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### Introduction

New visions of 4th Generation communication systems that are recently coming to fact and approaching the everyday life of human being, all going toward increase of capacity, data rate, coverage and reliability of services in response to raising demand to new applications and more complicated services.

The unified world of communications that moves toward convergence of services and technologies in telecommunication world and more specifically in internet and voice telephony and VoIP networks, all are approbating on some basics and most of them using a number of principles.

Next generation systems as their countenances beginning to be shaped, their common points started to appear. Most of them weather they are supported by IEEE , 3GPP or by other research communities and companies, agree on some essentials like, IP core networks with small variations and Multicarrier modulation formats specially OFDM and its derivatives as base of over air interface modulation schemes.

The Long Term Evolution of Universal Mobile Telecommunication Systems that proposed by 3GPP is just one of latest steps in an advancing series of mobile communication systems that uses Orthogonal Frequency Division Multiplexing as main technology for its radio networks.

OFDM is a modulation and multiplexing scheme at the same time. Its strength comes from immunity to multipath fading, Inter Symbol Interference and spectrum saving. OFDMA, SC-FDMA and MC-CDMA and etc that are used in new technologies, all are somehow related to OFDM, and use same principles.

In this dissertation we have introduced a novel method for enhancement of OFDM symbols by reducing overheads. In this chapter we gave a fast introduction of next generation communication systems and their relation with OFDM and why they rely on such scheme for their radio networks.

Afterwards in chapter two we went through background of OFDM technology and researches made on this domain. A brief introduction of general structure of an OFDM communication system is given in this part. The main blocks of such system are defined and brief history of technology given. Advantages and problems of this modulation scheme are presented and discussed.

In Chapter three we give a closer study on researches made on OFDM. The literature of technology has been revised in this part of dissertation. The study goes in between lines of system and channels and their specifications as it related to our study are discussed and then a brief revision on estimation of channel impulse response is given. Subsequently we will look over our main subject that is Guard interval of OFDM symbols and their benefits and variations and go through the scientific papers and researches that cover this part of system. In this section we run a one eye over most related works done on Adaptation methods for Cyclic Prefix and researches made so far on this area of science.

Fourth chapter is particularized to describe our designed system which is implemented later in MATLAB and simulates an OFDM communication system physical layer. Then our methods and techniques are explained in detail and multiple scenarios with different specifications are illustrated. All aspects of new adaptive system are covered in detail in this chapter. New added block which adds adaptivity to the system explained in detail and technical base which used in this method is demonstrated clearly.

Next chapter will contain a presentation of simulated results for various scenarios and different tested schemes. The complete in details graphs and results for each channel condition that related to specified schemes are given in chapter four. All aspects, like bandwidth effects and different Doppler amounts are also covered in detail. Ideas are given and tested and analysed in this part of dissertation.

Finally conclusions are made in chapter five and approaches are demonstrated and outcomes are discussed. Also in this chapter more aspects that should be covered in future researches and studies has been suggested and the directions for future work on our method were offered. We specify the researches that necessary to make these results a fact that can be applied in communication systems and taken benefit of.

Last pages cover the references and bibliography resources used to structure the thesis between your hands and further the management of this dissertation also included at the end.

### Aims and objectives

### Aims

The goal of this dissertation project is to find a robust and adaptive Cyclic Prefix for 4th generation communication systems which changes its length in reaction with environmental change based on estimation of channel delay spread that gives OFDM symbol capability of battling ISI with minimum resources possible and maximum symbol efficiency to meet the purposed bit error rate for mobile and multipath frequency selective time varying channels used in 4th generation mobile networks that use OFDM as basic modulation technique.

### Objectives

In order to meet required conditions for purposed Adaptive Cyclic Prefix method and reach needed quality of received signal the following steps are necessary for this project.

- Massive Background study to find available channel estimation methods, channel delay spread evaluation and ISI and ICI cancellation schemes in order to find most accurate Channel Impulse Response.
- Implementation of an OFDM communication system model in MATLAB to simulate the methods introduced that contain Transmitter, Channel, and Receiver and statistics measurement blocks.
- Implementation and simulation of different channels and equalization algorithms and finding a method for channel delay spread estimation.
- Investigation of CP length on channel estimation and equalization performances by measuring comparing the simulation results of different length CPs.
- Proposing a new Cyclic Prefix which can adaptively altered in response to channel variation.
- Review of introduced methods and optimization of code to reach maximum rate and best performance.
- And finally gathering results and comparison to last approaches and finalizing the final report.

### Background Study

In the past messages (information) have been conveyed by carrier pigeons, runners, etc. These methods were sufficient for data amount and distance of that age needs. Then electrical signals and communication is introduced that can bear messages to longer distances and much higher rates. New communication technologies were more reliable and energy and time saving. New services introduced by development of technologies like video conferencing, teleshopping and tele-banking and more and more.

Communication was one of the first applications of electrical technology. Today, in the age of fiber optics and satellite communication and cellular networks, communication systems remain at the leading edge of electronics. Probably none of electronics branch has as deep an effect on people’s everyday lives.

In order to communicate between any two points and form a communication system three main parts are necessary to be existed. First one is ‘Transmitter’, which generates the electromagnetic wave that carries the information and sends out the generated signal through channel toward receiver. The ‘Channel’ that carries transmitted signal and usually has destructive effect on passing wave. And finally a ‘Receiver’ which returns gathered electromagnetic wave and retrieves the original information. The wireless systems can be classified by type of electromagnetic signal that used by the system whether it uses a single tone frequency to carry information or it uses mixture of different frequencies.

### multicarrier versus single carrier

The process in which a lower frequency signal called baseband signal modifies the Amplitude, Frequency or Phase of a higher frequency signal called carrier is named modulation. The reverse process that retrieves the original signal from modulated carrier signal is called ‘Demodulation’.

The carrier signal always has higher frequency and mostly a single tone cosine signal. Modulation schemes are classified according to which property of carrier changed by data signal and whether they are analogue or digital. But regardless of these entire if they are using a single tone, like in inherited old systems they called ‘Single Carrier’ modulation and consequently single carrier communication system. Figure 2.1 shows a single carrier signal spectrum.

If more than one user wanted to share such system to communicate with others they will need a technique called Multiplexing to relay using of resources.

In the other hand we have systems called ‘Multicarrier’. As it can be understood from name in such modulation techniques and systems more than one frequency carriers are used to modulate information signal. The carrier signals could be generated individually but in most cases they are generated from same source to ensure of frequency synchronization and orthogonality.

Multicarrier systems are more immune to multipath fading, both frequency and time synchronization errors and narrow band noise. All these properties in addition to saving in guard band and lower latency and higher data rate make multicarrier systems more favourite for future communication systems.[1-1][1-2]

### Orthgonal frequency division multiplexing

OFDM is the most well-known multicarrier technique that can be considered both a modulation and a multiplexing method. It divides the spectrum to many subcarriers to modulate them with lower data rate streams. It uses available spectrum much more efficient than conventional single carrier modulation schemes. This efficiency comes from putting the subcarriers closer together or actually inserting them inside each other in a way to make their spectrum orthogonal to each other. Orthogonality means that each subcarrier’s spectrum has a null value in its adjacent subcarriers peak value and so on (Figure 2.2). The orthogonality makes the spectrum efficiency of OFDM 50% superior over traditional modulation schemes. [1-2][1-3]

The baseband modulation techniques are still available in OFDM and after mapping of data individually, the subcarrier generated by a Discrete Fourier Transform block to make sure of orthogonality and load data on them. This makes the synchronization easier and avoids frequency offsets. The figure 2.3 shows a general discrete domain OFDM system.

The following stages are obvious and form main parts of OFDM transmitter:

Mapper: As soon as user data is ready to transmit and comes through higher layers of system and arrives in physical layer, it will be mapped to its appropriate available states of baseband modulation like PSK or QAM. The available constellation points are determined from modulation order that itself pre-determined by system design or adaptively changes based on receiver feedback according to channel condition.

Each state in constellation map represents a group of data bits. There are different methods to assign the bits to states. Figure 2.4 demonstrates a 16-QAM constellation map with 16 states as it could be find out from name which a group of 4 information bits assigned to each state in simple binary order.

IFFT: Inverse Fast Fourier Transform that is used for its simplicity and accuracy is the main block of any multicarrier system including OFDM. It can be imagined as many parallel local oscillators that work exactly on adjacent “Orthogonal” frequencies. This orthogonality can be considered main feature of OFDM modulation that guarantees the avoidance of interference between adjacent subcarriers.

This block converts frequency domain states from mapped signals to their related time domain signal with orthogonal spectrum on modulated subcarriers. FFT/IFFT is a computationally efficient form of Discrete Fourier Transform which works by decomposition of mathematical approach of DFT to several lower order transformations and reducing the computational complexity. It converts frequency domain symbols to their time domain samples.

GI/CP Insertion: In OFDM there is no need for guard band frequencies due to time domain effect of channel by existence of IFFT and FFT but instead the consecutive symbols may interfere with followed ones due to channel delay spread. To avoid these phenomena a time guard interval inserted between two successive symbols coming from IFFT stage. This block is our stage of interest and covered in more detail later in this dissertation.

Then signal passes through a Digital to Analogue converter and converted to continuous time signal, then up converted to specified frequency and loaded to required part of spectrum and transmitted to channel.

In the channel signal will be attenuated, distorted, faded and induced by noise and interference. Different environments affect signal in different forms but all does one thing, all degrade the signal quality in a way that makes further processing in receiver to compensate such declination necessary. The channel part is very important in any communication system thence it covered in more detail in next section.

At the receiving part the antenna/s gather required amount of power from channel to form received signal. After some amplification and purification it will be down converted to baseband and then sampled by an Analogue to Digital converter. Then it applied to following main stages:

GI/CP removal: In this stage the added guard intervals are removed from OFDM symbols. This will cancel the effect of induced interference from delayed replicas of preceding symbols and reduce ISI.

FFT: Fast Fourier Transform that inverses the effect of IFFT and returns the frequency domain samples which represent modulation states. In fact the FFT and IFFT do same thing, because Fast Fourier Transform is implemented using a linear algorithm and works in both direction in the same way. The ‘Inverse’ prefix just used to acknowledge the frequency to time transformation at the transmitter and makes no change in real.

Equalizer: To compensate the channel effects the receiver contains one more important part. It actually encloses two subparts, Estimator and Equalizer. The receiver estimates the channel impulse response by using pre-known values called pilots or non-pilot algorithms and then tries to compensate it by applying reverse effect to the signal. This part is also covered later in channel section.

De-mapper: Finally samples goes through a demodulation block and translated to real data. This section does the inverse of modulation and performed in same order. But the difference is that the received states of signal suffering from random noise effects that are existed even after equalization also the fading effects company the signal due to non-perfect channel estimation.

### channel

One of the most important elements of every communication system is channel which signal passes through when it travels from transmitter to receiver. Signal can be affected by the channel during this period and its characteristics are modified by channel. Modification to signal varies depending on channel characteristics. There are many different channel models for wired and wireless transmission.

### wireless channel

First and most elementary challenge to any communication system especially broadband systems like OFDM comes from communication medium itself which signal propagates in form of electromagnetic energy between transmitter and receiver. A good understanding of wireless channel and its key specifications and physical parameters, is first step of analysing any telecommunication organism. It’s critical for suitable selection of Transceiver structure, its components and their settings and system parameters optimization.

Mobile wireless channel is severely affected by multipath propagation; the electromagnetic wave is reflected, scattered and diffracted, and arrives at the receiver via different paths as an incoherent superposition of many signals of same source with different delay times that are caused by the different path lengths of these signals.

The combination of these replicas of signals can be constructive or destructive depending on the phase change of each one which is itself function of time delays of each path. The mobile receiver moves through an interference pattern that may change within milliseconds and that varies over the transmission bandwidth. One can say that the mobile radio channel is characterized by time varianceand frequency selectivity. [1-4]

In next chapter we will go through more detailed view of channel effects on signal and how it can be compensated in receiver side by estimation of channel impulse response. A closer look also made to ISI effect on channel estimation and signal and how it is avoided by using Guard Interval. A study in literature of researches done in this domain is also given in next chapter.

### literature survey

In the previous chapter a brief study of multicarrier communication technology and particularly speaking OFDM was given. In this chapter a more detailed view is arranged to give reader the necessary information to understand the main idea of this thesis. The wireless channel discussed in detail and its impact on signal is studied. Then fading channels and their varieties are introduced and covered as part of literature overview. At the end we focus on the cyclic prefix technique and related previous researches in this area to emphasise the purpose of this dissertation.

Since a definition of a wireless channel is already given, the next step will be the understanding of how they really affect on transmitted signal. Free space model and two ray model are two most simple channel representations. In the following some more complicated channel specifications and models are introduced. Some of them are usually used in communication system simulations and better defines channel vandal effects.

### Awgn

In real world there is not any place where is not existed. Disturbance from mechanical and electrical machines, which is called man made noise, power lines, wired systems circuitries and more important the thermal noise generated systems themselves and counteraction between different transmission sources all are big random noise sources.

Noise in communication usually modelled with Additive White Gaussian Noise. If r(t) is received signal and s(t) is transmitted and noise denoted by w(t) the relation is as follows:

Noise as seen in formula is random number and added to original signal mathematically and that’s why it called additive and its spectral density power represented by ‘No’. It is called ‘White’ because its spectrum contains ideally all frequencies but if noise bandwidth limited it denoted by ‘BN0’ and called filtered noise.

Noise generation and modelling is a Gaussian process with zero mean. It means the noise values has opposite amounts and overall summation is zero but it implies the ideally the power of it infinite. The AWGN is mathematical fiction but it gives a good estimation of real life noise that affects the communication signals. We often use ‘Complex AWGN’ which means a random complex number is added to signal states which affect both magnitude and phase of signal.

### Fading channel

In channel signal experience other disturbing effects rather than additive noise. The most important one is ‘Fading’. There are two kinds of fading, large scale and small scale.

Large scale is due to path attenuation. We know that the free space attenuation caused by spread of energy on larger area during propagation. Free space path loss is main large scale fading effect and denoted by attenuation in received signal. Attenuation has multiplicative effect on signal and causes more severe changes in signal compared to random noise.

Small scale fading caused by interference of two or more versions of same signal arrived at receiver with different time delays. These slightly delayed replicas of same signal called multipath waves and combined with each other in receiver antenna and matched filter and cause wide differences in amplitude and phase of accepted signal.

The statistics of process above characterise the channel and most important part for channel model parameter specifications. A simple and regularly used process is achieved by the assumption that there are a large number of scatters in the channel that share in bringing about the signal at the receiver side. This approach leads to a complex-valued Gaussian process for the channel impulse response (CIR). The CIR has great importance in any communication system and its estimation can be considered as most important part of any receiver device. In the absence of line of sight or a dominant component, the process is zero-mean Gaussian process which is base of Rayleigh distribution systems. The magnitude of the corresponding channel transfer function is a random variable, for brevity denoted by , with a Rayleigh distribution given as following;

denotes the average power and phase is uniformly distributed in the range of [0 , 2π]. In the case where the multi-path channel contains a LOS signal or a dominant element in addition to the randomly distributed mobile scatters, the channel impulse response can no longer be modelled as zero-mean Gaussian process. For this kind of channel impulse response, the magnitude a of the channel transfer function has a Rice distribution given by following equation;

The Rice factor KRice is concluded from the ratio of the power of the dominant signal tap to the power of the scattered paths. I0 is the zero order modified Bessel function of first kind. The phase is uniformly distributed in the range of [0 2π]. The Rice distribution is not matter of interest for this report and is only covered to emphasise the difference its difference with Rayleigh distribution for mobile channels. Because in most cases the mobile wireless communication systems don’t contain a main LOS signal path between transmitter and receiver, Rayleigh distribution is usually used to represent their channel model [3-1].

### Delay spread & Inter sybol interference

### Delay spread

Consider a transmitted signal as given by Equation below;

Which illustrates the signal with carrier f0 modulated by complex amplitude of s(t) . Assuming that both transmitter and receiver are at rest (or the time variance is so slow that it can be neglected for the time under concern) and we can ignore any change in frequency of observation in receiver and thus Doppler shifts. But the delays τk= lk/c of the complex baseband signal s(t) → s(t − τk) for the different propagation paths for signal with length lknot ignored for this case. Then in the receiver the overall accepted signal is;

The delays of the carrier are already included in the phase θk. The complex baseband transmit and receive signals and are related by

is the impulse response of the channel. The corresponding channel transfer function is given by

Typically, the frequency response looks as shown in Figure 3.1. In the special case of two-path channels (N = 2), the transfer function shows a more regular behaviour. In this case, the power gain |H(f )|2 of the channel can be calculated as;

The transfer function is periodic with period |τ1 − τ2|−1. We may regard H(f ) as a random transfer function, or a stochastic process in a frequency variable. Frequency-shift invariance (which corresponds to neglecting Doppler Effect) can only be an approximation. Since the variable for this process is a frequency, there is a power density distribution as a function of a time variable τ that can be recognized as the delay time. This is known as channel delay power spectrum or channel delay profile. Figure 3.2 illustrates such a delay power spectrum SH(τ) corresponding to the process given by the Equations (3.10) and (3.11).

But, in real situations, the received signal is a continuous rather than a discrete (which is used to simulate the case in MATLAB) superposition of delayed signal components, resulting in a continuous delay profile SH(τ) as shown in Figure 3.2(b). Note that the delay power spectrum reflects the distribution of path length and their strength. One popular model for SH(τ) is an exponential distribution

for τ > 0 and zero elsewhere. The mean value τmof this distribution equals the delay spread denoted by Δτ. The exponential power delay spectrum reflects the idea that the power of the paths decreases strongly with their delay. This is of course a very rough model, but it can be refined by adding components due to significant distant reflectors [1-4]

### inter symbol interference

Generally speaking the abovementioned delayed replicas of a signal, interfere each other and make destructive effect on received symbol especially in high data rate communication. OFDM reduces such an effect by breaking one high data rate stream to multiple low speed sub-streams. This reduces the Tsymbol which consequently declines the fading effect on symbol.

But what if the preceding symbols delayed copies interfere the next one. This effect is called Inter Symbol Interference and reduces signal quality. This phenomenon is one of the major problems that Multicarrier systems suffer from. For a transmission system with maximum delay equal to τm the only way to have an ISI free reception is to satisfy the following condition;

This condition restricts the transmission speed which is overcome relatively in OFDM by multicarrier design. But still for avoiding ISI a Guard Interval is necessary and used to keep the channel delay spread destructive effects below required level. The GI in OFDM is further explored below.

### Channel estimation

Although OFDM solves many complications that were necessary in equalization of single carrier systems but still cancellation of channel fading effects on signal seems to be required. The first step to successfully apply this process is to have a good vision of channel condition and its effects on signal. Thus a estimation of wireless channel is essential.

The ‘blind estimation’ and ‘pilot aided estimation’ of CIR are two basic categories of estimation schemes. Since most of blind methods are computationally intensive and doesn't perform as good as training sequence methods, they're not usually used in our networks of interest that suffer from frequency selective time varying multipath channels. In such systems e.g. mobile cellular networks the CIR observed by client device changes in a small fraction of time which makes the use of ‘Blind Estimation’ relatively unpractical.

In mobile wireless channel that is mostly frequency selective fast fading channels, the pilot aided channel estimation is usually the dominant method neglecting of what kind of mathematical algorithm used. In this method the pilot distribution inside OFDM symbol plays an important role in estimation quality and decision of algorithm. The pilot arrangement inside data symbols is generally done in two ways. Block type pilots and comb type arrangement [3-11] [3-12] [3-13].

In Block arrangement all subcarriers loaded by pilot signal in defined periods within data symbols. The CIR estimated using these pre-known values and used to equalize data symbols between two blocks of pilot symbols and then CIR updated in next block.

But the disadvantage of block-type is when communication channel changes during transmission of data symbols nothing can be detected and error rate increase. This problem become critical in highly mobile environments that CIR changes approximately with each symbol received.

To overcome above mentioned problem in second method, part of subcarriers reserved for pilot signals in every OFDM symbol [3-11]. This is to satisfy the fast fading mobile environment signal equalization.

Different mathematical algorithms and practical methods applied to pilot symbols to obtain the estimated values of CIR coefficients whether the block type or comb type pilots employed. The Least Squares (LS) and Minimum Mean Square Estimation (MMSE) and Least Mean Square (LMS) are introduced as most practical methods to estimate channel response in pilot frequencies of comb-type sequences [3-11] [3-12] [3-13].

Their performance varies in different channel conditions, but they generally chosen to be used in communication systems based on trading between simplicity of implementation and minimum signal quality required. For instance the MMSE performs better in SNR gain over LSE but its major drawback is complexity of implementation.

The Interpolation of comb type can be done in several ways in order to derivate the channel response in data subcarriers from estimated CIR in pilot subcarriers. In other words since the comb-type pilot aided channel estimation only estimates the channel response in subcarriers which loaded by pilots there is a need for method to find channel response in data subcarriers in order to cancel the fading effect of channel on data symbols. This process called ‘Interpolation’. Linear Interpolation, second order interpolation, low pass FIR interpolation, spline-cubic interpolation and time domain interpolation are mostly used methods for this purpose.

Second order interpolation and time domain interpolation perform better than simple linear method and they have better BER. But the low pass FIR and spline-cubic methods are well implemented and more popular ways that also perform very well.

In [3-11] most of interpolation and estimation schemes are simulated over a Rayleigh fading and Auto Regressive based fading channel with different modulation orders. It proves that comb-type outperforms the block type pilot in rapid time-varying and highly mobile channels. It also demonstrates that low-pass interpolation performs much better among all other techniques due to minimizing of error between the interpolated data points and their ideal values. Moreover it illustrates that low-pass comb type estimation more robust for Doppler frequency increase.

### Guard interval & Cyclic prefix in OFDM

The interference makes the situation for channel estimation and compensation for fading channels worse. In order to make equalization as simple as it’s possible in OFDM, as we mentioned earlier a Guard Interval introduced to capture the delayed symbols replicas and prevent them from interfering the subsequent one.

Although most of Current OFDM transmission systems employ Cyclic Prefix as Guard Interval but there are several GI types are encouraged in literature. A method in which the ‘null’ guard interval inserted between two successive OFDM symbols has been studied in earlier literature to improve the transmission quality. This scheme called Zero Padded OFDM (ZP-OFDM) transmission. It is proposed and studied in [3-3].

In [3-4] the Pseudo Random Postfix (PRP) is proposed to replace the null samples in ZP-OFDM. In this method, a pseudo random sequence is inserted between each two symbols and it can be pre-known for receiver to exploit them for channel estimation, in addition to reducing ISI.

May be both most widely used and well known method, is Cyclic Prefix extension for OFDM symbols which is called CP-OFDM. In CP-OFDM a portion of OFDM symbol itself copied to the beginning of symbol as cyclic extension and guard interval. By doing this the symbol is cyclically extended from the original harmonic wave of the Fourier period Tsymby a guard interval of length Tgto become a harmonic of the same frequency and phase, but of duration T = Tsym+ Tg[1-4].

Figure 3.5 shows the cyclically extended OFDM symbol. This scheme has several advantageous rather than avoiding ISI. The better SNR gain and easier synchronization in both time and frequency make CP-OFDM more favourite over ZP-OFDM however small ripple caused by CP in power band prevents using of cyclic prefix in low power transmissions like UWB transmission systems [3-5].

In [3-6] a way of study of multicarrier systems and especially OFDM symbols are given without discussing any practical approach. This paper talks about statistics that can be obtained from second order characteristics of OFDM symbol and useful information that one can get from cyclostationary statistics of it, to employ the obtained information in different domains like frequency and timing synchronization. Furthermore it studies the effect of pilot carriers and cyclic prefix on such readings and observations and finally it formulates them in a new method.

A closer and more detailed study of Cyclic Prefix of OFDM is done in [3-7]. It supports the idea of introduction of CP to eliminate both Inter Symbols interference and Inter Carrier Interference (ICI). Where ISI comes from different symbols interfering each other, ICI is caused by interference of subcarriers in the same symbol. Since adding cyclic prefix gives a constant capacity loss, the common wisdom is to choose cyclic prefix to be roughly as the same length of channel delay spread.

### Adaptive Cp in OFDM literature

While cyclic prefix length kept as minimum as possible, large delays in signal may occur. Such delayed replicas cause a significant increase in ISI amount. The solution for this problem is to change CP length according to channel condition.

In [3-8] an adaptively changeable length CP is introduced to overcome ISI problem. The impact of CP length on the system bit error rate is studied. It is obviously distinguishable that the longer CP better signal performance but to harmonize this method with higher spectral efficiency, a new technique introduced to change the CP length adaptively and keep it as small as possible while meeting required quality of signal. This method is achieved by slight changes in sampling frequency that leads to increase of distance between spectral lines of OFDM symbol and extends the CP length. This frequency change may cause other disturbing problems on receiving signal that can be considered one of disadvantageous of this method

To overcome long channel delays and maintain better performance a new frame structure is proposed in [3-9]. The concepts of super-frame and sub-frame are introduced on the legacy frame structure basis of OFDM based WiMax. The proposed hierarchy of frames supports three different lengths for CP, short, normal and long. But still this system doesn’t introduce a complete flexibility and adaptation however it allows for sub-frames inside a super-frame to have different lengths of CP. Beside no methods are suggested for decision basis of choosing between supported CP lengths.

In [3-10] two different lengths of Guard Intervals are used for protecting two different symbols. The normal GI is used for data symbols and slightly longer ones for protecting pilot symbols. This is due to importance of pilot symbols for channel estimation that would give better quality if ISI can be completely avoided. The proposed system in [3-10] uses a Variable Length Pilot (VLP) that embedded periodically for channel estimation that uses a block type pilot aided algorithm.

The closest ideas are proposed in [3-14] and [3-15]. In [3-14] the writers propose a method to estimate channel Root Mean Square Delay spread. This scheme which is called AOFDM-VCPL exploits the pilot subcarriers to estimate channel Power Delay Profile (PDP). Then it calculates according to a criterion a suitable CP length and updates the OFDM frame size. First the Channel Frequency Response (CFR) is estimated by using of Maximum Likelihood (ML) algorithm in frequency domain. Then CFR translated to corresponding CIR by means of IFFT. The samples of CIR considered as power delay profile of channel and first ‘l’ elements which have higher values and chosen according to power percentage value, used to calculate RMS delay spread of channel by using mathematical algorithm. Then the CP length updated to twice of evaluated r.m.s. delay spread of channel and fed back to transmitter for following symbols.

The main disadvantage of this method of this method is noise impact on estimation process. The noise affects the CFR estimation based on pilots. Then the error value caused by noise carried to time domain and finally induces some error amount to estimation of delay spread. Thus the accuracy of CP length adaptation will be a dependent of CFR estimation algorithm which itself has different methods with various accuracy. Beside introduction of extra IFFT and r.m.s. calculator which uses matrix divisions and accumulations adds some complexity to the system. Another issue with this method the delay time to get final CP length because the estimation goes through four stages that three of them has complex mathematical algorithm which makes the fast update of CP length very hard.

In [3-15] which is based on [3-14] the r.m.s. and excess delay are also estimated with almost similar technique. In this technique the magnitude of PDP used to avoid error bias that caused by synchronisation errors. It also uses a channel estimation based algorithm like previous one. The channel frequency response estimated first using Least Squares algorithm. This kind of estimation noise susceptible to Gaussian noise and reflects the noise power in estimated channel response. To remove this effect they used a parabolic function to remove noise power. After noise cancellation IFFT used to obtain PDP of channel. According to this paper the synchronisation errors induce carrier dependent errors in estimation channel response. To avoid such a problem the magnitude of CFR used to derive the channel PDP. Then only first L taps used to manipulate r.m.s. and excess delay spread of channel. The CP length proposed to be larger than excess delay spread in [3-15] so it insures less interference in OFDM symbol. The proposed technique has same difficulties that [3-14] faces, however its accuracy increased by parabolic algorithm that estimates the noise power and removes major part of noise effect but the complexity of stages increased. Also the delay time for CP to be estimated is also increased by adding of noise power cancellation stage. Such complex mathematical stages could make implementation of this method in real time communication systems like mobile communications more difficult and cost inefficient.

After going through all relevant papers and researches which made in OFDM systems and particularly about Cyclic Prefix and its adaptation algorithms and methods, in next chapter a new simple algorithm which is more practical based and uses only few easily implementable stages are proposed and explored.

### Materials and Methods

Since the investigation of Cyclic Prefix and adaptation of its length is the main subject of this dissertation an implementation of OFDM transceiver is necessary to investigate the physical layer of a new generation communication system. As we learnt till now from what was mentioned the Orthogonal Frequency Division Multiplexing is chosen to be fundamental modulation scheme of most next generation communication systems due to its strength to channel disturbance and high data rate and etc. A general and simple transceiver implemented to simulate such system and investigate its performances in different channel conditions and further explore our new proposed methods and their performance compared to original ones.

### General Ofdm model

The proposed system design contains basic elements of what named before as general OFDM transceiver (figure 2.3). This transmission system which represents a simple OFDM based system’s physical layer modified to test the proposed guard interval.

At the beginning the system was implemented as a normal CP-OFDM with channel LSE equalizer then it is updated to a system with two transceivers working in parallel on same data stream with equal channel conditions. One is a conventional normal CP-OFDM as reference and second to investigate the proposed schemes and methods. In the following lines we will go step by step through different stages of designed system (figure 4.1) and their mathematical modelling with explanatory figures and flowcharts.

In above system there are few changes can be noticed, compared to figure 2.3 of basic OFDM system. Two ‘Pseudo Random Binary Sequence Generators’ (PRBSG) are added to the system; One for each one of transmitter and receiver. An Estimator, which is used for channel delay spread estimation, is also added to receiver part. In following sections the complete system details are explained.

### transmitter

In realized system that clearly shown in the figure 4. 1. The following stages are designed and coded in transmitter state; the new added stages which can be seen in different colour are added to the system to put into practice the new required operations.

### data Genration

When user data arrives in packets to MAC layer of any communication system it packed to frames before transmission. In this model a random binary data generator used to replace user data stream. The frame length depends on baseband modulation degree (BPSK, 4-QAM, 16-QAM, etc) and number of subcarriers in OFDM symbol which defined by FFT word length.

If the stream length is denoted by ‘M’ and modulation degree and number of subcarriers by ‘Q’ and ‘L’ then the following equation explains their relations neglecting pilot subcarriers or assuming them as normal data ( in real they are normal symbols that pre-know for receiver).

In the system under the investigation the number of subcarriers chosen to be 1024 that is average number used in 4G communications like LTE and WiMax however it alternates depending on circumstances from 64 subcarriers in some systems like WLAN to 4048 subcarriers in DVB communication systems.

### Mapping

In OFDM the modulation of binary stream to frequency domain symbols called maps. The modulator first sets the binary bits to groups according to modulation degree Q and then translates them to available constellation points. These points represented by magnitude and phase in a complex plain. Figure 4.2 demonstrates different mapping schemes that can be used with modulation of binary data design.

Each single symbol ‘SK’ now represents number of bits that particularly in this case for 4-QAM it is 2 and 4 sequential bits for 16-QAM. Any order of QAM or PSK can be used in this design and can be modified easily in order to investigate the effect of modulation order on signal quality. The 4th and 16th degree QAM are mostly studied in this system. The modulated symbol states are now mathematically written as complex states like equation 4-3 which consist of real and imaginary parts as it can be found out from figure 4.2.

Thus the generated bit stream now converted to trail of QAM symbols and denoted by. Letter ‘k’ used to distinguish that symbols are illustrate frequency domain amplitudes.

The number of symbols is converted to equally match number of subcarriers ‘L’ and ready to be loaded on them and carried out.

### pilot insertion

Pilots are pre-known symbols or bits by both transmitter and receiver that usually used for channel estimation and signal equalization in the receiver as we discussed it earlier. These symbols are inserted before the signal goes through IFFT. The number of pilot subcarriers and their arrangement depends on estimation algorithm and channel condition. In implemented system 128 pilot subcarriers used which comprise 12.5% of overall symbols and arranged in comb type method to handle and acclimatise with highly frequency selective mobile time variant channel condition. Pilot spacing between data carriers or pilot insertion rate is calculated like below;

To simplify and optimise designed system the pilot signal generated together with random data generation but their positions identified in both transmitting and receiving side and represented by pilot indexes ‘IP’ with steps equal to insertion rate which is 8 for implemented model with 1024 subcarriers and 128 pilot symbols.

### IFFt

After mapping and pilot insertion the subcarrier generated to carry mapped symbols. The key feature of OFDM relies on the fact that subcarriers can be generated at the same time and from same source in discrete domain using an Inverse Discrete Fourier Transform and particularly its efficiently implemented IFFT version.

Each subcarrier can be frequency formulised as a complex equation of 4-6. But in fact no carrier frequency is generated; the IFFT translates the signal states directly to their complex modulated carrier states.

Off course as appears from equation it represents continues time signal but when we assume that it sampled with Ts rate it could be changed to following discrete domain,

Which in discrete system with sampling time equal to, the replaced by and simply denoted by . Afterwards the amplitude of carrier replaced by symbol states and summarized together according eq. 4-8 for all subcarriers to generate complex time domain OFDM symbol.

The bandwidth of each subcarrier is a small portion of overall signal bandwidth and reversely related with symbol duration and defined as following.

That for designed model in this case with 10 MHz bandwidth (Bandwidth also flexibly can be changed in implemented system) and 50nSec sample period it is calculated and given 19.53 KHz. The phenomenon of parallel transmission of data on subcarriers leads to excessive increase in symbol duration with ratio of 1/L that for 1024 subcarrier case is equal to 1/1024.

Symbol duration increment to battle the channel delay spread, which causes ISI, in more efficient way is one of main advantageous of OFDM transmission. Figure 4.3 demonstrates how OFDM can stretch the symbol transmission period by parallel transmission of subcarriers and compared to single carrier which employs a wide bandwidth and smaller symbol duration

This amount can’t be increased illogically since it governed by another issue called coherence time which depends on maximum Doppler shift. If symbol duration goes over channel coherence time then channel impulse response changes during same bit transmission and may cause severe effects of received signal. But the FFT size and consequently symbol duration increment ratio can be tuned to channel conditions and system bit rate to have an optimized point.

### Gi/Cp insertion

As we mentioned earlier in this report OFDM declines ISI effects in data stream by parallel transmission but still two consecutive OFDM symbols can interfere. To overcome ISI in OFDM in the next stage of transmitter a Guard Interval in time domain inserted between every two symbols. In the implemented code the GI chosen to be Cyclic Extension of OFDM itself to further improve performance in case of ISI. Then the extended symbol could be written as following;

CP = [SL-G+1 SL-G+2 . . . SL | S1 S2 S3 . . . SL] (4-10)

CP represents the CP-OFDM signal that is finally ready to transmit through channel. Since our model works in baseband and discrete time in MATLAB, no D/A conversion took place and no up-conversion done and simply the final stream passed to channel object for processing. But in real world these symbols go through the pulse shaping filter and converted to continuous signal for transmission over antennas.

### Channel

Like pointed out earlier the channel model may be most important part of system design. It brings the platform for system simulation because each channel situation gives different reactions to designed system. The process of testing system on simulated channels gives a good vision how a designed system will work before it put into real.

Relying on this fact a wide range of channel models are implemented and simulated in designed transceiver. Starting by simple ‘AWGN’ then going through normal distributed random complex and standardized COST207, ending with Extended ITU channel profiles. First and simplest channel is Additive White Gaussian Noise, when it applied to transmitted signal; it adds a random complex noise to each subcarrier in a way that overall noise power gives required level of Signal to Noise Ratio.

This part of channel stays with us even in other channel models because it represents the basic channel effect that no communication channel existed in the world without it. Anywhere you go there are manmade noises, electrical power lines and several electric power systems are existed that generate lots of noise adding to that the leakage from other communication systems to one’s being designed.

where for discrete system it is demonstrated and implemented as follows;

The in is received signal in receiver antenna (here receiver stage block) and and stands for transmitted signal and random noise. The noise power depends on measured signal power in channel and applied SNR in the block.

### Fading effect of Channels

Since the main idea of research is improvement of OFDM over mobile wireless channels the fading channels are more realistic and they have more important role in our design. In channel block of transceiver, different Rayleigh distributed profiles are investigated. Three main classes implemented in the model and simulation switches between them.

### Random rayleigh

In [4-3] mentioned Rayleigh fading is defined a reasonable model when there are many objects in the environment thatscatterthe radio signal before it arrives at the receiver. It is a good model when many scatters are existed and no dominant path like LOS is available (that is very good approximation of mobile channels). Then each path gain is a random Gaussian process with zero mean and can be generated by a producing two independent uncorrelated numbers for real and imaginary part of which denotes channel impulse response.

Then input signal to channel (transmitted signal) convolved with using simple FIR filter with filter coefficients equal to . The length of filter which is identical to defines the number of taps or number of combined replicas of same symbol. Still the random noise is available thus the output signal from channel is like below;

### Cost 207

COST (European Cooperation in Science and Technology) is one of the longest-running European instruments supporting cooperation among scientists and researchers across Europe [4-4].

In COST 207 final report it defines tapped delay channel profiles for 2G GSM mobile in 900MHz band that later extended to DCS1800 band and became popular also for simulating UMTS and DVB-T mobile channels. It gives the power and delay profiles for various channel conditions and area situation like ‘Rural Area’, ‘Typical Urban’ and ‘Bad Urban’ and etc. Table 4.1 shows these amounts [3-1] [4-2].

Table4.1. Cost 207 Power Delay Profile

Environment |
Rural Area |
Typical Urban |
Bad Urban |
|||

1 |
Delay (nSec) |
Power (dB) |
Delay (nSec) |
Power (dB) |
Delay (nSec) |
Power (dB) |

2 |
0 |
0 |
0 |
-4 |
0 |
-7 |

3 |
100 |
-4 |
200 |
-3 |
200 |
-3 |

4 |
200 |
-8 |
400 |
0 |
400 |
-1 |

5 |
300 |
-12 |
600 |
-2 |
800 |
0 |

6 |
400 |
-16 |
800 |
-3 |
1600 |
-2 |

7 |
500 |
-20 |
1200 |
-5 |
2200 |
-6 |

8 |
1400 |
-7 |
3200 |
-7 |
||

9 |
1800 |
-5 |
5000 |
-1 |
||

10 |
2400 |
-6 |
6000 |
-2 |
||

11 |
3000 |
-9 |
7200 |
-7 |
||

12 |
3200 |
-11 |
8200 |
-10 |
||

13 |
5000 |
-10 |
10000 |
-15 |

In implemented design these profiles along with different Doppler Shift amounts used to build a Rayleigh channel object which applied to transmitted signal to create the channel fading effects on signal. Then random noise applied to reach required SNR level and afterwards signal fed to receiver.

### ITU channel model

Another wireless channel model which is implemented and investigated in our OFDM transceiver is Extended ITU channel model for Long Term Evolution UMTS system design.

ITU channel models used in the Third Generation Mobile communications. The main parameters to describe propagation models consist of delay spread in time units, multipath fading characteristics, path loss, and operating radio frequency. In ITU Models each environment was defined for two cases which have different probabilities of occurrence: a smaller delay spread and a larger delay spread case. The evaluation of LTE techniques demands channel models with increased bandwidth compared to UMTS models, to reflect the fact that the characteristics of the radio channel transfer function are connected to the delay time resolution of the recipient system. Specifically the ITU models covering an excess (maximum) delay spread from 35 ns to 4000 ns were chosen as a starting point, together with the Typical Urban (TU) model from GSM which has a maximum excess delay of 1000 ns. In this way, extended wideband models with low, medium, and large delay spread values could be acknowledged. The low delay spread gives an Extended Pedestrian A (EPA) model which is employed in an urban environment with comparatively small cell sizes, while the medium and large delay spreads give an Extended Vehicular A (EVA) model and Extended TU (ETU) model respectively. The ETU model has a large maximum excess delay of 5000 ns, which practically is not very typical in urban environments. Instead it applies to some extreme urban, suburban, and rural cases which occur rarely but which are important in evaluating LTE performance in the most challenging environments [4-1].

Table 4.2 shows the r.m.s. delay spread values for the three extended ITU models. It was also decided that the extended channel models are applied with low, medium, and high Doppler shifts, specifically 5 Hz, 70 Hz and 300 Hz, which at a 2.5 GHz carrier frequency correspond approximately to mobile velocities of 2, 30 and 130 km/h respectively.

Profile |
EPA model |
EVA model |
ETU model |
|||

Tap Number |
Excess Tap delay |
Relative Power |
Excess Tap delay |
Relative Power |
Excess Tap delay |
Relative Power |

1 |
0 |
0 |
0 |
0 |
0 |
-1 |

2 |
30 |
-1 |
30 |
-1.5 |
50 |
-1 |

3 |
70 |
-2 |
150 |
-1.4 |
120 |
-1 |

4 |
80 |
-3 |
310 |
-3.6 |
200 |
0 |

5 |
110 |
-8 |
370 |
-0.6 |
230 |
0 |

6 |
190 |
-17.2 |
710 |
-9.1 |
500 |
0 |

7 |
410 |
-20.8 |
1090 |
-7.0 |
1600 |
-3 |

8 |
1730 |
-12.0 |
2300 |
-5 |
||

9 |
2510 |
-16.9 |
5000 |
-7 |

Table 4.3.Extended ITU Model Tap delayed values [4-1]

### Receiver

After picking up signal by recipient antenna it down converted and sampled and goes toward Guard Interval Removal. In designed one since it is working in baseband there is no need for down conversion, also because system deals with discrete time the sampling stage also ignored however it used in channel block for bandwidth determination and filter implementation.

### CP/GI removal

In this stage received sequence RCP(n) goes through a matrix selector and cyclic extension symbols removed from received symbols which contain cyclic extension like below;

The length of CP is pre-known by receiver and agreed with transmitters one. After taking out these symbols the signal looks like below;

The delay spread effects of channel which causes signal to broaden in time and stretch to guard interval, are captured by this cyclic extension. By removing this part the delayed replicas of previous symbols are removed too and interference of the received symbol is avoided.

### FFT

Following stage is Fast Fourier Transform to retrieve frequency domain mapped symbols. This can be considered as OFDM receiver heart which demodulates the OFDM signal efficiently taking benefit of orthogonal spectrum of received signal subcarriers. As mentioned earlier it uses a linear algorithm to transform signal from time domain to frequency domain in below:

And the individually QAM modulated symbols are now recovered but the noise, changes and fading degradations also transformed with them;

### Channel Estimation and Equalization

Received symbols are now suffering from ‘fading effect’ and ‘additive noise’. If we remember transmitted complex states from equation 4-3 and the channel covolutional effect in time domain on them we can formulate the received symbol states as follows:

represents subcarrier complex channel gain and it appears to have multiplication effect on symbol. This is due to existence of FFT which translates time domain convolution to frequency domain multiplication. Unavoidable random noise also has a complex value and transformed with signal.

To compensate channels disturbing effect first we should have the channel impulse response for related subcarrier. The transmitted pre-known pilots now used to estimate. The simple Least Squares Estimation method has been chosen to be designed system’s one tap equaliser. In this algorithm the received pilot values are divided by pre-known transmitted values (eq. 4-20) taking the benefit of FFT to keep the operation as simple mathematical division.

The estimated values are then interpolated to data subcarriers using one of mentioned methods in previous sections, which is FIR low pass for this case. Afterwards the equalisation applied by dividing the received symbols by correspondent to particular subcarrier (eq. 4-21).

Equalisation with above algorithm has a small problem and that is bad noise performance because Xk contains random noise and translated in division process and causes to received signal have a noise level. There is no problematic noise enhancement or colouring, since both the signal and the noise will have their powers directly scaled by.

### Demapper

After equalization the symbols more similar to transmitted ones and contain less error and they are ready to demodulate to binary data. Demapper as it appears from the name takes the QAM signal states and translates them to binary bit stream. It works on same constellation map with same degree (for designed case 4-QAM or 16-QAM) as the Mapper works. But here due to channel and noise induced errors some symbols are retrieved in error and makes received binary sequence looks slightly different from transmitted data which this variations measured later to obtain Bit Error Rate as system performance indication.

The above OFDM transceiver designed to accommodate our Adaptive Cyclic Prefix algorithm that proposed in this research. This new scheme is explained in following section of this chapter.

### Proposed Adaptive Cyclic Prefix

The introduction of the cyclic prefix can entirely eliminate Inter-Symbol Interference as long as the CP length is longer than the channel delay spread. The CP avoids interfering of OFDM symbol blocks and makes the channel appear circular and permits low complexity frequency domain equalization. An apparent drawback of CP is that it adds overhead to symbol, which effectively reduces bandwidth efficiency.

In other words however cyclic prefix is elegant and simple but it is not entirely free. It comes with power and bandwidth penalty. Since G redundant symbols are added and transmitted, the OFDM signal required bandwidth increases from to In a similar way the transmit power budget increased with same ratio.The power required to transmit a symbol with cyclic extension is equal to dB. Thus for both power and data rate the loss is as below [3-2];

The increased power rather than resources consumption which itself is an important issue in the age of green technology and power resources saving can cause interference to neighbouring users in interference limited wireless systems. One alternative solution for power problem is to use zero prefix or what called zero-padded OFDM. One commercial system which uses this method is Multiband OFDM that is employed in UWB transceivers. So why everybody wouldn’t uses ZP-OFDM since it reduces power by mentioned ratio.

There are two reasons for not using zero prefix. As seen in the figure a tail caused by channel appears in this method and is added back to the signal where in CP-OFDM it can be ignored. Second the additional noise from this tail induced into the symbol causing a higher noise power with same ratio of power and rate [3-2]

Thus the designer of any system should take to considerations of these tradeoffs and decide to use of these methods. In WiMax and LTE systems the CP has been chosen to be used. In order to tolerate the loss of spectrum efficiency and power a new scheme for CP insertion for OFDM is proposed in this dissertation. In this method the length of Cyclic Prefix is adaptively changed. This Adaptation based on probing of channel with Correlation of Pseudo Random sequence.

“A set of values or elements that is statistically random, but it is derived from a known starting point and is typically repeated over and over. Pseudo-random numbers provide necessary values for processes that require randomness, such as creating test signals or for synchronizing sending and receiving devices in a spread spectrum transmission. It is called "pseudo" random, because the algorithm can repeat the sequence, and the numbers are thus not entirely random” [4-4].

PN sequence has very good correlation property which ideally should be like below;

Where the result of correlation for sequence ‘a’ with length ‘N’ and ‘m’ ones, is:

Where;

More information on correlation property of Pseudo Random Sequence can be found in [4-5]. Practical PN-sequences are generated by linear shift registers and has some lack of perfection including in correlation profile but still they has a unique autocorrelation outline that has an optimum on perfectly matched condition and falls below half elsewhere with relatively similar characteristic described by eq. 4-24 which is demonstrated in figure 4.5.

### Channel Delay spread estimation

Based on what mentioned above on PN-sequence a novel idea proposed in this dissertation to adaptively change CP length on estimation of channel delay spread basis done by a PN sequence probing algorithm. In this method some modifications have applied to GI/CP insertion in transmitter and GI/CP removal in the receiver and consequently the OFDM symbol looks slightly different. Figure 4.6 demonstrates the variations.

It can be figured out a PRBS generator is added to transmitter and receiver which may already existed in some systems for other purposes. The generated sequence replaces the normal CP every specified period to measure and track the channel delay profile which is shown in figure 4.7.

To further emphasise the importance of this adaptive method to take benefit of a fit length of cyclic prefix a numerical example is demonstrated bellow.

### Example:

In this example, the Minimum and Maximum spectrum loss due to Cyclic Prefix are calculated. A 10 MHz channel bandwidth considered. Maximum delay spread was assumed to be t =5micorsecond. It is known that for guard band size in WiMax the possible available values are G= {1/4, 1/8, 1/16, 1/32} and FFT word length of one of values L= {128, 256, 512, 1024, 2048}. In a symbol rate of 10Mega, a delay spread of 5micro affects 50 symbols, so a CP length of at least 50 symbols required.

The Minimum overhead will be for the largest number of subcarriers, so this leads to L=2048. Thus 50/2048 = 1/40.96 so the minimum guard interval of 1/32 is sufficient. Hence, the data rate and spectrum and power loss will be only 1/32.

The maximum overhead is for the case of lowest number of subcarriers L=128. In this case 50/128 > 1/4 and thus even the largest possible Guard Interval is not enough to preserve orthogonality and avoid ISI. To have ISI free for this environment minimum FFT length is 256 that cost ¼ loss of spectrum and data rate.

At the receiver also a PRBSG generates same sequence and a correlator used to track delayed replicas of sequence and record their footprints. The stronger the delayed versions of PN-sequence and OFDM symbol the longer declination time in excess delay outline and thus more ISI effect from channel and longer CP needed to avoid it. This is exactly the purpose of this method, to efficiently adjust the CP length to the channel delay spread and make a good trade of avoiding the ISI and saving spectrum and power at the same time.

Figure 4.8 illustrates the cross correlation profile between received signal and PN-Sequence. The optimum point clearly demonstrates the first and highest power received copy of transmitted signal. To clearly investigate this correlation profile and to make sure from outline two scenarios are investigated; first with all data carriers set to zero and second with normal random data. The result shows that the existence of data doesn’t affect correlation profile in a way to change probing.

### Normalization

After excessive investigation and simulations it has been found out that estimation based on graph of figure 4.8 has problem of dependency on PN length and consequently on highest value of correlation profile. In other words when delay spread value goes down thus CP length and then the generated PN sequence will be shorter. This phenomenon leads to lower optimum point of correlation profile which affects the threshold detection in next step. The dynamic threshold that based on percentage value of optimum point is also lacks the accuracy.

To get rid of this dependency and make the threshold more static and based on definition of delay spread an improvement made to correlation results before threshold crossing detection. The complete profile is converted to normal values and re-plotted like in figure 4.9.

### threshold detector

In Threshold detection stage the system takes the outputs of correlator and searches for optimum point and saves the value and index (position). This point is the best copy of signal received and could be considered as the first accepted one. Then it updates the threshold point to a power level which is defined by user and system sensitivity. Then it looks for first point which goes below the determined power level. When it finds it records the position and then measures the time delay between two points (figure 4.10). The found value is a good approximation of channel delay spread which is defined as : “The maximum excess delay (X dB) of the power delay profile is defined to be the time delay during which multipath energy falls to X dB below maximum. In the other words, the maximum delay is defined as, where is the first arriving signal and is the maximum delay at which a multipath component is within X dB of the strongest arriving multipath signal” [4-6].

The eq. 4-24a can be rewritten as eq. 4-25 when receiver generated PN-Sequence is correlated with received PN probing signal from channel;

But the in fact consists of accumulation of more than one signal which arrived at receiver through different paths with different complex gains of . Neglecting the random noise Thus we have as following;

By inserting the 4-26 in correlation of 4-25 the received probing signal correlation profile can be written as;

By a small replacement of equation we will have;

The coloured part of equation 4-28 is autocorrelation of PN-Sequence which is demonstrated in figure 4.5. The absolute value of overall correlation can be imagined as delayed copies of autocorrelation graph of figure 4.5 with different attenuation. This vision is illustrated in figure 4.11 that is completely similar to practical result of simulation in figure 4.8. By adding the threshold crossing detection of new scheme the and according to the definition the excess delay of channel can be estimated when the correlation result goes below specified level (X dB) and channel excess delay spread is estimated in a proper way.

After determination of channel delay spread the length of Guard Interval should be decided. A small timing synchronization added to estimated value to give a fair toleration chance to synchronization errors. This amount can be a percentage of TG or fixed according to system hardware possible potential error margin. Then the calculated amount is send as feedback to transmitter as it clearly demonstrated in figure 4.6.

By this method we make sure that CP length always longer than channel delay and captures ISI efficiently and at the same time, excessive duration of guard interval is saved. This leads to saving of spectrum and increases in spectral efficiency and consequently increasing of system throughput for data bits. The other issue is the power for transmission of extra CP symbols is saved which is also an important issue in the time of green technology. The disadvantage of new method is that its BER performance is slightly worse than conventional CP-OFDM which is we tried to improve in next updated version of this method. Further analysing is done in next chapter along with demonstration of results.

### Proposed GI 2: Zero-padded ACP

In this scenario an improvement technique is described to compensate the interference caused by insertion of PN-Sequence for probing purpose. In this method the GIs which is used for probing is divided by half. First half is used to insert PN test signal and second part nullified as it is shown in figure 4.12.

The new configuration has two major advantages:

Ø First the interference from PN sequence delayed replicas is captured by zero intervals and makes less effect on data symbols.

Ø Second the zero padded intervals after Probe signal makes the correlation results for pseudo random signal and made decision beyond it more accurate. It means this duration only contains the cross correlation results of received and transmitted sequence because the data carriers not participating in this period’s correlation result anymore and gives better results in obtaining channel delay spread. Consequently it will give more precise value for Cyclic Prefix length.

Of course the throughput and efficiency performance of the system will remain as it was and no significant changes will occur compared to first proposed scheme with no zero padding. The major change will be in Bit Error Rate Performance thus in results and analysis part of this method the discussion concentrates more on received signal quality and errors probability. The phenomenon can be figured out simply from the correlation profile similarity of Zero and Random data comparison in figure 4.8 and 4.9.

The second improved method simulation is investigated on same various channels which was used to investigate the first scheme but with more concentration on mobile and realistic channels.

In all scenarios and studied cases two transmitters and receivers are used which are working on same randomly generated data bits. They’re using same baseband modulation (4-QAM or 16-QAM), same number of pilots and channel estimation scheme. The signals are passed through same channel object and all details are kept similar to simply investigate just influences of wanted scheme on the system. The first transmitter uses a conventional CP-OFDM scheme just as described in first section of this chapter. Second transceiver uses our proposed modifications on OFDM symbol and used to inspect all aspects and scenarios examined.

After explanation of every small detail of designed symbols and introduction of different systems stages in this chapter the system implemented and simulated. The numerical details and corresponding results are gathered and analysed in next chapter.

### REsults and Data analysis

The development of a simulation code in MATLAB environment gave us the possibility to evaluate the proposed modifications behaviour in modelled channels accurately, to underline the advantages and weaknesses, and to propose improvements and future studies and guidelines.

Since in previous chapter we went through every detail of system and all aspects of transceiver and channel were covered, here in this part the concentration is mostly led toward mentioning just numerical values and details assumption and then simulation results demonstration and their analysis.

MATLAB software is chosen for implementation of our OFDM transceiver and related channel profile owing to its powerful tools and functions to properly put into practice various mathematical models related to our work.

“MATLABis auser interfaces, and interfacing with programs in other languages.” [5-1].

In MATLAB ‘.m’ file code implementation an OFDM system physical layer consisting of Transmitter, wireless channel model and Receiver, with probing and measurement plotting procedures built to meet our required objectives. Table 5.1 shows the default values employed for system parameters in code implementation of system.

Figure 5.1 demonstrates the BER performance versus SNR for conventional CP in different channel models starting with simple ‘AWGN’ ending with Rayleigh frequency selective fading. The MATLAB ‘AWGN’ function used along with ‘Measured’ command property to get proper SNR levels applied to signal. These graphs are presented to give a primary vision of function of basic OFDM transceiver that we introduced in last chapter.

It is obvious that worse channel condition signal experiences the more errors received signal has. According to that the random Rayleigh seems to be worst performance because all tapped delay replicas of signal have completely random gains and delays causing a huge amount of fading in signal and degrading of signal. The rural area has less scatters and fading of signal much less than a typical urban area thus the signal in rural area has better quality and higher BER performance. To apply more empirical channel models and have a good vision of system behaviour in other channels which are more practical and realistic the simulation ran for other channel models in mentioned standard models. Figure 5.2 shows the results for COST 207 and ITU Extended channel models.

The above graphs demonstrate clearly the characteristic of CP-OFDM in different empirical channel environments. In COST models by going toward urban areas the number of scatters and consequently the delayed signals and fading effect of channel increases. This would leads to noticeable decrease in system performance. The situation is completely similar for ITU defined channels. However they based on different empirical measurement on different logical basis but the outcome is quite similar if they applied to same system; the more we go toward highly inhabitant areas and higher mobile environment the more amount of signal fade we will experience.

Amount of user data being transferred in time unit which is called actual throughput of system is one of indications that can be used to demonstrate system performance. It is well known that new world technologies competing to increase this value as demand increasing for higher data rate services.

The main aim of this project is increasing the performance of OFDM symbol as we said earlier, and particularly improving of the system data throughput by adaptively changing the CP length and decreasing overhead while keeping BER performance as well as possible. The other problem which is solved by introduction of ACP is path delays longer than fixed CP length. When such a delay happens the ISI amount increases significantly, while ACP can handle such a phenomenon by increasing CP length adaptively. Figure 5.3 illustrates the Frame Efficiency, which is one of performance indication statistics, versus CP length of conventional CP-OFDM with new designed one that calculated from following equation.

For Normal OFDM symbols with fixed CP length it is very obvious that by increasing the CP length the overhead per symbols increases and consequently the FE decreases. But the case for Adaptive method is completely different. Its CP length only depends on estimated channel delay spread and since the channel under investigation had fixed delay profile with very slight changes the CP length and so overhead bits remains fixed and causes a steady and approximately flat FE. If we assume the 128 sample length CP for CP-OFDM that is fair length for a system with 1024 subcarrier and data rate around 150Mbps like WiMax or LTE, the new designed one completely outperforms the conventional CP-OFDM with about 10% better efficiency for this channel condition.

The results for adaptive transceiver in different channels as it appears follow the same style and performance. Best case for AWGN and worst for random Rayleigh. We should know that all these graphs refer to un-coded signal so the BER is much different with encoded signals that the quality of about <10-4 is necessary. In ACP-OFDM however the behaviour of results is quite similar to conventional CP-OFDM but numerical values reveal the fact that these outcomes are slightly worse than their correspondent channel conditions in CP-OFDM. To clarify this comparison figure 4-5 shows the one by one contrast between fixed-CP and Adaptive-CP schemes in some of mentioned channels.

New understandings can be seen in above figure. 5.5a shows that for ‘AWGN’ environment there is very slight difference between ACP and reference graph for CP-OFDM. The similarity of performance comes from absence of fading channel and delayed paths. Since no interference exists because of no delayed signals are completely close to each other. In medium channel conditions like ‘Rural area’ of COST models (graph 5.5b) or ITU-EPA model (graph 5.5d) the disadvantage point of ACP appears. In these cases the interference caused by PN signal comes to surface. The interference comes from affection of data carriers following probing PN-sequence by delayed replicas of PN signal itself. In fact it is noticeable that the reaction of proposed scheme to environmental change varies much slower compared to CP-OFDM that its performance declines rapidly by degradation of channel conditions. As we said in literature review when a delay spread of signal goes beyond CP length the signal faces deep fades and high level of ISI. This is the case for 5.5c with typical urban channel model where ACP handles the delayed signals and performs better than CP-OFDM although the PN signal interference is still available but unnoticeable.

In other words the PN-Sequence that replaced CP every 50 or any specified duration symbols to probe and estimate channel delay spread itself interferes into data subcarriers and induces error bits as well as loosing cyclical convolution effect made by CP in channel to further decrease signal quality However the improvement in system throughput in evident but still there is a slight degrade in performance in some channels thus an improvement is proposed to this ACP in next section to remove interference caused by PN signal.

Since the variation comes from PN-sequence, the insertion rate of this signal has major effect in amount of interference. Thus insertion rate influence explored by examining different insertion rates which is illustrated in

The outcomes from investigation of PN insertion rate prove our Idea that interference is major problem of this method. Thus an average amount of 50 symbols time chosen to insert probe sequence for all preceding and following simulations to study other aspects. It is a good assumption to react to channel delay changes and update CP length every 50 symbols, however for a more accurate assumption further study needed to find out the channel variations to predict the delay spread changes in channel. As we know in highly mobile and fast fading channels the CIR of channel changes approximately every symbol which makes use of block-type pilot insertion and channel estimation impossible but according to literature these changes doesn’t affect the delay spread of channel to be varies as fast as CIR and above assumption seems to be fair for such channels.

To further clarify the main advantage of new scheme which is spectral efficiency improvement, the graphs in figure 5.7 demonstrate the physical layer overall carried data versus time of ACP-OFDM with time compared to CP-OFDM with fixed CP lengths. The relation between frame efficiency and throughput defined as below

Ts denotes sample time and since frame consist of data symbols and overhead just like what equation 5-3 explains the relation between FE and Throughput is defined by;

Obviously and as we could predict from FE graph the ACP carries higher amount of user data within specified times. ACP detected the channel delay spread and updated the CP length according to that so it had smaller overhead amount and better data transmission efficiency although if another channel used with longer delay spread it would cause to ACP has longer length than may be 1/16 CP but it would have better BER than it because it catches long delayed signals and consequently the ISI.

### Zero padded Adaptive cyclic prefix

In this part the improvement made to proposed ACP which was suggested in relative part in methodology implemented and simulated. The results are promising to debug the weaknesses of ACP that was considered as interference of probe signal.

The improvement is simple; as shown earlier in chapter four the system upgrade was applied inserting zero signals between PN-Sequence and data carriers in symbols. The upgrade does not change the correlation results because like shown in figure 4.8 whether the data carriers loaded by zero data or random data the correlation property of PN-Sequence leads to a unique profile. The simulation is repeated with same assumptions and channel conditions. Figure 5.8 demonstrates graphs BER for different wireless channel models which new version of ACP-OFDM tested on. The CP-OFDM is also kept to be used as reference for system performance. The new scheme decided to be called Zero-Padded Adaptive Cyclic Prefix OFDM (ZPACP-OFDM

The result for a simple ‘AWGN’ channel is shown in graph 5.8a. The performance does not change because as we said in last part the lack of multipath propagation leads to no variation in signal performance between two cases but the slight degradation of signal that was existed in ACP has gone in ZPACP by inserting the null signal between data and PN sequence. These graphs prove previous predictions that proposed method performs better in worse channel conditions with large amount of scatters and large path delays. These channel models are more accurate for real world and practical frequency selective highly mobile channels.

The next channel contains few scatters with small path delay and related to a ‘Rural area’ mobile channel that is used earlier in first report and contains six taps with different gains and delays up to 50nSec, also the maximum Doppler shift set to 120Hz as an average mobile device speed for carries around 2GHz carrier frequency that are used typically in communication systems. This channel model represents a more accurate wireless channel for mobile wireless systems and gives closer assumptions to standards. The two other graphs are related to COST 207 ‘Typical Urban’ and ITU-ETU channel models.

The outcome from graphs of figure 5.8 is that the idea of zero-padding of PN-sequence is completely successful and completely removed the interference caused by probing signal. It shows null signal not only prevents the interference it also reduces the amount of noise induced in data followed by guard interval and increases the BER performance of OFDM symbols.

ZPACP-OFDM takes the advantage of null signal that gives a BER performance of one that in conventional ZP-OFDM while it also keeps CP in most of symbols and recreates cyclic convolution in the channel and has positive characteristics of CP-OFDM like better frequency and time synchronization properties and sharp signal power spectrum.

Figure 5.9 illustrates the result for simulation of system with for ‘Rural area’ channel model for both ACP and ZPACP to emphasise the significant improvement that occurred in signal quality. The results for zero padded one with its decedent are in significant difference as it can be seen from graphs. While the pure PN probe (green) was worse than conventional CP (Blue) the new zero padded versions (red) performs even better than conventional CP.

The pure PN sequence guard interval was suffering from interference of sequence itself with data symbol where the new one avoids this phenomenon by placing a null interval between PN sequence and data and still keeps the correlation property of guard interval in order to determine the channel Delay Spread.

The new zero padded update solves the problem of PN induced interference while it keeps the advantage of improving spectral efficiency and power saving for ACP guard interval scheme.

### Bandwidth effects

As the final design settled with ZP-ACP due to its better BER performance and same improvement to FE and system Throughput in next stage of project the influence of transmitted signal bandwidth is explored.

The study of BW aspect of system is found necessary since most of new generation communication and telecommunication systems are exploiting a flexible BW in their over air interference. Figure 5.10 illustrates the different bandwidth signals which is varied by using Ts property of Rayleigh channel object in MATLAB and investigated in COS207 ‘Typical Urban’ channel profile as an average channel model for mobile systems environment.

It can be seen that increase in signal bandwidth causes extra degradation of signal quality. This is due to significant increase of fading effects of channel with raising signal bandwidth. Because further the difference between signal bandwidth and channel coherence bandwidth deeper the fading of channel on the signal. It is known that the higher the communication bandwidth the more challenging the system design would be. Based on this fact, any broadband wireless system design should have a precise study of channel circumstances related to that system so it can override potential problems facing system in reality.

### conclusion & Future work

### Conclusion

A modified version of OFDM symbol and transceiver proposed in this dissertation. Then the proposed system is implemented in MATLAB simulation software and explored in detailed block level.

The modification has been planned based on demand for higher spectrum efficiency and reduced overhead and redundancy in OFDM symbols, while it maintains signal quality and BER performance of system. Power saving, which is main concern of newly introduced Green Radio in communication systems, is another aspect of proposed scheme. Reduction of power consumption made possible by reducing amount of overhead in each OFDM symbol of designed transceiver.

The Power Delay Profile of channel is estimated by using unique correlation property of a Pseudo Random Binary Number Sequence inserted in OFDM symbols guard interval periodically. Then excess delay of channel estimated and suitable Cyclic Prefix length is calculated based on channel spread delay. This operation changes the CP length adaptively and was named ACP-OFDM. Such an adaptive system reduces overhead by decreasing length of CP when long CP is not necessary. It saves the spectrum and power required to transmit these redundant bits. At the same time if long delays occurred in channel that is longer than normal fixed CP length, it stretches length of CP in a way that captures delayed signals and prevents ISI and improves BER performance of the system.

The investigation of simulation results of implemented code approves the fact that our system superior over conventional systems in power saving and spectral efficiency. The upgraded zero padded version called ZPACP-OFDM, which uses a null signal to split inserted PN sequence from data carriers, shown to have also BER performance advantage in most of wireless channel models used to simulate our designed system over conventional method in addition to spectral and power efficiencies.

As long as designing the proposed novel scheme of adaptive CP, the channel impulse response estimation for signal equalisation also studied in brief. LSE method used particularly for simplicity of its algorithm and lower affect on other system parts and signal processing stages.

The use of adaptive methods and algorithms such ZPACP-OFDM even made easier by introduction of Software Radio in 4th generation communication systems, which makes on the spot adjustment of any circuitry part of system simpler and quicker. This technology allows integrating adaptive algorithms like ZPACP to added and integrated in communication systems easily and efficiently.

The PDP estimator and CP adaptiser part of designed system also can be implemented easily by means of Reconfigurable Logic devices like FPGA and perform in higher speeds t o meet the need for higher data rates required in 4th generation communication technologies like LTE, WiMax and etc.

### Future Work

The designed system showed that performs better and more efficient than conventional fixed CP-OFDM systems in all investigated radio channels. But in order to realize a novel adaptive system and manufacture it commercially more stages should be completed first and more investigations and analysis needed to be done on the system.

The study of Doppler Effect on our proposed scheme is one of domains that seem to be necessary to have a complete vision of the system reaction to wireless environment circumstances especially in mobile communication systems that Doppler shift is a major challenge. Also there are more standardised channel models available which is designed for particular environments and or particular communication systems that can be used to simulate our proposed system to further study the response of adaptive algorithm in different channels.

In addition to above mentioned research areas a deep and detailed study of system from mathematical point of view can be useful to find out and improve strength and weak points, advantageous and disadvantageous of proposed system. This study also helps to obtain vulnerabilities and find proper solutions for them before progressing to other stages.

From different point of view, the inserted PN sequence also can be exploited to improve CFR estimation and compensation purposes in parallel with delay spread estimation of channel. In this case the PN signal can be used as block type pre-known pilot signals and used along with LSE algorithm or any other algorithm to add more accuracy to equalisation process of received signal. Such a joint algorithm can increase the BER performance of system significantly.

Afterwards a comparative research will be possible and helpful to examine our proposed scheme with relative studies made on adaptive methods particularly with designed systems in [][] to nominate proper method for real world implementation and highlight each methods weaknesses and strength points.

Next stage can be a practical model made by DSP or FPGA based integrated electronic boards to investigate the chosen proposed method realistic wireless channel along with frequency and timing synchronisation error impacts on the system.

These stages of research, study, analysis and simulations make the proposed system to get ready to be applied in next generation communication technologies that in need for more powerful, adaptive and flexible systems to increase data rates, connection reliability and reduce power consumption for high quality end user services and consumer electronics.

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