Orthogonal frequency division multiplexing


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Orthogonal frequency division multiplexing

  1. 1. Chapter-1 1. INTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM) is one of the latest modulationtechniques used in order to combat the frequency-selectivity of the transmission channels,achieving high data rate without inter–symbol interference. The basic principle of OFDM isgaining a wide spread popularity within the wireless transmission community. Furthermore,OFDM is one of the main techniques proposed to be employed in 4th Generation WirelessSystems. Therefore, it is crucial to understand the concepts behind OFDM. In this paper it isgiven an overview of the basic principles on which this modulation scheme is based. Due to the spectacular growth of the wireless services and demands during the lastyears, the need of a modulation technique that could transmit high data rates at highbandwidth efficiency strongly imposed. The problem of the inter–symbol interference (ISI)introduced by the frequency selectivity of the channel became even more imperative once thedesired transmission rates dramatically grew up. Using adaptive equalization techniques atthe receiver in order to combat the ISI effects could be the solution, but there are practicaldifficulties in operating this equalization in real-time conditions at several Mb/s withcompact, low-cost hardware. OFDM is a promising candidate that eliminates the need ofvery complex equalization. In a conventional serial data system, the symbols are transmitted sequentially, one byone, with the frequency spectrum of each data symbol allowed to occupy the entire availablebandwidth. A high rate data transmission supposes a very short symbol duration, conducingat a large spectrum of the modulation symbol. There are good chances that the frequencyselective channel response affects in a very distinctive manner the different spectralcomponents of the data symbol, hence introducing the ISI [1]. The same phenomenon,regarded in the time domain consists in smearing and spreading of information symbols such,the energy from one symbol interfering with the energy of the next ones, in such a way thatthe received signal has a high probability of being incorrectly interpreted. Intuitively, one can assume that the frequency selectivity of the channel can bemitigated if, instead of transmitting a single high rate data stream, we transmit the datasimultaneously, on several narrow-band subchannels (with a different carrier correspondingto each subchannel), on which the frequency response of the channel looks “flat”. Hence, for 1
  2. 2. a given overall data rate, increasing the number of carriers reduces the data rate that eachindividual carrier must convey, therefore lengthening the symbol duration on each subcarrier.Slow data rate (and long symbolSub channel index frequency. The frequency selective channel response duration) on eachsub channel merely means that the effects of ISI are severely reduced. This is in fact the basic idea that lies behind OFDM. Transmitting the data among alarge number of closely spaced subcarriers accounts for the “frequency divisionmultiplexing” part of the name. Unlike the classical frequency division multiplexingtechnique, OFDM will provide much higher bandwidth efficiency. This is due to the fact thatin OFDM the spectra of individual subcarriers are allowed to overlap. In fact, the carriers arecarefully chosen to be orthogonal one another. As it is well known, the orthogonal signals donot interfere, and they can be separated at the receiver by correlation techniques. Theorthogonality of the subcarriers accounts for the first part of the OFDM name.1.1 OFDM PrinciplesIn this section, the key points of OFDM are presented: the principles of a multicarrier(parallel) transmission, the usage of FFT and the cyclic prefix „trick”. We will also discussthe main challenges that this technique must deal with. The concept of multicarrier (parallel) transmission In a mobile radio environment, the signal is carried by a large number of paths withdifferent strength and delays. Such multipath dispersion of the signal is commonly referred 2
  3. 3. as„ channel-induced ISI”and yields the same kind of ISI distortion caused by an electronicfilter [2]. In fact, the multipath dispresion leads to an upper limitation of the transmission ratein order to avoid the frequency selectivity of the channel or the need of a complex adaptiveequalization in the receiver. In order to mitigate the time-dispersive nature of the channel, thefinding of the multicarrier technique was to replace a single-carrier serial transmission at ahigh data rate with a number of slower parallel data streams. Each parallel stream will bethen used to sequentially modulate a different carrier. By creating N parallel substreams, wewill be able to decrease the bandwidth of the modulation symbol by the factor of N, or, inother words, the duration of a modulation symbol is increased by the same factor. Thesummation of all of the individual sub channel data rates will result in total desired symbolrate, with the drastic reduction of the ISI distortion. The price to pay is of course veryimportant, since the multicarrier transmission seems to act as a frequency multiplexation,which will generate problems in terms of bandwidth efficiency usage. The things go howeverbetter than seemed, because in OFDM the carriers are orthogonal to each-other and they areseparated by a frequency interval of Δf=1/T. The frequency spectrum of the adjacent subchannels will overlap one another, but the carrier’s orthogonality will eliminate in principlethe interchannel interference that we feared of. OFDM is a promising candidate for achieving high data rate transmission in mobile environment. The application of OFDM to high data rate mobile communication system is being investigated by many researchers. Cimini (1985) proposed a cellular mobile radio system based on OFDM used with pilot based correction. It was shown to provide large improvements in BER performance in a Rayleigh Fading Environment. Introduction of OFDM into cellular world has been driven by two main benefits Flexibility: each transceiver has access to all subcarriers within a cell layer. Easy equalization: OFDM symbols are longer than the maximum delay spread resulting in flat fading channel which can be easily equalized. OFDM benefited from considerable research interest from the military applications and it had been used in several high frequency military systems such as KINEPLEX, ANDEFT and KATHRYN (Zou and Wu, 1995). 3
  4. 4. Also the introduction of Digital Audio Broadcasting (DAB) based on OFDM, successful test on OFDM for Digital Television Terrestrial Broadcasting (dTTb) and research on OFDM for HIPERLAN type II and Wireless ATM projects have increased the interested towards OFDM. For IMT-2000/UMTS, two OFDM air interface concepts, Band Division Multiple Access (BDMA) and OFDM by Telia, were presented to Study Committee (Ojanperä, 1998). Digital Satellite services are becoming popular and application of OFDM to the Satellite Mobile Channel was proposed by Fernando and Rajatheva (1998). OFDM used in DAB standard for CD- quality digital audio broadcast. One benefit of OFDM in a wireless communications system is that the receiver does not need to constantly adapt an equalizer as a single carrier system would. OFDM system shows much favorable properties such as high spectral efficiency, robustness to channel fading, immunity to impulse interference, capability of handling very strong echoes (multipath fading). The mobile radio channel suffers from multipath propagation and the channel is time variant, depending on the speed of the mobile station. Thus, Forward Error Correcting schemes should be used in OFDM system to improve the performance better. Application of suitable coding scheme to OFDM provides a diversity effect through exploitation of the multipath nature of the fading channel.1.2. Neccesity of PAPR: There are some obstacles in using OFDM in transmission system in contrast to its advantages. A major obstacle is that the OFDM signal exhibits a very high Peak to Average Power Ratio (PAPR). Therefore, RF power amplifiers should be operated in a very large linear region. Otherwise, the signal peaks get into non-linear region of the power amplifier causing signal distortion. This signal distortion introduces intermodulation among the subcarriers and out of band radiation. Thus, the power amplifiers should be operated with large power back-offs. On the other hand, this leads to very inefficient 4
  5. 5. amplification and expensive transmitters. Thus, it is highly desirable to reduce the PAPR. The other limitation of OFDM in many applications is that it is very sensitive to frequency errors caused by frequency differences between the local oscillators in the transmitter and the receiver. Carrier frequency offset causes a number of impairments including attenuation and rotation of each of the subcarriers and intercarrier interference (ICI) between subcarriers. In the mobile radio environment, the relative movement between transmitter and receivercauses Doppler frequency shifts, in addition, the carriers can never be perfectlysynchronized. These random frequency errors in OFDM system distort orthogonalitybetween subcarriers and thus intercarrier interference (ICI) occurs. A Number of methodshave been developed to reduce this sensitivity to frequency offset. 5
  6. 6. Chapter-2 2. LITERATURE SURVEY:2.1 OFDM Overview: The Orthogonal Frequency Division Multiplexing (OFDM) transmission scheme isthe optimum version of the multicarrier transmission scheme. In the past, as well as in thepresent, the OFDM is refered in the literature Multi-carrier, Multi-tone and FourierTransform. The concept of using parallel data transmission and frequency multiplexing waspublished in the mid 1960s. After more than thirty years of research and development,OFDM has been widely implemented in high speed digital communications. Due to recentadvances of digital signal Processing (DSP) and Very Large Scale Integrated circuit (VLSI)technologies, the initial obstacles of OFDM implementation such as massive complexcomputation, and high speed memory do not exist anymore. The use of Fast FourierTransform (FFT) algorithms eliminates arrays of sinusoidal generators and coherentdemodulation required in parallel data systems and makes the implementation of thetechnology cost effective (Weinstein and Ebert, 1971). The OFDM concept is based on spreading the data to be transmitted over a largenumber of carriers, each being modulated at a low rate. The carriers are made orthogonal toeach other by appropriately choosing the frequency spacing between them. In contrast toconventional Frequency Division Multiplexing, the spectral overlapping among sub-carriersare allowed in OFDM since orthogonality will ensure the subcarrier separation at thereceiver, providing better spectral efficiency and the use of steep band pass filter waseliminated. OFDM transmission system offers possibilities for alleviating many of the problemsencountered with single carrier systems. It has the advantage of spreading out a frequencyselective fade over many symbols. This effectively randomizes burst errors caused by fadingor impulse interference so that instead of several adjacent symbols being completelydestroyed, many symbols are only slightly distorted. This allows successful reconstruction ofmajority of them even without forward error correction. Because of dividing an entire signalbandwidth into many narrow sub bands, the frequency response over individual sub bands isrelatively flat due to sub band are smaller than coherence bandwidth of the channel. Thus,equalization is potentially simpler than in a single carrier system and even equalization may 6
  7. 7. be avoided altogether if differential encoding is implemented. The orthoganality ofsubchannles in OFDM can be maintained and individual sub channels can be completelyseparated by the FFT.2.2 General OFDM system:Since the spectra of an OFDM signal is not strictly band limited, linear distortions such asmultipath propagation causes each subchannel to spread energy into the adjacent channelsand consequently cause ISI. One way to prevent ISI is to create a cyclically extended guardinterval, where each OFDM symbol is preceded by a periodic extension of the signal itself.When the guard interval is longer than the channel impulse response or multipath delay, theISI can be eliminated. By using time and frequency diversity, OFDM provides a means totransmit data in a frequency selective channel. However, it does not suppress fading itself.Depending on their position in the frequency domain, individual subchannels could beaffected by fading.This requires the use of channel coding to further protect transmitted data.Coded OFDM combined with frequency and time interleaving is considered the mosteffective means for a frequency selective fading channel. Figure 2.1 illustrates the process of a typical OFDM system. 7
  8. 8. The incoming serial data is first converted from serial to parallel and grouped into x bitseach to form a complex number. The complex numbers are modulated in a baseband fashionby the IFFT. And converted back to serial data for transmission.A guard interval is inserted between symbols to avoid intersymbol interference (ISI) causedby multipath distortion. The discrete symbols are converted to analog and lowpass filteredfor RF up-conversion.The receiver performs the inverse process of the transmitter. One tap equalizer is used tocorrect channel distortion. The tap coefficients of the filter are calculated based on channelinformation (Zou and Wu, 1995).2.3 Peak to Average power Ratio (PAPR):OFDM has several properties, which make it an attractive modulation scheme for high speedtransmission links. However, one major difficulty is its large Peak to Average Power Ratio(PAPR). These large peaks cause saturation in power amplifiers, leading to intermodulationproducts among the subcarriers and disturbing out of band energy. Therefore, it is desirableto reduce the PAPR. · To reduce the PAPR, several techniques have been proposed such asclipping, coding , peak windowing, Tone Reservation and Tone Injection. But, most of thesemethods are unable to achieve simultaneously a large reduction in PAPR with lowcomplexity, with low coding overhead, without performance degradation and withouttransmitter receiver symbol handshake. The complex envelope of the OFDM signal,consisting of N carriers is given by (Müller and Huber, 1997),Where g(t) is rectangular pulse of duration T and T is OFDM symbol duration.Peak to Average power Ratio is defined by (Müller and Huber, 1997),From the central limit theorem, for large values of N , the real and imaginary values of S(t)become Gaussian distributed. The amplitude of the OFDM signal there for has a Rayleigh 8
  9. 9. distribution with zero mean and a variance of N times the variance of one complex sinusoid.Assuming the samples to be mutually uncorrelated, the cumulative distribution function forthe Peak Power per OFDM symbol can be given by (Müller and Huber, 1997), In literature, two kinds of approaches are investigated which assure that thetransmittedOFDM signal does not exceed the amplitude A0 if a given back off is used. The first methodmakes use of redundancy in such a way that any data sequence leads to the magnitude ofOFDM signal greater than A0 or that at least the probability of higher amplitude peaks isgreatly reduced. This approach does not result in interference of the OFDM signal. In thesecond approach, the OFDM signal is manipulated by a correcting function, which eliminatesthe amplitude peaks. The out of band interference caused by the correcting function is zero ornegligible. However, interference of the OFDM signal itself is tolerated to a certain extent.Peak to Average power Ratio effect is described by Peak Envelop and Crest-Factor (CF)which is defined as the square root of Peak to Average Power Ratio. Here, we will refer it asPeak to Average power Ratio (PAPR). In the following section, some significant methods toreduce PAPR are described.Block CodingA block coding scheme for reduction of PAPR proposed by Jones, Wilkinson and Barton(1994) is to find code words with minimum PAPR from a given set of code words and tomap the input data blocks of these selected code words. Thus, it avoids transmitting the codewords which generates high Peak Envelop Power. But, this reduction of PAPR is at theexpense of a decrease in coding rate. It has 2.48 dB with ¾ rate block code for four carriersignal. For large number of carriers, necessary code sets exist but encoding and decoding isalso difficult task. It is not suitable for higher order bit rates or large number of carriers.M sequences the use of m-sequences for PAPR reduction is proposed by Li and Ritcey(1997). This is done by mapping a block of m input bits to an m-sequences [C0… ..CN-1] oflength N=2m-1. This results in a code rate of (m/2m-1). The m-sequences are a class of (2m-1,m) cyclic codes obtained from a primitive polynomial of degree m over GF(2). Tellambura 9
  10. 10. (1997) showed that the achievable PAPR is only between 5dB to 7.3 dB for m between 3 and10. The problem with this approach is the extremely low rate for large values of m.Selective ScramblingEetvelt, Wade and Tomlinson (1996) proposed this technique to reduce PAPR. The methodis to form four code words in which the first two bits are 00,01,10 and 11 respectively. Themessage bits are first scrambled by four fixed cyclically inequivalent m-sequences. Then theone with the lowest PAPR is selected and one of the pair of bits defined earlier is appendedat the beginning of the selected sequence. At the receiver, these first two bits are used toselect the suitable descrambler. When a scrambled binary sequence with high proportion of1s or 0s is applied to N- point IFFT OFDM modulator, it will give a signal with high PAPR.A scrambled binary sequence of length 2N with a Hamming weight close to N will oftengenerate low PAPR. Selecting structured scrambled sequence is critical. PAPR is typicallyreduced to 2% of the maximum possible value while incurring negligible redundancy in apractical system.Clipping and FilteringDeliberate clipping is a simple approach and, since the large peaks occur with a very lowprobability, clipping could be on effective technique for the reduction of the PAPR (ONeilland Lopes, 1995). However, clipping is a nonlinear process and may cause significant inbanddistortion, which degrades the bit error rate performance, and out of band noise, whichreduces the spectral efficiency. Filtering after clipping can reduce the spectral splatter butmay also cause some peak regrowth (Li and Cimini, 1998). If digital signals are clippeddirectly, the resulting clipping noise will all fall in-band and can not be reduced by filtering.To avoid this aliasing problem, oversample each OFDM block by padding the original inputwith zeros and taking a longer IFFT. Filtering after clipping is required to reduce the out ofband clipping noise. The other approach to clipping is to use Forward Error Correcting codesand bandpass filtering with clipping (Wulich and Goldfeld, 1999). This method improves thebit error rate performance and spectral efficiency.Peak WindowingThe simplest way to reduce the PAPR is to clip the signal, but this significantly increases theout of band radiation. A different approach is to multiply large signal peak with a Gaussianshaped window proposed by Pauli and Kuchenbeeker (1997). But, in fact any window can be 10
  11. 11. used, provided it has good spectral properties (Van Nee and Wild, 1998). Since the OFDMsignal is multiplied with several of these windows the resulting spectrum is a convolution ofthe original OFDM spectrum with the spectrum of the applied window. So, ideally thewindow should be as narrow band as possible. On the other hand, the window should not betoo long in the time domain, because that implies that many signal samples are affected,which increases the bit error ratio. Examples of suitable window functions are the Cosine,Kaiser and Hamming window. Van Nee and Wild (1998) showed that PAPR could beachieved independent from number of sub-carriers, at the cost of a slight increase in BER andout of band radiation.Bandwidth Efficient Reduction of the Crest Factor (BERC)This procedure, the BERC scheme proposed by Pauli and Kuchenbeeker (1998) is tomultiply the envelope mE(t) with a weighting function b(t). Thus, we haveThe function b(t) is composed of a sum of Gaussian pulses.Gaussian pulses are chosen because they are optimally concentrated both in time andfrequency domain. tn denotes the position of a local maximum of the envelope mE(t) above acertain threshold S that is normalized to the root mean square value mEff. The coefficientsand are chosen in way that the envelop m (t) E does no longer cross the threshold SThe factor g is used for the optimization of the weighting function. A small value for g leadsto narrow band weighting function and higher bit error rate follows.Additive Correcting FunctionProposed by May and Rohling (1998), this approach is similar to peak windowing butadditive correction function is used instead of multiplicative correction function. OFDMsignal is modified in such a way that given amplitude threshold of the signal is not exceeded 11
  12. 12. after the correction. With the restriction that the correcting function dose not causes any outof band interference, the correcting function has been given with minimal power and thuscauses minimal interference power within the OFDM band.The corrected signal can be written as,This correction limits the signal S(t) to Ao at the positions tn of amplitude peaks.This function can correct an amplitude peak in the OFDM signal with minimal interferenceof the signal without any out of band interference. For practical application, however, theextent of the sinc function in time must be limited by windowing.Selected Mapping (SLM)Bäuml, Fischer and Huber (1996) proposed this method to reduce PAPR for a wide range ofapplications. Because of the statistical independence of the carriers, the corresponding timedomain samples v[k] ,k=1,… .D in the equivalent complex valued lowpass domains areapproximately Gaussian distributed. This results in a high peak to average power ratio.Because of varying assignment of data to the transmit signal, this method is called “SelectedMapping”. The core is to choose one particular signal, which exhibits some desiredproperties out of N signal representing the same information. Generating OFDM framesrepresenting the same information is as follows.After mapping the information to the carriers V[m] each OFDM frame is multipliedcarrierwise with the N vectors P(n), resulting in a set of N different frames with componentsThen all N frames are transformed into the time domain and the one with the lowest PAPR is 12
  13. 13. selected for transmission. To recover data, the receiver has to know which vector P(n) hasactually used and the number n of the vector is transmitted to the receiver as side information. This method can be used for arbitrary number of carriers and any signalconstellation. It provides significant gain against moderate additional complexity.Partial Transmit Sequence (PTS)The main idea of this scheme proposed by Müller and Huber (1997) is that thesubcarier vector is partitioned into V pairwise disjoint sub blocks ; v=1,… ,VAll subcarrier positions in , which are already represented in another subblock, are set tozero so thatRepresents the same information as Am, if the set { , v=1,… ..,V}is known for each . is complex rotation factors with 1 = m for v=1,… … ,VBased on them, a peak value optimization is performed by suitably choosing the freeparameters b(v) m such that PAPR is minimized for b (v) m . The b(v) m may be chosen withcontinuous valued phase angel.Then, the optimum transmit sequence isThis scheme requires that the receiver has knowledge about the generation of the transmittedOFDM in symbol period m. Thus, the set with all rotation factors b (v) m has to betransmitted to the receiver so that this one can derotate the subcarriers appropriately. Thisside information is the redundancy introduced by PTS. This is the distortionless scheme andit works with arbitrary and any type of modulation on them while inserting only littleredundancy. 13
  14. 14. Tone ReservationProposed by Tellado and Cioffi (1998), the PAPR is reduced by adding time domain signalsto the data sequences that lay in disjoint frequency space to the multicarrier data symbols.With this formation, optimizing the time domain signal leads to a convex optimizationproblem that can be transformed into a linear program (LP). Solving the LP exactly leads toPAPR reduction of 6-10dB, but a simple gradient algorithm could achieve most of thisreduction after a few iterations. These additive signals can be easily removed from thereceived signal without transmitter receiver symbol handshake.If we do not transmit data on all tone, i.e. some values of data vector are zero, we can usethese values for reducing PAPR. If data vector Xj=0 for j Î {j1,… jL}, then the transmittercan add any vector c that satisfies, cj =0 for j Ï {j1… jL} to the data vector and remove it atthe receiver.IDFT (X+C) = Q(X+C) =x+QC =x+c where Q denotes IDFT matrix.To minimize the PAPR of (x+c), we must compute the vector c* that minimizes themaximum peak value.Using gradient algorithm iteratively, PAPR can be reduced. This algorithm has complexity,O(N) and can be applied to any number of carriers. But, there is little increases in transmitpower and little data rate loss.Carrier Frequency Offset Another limitation of OFDM in many applications is that it is very sensitive tofrequency errors caused by frequency differences between the local oscillators in thetransmitter and the receiver. Carrier frequency offset causes a number of impairments. There are two deleterious effects caused by frequency offset; one is the reduction ofsignal amplitude in the output of the filters matched to each of the carriers and the second isthe introduction of inter carrier interference (ICI) from the other carriers which are now nolonger orthogonal to the filter. 14
  15. 15. Because, in OFDM, the carriers are inherently closely spaces in frequency comparedto the channel bandwidth, the tolerable frequency offset becomes a very small fraction of thechannel bandwidth. Maintaining sufficient open loop frequency accuracy can become difficult in links,such as satellite links with multiple frequency translation or mobile digital radio links thatmay also introduce significant Doppler shift. OFDM is orders of magnitude more sensitive tofrequency offset and phase noise than single carrier system (Pollet, Van Bladel andMoeneclaey, 1995).ICI counter measures are divided into three groups.The most commonly used method is frequency-domain equalization, which uses trainingsignals (Ahn and Lee, 1993).The time-domain windowing method can also reduce ICI through multiplying the transmittedtime-domain signals by a well-designed windowing function (Li and Stette, 1995).The third method is called the ICI self-cancellation scheme (Zhao and Häggman, 1996). A main feature of these methods is that bandwidth efficiency might be reduced eitherby training signals or by using redundant subcarriers Moose (1994) described the maximumlikelihood estimator of the carrier frequency offset, based on the observation of twoconsecutive and identical symbols. Li and Stette (1995) proposed a Windowing method to reduce ICI by cyclicallyextending by v samples the time domain signal associated with each symbol. The whole ofthe resulting signal is then shaped with the window function. It is important to note that DFTtransform in the receiver is N point whereas that in the transmitter is N/2 point. If v< N/2,then the signal corresponding to each symbol is zero padded at the receiver to give length N. The outputs of the DFT with even numbered subscripts, in which actual data ismodulated in transmitter, are used as estimates of the transmitted data and the odd numberedones are discarded. Because not all of the received signal power is being used in generatingdata estimates, the method has a reduced overall SNR compared with OFDM withoutwindowing. A number of different windows, including the Hanning window (Gudmundsonand Anderson, 1996), windows satisfying the Nyquist criterion, and the Kaiser window(Muschallik, 1996) have been used to reduce ICI. 15
  16. 16. Chapter-3 3. SYSTEM MODEL3.1 Configuration:Block diagram of lowpass equivalent representation of the overall simulation model is shownin Figure Transmitter SectionConvolutional CodeIn this study, the following convolutional encoder for (2,1,6) code with constraint lengthseven considered. 16
  17. 17. The Generator matrices for the encoder shown in Figure 3.2, is given by,The two outputs are read into a serial data stream.QPSK ModulationQSPK modulation is a bandwidth efficient simple modulation scheme widely used in digitaltransmission systems. It has been proposed to use in Third Generation wirelesscommunication system. The QPSK modulator is shown in Figure 3.3 and correspondingsignal constellation diagram is shown in Figure 3.4. 17
  18. 18. FFT ImplementationIn order to combat a multipath delay spread channel, the guard interval for the OFDM signalshould be longer than the multipath delay spread, max t (Ziemer and Wickert, 1997).Where is the fraction of the signaling interval, that is devoted to guard time and is guard interval and T is OFDM symbol duration.From these design criteria, the following equation can be derived to calculate the number ofsubcarriers (Ziemer and Wickert, 1997).Where Rc is the code rate, Rb is the bit rate, m is the bits per subcarrier and N is number ofsubcarriers & N=128. 18
  19. 19. OversamplingWhen calculating the PAPR, we have to consider the actual time domain signal that is inanalog form. The IFFT outputs, which are symbol spaced sampling values, will miss some ofthe signal peaks.If we calculate PAPR by using these sample values, then the calculated PAPR is less thanthe actual PAPR. This is an optimistic result and will not illustrate the real situation.However, they are enough for signal reconstruction.To account for this issue, oversampling is performed by low pass filtering the IFFT signaland then sampled at a higher rate. Now, the increased samples are close to the real analogsignal and calculation of PAPR based on these samples will give the true PAPR.3.3 Proposal to Reduce PAPRMotivation: PAPR increases when number of subcarrier increases. It can be shown that for abaseband OFDM signal with N subcarriers has a PAPR=N2/N =N (Leonard J. Cimini, 1997).One way to reduce PAPR is reduce the number of subcarriers as low as possible even when aPAPR reduction scheme is employed. The simplest way to reduce the PAPR is to clip theOFDM signal before amplification (O’Neill and Lopes, 1995). It is possible to remove thepeaks at the cost of slight amount of self-interference since large peaks occur with very lowprobability.However, clipping is a nonlinear process and may cause significant in-band distortion, whichdegrades the bit-error-rate (BER) performance, and out of band noise, which reduces thespectral efficiency. Filtering after clipping can reduce the spectral splatter and it is apromising technique to reduce PAPR (Li and Cimini, 1998). Another approach is theclipping with Forward Error Correcting codes. Wulich and Goldfeld (1999) showed theimproved performance in PAPR and spectral efficiency when clipping is used with a forwarderror correcting code. A different approach to clipping is peak windowing where large signal peaks aremultiplied by certain window function, which has good spectral properties (Van Nee andWild, 1998). Ideally, the window should be as narrowband as possible but it should not be 19
  20. 20. too long in the time domain. Examples of suitable window functions are the Cosine, Kasierand Hamming window.Methodology: Among the existing methods, Peak Windowing exhibits good properties such as verysimple to implement, independent of number of carriers, no affect in coding rate and largereduction in PAPR. In this study, peak windowing with forward error correcting codes willbe analyzed since it may compensate the increase in BER and give better performance thatcan be implemented in a small inexpensive mobile unit. Then, we propose a method to beused with peak windowing to reduce the PAPR further. Windowing parameters, window width and attenuation factor, should be selectedsuch a way that it will reduce the PAPR. However, it is difficult to find a relationshipbetween windowing parameters and PAPR since the PAPR is random. Generally, thewindow width should be small in order to avoid distorting many sample values and theattenuation factor should be selected by considering PAPR reduction and signal distortion.Further, it is necessary to relate OFDM parameters with peak windowing. In this study, we consider peak windowing method, by defining clipping ratio. Whenclipping is employed to reduce PAPR, the OFDM signal is clipped whenever it exceeds aclip level, A. Normalized clipping level, which is called clipping ratio (CR), is defined as (Liand Cimini, 1998),Where is the rms power of the OFDM signal and it can be shown that, for an OFDMsignal with N subchannels, for a baseband signal and for a bandpasssignal? (Li and Cimini, 1998).OFDM signal is multiplied by the window function when the signal peak exceeds theclipping level. Unlike the clipping, the OFDM signal within the windowing width ismodified. This results in a smoothed OFDM signal. The following modified Hanningwindow function is used in this study. 20
  21. 21. The PAPR reduction is achieved at the expense of bit error rate (BER) performancedegradation and the out of band radiation. On the other hand PAPR cannot be reducedbeyond a certain limit by removing peaks, as the average value of the OFDM signal, alsodecreases, which in turn increases the PAPR. This can be realized from the followingdefinition of PAPR. One simple way to reduce PAPR further is increase the average value ofthe OFDM signal. Here, we propose a method, called “Pre-amplification” to employ withPeak windowing to reduce the PAPR further.Peak windowing method concerns only removing the peak values, which have lowprobability of occurrence. OFDM signal exhibits some low values, we will call it "bottoms",with low probability of occurrence, like peaks. By increasing these bottoms above certainlevel, the average value of OFDM signal can be shifted up. This results in PAPR reduction.Basically, this is like inverted windowing. Now, the sample values are amplified and thus wecall it "Pre-amplification".In Pre-amplification, output signal from peak windowing is multiplied by the modifiedwindow function when the signal falls below the bottom level. Like, peak windowing, thesignal within the window width is modified. This will cause BER degradation and out ofband radiation. We analyze these effects in this study. The following modified Hanningwindow function is used in this analysis.3.4 Channel ModelThe typical mobile radio channel is one suffering from severe multipath fading and this leadsto severe degradation of the bit error rate (BER) performance. In an OFDM system, as thesignals in each channel are of low flow rate, having larger symbol duration, channel can beconsidered as frequency flat. This is true when the coherence bandwidth of the channel isgreater than the symbol rate. But, the real channel is frequency selective and the OFDMsystem exhibits diversity effect in a frequency selective channel. This is the major benefit inusing OFDM system in a multipath fading channel. 21
  22. 22. The impulse response of the multipath fading channel can be expressed as follows.Following assumptions are made before taking the frequency response of the impulseresponse in order to apply it in an OFDM system. 1. The channel is static during an OFDM symbol duration. 2. The delay between consecutive paths is equal to the sample duration (T). 3. AWGN posses same statistical properties both in time and frequency domain.Then, the frequency response of the channel can be expressed as follows.The multipath channel is assumed to be a symbol spaced taped delay line model andcharacterized by a multipath intensity profile. For practical purposes, the tapped delay linechannel model can be truncated at L taps given by (Proakis, 1995)where Tmax is the total multipath excess delay. Assuming a typical urban / suburban outdoorenvironment having 3ms multipath spread and T s s = 0.5m , we can model the channel withL =7 taps.The multipath intensity profile varies as physical channel changes with time. It is also varieswhen the receiver changes its relative position to the transmitter. Statistically, the differentmultipaths are assumed to follow exponentially decaying power delay profile.This can be realized by assigning different variances to noise sources of individual taps.The total average power of the channel is normalized to unity.Following exponential power delay profile is used to calculate average power of each taps. 22
  23. 23. The standard deviation of noise sources for each path can be expressed as,Mathematically a random signal with Rayleigh distributed magnitude and uniformlydistributed phase can be generated by generating its real and imaginary parts from twoindependent Gaussian noise sources, which have zero mean and identical variance. Theaverage gain of the channel is determined by the variance of noise sources, since the rmsvalue of the Rayleigh distributed envelope is m 2s where m s is the standard deviation of itsGausian components.The effect of Doppler shift due to the movement of the mobile station will be introduced byusing classical Doppler filters for filtering complex Gaussian noise samples. The Dopplerfilter is same for all taps since it is determined by the mobile speed and carrier frequency.Gaussian random numbers are generated and filtered by the normalized Doppler filter.Filtered samples are generated independently for each path. Then, the frequency response ofthe channel is obtained by taking the IFFT of the generated filtered samples of all paths. It isassumed that delay in the signal due to multipath arrival is equal to duration of symbol time.The average signal power and the total multipath power can be normalized to one, withoutloss of generality. Such a frequency selective fading channel model used for the simulation isshown in Figure 3.5.In addition to the fading caused by the channel, the signal is also distorted by noise. Thenoise variance depends on the b o E / N , code rate and spectral efficiency. The noisevariance can be expressed as) 23
  24. 24. where n is the modulation density of the digital modulation scheme being used.3.5 Receiver Section:The following assumptions are made in this study. · Perfect synchronization in the receiver · Receiver has the full knowledge of the channel.If we assume that the channel is static during an OFDM symbol duration, then the channel isslow fading and the received signal is obtained by multiplying the data sequence by channelfrequency response and adding additive white Gaussian noise. Then, the received signalcorrupted by both AWGN and multipath fading is given by,where {Zn} are zero mean complex Gaussian independent random variables representingAWGN. 24
  25. 25. BER Simulation MethodFor the bit error rate simulation , the Monte Carlo Method is used. Although this method isnot suitable for very low BER because of the increase in computer run time, this is widelyused to simulate cellular mobile systems. Figure 3.6 shows the implementation of Monte Carlo estimation procedure.Comparing the source data bits known from the transmitted sequence, with the outputdetected sequence bit provides an error bit. The BER is calculated by dividing the number oferror bits by the number of data bit 25
  26. 26. Chapter- 6 CONCLUSION: According to the simulations, OFDM appears to be a good modulation technique forhigh performance wireless telecommunications. Some factors were not tested here like peakpower clipping, start time error and the effect of frequency stability errors. The codification used for the system could be improved, just using block codesinstead of convolution codes, but this fact would be out of the standard. Also, the pilot signaldistribution could be modified to reduce the redundancy. Wireless LAN is a very important application for OFDM and the development of thestandard promises to have not only a big market but also application in many differentenvironments. 26
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