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This project investigates the effects of asynchronous Multiple Access Interference on the performance of an Orthogonal Frequency Division Multiple Access (OFDMA) wireless network in a multipath Rayleigh fading environment. The MAI destroys the orthogonality among subcarriers resulting in the degradation of the system performance. Studying and modeling the system, an accurate mathematical interference analysis is obtained regarding the signal that arrives at a reference receiver from all the active users. Having knowledge about the cyclic prefix (CP), FFT windows and their effects on an OFDMA wireless network, we will study the average system performance deriving mathematical expressions for the average signal error rate (SER) and the average bit error rate (BER). The study of the system performance will be held on different scenarios of users using the interference model.
For the broadband wireless access, which offers high rate wireless communication, OFDMA represents one of the most reliable techniques . However, due to its high sensitivity to time and frequency offsets a surge of research activities has been carried out in order to identify and take into account the key parameters that combat the drawbacks of the OFDMA improving the average system performance.
This project deals with orthogonal frequency division multiple access (OFDMA) wireless networks in a multipath Rayleigh fading environment. It focuses on the destruction of the orthogonality between subcarriers caused by the presence of asynchronous multiple access interference (MAI). The main purpose is the performance analysis of the system taking into account the MAI. As far as the performance measure is concerned, the central goal is to study the system performance for different scenarios of users and to achieve an improvement making use of extended cyclic prefix (CP) and FFT windows.
Wireless communication represents one of the most rapidly developing areas in the communication field  and concerns both the infrastructure-based and ad-hoc networks .
The wireless channel is characterized by randomness and requires special caution when using in telecommunication applications. There are many natural phenomena, such as reflection, diffraction and scattering, which result in non-deterministic behavior of the wireless channel. During the propagation of the signal through the wireless channel there are four basic natural phenomena, path loss, shadowing, multipath fading and interference that cause the distortion of the received signal , .
The three main multiple access techniques, with which multiple users can access the channel for transmission and communication, are the frequency division multiple access (FDMA), the time division multiple access (TDMA) and the code division multiple access (CDMA). According to these schemes, different users transmit at different frequency bands, time slots and using different codes respectively .
One of the most promising wireless access techniques is the orthogonal frequency division multiple access (OFDMA) which is a combination of OFDM multiplexing with a FDMA protocol . This technique has recently been implemented in new networking technologies such as the IEEE 802.16 standard and represents a transmission standard that divides the available bandwidth into narrowband orthogonal subcarriers. Its main characteristics are that more than one subcarrier can be assigned to one user, many simultaneous transmissions are allowed and if a subcarrier has bad quality for a user, it can be assigned to another user for whom it has good quality (dynamic resource allocation). Therefore, OFDMA provides multiuser diversity and flexibility, improves the quality of service (QoS) and is resistant in the multipath transmission due to the increased duration of OFDM symbols of every subcarrier. The OFDMA can be easily expanded to wideband transmission without the need for equalization . In addition, the subcarriers overlap each other making the network more spectrum efficient than FDMA system (Figure 1).
Figure 1: Comparison of OFDM and FDM technique 
Despite the subcarrier overlapping, there is no intercarrier interference because of the orthogonality among subcarriers. The orthogonality relationship is defined as shown in (1) , where only when , ,
where the bandpass signal is defined as (2)
and the equivalent lowpass signal of is defined as
It is essential to be mentioned that the orthogonality is maintained only if the received signal are synchronized . The cyclic prefix (CP) and the FFT window represent the basic tools of OFDMA networks as they can alleviate the inter-symbol interference (ISI), which is introduced by multipath impairments. A typical OFDM transceiver is shown in Figures 2a, 2b. Figure 2a depicts the OFDM transmitter, where the inputs (data symbols) are assumed to be in the frequency domain and their time-domain domain counterparts are generated applying inverse fast Fourier transform (IFFT) followed by CP insertion. In Figure 2b the OFDM receiver is illustrated, where firstly the CP is discarded and then fast Fourier transform (FFT) is applied on the useful symbol (data symbol) so that the original one is recovered.
Figure 2a: Typical OFDM Transmitter 
Figure 2b: Typical OFDM Receiver 
Despite the fact that the OFDMA system presents numerous advantages, some weaknesses of OFDM multiplexing and a number of additional difficulties have been observed in the OFDMA network, such as high peak-to-average power ratio (PAPR). Furthermore, it is characterized by high sensitivity to carrier frequency offsets and time misalignments (timing errors). In addition, whenever there are mobile users, Doppler distortions emerge due to the fact that the movement causes Doppler shift introducing frequency offset. The three latter disadvantages have one dramatic result, the destruction of the orthogonality and consequently the degradation of the system performance.
The frequency offset between the transmitter and the receiver is introduced by differences in frequency between the local oscillators  and/or the Doppler Effect . It destroys the orthogonality among the different subcarriers and causes intercarrier interference (ICI), as well as multiple access interference (MAI), and consequently multiuser interference (MUI) emerges. The equation (1) taking into account the frequency offset (Î”) is expressed as shown in the equation (4), which is non-zero even if Î”f*T= 1.
The time offset is induced by asynchronous different users' signals, which arrive at a reference receiver, and introduces MUI destroying the orthogonality. In that case, the equation (1) will be expressed as (5), where E denotes the duration of delay. The equation (5) can be zero only if , because
Due to user mobility, the frequency of the transmitted signal is spread and the Doppler Effect (Doppler Spread) emerges and destroys the orthogonality causing frequency spread and results in ICI . In that case, the equation (1) will be expressed as (6), where g(t) represents the occurrence of Doppler Effect.
Due to the time offset, frequency offset and Doppler Spread, robust multiuser frequency and timing synchronisation techniques are required in an OFDMA network. In this project, the destruction of the orthogonality caused by timing misalignments will be studied and analyzed.
1.3 AIMS AND OBJECTIVES OF THE PROJECT
The aim of the project is the performance analysis of orthogonal frequency division multiple access (OFDMA) wireless networks in a multipath Rayleigh fading environment, where asynchronous multiple access interference (MAI) occurs. The presence of MAI is due to the fact that signals from different active users arrive at a reference receiver asynchronously. The effect of MAI is the destruction of the orthogonality among subcarriers and consequently the performance of the system is being degraded. Considering several types of spatial distribution of users, the purpose is to study the performance of the system and the improvement of the performance using extended cyclic prefix (CP) and FFT windows.
The objectives of the project are the following:
The study of OFDMA wireless network in a multipath Rayleigh fading environment and the interference that occurs due to time offset.
The modeling of the system taking into account the effect of MAI, using a number of tools and making some assumptions.
The accurate mathematical interference analysis based on the received signal by the reference receiver, which is the superposition of all users' signals. The moment generating function (MGF) is used to simplify the mathematical analysis of the signal to interference and noise ratio (SINR).
The study of the system performance on different scenarios of user distribution using the interference model.
The theoretical analysis of the average system performance deriving mathematical expressions for the average signal error rate (SER) and the average bit error rate (BER), which represent the performance measures for the physical layer of communication systems.
The simulation of the model using MATLAB in order to verify the theoretical results and illustrate the possible performance improvement.
Considering the fact that a number of relevant studies have addressed the interference analysis and cancellation in OFDMA system, a comparison will be made between the results obtained by this project and the corresponding results by other previous research.
2. LITERATURE REVIEWS
2.1 SYMBOL TIMING MISALIGNMENT IN OFDMA SYSTEM
OFDMA is one of the most promising wireless access techniques for future broadband multiple access communication and has lately attracted interest from both research and industry . Although it is characterized by a number of essential advantages, such as high bandwidth efficiency and robustness against multipath propagation , one major drawback of OFDMA is its sensitivity to time asynchronism.
In OFDMA, the available channel bandwidth is divided into narrowband orthogonal subchannels  and as multiple users use different subcarriers, many simultaneous transmissions are allowed. Provided that the subcarriers overlap each other, the basic requirement for preservation of the orthogonality is the synchronisation of the signals that all users transmit; that is, the users should be synchronised. It is important to be mentioned that a cyclic prefix (CP) is inserted at the beginning of every transmitted symbol in order to absorb the delay spread that exists because of the multipath resulting in the preservation of orthogonality. The duration of CP is called guard time interval (Tg). However, in uplink scenarios of cellular-based OFDMA networks or in OFDMA ad-hoc networks the concept of synchronisation cannot be performed perfectly. Consequently, it results in multiuser interference (MUI) as symbol timing errors exceed Tg and the orthogonality is being destroyed .
2.2 RESEARCH ON INTERFERENCE AND PERFORMANCE ANALYSIS OF OFDMA TIME-ASYNCHRONOUS NETWORKS
Since OFDMA is a reliable solution for broadband wireless service systems , much research has been carried out in order to study the effect of timing errors and propose techniques to eliminate the MUI.
In 1992 Ruiz et al.  proposed the insertion of cyclic prefix (CP), which is a part of the OFDM symbol that is copied from the beginning of the symbol to the end , as a guard interval in order to avoid the intersymbol interference (ISI) during transmission. The CP has to be as long as possible  but a very large extension causes reduction of the transmission rate . Provided that CP length is not much longer than what is required to eliminate ISI, its use and extension are essential in
the OFDMA network as CP does not only avoid the ISI but also combat a part of the MUI resulted by the destruction of the subcarrier orthogonality , .
To investigate and overcome the problem of timing synchronisation in a typical random OFDMA uplink network in 1998 Nogueroles et al.  considered that a base station receiver implements an algorithm that cancels the successive interference. Using a random subcarrier assignment scheme they applied a combined MC-CDMA/FDMA coding scheme and analyzed three different system versions. At the first system version the users send signals to the base station without synchronisation causing a variation of the delay, whereas at the second system implementation there is synchronisation at the transmitters and possible delays occur because of the different users' positions in the service area. At the last system version as fully synchronisation is assumed at the base station, the users have to transmit at different time instance according to their positions. Important information that this model provides is that the performance, the capacity and the transmission rate perform a large variation at each different system version. However, the most significant conclusion from the implementation of that model is that ISI causes MAI which in turn destroys the orthogonality among the subcarriers .
 deals with the synchronization techniques for cellular OFDMA systems that have been proposed to eliminate the effect of time and frequency offsets. It is clear that the uplink transmission synchronization, which is much more difficult that the synchronization in the downlink case, is achieved through feedback techniques. Although these techniques represent an efficient solution to the time and frequency offset problem, there are difficulties related to the implementation of the techniques as the base station has to estimate numerous unidentified parameters and ways in which these parameters has to be utilized has to be found.
In  the effects of asynchronous MAI on the performance of the OFDMA uplink system are examined. The OFDMA network is centralized; that is, there is a base station, common for all users, with which they communicate. The wireless channels are assumed to be modeled as frequency-selective Rayleigh fading channels and the impulse response of every channel is modeled as a tapped delay line with a number of paths, which apply the wide sense stationary uncorrelated scattering (WSSUS) model. Additionally, it is assumed that the base station receives a signal which is the superposition of all transmitted signal. The transmitted signal arrives at the base station through independent channels. For the investigation of the timing error effects, it is assumed that the timing and frequency errors between users and the base station are completely independent and the frequency errors are ignored. The
basic tools for this approach are the timing misalignment and the consideration of a synchronous user group and an asynchronous one. Also, interleaved-type and block-type subcarrier allocation schemes are used and Gaussian approximation is used in the MAI analysis. The most important points of this model, which should be taken into consideration for the implement of any other model, are that the interleaved-type subcarrier allocation scheme is more sensitive to time offset problem and the performance can be examined with greater application ability for practical system parameters but an uplink synchronisation technique is required to certify that the errors lie within Tg. Unfortunately, this kind of synchronisation techniques can be applied only for cellular-based or centralized OFDMA networks and also they require the base station to calculate all times that the signals arrive as they are based on feedback control channel , .
Relevant research was carried out in , where the uplink of OFDM-FDMA systems is studied and ICI problem is addressed. A carrier frequency offset compensation method is proposed to combat the frequency offsets making the computational complexity of the method reduced when the number of users is increasing. However, the time offset problem is ignored assuming perfect timing synchronization.
In the OFDMA uplink scenario of , the system performance is considered in the presence of carrier, clock and timing errors. Although, in  timing errors are not ignored, it is assumed that these errors lie within the guard interval. Consequently, the interference due to time offset is not analyzed.
In contrast to centralized OFDMA systems,  refers to OFDM ad-hoc network (that is, without the existence of base stations). However, although a solution for OFDM ad-hoc networks is proposed, this solution concerns a new protocol which improves the throughput of the system applying request-to-send (RTS) and clear-to-send (CTS) on multiple control channels. In other words, this model deals with the media access control of OFDM ad-hoc networks assuming that the physical layer is characterized by perfect synchronisation and MAI does not occur.
In , the system performance analysis is developed regarding ad-hoc OFDM systems in a frequency selective fading environment and taking into account the effect of time offset on the performance of an OFDM receiver. A mathematical interference is presented and precise expressions for the average signal-to-interference ratio (SIR) are derived taking into account the effect of ICI and ISI. However, the system analysis concerns a single user OFDM. Therefore, the effects of the implementation of this method in an ad-hoc OFDMA network, in which there is a number of users, are unknown and cannot be predicted.
A lot of research is going on to find new synchronisation techniques for OFDMA which will provide improved system performance and will be characterized by low and not very expensive complexity. The synchronisation techniques for an uplink transmission meet significant difficulties compared with the corresponding techniques for a downlink transmission. Studying  and mainly the CP length, the DFT window length and positioning and the physical layer parameters for IEEE 802.16 Wireless MAN, it is obvious that the insertion of extended CP and DFT window is essential to preserve the OFDMA system synchronisation and restrict the time offset problem. However, extending CP and DFT window length should not be large in order to avoid experiencing other problems and unfortunately, that extension cannot be applied in any network .
As far as the right positioning of FFT window is concerned,  exhibits all the possible methodologies for the right selection of FFT window positioning in networks that apply the single-frequency network (SFN) technique. The OFDM receiver synchronisation is consisted of two stages; the 'initial synchronisation' at which the symbol rate and the receiver are aligned, and the 'secondary synchronisation' at which the FFT window is positioned for demodulation purpose. For the latter stage there are five different FFT window positioning methodologies which are the typical synchronisation, synchronisation to the strongest signal, synchronisation to the first signal above a threshold, the centre of gravity approach and the quasi-optimal strategy . The selection of a FFT window positioning strategy in OFDM receiver has to be made with caution as it considerably influences the network coverage probability . Additionally, the position of FFT window should be flexible in order to ensure that all the signals display orthogonality at the receiver .
In  the problem of MUI due to time misalignments is analyzed for the physical layer of OFDMA wireless ad-hoc networks. The main aim of  is the precise mathematical interference analysis focusing on the propagation delay and the spatial user distribution in order to investigate the limits of CP length increase so that the MUI can be eliminated and simultaneously the spectral efficiency may not be too decreased. The noise is assumed to be AWGN, the channel is modeled as a multipath Rayleigh fading channel and the service area is assumed to be circular with a reference receiver at the centre of the circle. Furthermore, both the interleaved and block subcarrier assignment schemes are used. Developing the mathematical interference analysis of the system, the average signal error rate and bit error rate is determined and consequently the average performance is presented. A very important point is that the particular mathematical analysis of MAI provides orthogonality between two carriers whenever there are two same successive symbols of the second carrier and it is completely independent of their time offset.
Moreover, it is important that the decision variables turn out to be conditionally complex Gaussian random variables without any approximation. "Hence, the known standard closed-form expressions of the bit or symbol error rates in AWGN channels can be used to obtain exact closed-form expressions for the "conditional probability of errors" which depend solely on the SINR". It is also worth mentioning that the basic tools are the extension of CP length and the implementation of dynamic FFT window positioning. Consequently, MAI is reduced and also using the cutoff rates and making simulations for several different order modulation schemes it is shown that the bandwidth efficiency can be determined, improved and can present a maximum point for sufficient CP length and dynamic FFT window positioning. An additional considerable point of that model is the optimum CP length dependence from the selection of subcarrier assignment scheme and modulation order, signal-to-noise ratio and the maximum propagation delay .
The methodology used in this project is based upon an OFDMA wireless network in a multipath Rayleigh fading environment and the MAI that occurs as a result of timing misalignments. The interference will be analyzed using the MGF function as a basic tool and the average system performance will be evaluated for various different scenarios of user distribution, following the network modeling. The CP and the FFT window will be used for eliminating the MAI in the OFDMA network, whereas the required tools for the simulation of the model are MATLAB and the Monte-Carlo Simulation method. With all the above consideration, the project is organized as follows:
STEP 1: Study and comprehension of the fundamental OFDMA principles and the interference that occurs in an OFDMA wireless network due to time offsets. In addition, studying and identifying the causes and the effects of the timing misalignments, as well as all possible ways that the users can be distributed in a service area, the model of the network can be constructed.
STEP 2: Modeling of the system. Taking into account the MAI due to time offsets and making some assumptions, such as perfect carrier frequency synchronization, the network model is developed in order to provide a complete inspection of the system. Through the network modeling the interaction of users can be observed, as well as the behavior of all system parameters is monitored. Furthermore, effects of possible changes in the system parameters might be predicted. Orthogonal subcarriers are assigned to the users who are located randomly around a reference receiver based on various different scenarios and multipath Rayleigh fading channels are assumed through which the transmitted signals arrive to the reference receiver. Extended CP and FFT windows are used as basic tools in order to eliminate the interference improving the overall performance.
STEP 3: Accurate mathematical interference analysis of the OFDMA wireless network. Taking into account the signal that arrives at a reference receiver as a superposition of all active users' signals, a precise mathematical analysis of MAI can be developed. Using certain mathematical tools, probability principles and models, as well as a specific function called "Moment Generating Function" (MGF) are required to express the interference mathematically. MGF function represents a mathematical tool that finds all the moments of a distribution. It will be used in this project for the reason that it simplifies the mathematical analysis of the cumulative distribution function of SINR. This simplification is achieved through the property of MGF that the result produced by the MGF functions of all independent random variables is equal to the MGF of the summation of these random variables .
STEP 4: At this step, various different scenarios will be generated representing the distribution of users in the service area. The purpose is the study of system performance for each scenario using the obtained interference model.
STEP 5: Deriving mathematical expressions for the SER and BER, the theoretical average performance of the system will be analyzed.
STEP 6: Simulation of the model with the aim of computing the performance of the system, verifying the theoretical results and illustrating possible performance improvement. The simulation will be carried out using the simulation tools MATLAB and Monte-Carlo Simulation, illustrated in the section 3.1. Moreover, in the section 3.1 the reasons for using MATLAB and Monte-Carlo Simulation in this project are clarified.
STEP 7: Comparison with relevant studies and extraction of conclusions regarding the analyzed model.
3.1 COMPUTER SIMULATION FOR WIRELESS COMMUNICATION
The most precise performance evaluation is in the case of hardware implementation and testing. However, this approach is not only complicated, but also it can easily introduce problems and the identification whether the problem is related to the hardware, the implementation or the design of the system is difficult . Consequently, before the process of hardware simulation, it is crucial to carry out computer modeling and testing.
The computer simulation is a branch of Applied Mathematics that represents a sophisticated tool, which imitate the real world operations . It is characterized by speed, convenience and affordable technology. By testing new algorithms and "what if" scenarios, enhancement of the speed in research and development is achieved and insights on the system or potential problems are gained . Additionally, using computer simulation diminishes the risk that regards modifications of a system or implementation of new systems . The simulation of this project will be accomplished through the use of MATLAB due to its important benefits, experience on this statistical software package gained from MSc and the licensed MATLAB access provided by university of Manchester.
MATLAB is a simulation software package, widely used in the electrical and electronic engineering community. This software contains basic programming functions, special and graph functions, as well as matrix operations. Therefore, it is very useful for mathematical manipulations, excellent production of graphs and efficient matrix operation processing without need for defining variables . In this project, Monte-Carlo Simulation will be used on MATLAB as a method for statistical computer simulation.
Monte-Carlo Simulation is an unbiased and consistent estimator , based on the use of repeated probabilistic trials . The probability approximation of certain outputs is the main objective of this method by using defined statistics and deterministic simulation. The idea of this approach relies on the "Law of Large Numbers" and its accuracy is strongly dependent on the number of trials.
4. PROJECT PLANNING
The available days for the dissertation execution are from 16th May until 6th September. The project planning is illustrated in Figure 4.1.
Figure 4.1: Gantt chart
Firstly, study of the OFDMA wireless network in the presence of time offset will be carried out.
Subsequently, the model of the under consideration OFDMA system will be built and the mathematical interference analysis will be developed.
Then, a number of user scenarios will be generated and tested through simulations regarding the system performance. It is worth mentioned that the research is theoretical. Consequently, as far as the project risk is concerned, by testing various scenarios some may be discarded or new assumptions and new scenarios may be considered in order to study and improve the system performance.
Afterwards, the model is compared with other models obtained by relevant research and conclusions are extracted from our evaluation.
The two final steps are the dissertation writing and possible corrections on the project.