# Timing Synchronization Techniques In Wireless Ofdm Systems Computer Science Essay

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The rapid development in the telecommunications sector with special emphasis on data transmission in secure and efficient ways encourages more research in this field. The purpose of this project is to be able to get a clear picture of all the factors involved in data transmission with special emphasis on receiving data through OFDM subcarrier system. Orthogonal Frequency Division Multiplexing is a multicarrier modulation method that uses broadband to transmit information divided over narrow bands in parallel. This method promises higher efficiency and benefit over the older and conventional single-carriers in keeping with the necessity to transmit more than one type of information and at high speeds in today's world. The paper will discuss the methods of synchronizing time and frequency during transmission to be able to receive data symbols with minimal error or interference.

## Introduction

The purpose of this project is to be able to build a secure and efficient data receiver based on the OFDM system. It will deal with time synchronization mechanisms in receiving and processing data symbols.

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The progress made in the last two decades in the field of wireless technology has been noteworthy. From the first of its kind, the 2G or 2nd Generation in digital mobile services has paved way for the latest in cellular wireless standard, the 4G or 4th Generation working group. The 4G wireless standard has a flexible channel bandwidth, between 5 to 40 MHz at a minimum data rate of 100Mbit/s across any distance. When the client is at a fixed place from the station, the data rate may go up to 1Gbits/s. To attain a smooth transition and seamless connectivity over heterogeneous networks while roaming, 4G requires multi-antenna and multi-user MIMO. Frequency-domain-equalization like Orthogonal Frequency Division Multiplexing or OFDM is needed to be able to utilize channels by using frequencies, selectively.

OFDM is widely prevalent as a modulation technique as it offers simple equalization, via a bank of multipliers unlike the complex equalization methods in single carrier modulation. This is accomplished by dividing the available spectrum into narrow bands of subchannels, thereby, preventing multipath fading or distortions. The subchannels are propagated parallel to each other. The use of a cyclic prefix is necessary to block Intersymbol Interference. However, it may be useful to remember that OFDM systems have a few drawbacks as well. These systems are very susceptible to carrier frequency offsets. If the transmitter and receiver use the same frequency, the subcarriers will be orthogonal. But, the outcomes of any frequency offset due to the instabilities of carrier frequency oscillators result in Inter-carrier Interference in the receiver.

The transmission of information from one point to another point is the main purpose of any communication system. The three basic components for telecommunications are transmitter, receiver and channel. In both digital and wireless communication networks, a modulator is required along with a transmitter and receiver and convertor. For wireless communication systems that operate in frequency selective fading environments the MIMO signalling process with OFDM can enhance the data rates. The base band signalling process requires several changes like frequency and time synchronization, tracking synchronization, MIMO detection and channel estimation, etc. to function. The implementation of a complete extension of MIMO with OFDM is possible using three transmitting and receiving antennas, as observed with IEEE 802.11a. Due to coupling between the transmitter and receiver, doubling of the system throughput can be achieved.

OFDM is so efficient in transmitting data over wide distances because it splits the base bandwidth into 'N' number of subchannels in narrow bands. These are transmitted parallel to each other. The transmitter uses IFFT or Inverse Fast Fourier Transform to generate the signals along the narrow subchannels, to distribute the signals as orthogonal carriers.

The addition of a suitable Guard Interval or GI along with the long symbol duration allows OFDM to be selective in picking up specific frequencies, which are faded in multipath system.

Cable or wireless systems use frequency division multiplexing or FDM, in a single transmission path, to transmit multiple signals at the same time. Data in the form of video, audio or text has a unique carrier or frequency range. The form of data will determine the frequency at which the information will be transmitted. In OFDM or orthogonal frequency division multiplexing, a set of data is transmitted using spread spectrum technique to distribute the signals over a number of carriers at unique frequencies. It is, therefore, sometimes referred to as multicarrier or multi-tone modulation. This allows demodulators to be frequency specific and prevents the interference from other frequencies. This method of distribution of data is efficient as it has high spectral capabilities and offers resistance to radio frequency interference and multipath distortion.

## 2.1: OFDM Fundamentals

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Broadcasting stations have to transmit multipath channels using several paths of different wave lengths. This causes interference between the multiple versions of a signal and it becomes difficult to get the original data without distortion. This is known as intersymbol interference or ISI. OFDM helps overcome these forms of interference and enhances the clarity in the reception of transmitted signals. This modulation technique is used in many parts of the world for digital TV. For example, digital audio broadcasting or DAB is used in Europe and ADSL, asymmetric digital subscriber lines are used globally. WLAN or wireless local area networks increasingly use OFDM technology for wireless communication from point to point and multi point configurations. According to the international standards for OFDM transmission, IEEE 802.11 uses OFDM in 5 to 8 GHz band.

Multiple input multiple outputs or MIMO OFDM uses multiple antennae to receive and transmit radio signals. It was developed by Iospan Wireless, based in San Jose using smart antenna and space and time processing techniques enabling high-capacity, NLOS or non-line of sight operations. MIMO OFDM uses base station antennas that do not have LOS to amplify the signal strength. Multiple antennas transmit small chunks of data to the receiver, in a process called spatial multiplexing, and the receiver has to process the data and put the pieces back together. The speed in transmission is enhanced by a number equal to the number of antennas used during transmission. This method uses the spectrum, resourcefully. Some types of OFDM are Flash OFDM, developed by Flarion and WOFDM by Wideband OFDM. OFDM is now used extensively for a number of high data rate communication systems, like DSL, WLAN, digital video broadcasting, 4G cellular systems and WiMax.

Fig 2: Transmission using MIMO OFDM

One area of concern for signal transmission is that the intersymbol interference or ISI becomes very strong as the number of symbols sent per second is increased and the channel delay spread increases as multiples of symbol time, Ts. Usually, NLOS systems that have to transmit over long distances suffer from large delay spreads. The concept of multicarrier modulation is simple and is a product of advancement to do away with ISI with high data rates. To obtain this, Ts or symbol time has to be greater than the channel delay spread, because change in the Ts can result in a huge bit error rate or BER. In recent times high data transfer rate is required by most channels resulting in smaller Ts when compared to the delay spread leading to high ISI. Multicarrier modulation breaks the high data rate into lower rate substreams (L) where Ts /L is greater than the channel delay spread. This gives us ISI free data.

L subchannels are transmitted orthogonally to maintain a total desired data rate; this is referred to as OFDM. In this instance the ISI in each subchannel is significantly smaller and can be done away with using a cyclic prefix. Cyclic prefix is part of the data symbol added to the beginning during guard interval. This makes the waveform start from time minus to prevent one subcarrier from interfering with another. This improves the robustness of multipath.

## 2.2: Single Path Relay

In adopting OFDM for cooperative relay networks single path relay and multipath relay come into the picture. Relays belong to a network of transceiver nodes located between the transmitter and receiver and help in the transference of information. On allocating equal power to each subcarrier and applying constant gain allocation for all subcarriers results show that equal power allocation for each subcarrier gives higher mutual information in a single path environment.

The amplify and forward gain algorithm for allocating constant power to all subcarriers gives poor result in a single path relay as the gap between the source or transmitter and receiver increases. There is an increase in the noise and channel distortion proportional to the distance as is evident in the bit error rates or BER and word error rates or WER. Decode and forward method gives a better performance as noise and distortion are minimized at each relay. In a multiple path relay network also decode and forward method yields better results than amplify and forward, but it is small when compared to single path environment.

## 2.3: Time Synchronization

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Examples of our workWhen demodulating an OFDM signal time and frequency synchronization is very important. This task is performed by the receiver. To do this the timing offset of the symbol has to be calculated to synchronize time with optimal timing instants and the carrier frequency has to be aligned accurately to the transmitted carrier frequency.

In OFDM certain margin has been left for time synchronization errors when compared to single carrier systems. In a time domain the IFFT or inverse fast Fourier transform modulates each symbol into a specific carrier. Frequency synchronization is more difficult to achieve as it has to be matched to the transmitted carrier frequency. The cyclic prefix neutralizes some of the effects of errors in timing synchronization. The timing offset has to be included by the channel estimator for each subchannel to minimize any loss in performance as the appropriate phase shift is applied by the FEQ.

Fig 4: Time synchronization in OFDM with two subcarriers

The project will research on the design and implementation of OFDM base band transmitter and receiver with special focus on reducing inter symbol and inter carrier interference and the use of guard intervals and cyclic prefix to reduce data error. This will be based on direct mathematical algorithms to minimize time synchronization errors in single path relay transmissions. At the end of this project we hope to be able to visualize an OFDM receiver which will incorporate time synchronization, channel estimation and equalization methods to receive information with minimal distortion from the original data sent.

## 3. Methodology

To achieve high data rates OFDM has been the technology that people depend upon. However, implementing receiver synchronization can be challenging as OFDM receivers are extremely sensitive to inter-carrier interference which can adversely impact its throughput and performance.

The project aims at exploring the means of minimizing time synchronization error in OFDM in WLAN. The methodology involves research on work done by other researchers in this field and drawing upon their knowledge and our experiments to establish a principle that will minimize interference and distortion of signals that may be put into use to improve wireless communication by increasing transmission efficiency. Mathematical algorithms and discussion will be a part of the methods used during this project. Verification of BER will be useful in testing the transmission efficiency at the receiver. In order to overcome all the distortions caused by frequency, timing and sampling errors one needs to be able to design a receiver to rectify these issues.

## 3.1: Techniques Used in OFDM

During transmission the receiver needs to perform two functions. One is receiver training and the other is receiver tracking. Receiver training allows for time and frequency synchronization, automatic gain control settings and channel estimation. When all these steps are complete the receiver will automatically switch to tracking operation in which it will correct any discrepancy in the data transmitted by the station and submit it to the MAC layer or Media Access Control. The MAC layer helps to break down data into a form that is transmitted across a network and can restore the original data when it reaches the destination. The MAC layer is the innermost layer of an OSI or Open systems interconnection model.

OFDM as mentioned previously uses the spectrum resourcefully. The data is distributed over several sub carriers to obtain better results. The fact that in OFDM, the subcarriers actually overlap with adjacent ones is proof of the spectral efficiency of OFDM. Certain techniques are used in addition to the reduced ISI in OFDM like interleaving, deinterleaving, forward error correction and channel estimation. This project will deal with some of these techniques in depth and look for ways of practical application.

## 3.2 Interleaving & De-interleaving

Interleaving is a method to rearrange or shuffle a string of data to get minimal loss of data in case of burst error during transmission. It helps the information to be distributed over time and frequency. In OFDM several inputs are interleaved and shared over different bandwidths to increase quality of reception. This data is decoded at the receiver's end to obtain the original signal. This can be better explained if we consider a video transmission and the clips are interleaved. In case of burst error where a series of data is misplaced in transit, it is easier to recover most of the data by correcting small gaps between clips after decoding. However, if the video clip had not been interleaved burst error would have resulted in the loss of the whole chunk of missing data that would not be retrieved by the forward error correcting codes.

Forward error correction methods or error detection and correction (EDAC) coding methods can rectify errors appearing uniformly throughout the data stream. The errors may be fading or noise impulses that appear in groups; when interleaved these bunches get distributed in a uniform manner which is easier to recover by the forward error correction method at the receiver after the message has been deinterleaved. Hence, forward error correction is an important step to check for errors in the transmitted data.

Channel estimation is a process to gauge the channel impulse response or CIR for a signal detector like MAP to successfully complete equalization. This reduces the inter-symbol interference to a great degree. There are a few types of channel estimation techniques like block type and comb type which will be discussed here in detail.

Guard interval helps to reduce time synchronization problems. It is beneficial to transmit several low-rate streams instead of a single high rate stream because low rate symbol modulation is not impacted as much by intersymbol interference or ISI, as a result of multipath propagation. As the duration between OFDM symbols can be long it is possible to insert guard intervals to minimize intersymbol interference.

Cyclic prefix is a part of the data set and is the repetition of the end symbols attached at the beginning of the stream, hence its name. It has two main functions: it acts as part of a guard interval and separates two streams of data, thus, eliminating ISI; it allows the linear stream to be structured in a circular fashion to be transformed to the frequency domain with the help of a discreet Fourier transform. Channel estimation and equalization are easier after adding the cyclic prefix.

The FFT or fast Fourier transform calculates the discrete Fourier transforms or DFT to find the spectrum of the signal. IFFT or inverse fast Fourier transform is used to transform the complex data set into a modulated and multiplexed signal that may be transmitted as a waveform. The algorithm for IFFT is almost the same as the algorithm for FFT mathematically, except for a sign change and the length factor, since DFT and IDFT are based on the same computations. The intrinsic features of FFT/IFFT in an OFDM system provide the orthogonal symbols. In the transmitter of an OFDM system, the input data is considered to be in frequency domain. IFFT is applied to the entire data set. All the symbols are then set on orthogonal sinusoid and added to give the output. At the receiver's ends, the reverse takes place using FFT.

The functions of FFT or discrete Fourier transform are almost the same as IFFT or inverse fast Fourier transform except for the difference in sign and scale factor 'N' equivalent to length. The execution time for IFFT also depends on the length of the transform. This is slower for prime numbers or ones which have large prime factors, however, are very fast for lengths with powers of two and ones that have small prime factors. For vectors of length 'N', the functions, Y=fft(x) and y=ifft(X) ican make the necessary changes to transform and inverse transform the given pair. The function may be represented as:

, where is N root of unity.

Fig 5: Base Band OFDM system for Transmitter and Receiver

Fast Fourier algorithm calculates the IDFT of vector x is: y=ifft (x). In the case of x being a matrix the IFFT returns inverse DFT to the matrix for each column.

When there is conjugate symmetry between the active dimension along vectors in x, the the output is real and the computation is much faster.

If x(i)= conj(x(mod(N-i+1, N)+1)) then an N element vector x is conjugate symmetric.

IFFT functions on the first non-singleton dimension if x is a multidimensional array.

y=ifft (X,n) returns the inverse DFT of vector x at the n-point.

y= ifft (X, [], dim) and y= ifft (X,n,dim) along the dimension dim, gives back the inververse dft of x.

y= ifft (..., 'symmetric') in IFFT treats x as conjugate symmetry along the active dimension.

y= ifft (...,'nonsymmetric')

The proposed methodology will be researched further and verification techniques will be used on model receiver. The next sections will deal with the discussion and practical implications of OFDM techniques in wireless transmission.

## 3.3 Time Domain Equalizer

The intersymbol interference ISI can be removed by using equalization methods which will enhance bit-by-bit error detection. Equalization is easy to achieve because they can resemble optimal behaviour closely. TEQ or time domain equalization is used to shorten the delay spreads to appropriately balance the cyclic prefix. This increases the transmission efficiency as the cyclic prefix can be short even for long delay spreads.

On the basis of the parameters given by IEEE 802.11a standard, TEQ can be explained better. The coding rate R is dependent on the data rate. So when the transmission rate is 48 Mbps the punctured convolution code along with coding rate is 2/3 and for 54 Mbps it is 3/4 (Yuan 2003).

## 4. Modulation in OFDM

To better understand the modulation and demodulation techniques of OFDM transceiver one needs to consider a simple multi-carrier system. OFDM was conceived from the techniques used for modulation and demodulation of a multicarrier communication system. This requires frequency division multiplexing or multi-tone. The data bandwidth is broken down into narrow non-overlapping sub-carriers that are transmitted parallel to each other. The sub-carriers are supposed to be narrow to reduce the intersymbol interference for a slow and flat fading effect. However, in an OFDM system, the carrier frequencies for each sub-carrier are different. These depend on

The pulse used for transmission in the subcarriers is made to be rectangular so that the conversion to IDFT and DFT can be carried out very easily. The name is orthogonal because the signals of the sub-carriers are orthogonal. The orthogonal pulse leads to a sin (x)/x curve of the spectrum. The spectrum in OFDM overlaps each other significantly which is why it is spectrum efficient. The need for synchronization between the transmitter and receiver is, therefore, very high to be able to maintain orthogonality and reduce error rates.

## 5. Receiving signals in OFDM

Fig 6: Receiver System in OFDM

As demonstrated in the baseband model, OFDM systems require the available frequency to be divided into several sub-carriers which are overlapping and orthogonal to ensure high spectral efficiency. The orthogonality can be maintained by adding a cyclic prefix which allows the signal to pass through a time dispersive fading channel with a minimal loss in SNR (signal to noise ratio).

The data signal in binary form must be grouped and coded and then mapped into a signal mapper. The data sequence is transformed into time domain by inserting a guard band. To avoid intersymbol (ISI) and inter carrier interference (ICI) a cyclic extension of time length larger than the expected delay.

To receive an OFDM signal after synchronizing long and short symbols, one must consider the plurality of the symbols. The method correlates a number of predetermined points of a long received symbol with corresponding points on the reference symbol. A peak is observed between the long symbol and reference symbol when the receiver exhibits time synchronization.

The received data signal is made to pass through the analogue-to-digital converter or ADC and the cyclic prefix is removed from it. A DFTN which is an N-point discreet time Fourier transform changes the data back to the frequency domain. After demodulation and channel decoding the data is recovered in the binary form.

In an ideal condition, when there is no interference at all, (Shen & Martinez 2006). This may be calculated from equations, and

This shows that data transmission using OFDM system is equivalent to data transmission over parallel channels. Fading channel of the OFDM system exhibits a 2D lattice of time and frequency. Thus, a need to design better channel estimators arises to give the best output between performance and complexity.

Two OFDM training symbols are used to achieve rapid timing synchronization and carrier frequency synchronization in less than two data frames. The first OFDM training symbol has odd number of sub carriers, while the second OFDM training symbol has only even number of sub carriers (Schmidl et al 1998).

## 5.1 Channel Estimation & Equalization

The Block type and the Comb type are the two basic 1D channel estimation processes in OFDM.

## Block type pilot channel estimation system

In the block type channel estimation system, slow fading channels are considered and pilot tones are incorporated in all subcarriers of OFDM systems in a particular time period. OFDM channel estimation symbols are transmitted from time to time through subcarriers. The purpose is to estimate the channel receiver to decode the received data within the block. The different types of estimation are: least square or LS, minimum mean-square error or MMSE and modified minimum mean-square error or modified MMSE.

LS estimation (Wu, Liu & Jing) uses l

MMSE estimator uses 2nd order statistics of channel condition to reduce the mean-square error. MMSE estimator is more efficient than LS. In cases of low SNR, it is especially useful. The drawback is the high complexity in MMSE estimator to invert or transpose the matrix every time the data changes (Shen and Martinez 2006).

Modified MMSE estimators are developed to reduce the complexity in MMSE.

## Comb Type Pilot Channel Estimation

The comb type system, on the other hand, is used to equalize channel changes from one OFDM block to the next. It can be achieved by inserting pilot tones into certain subcarriers of each symbol when the conditions of data subcarriers need to be estimated.

Comb-type pilot based channel estimation uses Np pilot signals for each symbol. These are uniformly inserted in X with S= N/ Np.

## LS Estimator with 1D Interpolation:

Linear interpolation may be given as

2nd Order interpolation is given by

Low pass interpolation may be used to pass original data through unchanged interpolations after adding 0s to the original sequence and allowing it to pass through an FIR filter.

Spline cubic interpolation gives a continuous polynomial curve.

Time domain interpolation is based on zero-padding and presents a high resolution interpolation. The estimated channel is transformed to time domain using IDFT:

IFFT

FFT

Gp (n)

Gp (n)

Hp(k)

H(k)

0

Fig 9: Time Domain Interpolation

ML Estimator or maximum likelihood estimator is given as computed from

PCMB Estimator is less complex than ML estimator, especially if 2M<Np. The PCMB estimator performs slightly better in MSE when SNRs are small.

There are other pilot aided channel estimators as well such as the simplified 2D channel estimators, iterative channel estimators and channel estimators for multiple antenna OFDM system.

Simplified 2D Estimators the pilots are incorporated into both the frequency and time domains using the principle of 2D filters. This kind of channel estimation gives better result than 1D, though the computation complexity and processing time is greater. An algorithm with two concatenated 1D linear interpolations on time and frequency can reduce the complexity of 2D channel estimation, sequentially.

Iterative channel estimators give robust output even when SNR is low. This is used to reduce complexity. The 2D transmission lattice (Shen & Martinez 2006) is divided into 2D blocks with the pilots being incorporated into each block.

Channel Estimator for OFDM with Multiple Transmit and Receive Antennas can significantly improve the quality and capacity of the subcarriers. OFDM system with multiple antennas faces a few issues with channel estimation as each tone for every receiver antenna has specific multiple channel parameters. This is overcome with the different tones for each channel by correlating and basing channel estimators on this correlation.

## 6. Timing and Synchronization Mechanisms

Synchronization of time and frequency is very important in OFDM to be able to retrieve the data without significant loss as ISI or ICI. Two ways of doing this is by adding subcarrier pilots to the frequency domain it is passed through IFFT and a cyclic prefix is added in time domain.

OFDM provides a definite advantage over more traditional multipath communication techniques. It uses the spectrum optimally and provides more resistance to multipath fading and data error due to different types of interferences. OFDM has to be synchronized suitably to be able to properly benefit from it. It is very important to correctly track the frequencies at the receiver to make sure that the orthogonality is being maintained at all times. Sampling has to be done at the correct time intervals so that the samples may be synchronized well. This will reduce the data errors considerably.

## 6.1 Symbol Timing Synchronization

A steep roll off metric for timing synchronization has been created and we will be focussing on that. The timing metric will have a robust synchronization detecting capability. Time domain and frequency domain training will have to be done. Frequency domain training will require a low peak to power average ratio of training symbol.

This may be achieved by either of two ways. The first method relies on suppressing the interference introduced by the training symbol pattern for multipath channels. The other method uses the maximum likelihood model and does not consider any interference. Signal to timing error gives an average interference power ratio when plotted against the shift in timing estimates. The synchronization, timing and frequency estimation as also the bit error rate performance may be presented using a Rayleigh fading channel (Minn et al 2003).

OFDM synchronization should be done according to the clock offset (Poole 2010) which requires the spacing between carriers to be used by the receiver to sample the received signal to be maintained by an internal clock rate. If the rates are different from those in the transmitter, the carriers will be increasingly removed from the correct rate that results in very high error rates.

## 6.2 Carrier Frequency Synchronization

Proper decoding of OFDM symbols received through multiple frequency bands entails accurate synchronization of the arrival time at the receiving end. Since the symbols are transmitted over bands with different frequencies it becomes difficult to estimate the related parameters. Mitsubishi Electrical Research Laboratories (2007) has come up with a synchronization technique to detect frequency packets and provide a carrier frequency offset.

To retrieve the information from its encoded form, the data has to be decoded. The most common algorithm is known as the Viterbi decoder. It is used effectively to shorten the path memory of the information sequence without affecting optimum performance. When the information is a long sequence, the delay due to decoding may be impractical at times. Hence the need to shorten the information sequence. The inclusion of guard interval and cyclic prefix, in relation to enhancing the efficiency of transmission has been discussed in the previous sections.

The OFDM receiver should be able to complete synchronization with the carriers of the OFDM signal with the help of the demodulator. If there are even minor frequency errors between the transmitting and receiving ends which may be caused by Doppler shifts due to relative movement between the transmitter and receiver, it may result in large frequency offsets. The demodulator needs to be synchronized so that the sum of carriers equals zero and the error rate is minimum. Therefore it is essential to maintain orthogonality to reduce synchronization errors.

## 6.3 Sampling Clock Synchronization

Time domain interpolation can be made to go through IDFT, zero padding and back to frequency domain. Sampling rate offset at the OFDM receiver can be performed only after timing and carrier frequency synchronization are complete. A method has been reported by del Castillo- Sanchez, et al in 2009, about estimating and correcting sampling clock frequency, carrier frequency and time. The results have been good without an increase in the complexity.

While synchronizing time and frequency over packet networks, one needs to have access to Primary Reference Clocks in different areas to synchronize at the end nodes. For bigger networks many nodes are present to access the primary reference clocks. The other nodes have to align with the reference clocks to have access to in-band or out-band links ( Ghaemi n.d.). For the in-band system payload data carries the timing details. However, the out-of-band mode uses dedicated timing packets that add to the data exchange traffic. Simple Network Time Protocol can work well in LAN as well as WAN environment and can run on real-time operations systems.

A major problem that affects radio communication systems when applying OFDM is time and frequency synchronization. Effective ways of synchronization will be able to reduce the data error rate to make the transmitting and receiving of digital data through OFDM systems more efficient. OFDM ensures that data error rates are minimized because of the protection it provides against fading, echoes, noise, reflections etc. OFDM uses the spectrum efficiently by transmitting the parallel subcarriers in a way that they overlap each other without causing any inter carrier interference. In order to utilize the spectrum effectively and keep up with the high data rate over wireless transmission systems, effective synchronization methods need to be developed periodically.

Time synchronization has to be followed stringently to avoid gain and inaccurate sampling. In case attention is not paid to strict compliance sampling will be incorrect and data error rate will be considerably increased and orthogonality will be impacted. The internal clock rate determines the sampling of the received signals and the carrier spacing within the receiver. If the clock rate differs at the transmitting end discrepancies will grow at each carrier level even if the first carrier is correct which will cause a higher error rate.

## 7. Advantages and Disadvantages of OFDM

There are numerous advantages of using OFDM in wireless telecommunications. Some of them are listed below:

Is adaptable to adverse channel conditions. Does not need very complex channel equalization algorithms.

The error coding techniques are efficient in retrieving some of the lost data affected by narrow band co-channel interferences.

Since each carrier carries a small amount of data intersymbol interference is reduced in OFDM.

Spectral efficiency is very high as the carriers overlap each other.

Timing errors are relatively low in OFDM.

It is of special advantage to broadcasters who use single frequency networks as OFDM improves the spectral usage.

There are certain disadvantages to using OFDM also. Here are some of them:

Frequency errors are of more serious consequences as OFDM is susceptible to frequency issues. It is sensitive to Doppler shift and if the frequency errors are not corrected the orthogonality of the carriers is affected at the receiving end.

OFDM requires a higher battery consumption for the linear power amplifiers to function that are less energy efficient than the non-linear amplifiers. Hence, the peak to average power ratio is quite high.

Cyclic prefix which is used to lower the intersymbol interferences reduces the overall spectral efficiency as they take up quite a bit of the spectral bandwidth.

We have looked at the pros and cons of using OFDM. By this analysis one may conclude that the advantages far outweigh the disadvantages as OFDM is fast becoming the backbone of digital telecommunication.

## 8. Conclusion

In this project so far, we have seen that to achieve orthogonality in receiving transmission one must consider the time and frequency synchronization to avoid inter symbol interference and inter carrier inference. This paper has looked at different techniques in which time synchronization can be achieved and effective means of receiving transmission in OFDM WLAN. The importance of guard intervals and addition of cyclic prefix to the data symbol has been stressed. It has also dealt with various channel estimation techniques to estimate the condition of the channels for estimating time and frequency gaps. Fast Fourier transform and Inverse FFT are used very effectively in OFDM to convert data symbols from analogue to digital and vice versa. Polynomial fitting helps in improving channel estimation in the LS method. Time domain interpolation can be made to go through IDFT, zero padding and back to frequency domain. At the end of this project I feel confident about being able to design a receiver that will manage time and frequency synchronization with least interference and error in the transmitted data symbols.

## 9. List of Abbreviations & Definitions

2G - Second generation: These are technologies in wireless communication.

4G - Fourth generation: Same as above.

ADSL - Asymmetric Digital Subscriber Lines: It is a technology that helps to transmit digital information at high speed and high bandwidth through phone lines. It is different from regular dial up connections as it is asymmetric and exploits the one-way nature of multimedia transmission by sending large amounts of information towards the user and allows only a small amount of information to be received from the user. It allows analogue information on the same line as well. This has wide scale utility in an urban area.

BER - Bit Error Rate: It is the percentage of error in bits received in comparison to the total number of bits transmitted. This is applicable only in telecommunication signals and is expressed in ten to the power, minus the coefficient of power.

CIR - Channel impulse response: It is a wind-band channel classification that has all the information required to motivate any type of signals or radio transmission impulses through the channel. The summation of amplitudes and delays of signals arriving at the receiving end at the same time causes the signals to be filtered.

DAB - Digital Audio Broadcasting: DAB is a technique of transmitting analogue audio signals that are converted to digital signals through channels having Amplitude Modulation or Frequency Modulation frequency range. DAB signals can be carried to several stations within the same frequency range. This technique gives enhance audio quality and reduced noise and other interference along with reduced multipath fading effects. DAB stations can have text format displays in which it is possible to see what number is coming up next.

DFT - Discrete Fourier transform: This is a specific Fourier transform which is used in frequency function to transform one function to another.

DSL - Digital Subscriber Line: DSL is a technology that helps to transmit digital data over cables of local telephone networks or lines. This service can be provided with ordinary telephones on the same telephone lines as DSL uses high frequency bands that separated through a filtering device.

FFT - Fast Fourier transform: It is an algorithm to calculate the discrete Fourier transform and the inverse Fourier transform. It divides a series into different lower frequencies. The changing of representation from time to frequency is called a Fast Fourier Transform.

ICI - Inter- carrier Interference: This is a typical kind of problem with OFDM systems. It is caused by time variation and frequency off-set and is resultant from sub-channels from the same data block of the same user. ICI problem becomes more acute in the presence of multipath fading.

IFFT - Inverse Fast Fourier Transform: A signal can be represented either as time or frequency. Changing the representation to frequency from time is called a Fourier Transform. The inverse Fast Fourier transforms simply reverses this operation, taking the signal from time back to frequency representation is IFFT.

ISI - Intersymbol Interference: This happens when one symbol interferes with other symbols creating distortions in a signal it causes errors such as noise and makes communication unclear. This phenomenon needs to be minimized by using filters at both the transmitting and receiving ends so that digital data is transmitted with least errors and interference.

GI - Guard interval: These are used to ensure that independent transmissions do not cause interference and distortions with one another in OFDM systems. Guard interval helps to protect sensitive digital data from interference such as delays, noise, echoes etc. To ensure least error each symbol is preceded by a guard interval because if the interference happens within this interval the receiver will be able to decode the data with minimal error.

MAC - Media Access Control: This is a unique number for the computer's hardware. When a computer is connected to the internet, a MAC address relates the computer's IP address to the MAC address on the LAN. It is used to maintain telecommunications protocol.

MAP - Maximum a Posteriori: It is an algorithm used in decoding information from each bit of data. It can be used to get information from each bit by using empirical data.

MIMO - Multi Input and Multi Output Systems: MINO is the device through which signals are signals are sent via multiple antennas unlike the FDM where signals are transmitted by a single antenna. This technique can increase the potential range of data transmission in WLAN environment.

N - Number of Subcarriers

NLOS - Non-line of Sight Operations: This is a term used in radio communication to mean a path that has partial obstructions such as buildings, trees etc across its path of transmission. It is also used to describe a channel between a transmitting and receiving antenna where there may be visual obstructions but where transmission of radio waves is possible and can be detected.

OFDM - Orthogonal Frequency Division Multiplexing: it is a technique that combines both modulation and multiplexing. OFDM technique it is applied only to one exclusive channel, where signals from the same source are split into several independent channels i.e. a sub-set of the main signals. Each channel is modulated by separate carriers and multiplexed into an OFDM signal for further transmission. Sub channels are multiplexed by either using frequency or the code division multiplexing technique.

OSI - Open systems interconnection: It is a model to standardize networking protocol in a logical structure. It is a set of agreements by various communication coordinators between computers and networks from different manufacturers and technologies. It promotes the use of standardized procedures for interconnections for different data processing systems.

TEQ - Time domain equalizer: This is used to minimize inter-block interference. The time domain equalizer helps in shortening the cyclic prefix and therefore, is able to reduce channel length.

Ts - Symbol Time:

WER - Word error rate: When large chunks of data like words are lost during transmission due to various interferences, this is known as WER.

WLAN - Wireless Local Area Network: It creates a link between multiple devices using a wireless distribution system like OFDM. It also provides a connection through an access node to the internet and can be moved around in the local coverage area and still maintain connection with the network.

WOFDM - Wideband Orthogonal Frequency Division Multiplexing

## 10. References for Images

Fig 1. OFDM transmitter - A flowchart to show how the information is transmitted across the OFDM subcarrier system.

Fig 2. Transmission using MIMO OFDM - Multiple antennas transmit small chunks of data to the receiver.

Fig 3. Sample wave form after addition of Cyclic Prefix - The addition of a cyclic prefix to counter the inter carrier interference changes the waveform as the wave starts from minus (-) time.

Fig 4. Time synchronization in OFDM with two subcarriers- two subcarriers with different wave times are synchronized.

Fig 5. Base band OFDM system for transmitter and receiver- A base band model of a transmission path and receiver path in OFDM.

Fig 6. Receiver system in OFDM - A flowchart to show the process of receiving information in an OFDM system.

Fig 7. Block type pilot channel estimation- Pilot lines are included in all subcarriers in a specific time period.

Fig 8. Comb type pilot channel estimation - Pilot lines are inserted in subcarriers of each symbol.

Fig 9. Time domain interpolation - A figure to represent zero-padding in time domain interpolation using inverse discrete Fourier transform.