Orthogonal Frequency Division Multiplexing 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 such as 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 transmission and reception of 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 such as 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 ( ).
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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 ( ).
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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.
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Figure ( ) showing the spectrum of CDMA
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 ( ).
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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).
One of the simplest methods to implement is Clipping and Filtering method where the large peaks are sorted off using the clipping technique. Filtering is then done to avoid the out-of-band radiation.
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).
References:
B.levng Patrick and chevng, "simulation of adaptive array algorithm for OFDM and adaptive vector ofdm system" Polytechnique of Virginia inisistute of university, 2002.
Li.X and J.L cimniy, "effects of the clipping and filtering and the filtering performance of OFDM', Letters of IEEE communications volume 2 and 5 131-133, 98.
H.Xiao, Anhua.J, Latif.L.U and J. Zhng. "companding transform for PAP reduction of OFDM signal" wireless communications IEEE transcations on volume 6, 2004.
Ochuaih and H. Imai, "A system approach to PAPR reduction in OFDM", proceedings to VTC 98, Canada 6-11, 1998.
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) * 2Ï€, 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 and stripped off at the receiver 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 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.
