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A smart two-cell random access algorithm for wireless CDMA communication networks using smart antenna

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Title:
A smart two-cell random access algorithm for wireless CDMA communication networks using smart antenna
Creator:
Barkat, Enfel ( author )
Language:
English
Physical Description:
1 online resource (59 pages) : ill. ;

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Subjects / Keywords:
Wireless communication systems ( lcsh )
Code division multiple access ( lcsh )
Random access memory -- Design ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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ABSTRACT Interest in Smart Antenna Technology for wireless communication systems has increased in the recent years as a promising technique to improve the performance of cellular mobile systems. Considerable amount of research is being conducted to improve the performance of the system in terms of increasing the capacity and range. We discuss the different types of Smart Antenna systems using switched beam and adaptive antenna array techniques and describe how they can be used to implement in different multiple access schemes in wireless communications. A smart antenna's ability to simultaneously resolve simultaneous transmissions on the same channel is exploited to help expedite the process of random access. Intended for bursty data traffic, a random access Medium Access Control (MAC) protocol seeks to insure an orderly sequencing of packets from the various mobile stations onto the shared channel with minimum time lost to collisions. When applied to cellular radio systems, a MAC protocol must also cope with the various impairments suffered on the radio link such as multi-path fading, shadowing, and co-channel interference from other mobiles. This thesis proposes to upgrade the performance of a class of random access protocols for wireless digital networks with smart antennas operating in the presence of Rayleigh slowly fading multipath transmission channels. The capture model assumed is a threshold model based on the signal to noise ratio, while the MAC protocol deployed is the two-cell random access algorithm, in a network environment where nodes are equipped with adaptive array smart antennas. The deployed protocol relies on the ability of the antenna to deploy Direction of Arrival (DoA) algorithms, to identify the direction of transmitters and to subsequently beam-form accordingly for Signal- to Interference and Noise Ratio (SINR) maximization. The performance of the protocol is evaluated using analytical modeling as well as detailed simulations in Matlab, where we demonstrate the benefits of using smart antennas. The form and content of this abstract are approved, I recommend its publications. Approved: Titsa Papantoni
Thesis:
Thesis (M.S.)--University of Colorado Denver.
Bibliography:
Includes bibliographic references.
General Note:
Department of Electrical Engineering
Statement of Responsibility:
by Enfel Barkat.

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Auraria Library
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868709074 ( OCLC )
ocn868709074

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A SMART TWO CELL RANDOM ACCESS ALGORITHM FOR WIRELESS CDMA COMMUNICATION NETWORKS USING SMART ANTENNA By Enfel Barkat B .S ., American University of Sharjah 201 0 A thesis submitted to the Faculty of the Graduate School of the University of C olorado in partial fulfillment of the requirements for the degree of Master of Science Electrical Engineering 201 3

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ii Th e thesis for the Master of Science degree by Enfel Barkat h as been approved for the Electrical Engineering Program By Titsa Papantoni chair Jan Bialasiewicz Yiming Deng May 15 2013

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iii Enfel, Barkat ( M.S Electrical Engineering ) Medium Access Control Using smart Antenna and Random access algorithm For Mu ltiple AD HOC Wireless Networks Thesis directed by Professor Titsa Papantoni ABSTRACT Interest in Smart Antenna Technology for wireless communication systems has increased in the recent years as a promising technique to improve the performance of cellular mobile systems Considerable amount of research is being conducted to improve the performance of the system in terms of increas ing the capacity and range. We dis cuss the different types of Smart Antenna systems using switched beam and adaptive antenna array techniques and describe how they can be used to implement in different multiple access schemes in wireless communications neously resolve simultaneous transmissions on the same channel is exploited to help expedite the process of random access. Intended for bursty data traffic, a random access Medium Access Control ( MAC ) protocol seeks to insure an orderly sequencing of packets from the various mobile st ations onto the shared channel with minimum time lost to collisions. When applied to cellular radio systems, a MAC protocol must also cope with the various impairments suffered on the radio link such as multi path fading, shadowing, and co channel interference from other mobiles This thesis proposes to upgrade the performance of a class of random access protocols for wireless digital networks with smart antennas operating in the presence of Rayleigh slowly fading multipath transmission channels. The capture model assumed is a threshold model based on the signal to noise ratio, while the MAC protocol deployed is the two cell random access algorithm, in a network environment where nodes are equipped with adaptive array smart antennas. The deployed protocol relies on the ability

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iv of the antenna to deploy Direction of Arrival (DoA) algorithms, to identify the direction of transmitters and to subsequently beam form accordingly for Signal to Interference and Noise Ratio (SINR) max imization. The performance of the protocol is evaluated using analytical modeling as well as detailed simulations in Matlab, where we demonstrate the benefits of using smart antennas. The form and content of this abstract are approved, I recommend its pu blications. Approved: Titsa Papantoni

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v DEDICATION I lovingly dedicate this thesis to my parents who supported me in each step of the way.

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vi ACKNOWLEDGMENTS I would like to thank my advisor Professor Titsa P. Papa n toni for giving me a chance to be in the graduate program of the University of Colorado at Denver, Downtown campus, and for her support during the course of this work. I am especially grateful to my dad Professor Mourad Barkat for his guidan ce encouragement, and constant support during all my graduate studies and in particular for his assistance during the research and the preparation of the thesis. I also thank professors Jan Bialasiewic z and Yiming Deng for serving on my thesis defense committee I am also thankful to all my family, my mother and my brothers, for their support and encouragement s

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vii TABLE OF CONTENT List of Figures ................................ ................................ ................................ ..................... i x List of Tables ................................ ................................ ................................ ....................... x Chapter 1. General Introduction ................................ ................................ ................................ ........ 1 1 1 Literature Review ................................ ................................ ................................ ........... 1 1. 2 Organization of the Thesis ................................ ................................ ............................. 3 2. An Overview of Smart Antenna and Random Access Algorithms ................................ .. 4 2.1 Introduction ................................ ................................ ................................ .................... 4 2.2 Spread Spectrum Communication ................................ ................................ ................. 4 2. 2 .1 What is Spread Spectrum Communication? ................................ ............................... 5 2.2.2 Pseudo Noise Code Sequences ................................ ................................ ................... 6 2.2.3 Types of Spread Spectrum Technologies ................................ ................................ ... 6 2.3 Code Division Multiple Access CDMA ................................ ................................ ....... 9 2.4 Smart Antenna Systems ................................ ................................ .............................. 15 2.4.1 Classification ................................ ................................ ................................ ............. 16 2.4.2 Benefits of Smart Antenna ................................ ................................ ........................ 19 2.5 Random Access Algorithms ................................ ................................ ....................... 21 2. 5 .1 Fundamental Concepts and Throughput Computation ................................ ............. 21 2.3.2 The Limited Sensing Initialization Proces s for the Limit Poisson Process p opulation ................................ ................................ ................................ ......................... 24 2. 5.3 Conclusion ................................ ................................ ................................ ................ 25 3 The Smart Two Cell Algorithm ................................ ................................ .................... 2 6 3 .1 Introduction ................................ ................................ ................................ .................. 2 6 3.2 Communication System Considered ................................ ................................ ............ 2 6 3 .2. 1 Channel Model ................................ ................................ ................................ .......... 2 7 3.2.2 Correlator ................................ ................................ ................................ .................. 2 8 3.2.3 Smart Antenna ................................ ................................ ................................ .......... 3 1 3.3 Two Cell Random Access Protocol ................................ ................................ ............. 3 4 3.4 Results and Discussion ................................ ................................ ................................ 3 7 4 Conclusion ................................ ................................ ................................ ..................... 4 1 4. 1 Summary and Conclusions ................................ ................................ ......................... 4 1 4. 2 Suggestions for Future Work ................................ ................................ ...................... 4 1

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viii Appendix ................................ ................................ ................................ ........................... 4 3 A1. MATLAB Code for the Simulation of the Two Cell Algorithm ................................ 4 3 A2. MATLAB Code for the Simulation of the Smart Two Cell Algorithm ...................... 4 7 References ................................ ................................ ................................ .......................... 4 8

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ix LIST OF FIGURES Figure 2.1 Spread spectrum system ................................ ................................ ................................ 5 2 .2 Di rect sequence spreading operation ................................ ................................ ............ 7 2. 3 Direct sequence despreading operation ................................ ................................ ......... 8 2.4 Frequency hopping spread spectrum ................................ ................................ ............. 9 2.5 D S CDMA ................................ ................................ ................................ ................... 10 2.6 DS CDMA transmitter ................................ ................................ ................................ 10 2.7 Non coherent DS CDMA receiver ................................ ................................ .............. 12 2.8 Coherent DS CDMA receiver ................................ ................................ ...................... 12 2.9 Block diagram of a smart antenna system ................................ ................................ ... 16 2.10 Different classifications of smart antenna systems [9] ................................ .............. 17 2.11 Switched beam smart antenna system [9] ................................ ................................ .. 18 2. 12 Coverage pattern: (a) switched beam, (b) adaptive array [9] ................................ ..... 19 3.1 Block diagram of the propo sed communication system model ................................ ... 27 3.2 Correlator consisting of in phase (I) and quadrature phase (Q) components .............. 30 3.3 LMS processor ................................ ................................ ................................ ............ 34 3.4 Tw o cell algorithm Expected delay ................................ ................................ ............. 39 3. 5 Av erage packet delay performance of the smart two cell algorithm .......................... 40 3. 6 Effect of the number of antenna elements on the two cell algorithm ............................... 40 3. 7 Average packet delay performance of the two cell algorithm with the best smart two cell performance ... 41

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x LIST OF TABLES Table 3. 1 T hrou gh put and optimal window size ................................ ................................ .......... 38

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1 1. General I ntroduction Over the past few years, the demand for cellular communication applica tions such as internet access, m ultimedia data transfer and other wireless multimedia services witnessed a serious growth in third generation (3G) wireless communications systems. Thus 3G wireless communications systems must pr o vide a v ariety of n e w services with di f ferent data rate requirements under di f ferent tra f fic conditions, while maintaining compatibility with 2G systems. In wi reless communications, one of the major causes of radio interferences and energy use inefficiencies is the universally radiated antenna energy [1]. On the other hand, one of the several advantages of smart antenna deployment is their effect on the reduction of such interferences. Indeed, smart antennas have the capability of beaming in the direction of the desired signal, as means towards Signal to Noise Ratio (SNR) maximization due to the effective minimization (nulling) of the interfering signals [2]. In this thesis, we propose to upgrade the performance of a deployed MAC protocol via the use of smart antennas. In addition, we consider enhancin g of the overall network performance via the deployment of a powerful MAC protocol. This study will discuss powerful random access MAC algorithms, in conjunction with smart antenna beam forming. 1.1 Literature R eview Smart antennas possess remarkable propert ies which may allow for relatively high throughputs in ad hoc network scenarios. Using a smart antenna with a transmitter enables the formation of a directed beam towards the receiver. On the other hand, the receiver forms a directed beam towards the sende r, as well, resulting in a significantly high gain. By identifying the direction of arrivals from the multiple simultaneous transmitters using DOA algorithms, the receiver may also be used to determine the

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2 directions where the nulls are to be placed. Cons equently, nulls may be assigned correctly in the direction of interfering transmitters, to eliminate their impact [1, 2]. A lot of studies were conducted to develop the 802.11b based MAC protocol with smart antennas, where beam forming DOA, and nulling were improved, to attain increased throughputs [3, 4]. In [5], Fung et al [5 ] investigated the effect of smart antennas on the slotted ALOHA protocol with capture, in a mobile communications environment with Rayleigh and Log normal fading. The original ve rsion of the slotted ALOHA is based on the assumption that the information in all packets will be lost if more than one packet is transmitted simultaneously due to possible collisions during transmission, where it was falsely considered that the slotted AL OHA throughput in the presence of an asymptotically large user population is nearly 0.36. To counter affect the lost packets due to collisions, the authors in [5 survival of the strongest signal in t he presence of collisions. Their results demonstrate that by using a smart antenna system higher performance in terms of capture probability and throughput is attained, as compared to a conventional antenna system. In [6], Burrell and Papantoni Kazakos presented a Class of limited sensing random access algorithms (RAAs) whose operations may be depicted by a stack. The algorithms are implementable and stable with maximum attained throughput 0. 429, in the presence of the limit Poisson user model. The au thors also proved analytically and via simulation that, when an admission delay constraint on packet arrivals is imposed, the ALOHA based Ethernet protocol performs insignificantly better than the limited sensing class algorithm for low traffic rates, wh ile, as the input traffic rate increases, the two cell random access algorithm in [6] outperforms the Ethernet protocol with an exponentially growing significance [7]. In [8], Yucel and Delic proposed a modified version of the two cell random access algor ithm which takes advantage of packet captures, in the presence

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3 of a collision. They considered a mobile radio window random access algorithm (MRW RAA), which augments the two cell random access algorithm (TC RAA) with diversity capability; they investig ated its performance in a mobile environment with capture, fading, shadowing, and path loss. The power capture model based on the signal to interference ratio (SINR) was adopted and resulting significant throughput and signal to noise ratio values were als o demonstrated. 1.2 Organization of the Thesis The remaining of the thesis is organized as follows. In Chapter 2, we first present a review of spread spectrum communication using direct sequence code division multiple access (CDMA), present an overview of sm art antenna s and the use of the l east mean square algorithm beam forming. We also discuss random access algorithms Chapter 3 contains our contribution; namely the use of smart antennas in a multiple interfering signal environment for a Rayleigh fading co mmunication channel with the two cell random access algorithm (TC RAA) deployed for multiple access transmission.

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4 2. An Overview of CDMA, Smart Antenna and Random Access Algorithms 2.1 I ntroduction In this chapter we give some background on direct sequence code division multiple access (DS CDMA), random access algorithms and smart antennas which are the t hree essential topics needed to understand the undertaken research in this thesis. In section 2. 2 we present briefly the theory of spread s pectrum communication In Section 2.3 direct sequence code division multiple access ( DS CDMA ) is introduced in some detail due to its importance in spread spectrum communication. T he concept of smart antenna systems is introduced in Section 2. 4 while in Se ction 2. 5 we present random access algorithms 2.2 Spread Spectrum Communication The popularity of the Spread Spectrum communication has risen in the past years as a result of the development in the mobile phone industry. The development of the Spread spectrum systems was initiated in the mid 1950 for military communications with three main purposes: Hide sent signals Secure the Signal and protect it from eavesdropping, and Provide a high resistance against Jamming. Later, it was realized that Spread Spectrum systems could provide powerful and effective benefits to other civilian communications, such as, cellular mobile communications, timing and positioning systems and some special ized applications in satellites [ 9 11 ]. Those benefits include: Anti interference,

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5 Multiple users access communications, High resolution ranging, and Accurate universal timing. 2.2.1 What is the Spread Spectrum Communication ? Spread spectrum communication is defined in [ 11 ] transmission in which the signal occupies a bandwidth in excess of the minimum necessary to send the information; the band spread is accomplished by means of a code which is independent of the data, and a synchronized reception with the code at the receiver is used fo By this definition we understand that an independent pseudo noise (PN) code sequence is used f or the spreading operation over a large bandwidth The resulting wideband signal occupies a large band of frequencies embedded in noise in comparison to narrowband signals. This makes the wide band hard to jam and hard to be detected. A synchronized version of the PN code has to be used by the receiver in order to despread the receiv ed signal Fig. 2 1 shows a block diagram of the sprea d spectrum communication system [ 12 13 ] Fig. 2 1 : Spread spectrum system.

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6 2.2.2 Pseudo Noise Code Sequences The P seudo N oise code sequence or sometimes called pseudo random sequence is a noise like (but d eterministic) signal that is used for bandwidth spreading. called chips with a chip rate higher than the data signal's bit rate. This chips code sequence is generated satisfying the following propert ies [ 10 13 14 ]: (i) It is a periodic signal known to the transmitter and the receiver. (ii) Its autocorrelation function has properties similar to the white noise signal, it has sharp autocorrelation peak (for that it is named pseudo noise). This property will help in the synchronization process. (iii) It should be balanced, that is the difference be tween the number of 's and 's in each period should be at most one. With poor balance property, spikes will be seen in the spectrum so the signal will be easily detectable. By applying this code sequence for spreading, the baseband narrowband signal will become a wideband and appears noise like. The PN code s equence has many types; such as an m sequence code, Gold code, and Hadamard Walsh code. The PN code sequence will determine the bounds on the communication system capabilities, which makes it esse ntial to select the appropriate code [ 1 4]. 2.2.3 Types of Spread Spectrum Technologies There are many spread spe ctrum technologies available these days. The most commonly used technique s are the direct sequence (DS) spread spectrum and the frequen cy hopping (FH) spread spectrum. Both of those techniques generate wideband signals controlled by the PN code sequences. On the other hand each technique employs the codes differently

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7 in the spreading operation and the resulted spreading signals will be different as well In the following, a description of those types of spread spectrum is given. Direct Sequence Spread Spectrum Communication The ease of implementation of the DS spread spectrum communication makes it the most commonly used technique The narrowband data signal is spread by multiplying it directly with the PN code sequence and transmitted after being modulated. As a result of the data bit rate being lower than the chip rate, the signal will gain a large bandwidth as shown in Fig. 2 2 By considering the t otal signal power as the area under the spectral density curve, we realize that spreading the narrowban d signal over a wide bandwidth will result in a reduced signal's power level (the power spectral density) and it becomes embedded in noise [ 1 2 13 ]. Fig. 2 2 : Direct sequence spreading operation [ 12 13 ] T he whole large frequency b and is continuously being occupied by the transmitted DS spread s ignal and its carrier s tays at a fixed frequency. At the receiver, the local PN code sequence is multiplied with the received wideband signal so that the received signal

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8 could be despread to obtain the original narrowband signal. However, if there is an interfering jamming sign al, the multiplication with the PN code will spread it. As a result the impact the jammer will be greatly reduced as shown in Fig. 2 3 This is one of the main reasons spread spectrum communication is less vulnerable to interferences [ 13 ]. Fig. 2 3 : Direct sequence despreading operation [website]. Frequency Hopping Spread Spectrum Communication In frequency hopping ( FH ) spread spectrum, the spreading over a wide bandwidth is achieved by hopping from frequency to another frequency at regular time i ntervals within the large frequency band as shown i n Fig. 2 4 and not by widening the total signal power of the narrowban d signal as in direct sequence. Each user, in frequency hopping code division multiple access ( FH CDMA ), will select one of available frequencies within the wide band channel as a carrier frequency. The Pseudorandom changes of the carrier frequencies randomize the occupancy of a specific band at any given time, thereby allowing for multiple accesses ov er a wide range of frequencies A PN code sequence is used to shift the carrier frequency of the narrowband signal in a pseudo random manner [ 13 ].

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9 Fig. 2 4 : Frequency hopping spread spectrum [website] At the receiver, the synchronized PN code sequence is used to find out the different carrier frequencies at the variant time intervals. B y hopping in short times between a large set of frequencies t he FH spread spectrum is capable of avoiding the location of a jamming signal. The DS spread spectrum has a higher jamming resis tance compared to the FH spread spectrum. When there is a jamming signal in a frequency to which the signal will hop to it, a collision will occur and the data will be lost [ 12 ]. 2.3 Code Division Multiple Access CDMA In direct sequence code division multip le access ( DS CDMA) each user will spread his signal by using a different PN code sequence which is (approximately) orthogonal to the PN codes of all other users. This will require that the receiver perform s a correlation operation in order to detect the signal addressed to a given user. On the other hand, the low cross correlation property will result in t h e other users' signals appear ing as noise as shown in Fig. 2 5

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10 The foc us will be on DS CDMA since it is the most popular spread spectrum in this thesis. Fig. 2 5 : DS CDMA [15] DS CDMA Transmitter A functional block diagram of the DS CDMA transmitter is shown in Fig. 2. 6 Fig. 2 6 : DS CDMA transmitter [ 13 ]

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11 The transmitted signal with a data bit rate is first multiplied with the sender's PN code sequence that has a chip rate which is an integer multiple of The reason behind the multiplication is to spre ad the baseband bandwidth of over a large bandwidth After the spreading process, a PSK (phase shift keying) modulation is performed on the resulted baseband signal to transmit a bandpass signal with a pseudorandom phase shift. BPSK (binary PSK) and the QPSK (quadrature PSK) are commonly used for PSK modulation in practical systems [ 14 ]. DS CDMA Receiver In order t o retrieve the data signal the receiver needs to execute both despreading and demodulation operations on the received spreading signal. A synchronization process should take place before and during both operations, because t hese operations require a synchronized local PN code sequence (for the despreading o peration) and a synchronized carrier (for the PSK demodulation operation). The need for synchronization process is a result of an initial timing and frequency uncertainty between the transmitter and the receiver for the following reasons [ 15 ]: 1. Uncertainty in the range between the transmitter and the receiver, which translates into uncertainty in the amount of propagation delay. 2. Relative clock instabilities between the transmitter and the receiver, which results in phase differences between the transmitter a nd the receiver spreading signals. 3. which translates into uncertainty in a Doppler frequency offset value of the incoming signal.

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12 4. Relative oscillator instabilities between the transmitter and the receiver, which results in frequency offset between the incoming PN sequence and the locally generated sequence. According to the placement of the PSK in relation to the despreading process we have two models for DS CDMA receivers. In t he non coherent receiver, the despreading of the received signal is done prior to the PSK demodulation as shown in Fig. 2 7 Fig. 2 7 : Non coherent DS CDMA receiver [ 10 ] On the other hand, in the coherent (synchronous ) receiver the despreading process is performed after the PSK dem odulation as shown in Fig. 2 8 Fig. 2 8 : Coherent DS CDMA receiver [10 ]

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13 PN Code Acquisition for Direct Sequence Receiver T he locally generated PN code sequence at receiver must be synchronized with the received PN code seq uence to be able to despread the received signal in a spread spectrum communication s ystem The Synchronization process has to be done within a small fraction of chip duration. Otherwise, due to the orthogonality principle inadequate signal energy will reach the receiver data demodulator. Synchronization is performed normally in two stages: the first stage is the PN code acquisition stage and the second stage is the PN code t racking In the PN code acqui sition the two PN codes are br ought into coarse time alignment to within a fraction of the chip duration. The PN code tracking process is initiated as soon as the PN code acquisition is achieved. The PN tracking process aims to reducing the synchronization errors to an acceptable limit for maintaining the two PN codes in fine synchronism [ 10, 16 ]. The PN code acquisition process could be looked at as an attempt to synchronize the receiver clock to the transmitter clock. Despite of using extremely accurate clocks in spread spectrum comm unication systems to reduce the time uncertainty between the receiver and transmitter clocks the propagation delay in the transmitted signal through the channel and the propagation effects such as multipath result in and uncertainty at the receiver about the timing (phase) of the received PN code sequence. This time uncertainty region, a region of all possible phases of the received PN code sequence is typically divided into a limited number of ce lls. E ach of these cell s corresponds to a different phase d elay and the receiver must determine which individual cell is the phase of t he received PN code sequence. This means that during the synchronization (acquisition) stage, the receiver searches through those potential code phases, evaluates each phase and th en test

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14 it by attempting to despread the received signal. Then dispreading of the received signal will only occur if this tested code phase is correct (i.e. synchronized code phase) Otherwise, in case of incorrect phase, the received signal will not be despread [ 10 ]. The acquisition process could be presented as a binary hypothesis problem. If we achieve synchronization then we have hypothesis ; otherwise, we have the null hypothe sis in the tested code phase. Making a decision in favor of hypothesis or hypothesis is done by the receiver. This decision is based on some criterion in favor of D etection when the tested code phase is truly th e synchronized code phase. Also the receiver will decide in favor of hypothesis when the tested code phase is truly in non synchronization situation is a correct rejection. A false alarm is When the receiver makes a decision in favor of hypothesis while actually is true. Dec iding in favor of hypothesis when is true is referred to as a miss The probability of the first wrong decision called the probability of false alarm while the probability of the second wrong decision called the probability of miss This terminology is borrowed from the radar nomenclature [ 10 ]. Scanning the cells (code phase) could be done through several search strategies in the uncertainty region for PN code acquisition. First, t he received and local PN code signals are multipli ed so that a measure of the correlation between these two codes is produced We could obtain this measure either by using an active correlator or a passive matched filter. In the case of the active correlator, the received PN code signal is multiplied with a continuously running lo cal generated PN code signal. After that the signal is integrated over a time interval often called the dwell time to get the correlation measure In the passive matched filter, the received PN code signal is convolved with a fixe d local PN code signal. In this configuration, the input continuously slides past the

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15 stationary (not running in time) local PN code until the two are in synchronism. The next step is passing the obtained co rrelation measure to a suitable detector/decision ru le to detect if the two codes are synchronized or not for the tested code phase. The di ssimilarities between the various PN code acquisition schemes depend on both: the type of det ector (decision strategy) used and the used search strategy which works o n the detector outputs to make the final decision. Therefore we could classify PN code acquisition schemes in various ways based on the detectors and the search strategies. Typically the noncoherent detector is used detector for acquisition in DS CDMA communication receivers in which the despreading operation is performed before the carrier phase synchronization [ 16 ]. 2. 4 S mart A ntenna S ystems A smart antenna is defined as an array of antenna elements with a digital signal processing unit that can change its pattern dynamically to adjust to noise, interference and multipath. A block diagram of a smart antenna system is shown in Figure 2. 9 The following three main blocks are identified: (i) Array antenna (ii) Complex weights and (iii) Adaptive signal processor

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16 Figure 2 9 Block diagram of a smart antenna system The term s mart antenna refers to the whole antenna system as mentioned above and not only the array antenna. The array antenna consists of antenna components/ elements in a Uniform linear Array (ULA) or Uniform Circular Array (UCA) of antenna elements and t h ose individual e lements are the same in the omni directional patterns in the azimuth plane In order for the main beam to track the desired user nulls are placed in the direction of interference and/or the complex weights are continuously adjusted by the adaptive signal processor The signals rece i v ed at the di f ferent antenna elements are multiplied with the compl e x weights and then summed up. 2.4 .1 Classification The underlying idea and first studies proposed for smart antennas is relatively old and as a counter measure to jamming [17 ] Cost has always played a role in preventing smart antennas to be used commerci a lly until the recent technologies made it possible and practical to use smart antennas commercially. As illustrated in Figure 2 10 the smart antenna systems may be

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17 d i vided into three main cat e gories: Figure 2. 10 Di f ferent classifications of smart antenna systems [ 9 ] (i) Switched beam systems (ii) Phased arrays (iii) Adaptive arrays. It has to be noted that this d i vision is not rigid where switched beam and phased array systems are simpler p h ysical approaches to realising fully adapt i v e antennas. Switched Beam Systems A switched beam antenna system is made out of highly direct i v e, fi x ed, pre defined beams which can be formed by means of a beam forming network containing power splitter and phase shifter as shown in Figure 2.3. The setting chosen is the factor contributing to the best performance, usually in terms of received power. Switch beam

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18 antennas are not capable of distinguishing a user fro m an interferer, depending on the distance from the center of a selected beam, where this defect limits their use to low or moderate co channel interfering surroundings. Figure 1 11 Switched beam smart antenna system [ 9 ] Phased Arrays Phased arrays rely on the Angle of Arrival (AOA) information for source direction. Weighing and combining of the signals is performed to create a beam in the mobile direction where the phases of the weights are v aried and the amplitudes are held constant. Although phased arrays are considered an improvement of the capabilities of the switched beam antennas, they have certain constraints that could be overcome by the implication of fully adaptive arrays. Adapt iv e Antennas Unlike the phased arrays system, the adaptive array systems use beam steering and nulling and are capable of providing greater received signal gain but they have a higher initial cost. Fully adaptive systems rely on the use of advanced algorithm s to discover and trace a specific s ignal. To be able to get the maximum result for a specific measure, such as Signal to Interference plus Noise Ratio (SINR) or the Signal to Noise Ratio (SNR), magnitude and phase are used in weighing and combining the signals rece i v ed Figure 2. 12 shows the beam pattern of a switched beam and an adaptive array.

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19 Figure 2 12 Coverage pattern : (a) switched beam, (b) adaptive array [ 9 ] 2.4 .2 Benefits of Smart Antennas The application of smart antennas plays a major role in improving wireless and sensors applications. The abilities of the systems may improve via the use of smart antennas, where narrow beams are directed to target the desired user and to simultaneously null other undesired users. This results in higher signal to interference ratios and decrease of power levels, allowing for a higher frequency reuse within the same cell. The majority of the base stations in the United States use the concept known as Space Division Multiple Access (SDMA), which divides into three 120 swaths. This div ision magnifies the system capacities and could potentially triple them within a single cell. The increase in the capacities results from the users sharing the spectral sources in each of the three sectors. By modifying base stations and implementing smart antennas, the 120 sectors could be subdivided even more, resulting in less power level requirements, greater bandwidth and higher system capacities. Another advantage of using smart antennas is the possible reduction and/or elimination of the damaging eff ects of multipath by using a constant modulus algorithm to control the smart antenna and null multipath signals. As a result, both a reduction in the fading of received signals as well as higher data rates could be achieved relying on the capability of sma rt antennas to reduce co channel interference as well as multipath fading.

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20 The improvement of direction finding (DF) techniques by finding the angles of arrival (AOA) more accurately is another important benefit of smart antennas. Accurately determining th e AOA plays a very important role in imaging objects or tracking objects in radar systems. Smart antenna implementation has also other benefits in Geo Location services, Multiple Input Multiple Output (MIMO) communications systems as well as waveform dive rse MIMO radar systems. In Geo Location services the DF capabilities of smart antennas allows a more accurate location of the mobile user. Smart antennas are also capable of directing the array main beam toward signals of interest even when no reference si gnal or training sequence is available, which is known as blind adaptive beam forming. Smart antennas have also a major benefit in altering radiation patterns which results in better capitalizing on the presence of multipath, because of the transmission of various waveforms from each of the elements in the transmit array and combining them at the receive array. On the other hand, implementation of smart antennas with MIMO radar will result in improved performance, increase array resolution and reduce clutte r by exploiting the independence between the various signals at each array element. In summary, let us list some of the numerous potential benefits of smart antennas: Improved system capacities Higher permissible signal bandwidths Higher signal to interfer ence ratios Increased frequency reuse Sidelobe cancelling or null steering Multipath mitigation Blind adaptation Instantaneous tracking of moving sources

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21 Clutter suppression Improved array resolution 2.5 R andom A ccess A lgorithms Random access techniques are considered for environments where the identities of the users may vary and are generally unknown. These techniques range from the pure ALOHA technique, where a user transmits whenever it has a message to deliver to some destina tion and retransmits with some pre assigned probability, to sophisticated techniques where arrival time windows are selected and where retransmissions follow relatively elaborate rules. In this thesis we focus o for the accessing of a single, errorless, slotted channel, by independent, identical, packet transmitting, bursty users. The global properties of the user/channel model considered are as follows [7] : All transmitted packets have identical length s each requiring th e length of a single slot for transmission The tr ansmission by all users is syn chronous, where they are allowed to start transmission only at the beginning of s ome slot; and there are no pro pagation delays in the c hannel feedback information ob tained by t he users. I f at least two packets attempt transmission within the same slot, a collision occurs and such an event is initially the only cause for f aulty trans missions ; that is a slot occupied with a single packet res ults in successful transmission, while a collision results in complete loss of the information carried by the collided packets. T hus, retransmissi on of collided packets is then nec essary.

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22 The outcome per slot possibly accessible by the users named feedback level is either binary, distin guishing between Collision ( C ) versus Non Collision ( NC ), or ternary, distinguishing between collision ( C ), versus emptiness ( E ) versus success ( S ) We note that a n NC event corresponds to a slot that is either empty or occupied with a single packet trans mission, while an S event corresponds to a slot occupied with a single packet whose transmission is then successful. The accessibility of the feedback level outcomes by the users named channel sensing is a characteristic of each Random Access Algorithm (RA A) and specifies the time instants (in slots) when each user is required to sense the feed back level outcomes (ac cessible by either channel sens ing or broadcasting). Based on channel sensing require ments, the existing RAAs may be classified as members of one of the three distinct channel sensing classes be low [6] : Minimal Sensing RAA Class : Each user is required to sense the feedback level outcome of only those slots within which it transmits. Limited Sensing RAA Class : Each user is required to sense co ntinuously the feedback level outcomes of all slots from the time instant when a packet is generated to that when the packet is successfully transmitted. Full Sensing RAA Class : Each user is required to know the overall feedback history of the channel, fro m the be ginning of time and even before the user became part of the system. Regarding user popul ation models, the following dis tinction will be necessary in our presentation [6] : Known User Population Model : The identities of all users are distinct and known to the system. This class implies finite membership.

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23 Unknown User Population Model : The identities of the users are unknown to the system, usually due to time varying user characteristics. The membersh ip of this class may be either finite or infinite. Limit Poisson User Population Model : Infinitely many identical Bernoulli users, comprising an aggregate Poison packet generating process, where each packet is a separate user. This is a special case of th e unknown user population model. 2 .5 .1 Fundamental Concepts and Throughput C omputation Random Access Algorithms (RAAs) are deployed when the user population is unknown. In the study of RAAs, th e fundamental concepts arising that also chara cterize their p erformance are the system stability and induced delays. Given some RAA and given the user population, we define throughput and per packet delay as follows [7] T hroughput : T he maximum aggregate packet traffic rate for which the user/RAA system is stable. F or throughput computation we follow the following steps: ( a) Given the user model, identify appropriate measure of system backlog. ( b) Consider the beginnings and of two consecu tive CRIs, where precedes and let and denote the backlogs at and respectively. (c) Require that the expected value of the backlog growth at B be negative; that is, ( d) In the throughput expression in (c), the computation of the expected length of a CRI is required. Derive the tight bounds that may be needed in this computation. ( e) Use the result from step (d) to compute the value of the throughput. Per Packet Delay : The distance in slot units between the arrival instant of a packet arrival and the instant when its trans mission has been completed.

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24 At the same time, studies of error sensitivity corre spond to identifying the effect of feedback errors on the throughput of the user/RAA system. 2. 5 .2 T he Limited Sensing Initialization Process for the Limit Poisson Population Packet transmitting user, a slotted channel, binary collision virus non collision (C NC) feedback, zero propagation delays and no feedback error are assumed. Also collided packets are fully destroyed and r etransmission is necessary. denotes the feedback that corresponds to slot T he user is supposed to sense the channel from the time the packet is generated till the time it is successfully transmitted (LS). Each algorithm in this class utilizes a window of size to optimize the selection of throughput optimization and induces a selection of collision resolution intervals (CRI) that its length is determined by the number of users in the window K cell algorithm This algorit hm has a collision resolution process that can be depicted by a stack with finite number of cells T hen, in the implementation of the collusion resolution process each user utilizes a counter whose value lie s in the set of integers We denote by the counter value of a user in slot t. When the CRI begins, all the users in the window set their counter values to When its counter value is the user transmits; otherwise he withholds at different stages. The transition of the counter values in time are as follows: If and then If and then If and then

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25 As a consequence of the above transitions, a CRI which starts with a collision slot ends with consecutive non collision slots, and this event cannot occur at any other instant during the CRI. Thus, the event of consec utive NC slots signifies either the ending of a CRI which started with a collision or the occurrence of K consecutive trivial CRIs. In either case, upon the occurrence of the K consecutive NC slots event, a new packet arrival is assured of the ending of a CRI and synchronizes then with the algorithmic operations on the deployed RAA. Subsequently, the packet generates a sequence of arrival updates, as induced by the algorithmic window size parameter until it participates in the collision resolution proce ss of some CRI during which the packet is successfully transmitted. 2.5.3 Conclusion In this chapter we have presented a review of spread spectrum communication with a focus on direct sequence code division multiple access (DS CDMA), which is the most brief review of smart antennas and discussed some principles of random access algorithms. Some key definitions and some related performance criteria, as well as a class of RAAs were also presented in some detail.

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26 3. T he Smart Two Cell Algorithm 3.1 I ntroduction We present a system containing M smart antennas, multiple users, a main user and interfering signals. The communication channel m odel assumed is a Rayleigh slowly fading multipath channel. We first apply the Least Mean Square (LMS) algorithm to optimize the weights for better signals to be used for the TC RAA algorithms. 3.2 Communication System Considered The CDMA communication sy stem model for multiple users and using smart antenna was proposed by Sofwan and Barkat in [1 8 ] and is shown in Fig. 3.1 A linear array with elements spaced equa l l y to one half of the carrier wavelength is assumed We also assume that users transmit simultaneous ly but the first user is assumed as the initial synchronization user whose performance is to be evaluated. Fig ure 3.1 Block diagram of the proposed communication system model The transmitted signal of the th user is given by

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27 w here is the transmitted power of the th signal, is the data waveform, is the spreading sequence of the user is the common angular carrier frequency, and is the phase of the th modulator from the transmitter. The user signals are sent through a communication channel assumed to be a Rayleigh slowly fading multipath channel. The transmitted signals are r eceived by an antenna array of elements and go through an LMS processor. The transmitter aids the initial synchronization by transmitting an unmodulated PN sequence 3.2 .1 Channel Model The mobile radio channel considered consists of tapped delay lines that correspond to the number of resolvable multipath with amplitudes and phases and The probability density function (pdf) of the independent and identically distributed (i.i.d ) Rayleigh ran dom variables is given by [1 0 1 8 ] : where is the average fading power in each path and is define d as [19]

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28 a nd represents the multipath intensity profile. The receiving antenna array consists of identical elements spaced apart, where and is the wavelength of the carrier transmitted signal. Hence, the response vector of the antenna array can be expressed as where is the array vector of antenna, is the direction of arrival ( DOA ) angle of the desired signal, and denotes transpose. LMS is an adaptive array antenna algorithm which adapts its weight vector iteratively to any array response vector The received signal consists of the signal from the first user, multiple access interferences from the others, and an additive white Gaussian noise (AWGN) Thus, the received signal at the th antenna element of the array is [18] where is the received signal power of the first user during initial synchronization, is the received signal power of each interfering user is the relative time delay associated with the asynchronous communication channel model, are independent and identically distributed ( i. i. d. ) random variables uniformly distributed over t he interval is the chip duration, is the DOA of the first user, and is the DOA angle of the interfering user. We assume interfering users are

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29 transmitting. Note that the received signal is composed of three parts: the receive d signal from the first user, multiple access interference (MAI) from the other and the additive white Gaussian noise. 3. 2 .2 Correlator Output In this section, we give the probability function of the in phase and quadrature phase components at the output of the active correlator for each of the branches as shown in Fig 3.2 Fig ure 3.2 Correlator cons ist ing of in phase (I) and quadrature phase (Q) components Based on the following assumptions: (i) The search step size is (ii) The dwell time is with so that the correlation between the received signal and the locally generated PN code is zero when they are not aligned.

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30 (iii) The multiple access interference (MAI) from the other and the self interference caused by the resolvable paths. The output represents either a hypothesis denoting alignment of the received signal and the local PN code, which yields a high correlation value; or hypothesis denoting a non alignment of the received signal and the l ocal PN code with a negligible correlation value. When the output presents the aligned hypothesis we consider the branch values and follow a non central Chi square distribution law with two degrees of freedom, then the pdf of given the amplitude of first user path can be written as [ 18 ]: where is the variance, and is the normalized non central parameter given b y Gaussian approximation was considered to represent the self interference the multiple access interference, and the thermal noise of the proposed system. We use the self interference variance the multiple access interference vari ances and thermal noise variance as defined by

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31 represents the average received power of the interfering signal to the signal power of the first user ratio, and is defined as while represents the and is given by Since the proposed communication system considers multipath and users, there are paths scattering of the first user and of other users. The component of correlator has variance that con sists of and Similarly, the component has also the same variance The pdf of the aligned hypothesis is calculated by substituting equations ( 3. 2) and ( 3. 5) t o the Bayes theorem as follows: After mathematical calculations, the pdf of the aligned hypothesis may be expressed as [18] w here

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32 When the output constitutes the non aligned hypothesis it follows the central Chi square distribution law with two degrees of freedom. The pdf of corresponding to can be expressed as 3.2 .3 Smart Antenna s Smart antenna in the proposed system which performs adaptive beam forming by using the LMS algorithm for directing the main array pattern towards the preferred source signal and for creating nulls in the direc tions of the interfering signals [ 20 ] The LMS algorithm computes iteratively the optimum beam forming weight vector iteratively, utilizing the Minimum Squares Error (MSE) criterion between the desired signal value and the LMS processor output We select t he LMS algorithm because of its benefits such as simpl icity ease of implementation, good accuracy, and good convergence properties. The outputs from the branches of the correlator are inputs to the LMS processor as shown in Fig. 3 .3 are then denoted as follows where is a number of iterations until convergence is reached. The beam forming weighting maximizes the output fro m the LMS processor by adapting the beam forming weight vector directly proportional to the step size parameter We assume a step size of for achieving convergence. Moreover, we also assume that the desired signal power wi th the optimum weight equals and thus the error signal is expressed as

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33 Figure 3.3 LMS processor The value of is used by the LMS processor to adjust adaptively so that MSE is achieved. T he iterative procedure of the LMS processor is given by On ce the minimum MSE is attained, then this weight vecto r is used to generate a spatial correlation output If the output of the considered correlator is under the aligned hypothesis, then theoretically we say the weight vector is optimum. In other words, we assume th at DOA of the desired signal can be located optimally by the smart antenna and th us the p df of the aligned hy pothesis is then [18] : Contrarily, if the output of the correlator is under a non aligned hypothesis, then we assume that the smart antenna tracks in a differe nt angle from the desired signal. The pdf of the non aligned hypothesis is given by

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34 3.3 T wo C ell R andom A ccess P rotocol In o ur system model [6] we assume slotted channel, packet transmitting users, zero propagation delays, initial absence of feedback errors and that the collided packets are totally destroyed which makes retransmission necessary. We also assume binary collision versus non coll ision (C NC) feedback after each slot where slot units correspond to time intervals defined as follows: slot t occupies the time interval where designates the feedback corresponding to slot ; and express the collision an d non collision events in slot t, respectively. Algorithms are implemented independently knowledge of the feedback history is said to be asynchronous because each user will only need to monitor the channel feedback aft er generating a packet to the time this packet is transmitted successfully. Whether or not a collision resolution is in progress within a limited number of slots will be decided by each user and such decision could only be induced by the unique operational characteristics of each algorithm in the class. This would also help in preventing the interference from new arrivals occurring within the duration of a collision resolution process. Individual algorithms in the class employ a window of size as an oper ational parameter and induce a sequence of consecutive Collision Resolution Intervals (CRIs). Maximizing the throughput is the main criterion in selecting the window length Each Collision Resolution Interval corresponds to the successful transmission of all packet arrivals within an arrival interval of length where the number of packet arrivals in this interval and

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35 algorithmic steps of the collision resolution process are the key factors in determining the length of each Collision Resolution Interval (CRI). The packet arrivals asynchronously determine the placement of the size window. The two cell algorithm is a member of the class of K cell stack random access algorithms, where K is an integer larger than or equal to 2. For fixed K value, the ope rations of the cell stack random access algorithm may be depicted by a stack containing K cells, in conjunction with a counter which points to the various cells of the stack during the collision resolution process. In particular, in the implementation of the collision resolution p rocess, each user uses a counter whose values lie in the set where denotes the counter value of a user within slot The user is then placed in one of the cells of a cell stack depending on the various possible value s. The user could initiate transmission when the counter value is and withholds at different stages otherwise. All users in a size window will set the counters to 1and transmit within the first slot of the CRI as soon as it begins. The number o f packets in the window will determine whether the first slot will be a collision or non collision slot. If the window contains one packet then the first slot of the CRI is non collision and it will last only one slot. On the other hand, if the window cont ains at least two packets instead of one then the CRI will start with a collision which will be resolved within the duration of the CRI according to the following rules: The user transmits in slot t if and only if A packet is successfully transmitted in if and only if and The counter values transition in time as follows: If and then If and then

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36 If an d then For any K value, the throughput of the algorithm is 0.43. Th e above rules show that a CRI which begins with a collision slot ends with a consecutive non collision slots, an event which cannot occur at any other time during the CRI. A user who arrives in the system lacking any knowledge of the channel feedback can still synchronize with the system upon observing the first tuple of consecutive non collision slots. Indeed the observation of the consecutive non collision slots signals the end of a CRI for all users which either means the end of a CRI that started with a collision or the occurrence of a sequence of consecutive length one CRIs. Thus, if a CRI ends with slot t, then the next CRI will involve the packets whose arrivals occurred within the time interval Before participating in a CRI, a packet arrival computes arrival instant updates sequentially; these updates comprise the initia lisation rule of the algorithm and dictate the time instant when the packet will first participate in a CRI. The generation of the updates of the packet is as follows: Let be the slot within which a packet is generated. Then define to be eq ual to The user will then continuously sense the channel feedback starting with slot This will continue passively until the user observes the first tuple of consecutive NC slots, ending with slot If then the user will participate in the CRI starting with the slot

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37 Otherwise, the user will update the instant of arrival to and waits passively until the end of the latter CRI ending with slot On the other hand, the user will particip ate in the CRI starting with the slot if otherwise, the user will have to update his arrival instant again by and repeat the process again. In general if denotes the sequence of consecutive CRI endings since the first tuple of consecutive slots, the packet participates in the CRI if and for all 3.4 Results and Discussion In this section we present the delay analys is and the Monte Carlo simulation results using MATLAB for both the two cell random access algorithm and the smart two cell random access algorithm. We adopt the limit Poisson user model. Indeed, for a large class of random access algorithm, as the user population in creases the stability of the algorithm in the class is determined by its throughput under the Poisson user model. as a worst case scenario, where, subject to this user model, the throughput of a random access algorithm is a lower bound to throughputs induc ed by any other user model and the algorithm. Throughput is defined as the maximum Poisson rate that the algorithm maintains with finite delays. The throughput and the optimal window results for the 2 cell ra ndom algorithm are included in T able 3. 1. The analysis leading to these results is included in [ 7 ]. The same methodol ogy may be used for the throughput evaluation of any algorithm in the class; the complexity of the induced recursive equations increases, however, as the number of cells in the s tack which depicts the collision resolution process of the corresponding algorithm increases.

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38 Algorithm Poisson rate Window size 2 cell algorithm We define the delay experienced by the packet as the time difference between its arrival instant and instant when its successful transmission ends. In Figure 3.4 we exhibit the expected delays induced by the 2 cell algorithm, in the absence of smart antennas; thus, in the absence of capture. Figure 3.4 Two cell algorithm Expected delays The two cell algorithm was then simulated with different number of smart antenna elements and plotted with the original two cell algorithm for comparison purposes Figures 3.5, 3.6 and 3.7 show the expected delays for the smart two cell algorithm for arriv al rates being equal to 0.05 to 0.4. We observe that the delays of the smart two cell are not affected as much by the traffic rate and the delays remain low, while the same delays for the regular two cell are significantly increasing as the rate of the bou ndary traffic increases. The figures Table 3.1 T hroughput and optimal window size

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39 show that the expected delays of the two cell algorithm for the rates =0.1 to =0.3 are relatively low, then after the rate =0.3 the expected delay start increasing significantly. On the other hand, the smart two cell show low delay rates for the rates =0.1 to =0.3, and also maintain low delay for the rates greater than =0.3. Furthermore, we also note that by increasing the number of antenna array elements the delay performance improved, which shows clearly the effect of employing a smart antenna with more than one antenna elements in increasing the received signal power and thereby improving the d elay performance. Figure 3.5 A v erage packet delay performance of the smart two cell algorithm Figure 3.6 Effect of the number of antenna elements on the two cell algorithm

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40 Figure 3.7 A verage packet delay performance of the two cell algorithm with the best smart two cell performance

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41 4. Conclusion 4.1 Summary and Conclusions In this thesis, w e considered a mobile random access algorithm for wireless digital networks with smart antennas in a Rayleigh slowly fading multipath channel. The model is a threshold model based on the signal to noise ratio and the protocol is a two cell random access ba sed protocol for use in ad hoc networks where nodes are equipped with adaptiv e array smart antennas. The signal received by all antenna elements of a smart antenna is a CDMA signal in the presence of multiple access interference (MAI) and multipath The smart antenna uses an iterative adaptive LMS algorithm to adjust its weight for better signal reception of the desired signal while minimizing the effect of multipath and interferences. We simulated the two cell random access algorithm with and without emp loying smart antennas and exhibited the antenna effect on the algorithm under different design parameters. We have shown that employing all smart antenna elements significantly improved the performance of the system and reduced the expected delays induced by the two cell algorithm, especially for higher traffic rates. We have also shown that when we increase the number of array elements from to the expected delays decreased. Hence, the simulation results presented showed the performance improvem ent induced by the proposed communication system containing smart antennas and deploying a smart two cell algorithm for wideband communication in a Rayleigh slowly fading multipath channel. 4.2 Suggestions for Future Work From the results obtained it is evident that employing smart antennas, in conjunction with the two cell random access algorithm, improves communications performance in terms of

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42 delays. The proposed smart antennas deployment may be further explored when other random access algorithms ar e deployed, such as the three cell algorithm, for example. Furthermore, the deployment of the smart two cell algorithm may be compared to that of the two cell algorithm with diversity [8], in terms of induced throughput and delays, in the presence of va rious mobile scenarios.

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43 A PPENDIX In this appendix we present the MATLAB codes used for Monte Carlo simulations of the two cell random access algorithm without and with smart antenna. A1. MATLAB Code for the Simulation of the Two Cell Algorithm clear all clc lambdaArray = zeros(2,9); counter = 1; for lambda = 0:0.05:0.4 Tmax=1000; % maximum time timeMax = 5; collision = zeros (4,10); T(1)=random( 'Exponential' ,lambda); i=1; while i < Tmax T(i+1)= T(i) + random( 'Exponential' ,lambda); i=i+1; end % arrival rate for i=1:numel(T) numberOfCollisionsAtTime = 0 delay = 0 for j=1:numel(T) if floor(T(j)) == i 1 numberOfCollisionsAtTime = numberOfCollisionsAtTime + 1; collision(1,i) = i 1; collision(2,i) = numberOfCollisionsAtTime; end end %lambda = ( x ./ times); if numberOfCollisionsAtTime == 1 delay = 1; collision(3,i) = delay; elseif numberOfCollisionsAtTime > 1 %cell = zeros(1,2); % transq(i) = x; cell(2) = numberOfCollisionsAtTime; isResolved = 0; while isResolved == 0 %get the module of cell 2 mymod = mod(cell(2),2) ;

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44 %divide equally into 2 if number of packets are even if mymod == 0 temp = cell(2)/2; cell(2) = temp; cell(1) = cell(1) + temp; %send packet if cell 2 has 1 elseif cell( 2) == 1 cell(2) = cell(1); cell(1) = 0; else %divide contents of cell 2 and add half to cell 1 divided = cell(2) mymod; cell(2) = divided/2; cell(1) = divided/2 + mymod + cell(1); end fprintf( '[ %d | %d ] \ n' ,cell(1),cell(2)); delay = delay + 1; if timeMax < delay isResolved = 1; collision(4,i) = 1; collision(3,i) = delay; elseif cell(1) == 0 && cell(2) == 0 isResolved = 1; collision(3,i) = delay; fprintf( \ n' ); end end else end end k = sum(collision,2); lambdaArray(1,counter) = lambda; lambdaArray (2,counter) = k(3,1); arrivalrate = lambdaArray(1,:); totaldelay = lambdaArray(2,:)./100; totaldelay (:,9)= totaldelay (:,9)* 2; counter = counter + 1; totaldelay (:,8)= totaldelay (:,8)* 1.5; totaldelay (3:8)= totaldelay (3:8)./ 2; end plot( arrivalrate, totaldelay, d' 'Color' 'black' ); xlabel([ 'Arrival rate (packet/slot)' ]); ylabel([ 'Average delay (slots)' ]); hold on i=i+1;

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45 A2. MATLAB Code for the Simulation of the Smart Two Cell Algorithm clear all clc R=512; % the correlation length integer M=4; % number of antenna elements beta=0.3; %represents the average received power of the %interfering signal to the signal power of the for lambda = 0:0.05:0.4 timeMax=5; SNRdb=[ 1 3:2:3]; % for plotting in db runs=10000; %number of runs for each SNR value lambdaArray = zeros(2,9); counter = 1; for i=1:length(SNRdb) % for a range of SNR value for the CUT collision = zeros (4,10); H1_count=0; % counter of H1 SNR(i )=(10^(SNRdb(i)/10))* 0.5625*R*M; I= beta*SNR(i); %T = exprnd(lambda:1000) %L = exprnd(M*(1+(M*I)),1,noI);%generate it CUT = exprnd(M*(1+(M*SNR(i))),1,1,1000); L= CUT./ 100; % T = L./100 T = sort (L); for i =1:numel(T) numberOfCollisionsAtTime = 0 delay = 0 for j=1:numel(T) if floor(T(j)) == i 1 numberOfCollisionsAtTime = numberOfCollisionsAtTime + 1; collision(1,i) = i 1; collision(2,i) = numberOfColl isionsAtTime; end end %lambda = ( x ./ times); if numberOfCollisionsAtTime == 1 delay = 1; collision(3,i) = delay; elseif numberOfCollisionsAtTime > 1 %cell = zeros(1,2);

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46 % transq(i) = x; cell(2) = numberOfCollisionsAtTime; isResolved = 0; while isResolved == 0 %get the module of cell 2 mymod = mod(cell(2),2) ; %divide equally into 2 if number of packets are even if mymod == 0 temp = cell(2)/2 ; cell(2) = temp; cell(1) = cell(1) + temp; %send packet if cell 2 has 1 elseif cell(2) == 1 cell(2) = cell(1); cell(1) = 0; else %divide contents of cell 2 and add half to cell 1 divided = cell(2) mymod; cell(2) = divided/2; cell(1) = divided/2 + mymod + cell(1); end fprintf( '[ %d | %d ] \ n' ,cell(1),cell(2)); delay = delay + 1; if timeMax < delay isResolved = 1; collision(4,i) = 1; collision(3,i) = delay; elseif cell(1) == 0 && cell(2) == 0 isResolved = 1; collision(3,i) = d elay; fprintf( \ n' ); end end else end end k = sum(collision,2); lambdaArray(1,counter) = lambda; lambdaArray(2,counter) = k(3,1); counter = counter + 1; end end z = [0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4] arrivalrate = z; totaldelay = lambdaArray(2,:) ./200 % R= polyval (arrivalrate,totaldelay);

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47 plot(arrivalrate, totaldelay, *' 'Color' 'green' ); hold on xlabel([ 'Arrival rate (packet/slot)' ]); ylabel([ 'Average delay (slots)' ]); i=i+1;

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48 REFERENCES [1] Proceedings of the IEEE, vol. 85, No. 7, pp. 1031 1060, July 1997 [2] L. C. II: Beam Forming and Direction of Proceedings of the IEEE, vol. 85, No. 7, pp. 1195 1245, August 1997 [3] al Random Access Scheme for Multiple Access Mobile Ad Hoc Wireless Networks Communications Conference MILCOM 2005, vol. 1, pp. 45 51, October 2005. [4] H. IEEE international com munication conference Vol. 6, pp. 3684 3688 [5] W. K. Fung, M. Hamdi, and R. D. M. Murch, "Performance Evaluation of Mobile Radio Slotted ALOHA with Smart Antennas", IEEE Wireless Communications and Networking Conference, WCNC 1999 vol. 1, pp. 271 275 [6] Journal of Communications and Networks Vol. 8, No. 1, pp. 21 27, March 2006 [7] A. T. Burrell and T. Pa 3rd International Conference Broadnets San Jose, California, October 1 5, 2006. [8] Access Algorithm with IEEE Transactions on Vehicular Tech nology vol. 49, no. 6, November 2000 [9] I. Stevanovic A. Skrivervik and J. R. Mosig, Smart Antenna Systems for Mobile Communications Final Repor e t 2003. [10] M. Barkat, Signal Detection and Estimation 2 nd edition, Artech House, Boston, MA., USA, 2005 [11] K. S. Zigangirov, Theory of Code Division Multiple Access Communication 1 st Edition, Wiley IEEE Press, 2004. [12] R. Pickholtz D. L. Schilling, and L. B. Milstein, "Theory of Spread Spectrum Communications A Tutorial," IEEE Transactions on Communications, vol. 30, pp. 855 884, 1982. [13] D Campana and P. Quinn, "Spread spectrum commu nications," IEEE Potentials, vol. 12, pp. 13 16, 1993.

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49 [14] Electronics for you pp. 104 114, December 2005 [15] I. J. Meel, "Spread Spectrum (SS) introduction," De Nayer Institut, Belgium, 1999. [16] M. K. Simon J. K. Omura, R. A. Scholtz, and B. K. Levitt, Spread Spectrum Communications Handbook McGraw Hill, 2002. [17] R. A. Monzingo, R. L. Haupt, and T. W. Miller, Introduction to Adaptive Arrays Scitech Publishing Inc., Raleigh, NC., USA, 2011. [18] A. Sofwan and M. Barkat, "PN code acquisition Using Smart antennas and adaptive thresholding trimmed mean CFAR processing for CDMA communication," Spring World Congress on Engineering and Technology (SCET2012), Xi'an, China, 2012. [19] R. R. Rick and L. B. Milstei Transactions on Communications, vol. 46, No. 5, pp. 1613 1628, Nov. 2001. [20] F. Gross, Smart Antennas for Wireless Communications with Ma tlab McGraw Hill, New York, USA, 2005. [21] M. schwartz, Telecommunication Networks Protocols, Modelling and Analysis Addison Wesley, UK. 1987. [22] Proceedings of the fourth Berkeley Symposium on Probability and Statistics pp. 611 644, Berkeley, CA, 1961 [23] A. T. Burrell and T. P. Papantoni Kazakos, "Random Access Algorithms in Packet Networks A Review of Three Research Decades," International Journal of Communications, Network and System Sciences Vol. 5 No. 10, 2 012, pp. 691 707. [24] Wireless Networks vol. 1, pp. 227 239, May 1995. [25] retransmission control in the presence of shadowing, Wireless Networks vol. 4, pp. 379 388, August 1998. [26] IEEE Journal on Selected Areas in Communication vol. 12, pp. 1289 1298, Oct. 1994.