# Training Design For Repetitive Slot Based Estimation Computer Science Essay

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In this project, we mainly focus on optimal RS preamble design by means of Cramer-Rao bound averaged through the channel, which is assumed as Rayleigh. We show that the multipath diversity gain and number of unknowns to be estimated by the most preferable value of J, which is a trade-off in between them. We also show that the enhanced power loading schemes are proposed as it is not optimal to load the uniform power for active sub carriers (with uncorrelated case in contrast). With higher signal to noise ratio (SNR) the proposed power loading system allocates more power to active sub carriers. The CRB-based theoretical results can be supported by the maximum probability estimator which is the result of simulation-based performance. The wireless systems employing the OFDM modulation is a key challenge in estimating the carrier frequency offset (CFO). This CFO estimation is carried out using a preamble number, say J, of repetitive slots (RS).

For wireless LAN's such as IEEE 802.11a, it has become the standard choice for Orthogonal frequency division multiplexing (OFDM). It is also being considered for several IEEE 802.16 and 802.11 standards. The OFDM fame arises from the complexity of balanced transceiver, and the granularity of the time frequency that it offers. Even then, it continues to be a serious challenge for synchronization. Here assuming ideal frame and timing synchronization, we focus on the synchronization of carrier frequency offset (CFO).

The estimation techniques of CFO may be classified as Pre-FFT known as time domain technique or Post-FFT known as frequency domain technique. The fractional part will be corrected and identified when the latter is utilized to approximate the integer part of the CFO. The fractional part of the CFO can be estimated by the time-domain methods. Some of these methods can even estimate the CFO's integer part. Time-domain methods are classiï¬ed from those that utilize the time-diversity provided by the cyclic preï¬x, those that rely on pilots or null sub-carriers (NSC) ignoring the cyclic preï¬x, and the blind approaches of the information bearing symbols that exploit the non-Gaussianity.

The estimation of Data-aided CFO in existing OFDM systems of repetitive slots (RS) employs a preamble made of a number, lets say J. After deactivating all sub-carriers the preamble is obtained using one OFDM symbol except those frequencies which are the integer multiples of J. In the absence of virtual sub-carriers, it will be shown that the maximum likelihood (ML) estimator of CFO which is based on RS is identical to the ML estimator which is based on NSC.

Using the CramÂ´er-Rao bound (CRB) as a metric, the virtual subcarriers are deactivated (the subcarriers which are at the edges of allocated frequency band) in order to avoid the interference with the adjacent design preamble systems. This involves the loading of power and optimization of J. The gain of multipath diversity and the number of unknowns to be estimated can be shown using the optimal value of J, which is a trade-off in between them. In case of uncorrelated channel taps, Uniform loading of power is optimal. We also show that the power loading is no longer optimal and better power loading schemes are proposed in case of uniform correlated channel taps.

## 1.2 Scope of the Project:

In the context of OFDM systems, the main project objective is to examine the estimators of CFO performance based on a single repetitive-slot pilot symbol. On the performance of estimation closed form expressions are provided, which illustrates the impact of multipath diversity by assuming a Rayleigh channel. Insights are provided using the Cram`er-Rao bounds, which shows how it can be designed using the preamble.

## 1.3 Literature Survey:

The most usable technique to attain a high performance communication on OFDM Transceiver is IEEE 802.11a and IEEE 802.11b. By under going few modifications on Transceiver behaviour we can evaluate an IEEE 802.11g against several impairment links as frequency offset, Inter-carrier interference, phase noise, etc.

In this document we mainly focus on the analysis of simulation results applied on WLAN OFDM Modulation using link impairments. To evaluate the phase noise and frequency Offsets Effects on OFDM 802.11g Transceiver, we mainly use the power of ADS 12005A simulation technique.( Mourad Melliti, Salem Hasnaoui, Ridha Bouallegue, April 2010)

The estimation for single user transmission and single carrier can be considered by carrier frequency offset by frequency selective channel. It is important to design the performance of optimize CFO when training is mainly devoted to frequency-selective channel. In this paper we show the training sequence, which minimizes the cramer-Rao bound related with the averaged over the channel statistics and the carrier frequency offset following a correlated channel model of Ricean fading. The improvements of standard pseudo random white training sequence can be compared by simulation results. (Philippe Ciblat, Pascal Bianchi, and Mounir Ghogho ).

In MIMO OFDM systems we mainly use the common training signal design corresponding estimation methods for carrier frequency offset and frequency selective channels. In designing a training signal, the training structure develops the signal which yields to low complexity estimation methods though the optimality of signal is maintained. The channel estimation is based on least squares approach while Frequency offset estimation is based on linear unbiased estimation principle. The signals like pilot-only training signal and pilot data multiplexed signals can be applied to proposed training signal and estimation methods. The frequency offset estimation range can be flexibly adjusted. The Cramer-Rao bounds or theoretical minimum mean square error performances are very close to proposed systems (Al-Dhahir and Minn ).

## 1.4 Existing System

The estimation of Data-aided CFO in existing OFDM systems of repetitive slots (RS) employs a preamble made of a number, lets say J. After deactivating all sub-carriers the preamble is obtained using one OFDM symbol except those frequencies which are the integer multiples of J.

## Disadvantages

Loading of power is not optimal.

It is critical to do Synchronization.

## 1.5 Proposed System

Using the CramÂ´er-Rao bound (CRB) as a metric, the virtual subcarriers are deactivated (the subcarriers which are at the edges of allocated frequency band) in order to avoid the interference with the adjacent design preamble systems. This involves the loading of power and optimization of J. The gain of multipath diversity and the number of unknowns to be estimated can be shown using the optimal value of J, which is a trade-off in between them. In case of uncorrelated channel taps, Uniform loading of power is optimal.. We also show that the power loading is no longer optimal and better power loading schemes are proposed in case of uniform correlated channel taps.

## Advantages

More power loading to activated sub carriers

High signal to noise ratio.

Multipath diversity gain and numbers of unknowns can be estimated by providing a tradeoff in between them.

## 1.6 BLOCK DIAGRAM

Interpolator

Derotator

Integrator

Fractional freq offset acquisition

Scaling

NCO

FFT block

FEQ

Coarse symbol boundary detection

FFT window

Pilot Extraction

Channel Estimation

Integer freq offset acquisition

WLS Estimation

Low pass filter

## CFO Estimation

## Effects of CFO:

The presence of the carrier frequency offset (CFO) will introduce severe inter-carrier interference (ICI), which, if not properly compensated, would significantly degrade the system performance

## NCO:

AÂ numerically controlled oscillatorÂ (NCO) is an electronic system which synthesizes a range of frequencies from a fixed time base. The name is anÂ analogyÂ with "voltage-controlled oscillator".

## Capabilities and Limitations:

Unlike aÂ phase-locked loop-based analogÂ frequency synthesizer, it has a capability to synthesize a wide range of is précised frequency ratio. The NCO has a proportionality to generate spectral side bands and time base frequency on the other side. By which, we can compare both the upper side band attenuated with lower band side. Therefore, we use the upper sideband in frequency synthesizer to be successful.

The communication systems based on NCO are more attractive because they are of phase continuous while receiving signal from NCO based transmitter.

## Operation:

The major steps which are generally used in NCO operation are:

1. The main aim of a "phase accumulator", is to perform the role of a digital waveform which generators by incrementing a phase counter per every sample increment.

2. A "phase-to-amplitude converter", is to implement the form of memory to ROM(read-only memory). By which, we can read the values by an waveform table can be helpful to create the waveform at a desired Phase offset.

3. A DACÂ digital-to-analog converterÂ is needed, for an desired analog output. To produce an analog output waveform the sample sequential values are extracted and sent to digital to analog converter.

4. The wave form of the digital to analog converter needs to filtered by an analog filter to remove DAC glitches and aliasing. Then, the wave form is directly used for an input of further digital signal processing.

Thus, we can produce the frequency ratios limited only to calculate the phase accuracy of the arithmetic. By this means we can get the frequency-agile and phase of NCOs. Insignificantly, modulated outputs can be produced to frequency, phase and quadrature.

The numerical-controlled oscillator is also known as NCO17. The carrier frequency error generates a signal which oscillates on increasing or decreasing of frequency error which depends on addition circuit 16.The increasing of oscillation frequency error correction will be supplied to the positive value and decreasing oscillation frequency will be supplied to the negative frequency error value. When the error signal of frequency error value is zero then the oscillation frequency becomes stable.

Furthermore, the two different channel conditions of optimal weights are derived. By this we can estimate the carrier frequency offset as well as timing offset both simulation and analysis represents the least squares algorithm accurately and effectively of ofdm signals in multipath fading.

Although OFDM can deal with multipath propagation efficiently, through proper parameter selection, it still suffers from time selectivity of the radio channel due to movement of the transmitter, the receiver or both. Therefore it is important to accurately estimate the constantly changing radio channel in order to demodulate the transmitted data successfully. Pilot symbol assisted channel estimation, whereby known data symbols -in this paper is called as pilot symbols- are transmitted to be used to estimate the radio channel is favored in, for example, 802.11 a/g standards.

These pilot symbols are inserted at the beginning of a packet to be transmitted and being used to estimate the radio channel by the receiver.

The more pilot symbols transmitted, or equivalently more energy, the more accurate the channel estimates will be, until it saturates, i.e., increasing pilot symbols will not improve the channel estimation accuracy. However, increasing pilot symbols will increase the transmission overhead, which is not desirable.

To gain the benefit of having more pilot symbols without having to transmit additional pilot symbols we can use the randomly modulated data symbols as pseudo-pilot symbols. Pseudo-pilot symbols are generated by performing data decision on the (randomly modulated) data symbols such that the modulations become known to the receiver. These pseudo pilot symbols are later on used to re-estimate the radio channel to improve the accuracy.

## Interleaving:

InterleavingÂ is a way to arrangeÂ dataÂ in a non-contiguousÂ way to increase performance.

It is used in telecommunications:

Time division Multiplexing,Â Data transmission,Â Error correction.

Computer Memory

Disk storage

Interleaving is the data communication mainly used in, radio transmission, multimedia file formats, radio transmission (for e.g. in satellites) or by ADSL. The interleaving of digital signal data is sometimes used to refer to the interleaving ofÂ digital signalÂ data. It is also used for multidimensional data structures.

Interleaving is used in digital data transmission technology to protect the transmission againstÂ burst errors. Interleaving can help to stop the errors that overwrite a lot bits in row, so it is typically used for error correction scheme that expects errors to be more uniformly distributed.

Data often transmits with error control bits that enable the receiver to correct a certain number of errors that occur during transmission. If a burst error occurs, too many errors can be made in one code word, and that codeword cannot be correctly decoded. To reduce the effect of such burst errors, the bits of a number of code words are interleaved before being transmitted. This way, a burst error affects only a correctable number of bits in each codeword, and the decoder can decode the code words correctly.

This method is often used because it is a less complex and cheaper way to handle burst errors than increasing the power of the error correction scheme.

## Assumptions in this Project:

Usage of cyclic Prefix

The response of the impulse channel is shorter than cyclic prefix.

As the channel effects with Slow fading then the time-invariant occurs over the symbol interval

The transmitted pulses are in Rectangular Windowing.

Synchronization is perfect from transmitter and receiver

, Gaussian channel noise ,Additive, white.

## CHAPTER 2

## 2.1 ABOUT OFDM:

Frequency division multiplexing (FDM) broadcasts several signals together over single path like a wireless system or a cable. Every signal moves in its own carrier frequency which can be modulated by text, voice, video etc. The data is distributed over several carriers which are spaced at different frequencies which provide orthogonity allowing the demodulators to view its frequencies rather than viewing other frequencies. OFDM has many advantages like lower multi-path distortion, high spectral efficiency and resiliency to RF interference. OFDM is of use as there are multiple channels in a global transmission system i.e. the signal transmitted is received at the receiver making use of different paths of different lengths. The original information cannot be extracted very easily as it contain multiple versions of interference of signal. OFDM is also termed as discrete multi-tone modulation or multi-carrier modulation which is used for the digital televisions in Japan, Australia and Europe.( Karmakar, Dooley L, & Mathew M. . (2008)

## OFDM Description:

In particular from the wireless LAN (WLAN) group standards over the past several years OFDM has received significant consideration from the general wireless community. To provide high reliable data rates for WLAN's, OFDM is selected as the best waveform by the groups of ESTI BRAN and IEEE802.11a. The fame of this OFDM has further increased by the recent selection of IEEE 802.11g committee as the modulation to extend the data rates of Wi-FI WLAN and IEEE 802.11b successful standards.

The most important reason for which OFDM is such a popular choice is, it can able to handle the distortions essentially which are most common in the wireless environment without the requirement of complex receiver algorithms. In particular the environment of WLAN and the wireless environment present a harsh channel for communications as it turns out. In both the time domain and as well as the frequency domain the conventional methods of modulation suffers from multipath. Multipath causes the group of frequencies to be attenuated and shifted in relative to each other in phase which distorts the symbol severely in the frequency domain. The multipath smears adjacent symbols basically into each other in the time domain. With the use of expensive adaptive filters, the typical systems can overcome these problems.

In order to oppose the inherent smearing time domain, OFDM employs a guard interval between the symbols and uses a group of signals which are narrowband in order to pierce through this environment. This makes the system of OFDM to maintain strong performance and allow the systems receivers to use lower complexity. In simple, we can say that OFDM is a accepted choice as it delivers strong performance without the need for complex algorithm receivers in multipath.

OFDM has both advantages and disadvantages with any waveforms, but the disadvantages of OFDM can overcome with careful design choices by using many modern wireless applications. Therefore, OFDM obtain one of the best fit in performance for wireless environments like WLAN's where multipath is the primary impairment to reliable communications and for optimizing cost. (Sinem Coleri, Mustafa Ergen, Anuj Puri, and Ahmad Bahai sep 2008)

## 2.3 OFDM Bundle:

An OFDM signal is a bunch of carriers with narrowband transmitted parallel from the same source at different frequencies. This modulation technique can be named as "multicarrier" rather than a conventional "single carrier" schemes.

Every single carrier, generally termed as subcarrier, conveys information modulating the amplitude and phase of the subcarrier over the signal duration. Thus it is clear that each individual carrier uses either Quadrature-Amplitude-Modulation (QAM) or Phase-Shift-Keying (PSK) to transmit information similar to that of conventional single carrier systems.

Multi-carrier systems or OFDM uses subcarriers consisting of low symbol rates in huge number. Each subcarrier is made non-interfering or orthogonal by maintaining the spacing between them as inverse to duration of the symbol. This spacing is the minimum spacing which is used by not creating the interference.

The OFDM system should modulate and demodulate each and every subcarrier which can be done easily through Fast Fourier transform (FFT). FFT is very efficient method that modulates and demodulates the parallel carriers in a group instead of repeating the process for each sub carrier.

From the figure shown below (Figure 1a), OFDM system converts the serial stream of symbol of QAM or PSK information to a parallel stream of size M which is then modulated to subcarriers of M making use of N size inverse FFT (N â‰¤ M). The inverse FFT outputs N form a stream of data undergoing serialization process which can then be modulated using a subcarrier. It should be noted in this process that inverse FFT of N point can modulate to N subcarriers. The difference N-M individual carriers when M is less than N are not included in the output stream as these should be modulated with zero amplitude. As an example, the IEEE802.11a standard indicates that 52 out of 64 (considering M= 52 and N=64) subcarriers are likely to be modulated by the OFDM transmitter.

## 0FDM Transmitter

Figure 2.3a: Block diagram of a simple OFDM transmitter tter.

It appears that the combination of outputs of inverse FFT's at the transmitter creates interference resulting in noise between individual carriers but the non-interfering or orthogonal spacing separates receiver from single subcarrier. Figure 1b shows the process taking place at the receiver end. The data received at the receiver end is split into parallel streams N which are then processed with FFT of size N. The FFT of size N employs filters that match to the subcarriers of N. the output of FFT undergoes serialization and converted to a data of single stream which is then decoded. The receiver serializes only M subcarriers having data when M is less than N as there are lesser subcarriers than N used at the transmitter.

## 0FDM Receiver:

Figure 2.3b: Block diagram of a simple OFDM receiver.

## 2.4 Multipath Challenges:

Multipath distortion serves as a key challenge to many wireless systems including OFDM-based WLAN architecture. The occurrence of this distortion at the receiver is due to the reflection of a portion of transmitted signal energy by the objects in environment. The figure shown below (Figure 2) is from a WLAN environment with multipath scenario.

Figure 2.4: Multipath reflections, such as those shown here, create ISI problems in OFDM receiver designs

The reflected signals with multipath scenario reach the receiver with different phases, different time delays and different amplitudes. Individual components of frequency is added constructively and destructively based on the comparative phase change between the paths reflected. As a result, the frequency domain of the signal received is shaped by a filter corresponding to multipath channel. There may be some transmitted signals which are attenuated and the other signals have a comparative gain.

In the time domain there are several copies of the signal differing in time delays. This difference in times between the two paths indicates the interference and overlap of symbols resulting in Inter-Symbol Interference (ISI). So, WLAN architectures should be build in such a way to avoid these distortions in demodulator.

It is known that OFDM system depends on subcarriers with multiple narrowband. In such environments, each subcarrier locating at frequencies which are attenuated by the multipath is received at very low signal strength. But for the majority of multipath environments, it affects only a small part of the carriers consequently increasing the error rate of a part of data transmitted. In addition, error correction coding and interleaving improves the robustness of OFDM in multipath. Let us go into the details of error correction coding and interleaving below. Sarma, K.K.,Â Mitra, A.,Â 2009.

## 2.5 Error correction and Interleaving:

Redundancy into the transmitted stream of data is made through error correction coding which allows the missing bits to be corrected or the bits with errors.

An example to this would be to repeat the bits containing information which is called repetition code. Higher rates of error correction can be achieved when the structure of repetition code is simple as more complicated type of redundancy can be used. In OFDM, error correction coding implies carrying each bit of information on to the number of subcarriers; accordingly the information bit can reach the destination unharmed even if any of the subcarriers is weakened.

Interleaving is another technique used to reduce the error rate in the subcarriers. This process changes the order of the bits transmitted. In OFDM systems, the information bits which are adjacent in time domain are allowed to transmit the subcarriers in frequency domain. In a way this helps to distribute the errors on subcarriers to spread in time allowing to convert small number of long error into large number of small errors. These short errors are then corrected using error correcting codes.

## 2.6 Details about Error Channels

2.6.1 Binary Symmetric Channel

The most common communication channel used in information theory and coding theory is the binary symmetric channel (BSC). In this theory, the receiver receives a bit when the transmitter sends a bit (1 or 0). It will be flipped with the crossover probability or a smaller probability even though it is assumed that the bit is transmitted appropriately. In information theory this channel is used commonly as it is one of the channels which is simple to analyze.

A binary symmetric channel with a crossover probability p and denoted by BSCp, is a channel with a binary input and the binary output and error probability p; i.e, if X is the variable which is transmitted randomly and Y is the variable which is received, then the channel which is characterized by the conditional probabilities are

Pr( Y = 0 | X = 1) = p

Pr( Y = 0 | X = 0 ) = 1-p

Pr( Y = 1 | X = 1 ) = 1-p

Pr( Y = 1 | X = 0 ) = p

The receiver can exchange the output if p>1/2 (i.e, interpret 1 when it sees 0, and vice versa) and attain an equivalent channel with a crossover probability 1-p â‰¤ Â½ when it is assumed to be 0 â‰¤ p â‰¤ Â½.

## 2.6.2 Binary Erasure Channel

Coding theory and information theory uses a binary erasure channel (or BEC) which is a widespread communications channel model. In this model, the recipient either receives the bit or it receives a message that the bit was not expected ("erased"), which the sender transmitted a bit (either a zero or a one). To evaluate it is one of the simplest channel which is commonly used in information theory.

Packet erasure channel is closely correlated to the binary erasure channel which shares several related theoretical outcomes with the binary erasure channel.

The BEC is a binary channel i.e., it can only send one of the two symbols (usually either 0 or 1). A non binary channel would be able to transmit more than two symbols (maybe even an infinite number of choices). At times the bit may get "erased" when the channel is not perfect i.e., the bit may get scrambled so the recipient never understands what the bit was.

The BEC is, in a sense, error-free. Contrasting the binary symmetric channel, it is 100% assured that the bit is accurate when the receiver receives a bit. The only disorder arises once the bit is scrambled.

This channel is regularly used by theorists because it is one of the simplest noisy channels to evaluate. To a BEC a lot of troubles in communication theory can be condensed.

## 2.6.3 Error detection and correction

Definitions of error detection and error correction:

During transmission of data from the transmitter to receiver the errors caused by noise or other losses, error detection is the facility to identify the existence of these errors.

Error correction is the supplementary facility to rebuild the new, error-free data.

There are two essential ways to design the channel code and protocol for an error correcting system:

Automatic repeat-request (ARQ): The transmitter sends an error detection code and the data, receiver from the other end check for errors and requests erroneous data for retransmission. In several cases the request implied, the receiver from the other end transmits an acknowledgement (ACK) of received data which is appropriate and the transmitter again sends the data which is not acknowledged in a sensible phase of time.

Forward error correction (FEC): The transmitter sends the coded message which is encoded with an error correcting code (ECC), and the receiver from the other end decodes the data into the most plausible data. The receiver never sends any acknowledgements back to the transmitter. The codes are intended, so that it would receive a senseless amount of noise to trap the receiver without understanding the data correctly.

It is feasible to merge the two, as a result that major errors are detected and retransmission requested and insignificant errors are corrected with no retransmission. The blend of two is called "hybrid automatic repeat-request".

## 2.6.4 Error detection schemes

To attain error detection several schemes exists. The common design is to include some redundancy, i.e., some additional data, to a message or communication, which enables finding of any errors in the delivered message. Mainly such error-detection schemes are organized: the transmitter directs the unusual data bits with the attachment of fixed number of check bits, which is a derivative from the data bits by various deterministic algorithms. The output of the received data bits is compared with the received check bits by applying the same algorithm at the receiver end. If these results do not match it seems that during the transmission an error has occurred at some point. In a scheme the original data was transformed into an encoded data which has at least as many bits as the original data that uses a "non-systematic" code, such as some raptor codes.

In general, to calculate the redundancy some hash function may be used. However, some functions are of mostly widespread use, due to their correctness of detecting certain kinds of errors or their simplicity, such as the cyclic redundancy check's show in detecting rupture errors.

Other mechanisms of adding up redundancy are "repetition schemes" and "error-correcting codes". Repetition schemes are very simple to execute and are quite ineffective. The number of errors that can be detected can be guaranteed by Error-correcting codes.

## 2.6.5 Repetition schemes

On this scheme variations exist. Given a stream of data that is to be transmitted; the data is broken down into block of bits and in transmission each block is transmitted several encoded number of times. For example, if we would like to transmit "1011", we might duplicate this block three times each.

Suppose we send "1011 1011 1011", and this is received as "1010 1011 1011". As one set is not the matching as the other two sets so we can find out that an error has occurred. If the error occurs in exactly the same place for each set, this scheme is not very effective and efficient and can be subjected to problems. (e.g. "1010 1010 1010" in the example above will be detected as correct data in this scheme).

However this scheme is very simple, and is in reality used in various transmissions of number stations.

## 2.7 Parity schemes

## 2.7.1 Parity Bit

The parity bit is mainly used for error detection which can detect only odd number of errors. The data in a stream is broken into number of bits, then the bit one is counted. The bit 1 is based on odd or even then the parity bit is set.( This system is called as even parity or odd parity).On the basis of Hamming code the tested blocks overlap the parity bits and used to isolate the error and can also correct the affects on single bit.

A parity scheme contains limitations as, odd number of bits like (one, three, fiveâ€¦etc) and even number of bits (two, four, six and so on) are flipped, even though the data is corrupted the parity bit appears to be correct. The mechanism on parity bit on extensions and variations are vertical and horizontal and undergoes diagonal, dual and double parity redundancy checks used in RAID-DP.

## Checksums: It is a sum of arithmetic sum of message code words of fixed length (For example, byte values). By means of a ones-complement prior to transmission as redundancy information the sum is often negated in Oder to detect the errors resulting in all zero messages. It includes longitudinal redundancy checks; parity bits, and check digits. In few check schemes like verhoeff algorithm and luhn algorithm are designed to detect errors on humans writing down or remembering identification numbers.

Cyclic redundancy checks: In CRC the data in block coefficients of polynomial over a finite field divides by a fixed, predetermined polynomial. The redundancy for the message serves by the remainder of the division. It is favorable properties mainly suited for detecting burst errors. They are widely used to implement in hardware and in various protocols.

## 2.8 Handling ISI:

ISI is the time-domain counter part of the multipath or spreading of one symbol into the next. By adding a "guard interval" to each and every symbol, OFDM elegantly manages this sort of multipath deformation. This "guard interval" is normally a cyclic or periodic extension of the essential OFDM symbol. In other words, although it carriers no 'new' information, it looks similar to the rest of the symbol.

Since no new information is conveyed, the receiver can still be capable to divide and decipher the subcarrier and disregard the 'guard intervals'. When the guard interval is considered to be longer than any smearing due to the multipath channel, the receiver is capable of eliminating ISI deformation by dumping the unnecessary guard interval. Hence, ISI is removed with almost no added receiver difficulty.

As it reduces the amount of energy existing at the receiver intended for channel symbol decoding, it is significant to note that removing the guard interval does have an effect on the noise efficiency. Further, it reduces the data rate since no new information is enclosed in the additional guard interval. Thus, while maintaining the enough multipath protection the guard interval will be made as short as feasible by the good quality system design.

Why the single carrier system does use the guard interval? The single carrier removes the ISI by addition of guard interval between each and every symbol. However, it has severe impact on the data rate for single carrier than the OFDM. As, OFDM uses a bundle of narrow subcarriers, the frequency width of the subcarrier is inversely proportional to the symbol duration which obtains high data rates with relative long periodic symbol. Therefore it has a little impact on data rate by addition of a short guard interval.

Individual carrier systems having equivalent bandwidth of OFDM should use symbols with small duration. Therefore, the data rate will have a greater effect with the addition of guard interval to the channel spreading.

In brief, OFDM is suitable for those wireless systems which have multipath propagation scenario as a key source of distortion as seen in a WLAN environment. Combining multiple narrow subcarriers with error correction coding and interleaving permits the OFDM system to operate with good results even in a multipath propagation whereas the guard interval at the receiver gives a comparatively easy way of eliminating inter-symbol interference. The design of high rate and reliable wireless communication systems is possible by combining the above features and reducing the complexity of traditional single carrier systems.

## 2.9 Multipath propagation

## Multipath propagation is one of the causes for inter-symbol interference in which the transmitted wireless signal is received at the receiver end through several paths. This can be caused due to refraction, reflection i.e. bouncing off the signal due to various reasons and atmospheric effects. These are of various paths, some effects slows down the signal rate resulting in the arrival of each signal at different times. Consequently, some of the symbols overlaps with the consecutive symbols avoiding correct detection of the symbol. These multiple paths also undergoes phase and amplitude distortions causing interference with the signal.

## 2.10 Band limited channels

Transmission of a signal through a channel with band limitations i.e. having zero frequency response above the cut off frequency, is one of the major causes for inter-symbol interference. Transmitting a signal in such limited band frequency results in attenuation of amplitude of frequency component by the channel to the frequencies lower than the cut off frequency and amputation of frequency components above the cut off frequency.

The shape of the pulse arriving at the receiver end is affected by filtering of frequency components. The rectangular pulse filtered is effected in a way that it not only changes the pulse shape of one symbol period but also effects all the consecutive symbol periods. If a message has been transmitted through this channel, pulse spreading of each symbol overlaps with the successive symbols.

This filtering of the transmitted signal affects the shape of the pulse that arrives at the receiver. The effects of filtering a rectangular pulse; not only change the shape of the pulse within the first symbol period, but it is also spread out over the subsequent symbol periods. When a message is transmitted through such a channel, the spread pulse of each individual symbol will interfere with following symbols.

Both wireless and wired communications support band limited channels as opposed to the multipath propagation scenario. The system tends to be pose limitations due to the transmission of a bundle of individual signals in one cable/area allocating a part of total bandwidth to each signal. In wireless systems, a portion of bandwidth in electromagnetic spectrum is allocated for transmission. As an example, FM radio is mostly transmitted in the frequency range of 87.5 MHz - 108 MHz range. This frequency allocation is typically managed by the government for example for USA it is administered by Federal Communications Commission (FCC). In a wired system like an optical fibers, the cable owner decides this allocation of frequency.

The physical properties of the medium can also cause limitation in bandwidth. For example, in a wired system the cable used may have a certain frequency limitation i.e. cut off frequency upon which the signal cannot be broadcasted. Certain communication systems require transmitting signals beyond the cut off frequency overcoming the interference caused due to bandwidth limitations. Such systems use pulse shaping technique to serve this necessity. Communication without ISI is possible for a flat frequency response and finite bandwidth of a shaping filter. Adaptive Equalizer is generally used to balance the frequency response as the channel response is not known in advance.

## 2.11 Effects on eye patterns

The inter-symbol interference in a data transmission system or a PCM can be studied practically by applying the received symbol to the oscillator's vertical deflection plates and also applying saw tooth wave at the rate T of the transmitted symbol which is 1/T to the oscillator's horizontal deflection plates. The symbol displayed as a result of these processes is termed as an eye pattern as it resembles human eye and the internal region of this eye pattern known as eye opening. Eye pattern which is obtained from the above technique gives a wide range of information about the particular system.

The sample of time interval of the received wave with no error from inter-symbol interference is given by the width of the eye pattern. The time at which the eye opens to its widest can be regarded as the preferred time for sampling of the signal.

The rate of closure of eye varying sampling time determines the sensitivity of the system to the timing error.

Margin over noise can be measured with the height of the eye opening at a particular time of sampling.

The graphical presentation of the characteristics of signal can be given by overlapping of an eye pattern with several samples of a signal. The figure shown below (Fig: 2.11a) is the binary phase-shift keying (BPSK). In the figure, amplitude of -1 is represented by 1 and the amplitude of +1 is represented by 0. Centre of the image contains current sampling time and the edge of the image contains next and previous sampling times. The transitions of the symbol from one to zero, one to one and so on can be seen in the diagram.

The distance between the point at zero amplitude and the point at the signal can be given as Noise margin which intern is given as the amount of noise that the receiver require to result in an error. The signals tends to be better if the sampling time is farer from the zero amplitude. In order to interpret a signal appropriately, the signal should be sampled at the cross of one to zero and zero to one transitions. Similar to the above case, the farther the points are, the better is the signal and can withstand to the errors at this time of sampling at the receiver end.

The eye pattern of the binary phase shift keying system (BPSK) operating in a multipath scenario effected by ISI can be shown in the figure (Fig: 2.11 b). It can be seen that there is a loss of actual signal due to the effects of distortion of the signal. It also results in the delay of signal to be received at the receiver. The noise margin of the system is also reduced showing the poor performance of the system.

Fig: 2.11a The eye diagram of a binary PSK system

Fig: 2.11b The eye diagram of the same system with multipath effects added

## 2.12 Countering ISI

## Several methods have been designed in data storage and telecommunication to solve the inter-symbol interference problems. Systems should be designed in a way to shorten the impulse response which results in a smaller amount of energy of one symbol interfering with other symbol.

A successive raised-cosine impulse with zero inter-symbol interference has been demonstrated in the figure.

Having guard period in time domain with separate symbols.

To undo/reduce the channel effect by applying inverse filter, this can be achieved by applying an equalizer in the receiver end.

To estimate the series of symbols transmitted via the Viterbi algorithm by applying a series detector in the receiver side.