The original data block is regenerated back by performing quite reverse operation at the receiver. SLM technique is implemented by using Z inverse discrete fourier transform (IDFT) operations and by using the bits of side information which is [log 2 Z] for each block of data. This method is applicable for different type of modulation schemes and as many number of sub-carriers. The number of phase sequences Z and their design are the important factors for reducing the PAPR for SLM technique.

Two problems are associated with SLM technique which is firstly the side information that has to be supplied for the receiver among the selected candidate blocks such that sent information is not distributed. Due to the providing of such information to the receiver the error occurrence is reduced. Secondly lot of inverse fast fourier transform's (IFFT) are required for the generation of 'Z' candidates. Significantly side problems occur due to this facility. Thus providing the side information to each candidate for generating small peaks will apparently reduce the user bandwidth.

## Tone Reservation method:

Tone Reservation method is also one among the other methods that is used to reduce the PAPR in OFDM systems. Here in this method it is based on summing up of data-block dependent time signal with the original multi-carrier signal in order to reduce the large peaks of the multi-carrier signal. The time domain signal can be computed at the transmitter side and stripped off at the receiver side with ease. The sub-carriers which are optimized for the PAPR reduction are not allowed to send the information by the transmitter. The main objective is to reduce the PAPR which can be done by finding the time domain signal that has to be added to the real time domain signal 'x'.

Suppose if a frequency domain vector Z is added to X; Z = [Z0, Z1, Z3 , ..., ZN-1] T , then the time domain signal is shown as x + z = IDFT {X + Z}, where z implies to the time domain signal due to Z. The data blocks of X and peak reduction vectors Z are restricted in tone reservation technique to let them remain in disjoint frequency spaces. In Z the L non-zero positions are known as peak reduction carriers (PRCs). The additional signals won't create any distortion due to the Orthogonality of the sub-carriers.

## Comparison of above three methods:

## Partial Transmit Sequence:

PTS method requires large number of IFFT blocks, which leads to the complexity of the system.

It requires more number of 'm' blocks in addition after the IFFT block operation in order to reduce high peak-to-average-power-ratio (PAPR).

More number of IFFT blocks as well as the introduction of additional 'm' blocks results in the complexity of the system.

## Selective Mapping:

Like PTS method this method also requires more number of IFFT blocks for the operation of the system.

Here masking method is used for the detection of the received signal.

In this method, during transmission additional side information has to be sent for the indication of the masking pattern.

The additional side information which is sent has to be protected from distortions.

Due to all these, the system design will become more complex to implement.

## Tone Reservation:

Unlike SLM method, tone reservation (TR) technique won't make use of any extra side information.

Unlike the above two methods, TR doesn't need more number of IFFT blocks, indeed it makes use of only one IFFT block for the implementation.

It needs more iteration to be done after IFFT block.

It has no receiver block which means that it won't require any receiver section in its design.

It is less complex, indeed simple compared to other methods.

## Orthogonal Frequency Division Multiplexing

## What is OFDM?

OFDM is a multicarrier modulation technique in which multiple signals are transmitted simultaneously thus dividing the whole bandwidth into a number of frequency channels which are distributed equally. Thus it splits a high-rate data stream into a low-rate data stream transmitted over a large number of subcarriers. Subcarriers are used for the transmission of the data to each one of the frequency bands such that the subcarriers are orthogonal to each other. Thus a large number of subcarriers are responsible for the transmission of the user information where each subcarrier is modulated by a less data rate, where subcarriers with less data rate results in the increase of symbol duration which decreases multipath delay.

In OFDM the condition of Orthogonality is maintained mainly for the elimination of crosstalk. This can be achieved by placing the subcarriers very close to each other, but they are independent to each other. Thus by placing the subcarriers close to each other results in the effective use of the bandwidth where more saving of the bandwidth takes place. In this manner even for the same bandwidth high data rates can be achieved. Thus OFDM can be differentiated from conventional multicarrier technique such as Frequency Division Multiplexing (FDM). The spectrum of OFDM can be shown in the figure ( ) when compared to FDM which saves the bandwidth.

The figure ( ) represents the spectrum of the conventional FDM

The figure ( ) represents the spectrum of the OFDM

Thus OFDM makes use of closely spaced subcarriers thus saving the bandwidth when compared to the conventional FDM.

## Advantages of OFDM:

Makes use of the frequency spectrum very effectively by allowing the sub-carriers to overlap with each other.

OFDM is used for the reduction or elimination of the inter symbol interference (ISI).

In OFDM FFT/IFFT blocks are used for preventing the sub-carriers to interfere with each other.

OFDM is robust towards the narrowband interference which affects other sub channels.

OFDM is robust towards inter symbol interference (ISI) and fading which arises due to the multi-path propagation.

Saving of bandwidth compared to the other modulation schemes such as frequency division multiplexing (FDM).

Channel equalization is simple compared with other single carrier systems.

OFDM is robust against multi-path environment.

## Disadvantages of OFDM:

Large peak-to-average-power-ratio (PAPR) due to the adding up of large number of sub-carriers.

Reduction in the efficiency of the RF power amplifier.

Introduces in-band distortion.

Introduces out-of-band distortion which results in inter symbol interference (ISI) caused due to the leakage of power spectrum.

## OFDM Applications:

Digital Audio Broadcasting-Terrestrial (DAB-T)

Digital Video Broadcasting (DVB)

Wireless LAN IEEE 802.11a, 802.16 standards

Hyper LAN's

Asymmetric Digital Subscriber Line (ADSL)

## Digital Audio Broadcasting-Terrestrial (DAB-T)

OFDM is the technology used in DAB-T. It has been specially designed for the digital audio modulation schemes and to contend with multipath interference of the mobile receivers.

## Digital Video Broadcasting-Terrestrial (DVB-T)

OFDM is implied in Asia and Europe for the purpose of broadcasting digital video such as DVB-T. As recommended by the European commission, almost all television that has been adopted for the users have to use a transmission system which has been standardized by one of the recognized standardized body in Europe.

## Wireless LAN's

OFDM find its extensive use in some of the wireless LAN standards such as IEEE 802.11a/g/n and in WIMAX.

## Asymmetric Digital Subscriber Line (ADSL)

OFDM technology is also used in ADSL. Here data connections are achieved at a very high speed making use of the copper wires. Attenuation affects the long copper wires when used at higher frequencies. This is main reason behind the implementation of OFDM which is resistive to frequency attenuation and narrow-band interference

## Generation of OFDM signal

## IEEE 802.11a WLAN Physical Layer

IEEE 802.11a physical layer is used for the generation of the OFDM signal. A new form of modulation scheme known as OFDM has been introduced to the wireless world by this standard. Thus with the introduction of OFDM higher data rates were provided compared to that of the other modulation schemes. It also provides higher data rates in a smaller bandwidth. IEEE 802.11a used the frequency bands from 2.4GHz to 5GHz band. This 5GHz band is further subdivided into two areas; 5.15GHz-5.35GHz and 5.725GHz-5.825GHz. 802.11a separated both these areas into 12 carriers which are overlapping with a spacing of 20MHz.

## Blocks used for the OFDM generation:

For generating OFDM signal, some of the blocks in IEEE 802.11a have been used. The blocks are mentioned in the figure below.

(figure)

## Variable Rate Data Source

It consists of 4 sub-blocks. They are:

Mode: It is an input port for a subsystem.

Source Enable: In this block indexing is done. Then the signal is compared for its relational operation. The relational block accepts real or complex signals of any data type as supported by Simulink. The output of the relational block is set to be frame based. Then an unbuffer is used for converting input frames into scalar outputs. It unbuffers the inputs according to the rows. Here the blocks adjust the output rates such that the sample period is same at both the input and the output. Then the resultant data is given to the output port of the subsystem.

Binary Source: This block enables the binary data to be transmitted to the next set of blocks.

Buffer: This block is used for buffering the input to a smaller or larger frame size. It redistributes the input samples to a frame size smaller or larger than that of the output frame size.

Tx bits: It is the output port of the subsystem used to transmit the output samples from buffer to the other block.

## Modulator Bank

The signals taken from the output of the data source block are sent to the modulator bank block.

## OFDM Symbols

This block consists of a sub block named Reshape. Reshape block is used to change the magnitude of the signal. It makes changes to the dimensions of the signal to the given specified dimensions. For example it converts a 2-D array matrix into a 1-D array matrix. Then the output of the reshape block is given to the OFDM frames block.

## Training

This block consists of two sub blocks. They are:

Training Sequence: This block is mainly used for the generation of a constant value. It generates real constant values or complex constant values depending on the parameter settings. The dimensions and elements of output block are same as that of the 'constant value' parameter. If the output of the block has to be a 1-D array, then the 'Interpret vector parameters as 1-D' has to be selected. Otherwise the constant value field is treated as a matrix.

Frame Conversion: This block is used for setting the parameter of the output signal to be a frame-based.

## Pilots

This block contains three sub blocks.

PN Sequence Generator: This block is used for generating pseudo random sequences which are also called as pseudo random binary numbers. Pseudo noise sequence is used in direct sequence spread-spectrum system. A shift register is used for generating pseudo noise sequences.

Unipolar to Bipolar Converter: This block converts the unipolar input signal into a bipolar output signal. The range of integers is between 0 and N-1. If the input signal contains integers between 0 and N-1, N is N-ary number parameter, then the output signal comprises of integers between -(N-1) and N-1.

Reshape: The output of the unipolar to bipolar converter is given to the reshape block. Here this block is used for changing the magnitude of the signal. It changes given input signal to other dimensionality output signal. Output dimension parameter field is used for specifying the dimensions of an output signal.

## Assemble OFDM Frames

It consists of three sub blocks.

Select Data Block: This block is also known as multiport selector block. This block is used to extract multiple sets of input rows or columns to multiple output ports. If the 'Select parameter' is set to rows, then matrix rows are selected and all the elements included on the rows are chosen. If 'Select' parameter is set to columns, then matrix columns are selected and all the elements included in the columns are chosen. The input rows and columns can appear as many times in any one of the outputs or they might not appear at all.

The output from the pilot block is given as input to the assemble subcarrier block by multiplying it with a constant value gain. Here both the input and constant gain can be a scalar, vector or a matrix. For the gain parameter the value of the gain is '-1' and the multiplication is done element-wise as specified by the multiplication parameter block. Here the output data type can be selected as 'same as input' as indicated in the 'output data type mode'.

Other block called Zero DC is also used which generates a constant value which can be real or complex and is selected as frame-based by the frame conversion block.

Assemble Sub carriers: This block is also known as a matrix concatenation block which is used to concatenate input vertical-wise. The output from Pilot block and Zero DC block are given as input to this block. This matrix concatenation block concatenates inout matrices along row-wise or column-wise. Here if the inoput given is frame-based, then the output is also frame-based. Else, the output is sample-based. If the concatenation method parameter is selected as vertical, them the matrix is concatenated column-wise. Here same column dimensions have to be possessed by the inputs for vertical concatenation, but they may have different row dimensions.

Prepend Training Sequence: This block is used for the horizontal concatenation of the matrix. The output from training block is given as input to this block. Here this matrix concatenation block concatenates input matrices along column-wise. If the inputs given to this block are frame-based, then the output is selected as frame-based; otherwise sample-based. Here the matrix is concatenated row-wise as the concatenation method parameter is selected as horizontal. Here the dimensions possessed by the input must be the same as that are possessed by the row, instead they may have different column dimensions.

Zero Pad: This block is used for zero padding the matrix along row-wise or column-wise. Here by doing zero padding the dimensions of the input changes from Mx-by-Nx to My-by-Ny. Here the padding can be done at the end of the row or at the end of the column. The number of output rows can be given using the 'Number of output rows' parameter.

## IFFT

## Append Cyclic Prefix

This block consists of other sub block.

Add Cyclic Prefix: This block is used for selecting input elements from a matrix or a vector. This Selector block generates output elements selected of an input matrix or vector. This block accepts the matrix signals as input. If the input type is matrix, the selector block outputs a matrix of elements selected form the input matrix. The block specifies the row and column indices of the elements to be selected either from rows and columns parameters or from external signals. Here the 'Source of row indices' and 'Source of column indices' is selected as internal.

## Multiplex OFDM Frames

The output of append cyclic prefix block is given as an input to the Multiplex OFDM Frames block. This block consists of a sub block called reshape. This block is used for changing the dimensions of a signal. It changes the dimensionality of an input signal to the other dimensionality output signal. The dimensionality of the output signal is set by using the 'Output dimensionality' parameter. For instance, this block can be used for changing M-element vector to a 1-by-M or M-by-1 matrix signal and vice versa.

## Multipath Channel:

Unbuffer: This block is used to unbuffer the input frame into a sequence of scalar outputs. It unbuffers an Xi-by-Y frame-based input into a 1-by-Y sample-based output. This means that the inputs get buffered according to row-wise such that each row of the matrix develops into an independent time-sample in the output. Here the rate of receiving of inouts by the block is normally less compared to the rate at which it produces the outputs.

Complex to real imaginary: This block is used to convert the input signal which is complex in nature into its real and imaginary parts. This block accepts an input signal of complex value and gives an output which is either real and imaginary or only real or only imaginary, depending on the output parameter setting. Here if the outputs are real, then they possess the data types same as that of the complex input and vice versa. Here the input can be an array of complex signals in which the output signals are the arrays of the same dimension. The real output consists of the real parts of the complex output where as the imaginary output consists of the imaginary parts of the corresponding complex input elements.

To Workspace: This block is used ti write the data into the workspace. It writes its output to an array or structure which has the name mentioned using the blocks parameter called 'Variable name'. Here the parameter called 'Save format' is used for determining the format of output which can be an array or a structure. If option array is selected, then this block saves the input as an M-dimensional array where 'M' has more dimensions than that of the input signal. Suppose if the input signal is 1-Dimensional array, then the array of the resulting workspace will be 2-Dimensional. Similarly the dimension of the workspace becomes 3-Dimensional if the input signal is of 2-Dimensional. Here we select the output format as an array.

## Aim of the project

The main aim of this project is to reduce the peak -to-average-power ratio (PAPR) in orthogonal frequency multiplexing (OFDM) systems. For this purpose clipping and filtering technique is used for reducing the PAPR which is a major drawback in most of the OFDM systems. Normally OFDM signals contains large number of sub-carriers which results in large number of peaks. These peaks allows for the large PAPR. For reducing these peaks Clipping method is implemented. But clipping introduces in-band and out-of-band radiation causing problems for other users and resulting in inter-symbol-interference (ISI). So in order to reduce these effects filtering technique has been used which eliminates the effects that are caused due to the implementation of clipping method.

## Software used for implementing coding

This project has been implemented in MATLAB software which is user-friendly and used for getting effective results.

## About MATLAB:

MATLAB® is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. Typical uses include

Math and computation

Algorithm development

Data acquisition

Modelling, simulation, and prototyping

Data analysis, exploration, and visualization

Scientific and engineering graphics

Application development, including graphical user interface building

MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar non-interactive language such as C or Fortran.

The name MATLAB stands for matrix laboratory. MATLAB was originally written to provide easy access to matrix software developed by the LINPACK and EISPACK projects. Today, MATLAB engines incorporate the LAPACK and BLAS libraries, embedding the state of the art in software for matrix computation.

MATLAB has evolved over a period of years with input from many users. In university environments, it is the standard instructional tool for introductory and advanced courses in mathematics, engineering, and science. In industry, MATLAB is the tool of choice for high-productivity research, development, and analysis.

MATLAB features a family of add-on application-specific solutions called toolboxes. Very important to most users of MATLAB, toolboxes allow you to learn and apply specialized technology. Toolboxes are comprehensive collections of MATLAB functions (M-files) that extend the MATLAB environment to solve particular classes of problems. Areas in which toolboxes are available include signal processing, control systems, neural networks, fuzzy logic, wavelets, simulation, and many others.

## Simulink

In this project we also make use of the IEEE 802.11a WLAN Physical Layer which is loaded in the simulink section of the MATLAB. This model is used to generate the OFDM signal.

## About Simulink:

Simulink is a software package for modelling, simulating, and analyzing dynamic systems. It supports linear and nonlinear systems, modelled in continuous time, sampled time, or a hybrid of the two. Systems can also be multi-rate, i.e., have different parts that are sampled or updated at different rates.

## Tool for Simulation:

Simulink encourages you to try things out. You can easily build models from scratch, or take an existing model and add to it. You have instant access to all the analysis tools in MATLAB®, so you can take the results and analyze and visualize them. A goal of Simulink is to give you a sense of the fun of modelling and simulation, through an environment that encourages you to pose a question, model it, and see what happens.

Simulink is also practical. With thousands of engineers around the world using it to model and solve real problems, knowledge of this tool will serve you well throughout your professional career.

## Research Methodology:

In this process the first and foremost step is the generation of the OFDM signal for the implementation. Here IEEE 802.11a WLAN Physical Layer model which is made available in simulink blocks in Matlab has been used to generate the OFDM signal.

OFDM signal which has been obtained from the above model consists of large peaks which can't be handled by the power amplifier. These peaks will result in large peak-to-average-power ratio (PAPR). This will tend to result in the degradation of the system and power leakage effects etc.

So the OFDM signal thus obtained has to be calculated for its PAPR and then clipping method has to be implemented for the thus generated OFDM signal. After the implementation of the clipping technique the graph for cumulative complementary distribution function (CCDF) versus peak-to-average-power ratio (PAPR) has to be plotted for both the signals. Here CCDF will be shown in amplitude and PAPR will be in power 'dB'. Here clipping method is implemented by doing some coding in MATLAB.

After the calculation of PAPR of the OFDM signal, clipping and filtering method has to be implemented for the OFDM signal in order to reduce the peaks. Then PAPR has to be measured after clipping.

The OFDM signal which is clipped results in unwanted spectrum leaking into the side lobes causing inter-symbol-interference (ISI) thus affecting the other users.

So filtering technique will be implemented to reduce all those problems that were caused due to the implementation of clipping method.

After the implementation of both clipping and filtering mechanisms which helps for the reduction of large peaks and unwanted spectral leakage, PAPR values are to be calculated. Thus CCDF vs PAPR has to be plotted for all the three signals; original OFDM, Clipped OFDM and filtered OFDM signals.

The CCDF vs PAPR curves thus plotted shows the amount of PAPR thus gained or lost.

All the values of PAPR have to be noted down to show the amount of total PAPR gained.