Mathematics remains a subject many students fail to become competent in by the time they graduate from high school. Most students often require one on one, individualized tutoring to help them reach competence. That remains a challenge since most classrooms are understaffed and underfunded, frequently having only one teacher in a overpopulated classroom. One strategy that has been used to alleviate some of this over reliance on the teacher has been faded worked examples, or fading. Fading is the successive removal of the last steps in a series of problems until the student is solving problems completely on their own. The current study aimed to determine whether fading improves learning, and for whom. The goal was to compare fading with business as usual (control), worked examples with self-explanations, and fading with self-explanations. Specifically, I was interested in the following research questions: (1) Do the three experimental conditions differ in promoting posttest scores on surface area and volume? (2) Do the three experimental conditions differ in promoting conceptual knowledge and procedural knowledge of surface area and volume at posttest? and (3) When interaction terms are created between student profiles and conditions within regression analyses, which profiles explain significant variance in posttest scores? Repeated measures analysis of variance, principle axis factor analysis, and simple linear regressions were used to examine the differences between conditions at posttest, to create propensity scores, and to determine whether there were any interactions between propensity scores and conditions. Results indicated a significant effect of fading on posttest scores. A regression with propensity factors indicated that the fading conditions appeared to benefit low propensity students moreso than high propensity students. Findings are discussed in terms of educational implications and future research that can complement these findings to contribute to future research. / Educational Psychology

yes / Empirical modeling of wireless fading channels using common schemes such as autoregression and thefinitestate Markov chain (FSMC) is investigated. The conceptual background of both channel structures and the establishment of their mutual dependence in a confined manner are presented. The novel contribution lies in the proposal of a new approach for deriving the state transition probabilities borrowed from economic disciplines, which has not been studied so far with respect to the modeling of FSMC wireless fading channels. The proposed approach is based on equal portioning of the received signal-to-noise ratio, realized by using an alternative probability construction that was initially highlighted by Tauchen. The associated statistical procedure shows that afirst-order FSMC with a limited number of channel states can satisfactorily approximate fading. The computational overheads of the proposed technique are analyzed andproven to be less demanding compared to the conventional FSMC approach based on the levelcrossing rate. Simulations confirm the analytical results and promising performance of the new channel modelbased on the Tauchen approach without extracomplexity costs.

Proliferation of new wireless technologies has rekindled the interest on the design, analysis and implementation of suboptimal receiver structures that provide good error probability performance with reduced power consumption and complexity particularly when the order of diversity is large. This thesis presents a unified analytical framework to perform a trade-off study for a class of hybrid generalized selection combining technique for ultra-wideband, spread-spectrum and millimeter-wave communication receiver designs. The thesis also develops an exact mathematical framework to analyze the performance of a dual-diversity equal gain combining (EGC) receiver in correlated Nakagami-m channels, which had defied a simple solution in the past. The framework facilitates efficient evaluation of the mean and variance of coherent EGC output signal-to-noise ratio, outage probability and average symbol error probability for a broad range of digital modulation schemes. A comprehensive study of various dual-diversity techniques with non-independent and non-identical fading statistics is also presented. Finally, the thesis develops some closed-form solutions for a few integrals involving the generalized Marcum Q-function. Integrals of these types often arise in the analysis of multichannel diversity reception of differentially coherent and noncoherent digital communications over Nakagami-m channels. Several other applications are also discussed. / Master of Science

Wireless has proved to be one of the most important and fastest growing fields of communications especially during last few decades. To achieve reliable communication, we model a wireless system to analyze its performance and to find ways to improve the reliability of a particular system. Extensive research is being done to accurately model wireless systems, and to achieve better performance. Simulation techniques have been in use for many years to support the design and evaluation of electronic communication systems. Over the past few decades, Computer Aided Design (CAD) techniques (including both computerized analytical techniques and simulation) have matured, and are now usually applied at some point in the system design/development process. The aim of this thesis is to find efficient algorithms that can model third generation wireless channels in a discrete sense. For modeling these channels, mathematical tools known as hidden Markov models are used. These models have proved themselves to be very efficient in many areas of electrical engineering including speech recognition, pattern recognition, artificial intelligence, wavelets and queuing theory. Wideband Code Division Multiple Access (W-CDMA) wireless communication parameters including channels fading statistics, Bit Error Rate (BER) performance and interval distribution of errors are modeled using different Markov models, and their results are tested and validated. Four algorithms for modeling error sources are implemented, and their results are discussed. Both hidden Markov models and semi-hidden Markov models are used in this thesis, and their results are validated for the W-CDMA environment. The state duration distributions for these channels are also approximated using Phase-Type (PH) distribution. / Master of Science

Since the 1950s, hidden Markov models (HMMS) have seen widespread use in electrical engineering. Foremost has been their use in speech processing, pattern recognition, artificial intelligence, queuing theory, and communications theory. However, recent years have witnessed a renaissance in the application of HMMs to the analysis and simulation of digital communication systems. Typical applications have included signal estimation, frequency tracking, equalization, burst error characterization, and transmit power control. Of special significance to this thesis, however, has been the use of HMMs to model fading channels typical of wireless communications. This variegated use of HMMs is fueled by their ability to model time-varying systems with memory, their ability to yield closed form solutions to otherwise intractable analytic problems, and their ability to help facilitate simple hardware and/or software based implementations of simulation test-beds. The aim of this thesis is to employ and exploit hidden Markov fading models within an iterative (turbo) decoding framework. Of particular importance is the problem of channel estimation, which is vital for realizing the large coding gains inherent in turbo coded schemes. This thesis shows that a Markov fading channel (MFC) can be conceptualized as a trellis, and that the transmission of a sequence over a MFC can be viewed as a trellis encoding process much like convolutional encoding. The thesis demonstrates that either maximum likelihood sequence estimation (MLSE) algorithms or maximum <I> a posteriori</I> (MAP) algorithms operating over the trellis defined by the MFC can be used for channel estimation. Furthermore, the thesis illustrates sequential and decision-directed techniques for using the aforementioned trellis based channel estimators <I>en masse</I> with an iterative decoder. / Master of Science

No / Two training schemes namely the orthogonal pilot scheme (OPS) and the superimposed pilot scheme (SPS) are compared in terms of achievable rates in multiple-antenna fading channels with memory. For both schemes, we show that the achievable rate depends on the number of antennas, signal-to-noise ratio (SNR) and fading speed via the channel estimation error variance and the fraction of time for data transmission. To guarantee positive achievable rates, we show that for the OPS the number of transmit antennas that can be accommodated is limited by the fading speed whereas for the SPS the number of antennas can be arbitrary. For most antenna configurations, we observe that while the SPS is superior in the low-SNR and fastfading regimes, the OPS is superior in other regimes. However, for a few number of antennas (e.g., single antenna), the SPS may also be superior in the low-SNR and slow-fading regimes.

Satellite systems in the 20/30 GHz band are very susceptible to outages due to rain-induced fades. In order to reduce the impact of these fades, it has been proposed that the power of the uplink station transmitter be adjusted during the fade to compensate. This dissertation will explore some of the issues involved in implementing this uplink power control (ULPC). Fade slope is examined as a parameter to predict signal strength during a fade. A fade slope model based on fade physics is presented, but it strongly suggests that fade slope is not an appropriate parameter for ULPC. Real time scaling of attenuation from the downlink to the uplink shows more promise for ULPC. Differences in drop size distributions during a rain storm will result is different scaling factors. If the downlink attenuation is limited to 6 dB at 20 GHz, real time scaling can be accomplished. A scaling type ULPC algorithm driven by downlink attenuation is tested on 66 hours of OLYMPUS 20/30 GHz fade data. A similar algorithm driven by uplink attenuation is tested and the performance of the two algorithms is presented and compared. / Ph. D.

Made available in DSpace on 2016-04-29T13:18:05Z (GMT). No. of bitstreams: 1 Cristiano Cedra.pdf: 426189 bytes, checksum: 6e02c6a26fd210dcadb0b0ef68cc7260 (MD5) Previous issue date: 2007-04-25 / The free throw is a kind of basketball shot and it occurs as a result of breaking some of the rules of the game. Approximately 25% of all points earned in a basketball game come from free throws. In basketball teaching or practicing, free throws are usually the first kind of shot taught, forming the basis for more advanced shooting techniques. Despite its importance, average free throw accuracy has been below 70%; only a few players have managed to achieve a higher average. In this paper a new method of free throw training is presented by progressive and gradual techniques aimed towards specifications changes in materials used in training (in this case, the diameter of the basketball rim and its height). Starting from basic conditions (larger diameters and lower baskets) to those seen as more complex (basketball s official specifications), trying to reach gradually the average accuracy in professional basketball free throwing. In this research, 12 athletes aged from 13 to 14 years old were chosen from a competitive basketball team to participate in it. Then, they were submitted to two stages at the baseline condition. In the first stage, 39 sessions of 10 free throws were shot in each session. In the second stage, the athletes had 13 sessions of 30 shots in each session, out of which 10 were shot from the official free throw line, 10 from an intermediate distance between the free throw line and the basket and the last 10 were shot very close to the basket. After this stage, the athletes were divided into two groups: group 1 was submitted to an intervention related to the diameter of the basket and group 2, to an intervention related to the height of the basket. The fading procedure was identical for both groups that went through the multielement baseline design. Each athlete went through 9 fading practice stages, and, in every stage, should score at least 70% of the free throws to go on to the next stage. Stage 1 was carried out using a closer distance to the basket and a larger diameter (group 1) or a lower height (group 2). Progressively, the distance was increased, passing through the intermediate distance until reaching the official free throw distance, keeping to the same diameter and height specifications. When the athlete reached the official distance, he would go back to the starting line and resume his shooting but now the diameter and height would be set to the intermediate specifications. Gradually, the athlete should reach the official distance and specifications of basketball. The next stage was identical to the baseline condition and had the purpose of evaluating whether the results achieved in the last modified stage would last once the treatment was removed. Analyzing the results, it is made clear that practicing shots through repetition did not produce the results expected in the selected group, at best, it only established their previous marks. Being exposed to different distances without using progression through fading also did not bring improvements to the performance of the athletes and the level of accuracy in the closest distance was higher than in the intermediate distance, which was also higher than in the official distance suggesting that distance is a decisive factor when evaluating basketball shots. While group 1 achieved an overall improvement throughout the practice, some of the athletes in group 2 actually showed a loss in performance, suggesting that the diameter of the rim is, in fact, a more critical factor than the height of the basket. The fading procedure has brought improvements to the level of accuracy of the evaluated athlet / O lance livre é um tipo de arremesso do basquetebol e ocorre como conseqüência a algumas infrações à regra deste jogo. Aproximadamente, 25% dos pontos do jogo de basquetebol vêm do lance livre. No ensino e treinamento do basquetebol é o primeiro tipo de arremesso a ser ensinado servindo de base para os demais. Apesar da sua importância, as médias de acertos nestas situações tem sido inferiores a 70%, apenas alguns jogadores atingem médias superiores. Neste trabalho apresentamos um novo método de treinamento de lances livres através das técnicas de mudança gradual e progressiva das alterações nas especificações dos materiais utilizados nos treinos (no caso, o diâmetro do aro da cesta e a altura da cesta), indo de condições consideradas como mais simples (diâmetros maiores e cestas em alturas mais baixas) para aquelas vistas como mais complexas (especificações oficiais), tentando, gradualmente, atingir o objetivo de acertos dos arremessos de lances livres na cesta oficial do basquetebol. Foram participantes desta pesquisa 12 atletas, com idade entre 13 e 14 anos, integrantes de uma equipe competitiva de basquetebol. Estes foram submetidos a duas fases na linha de base. Na fase 1, realizaram 39 sessões com 10 arremessos de lances livres em cada sessão. Na fase 2, realizaram 13 sessões com 30 arremessos em cada sessão, sendo 10 da distância oficial de lance livre, 10 de uma distância intermediária entre a linha do lance livre e a cesta, e mais 10 bem próximos da cesta. Após esta etapa, os atletas foram divididos em dois grupos: o grupo 1 foi submetido à intervenção relacionada a dimensão diâmetro da cesta; e o grupo 2 à intervenção relacionada a dimensão altura da cesta. O procedimento de fading ou esvanecimento foi idêntico para ambos os grupos que passaram pelo delineamento de linha base múltipla entre participantes. Cada atleta passou por 9 fases de fading, e, em cada uma delas, deveria acertar pelo menos 70% dos arremessos para progredir para a fase seguinte. A fase 1 era realizada com distância próxima da cesta e diâmetro maior (grupo 1) ou altura menor (grupo 2). Progressivamente, a distância era aumentada, passando pela distância intermediária até chegar à distância oficial do lance livre, mantendo-se a mesma especificação da dimensão diâmetro ou altura. Quando o atleta chegava à distância oficial, ele voltava a arremessar de bem próximo da cesta, mas agora com a dimensão diâmetro e altura com especificações médias. Gradualmente, o atleta deveria chegar à distância e dimensão oficiais do basquetebol. A etapa seguimento foi idêntica à etapa de linha de base e tinha como objetivo avaliar se os resultados produzidos na última fase da intervenção se mantinham após a retirada do tratamento. Nos resultados, percebemos que a repetição do ato de arremessar não produziu melhoras no desempenho dos atletas avaliados, no máximo, estabilizou seus resultados. A exposição a diferentes distâncias sem a utilização da progressão através do fading também não produziu melhoras no desempenho destes atletas e o índice de acertos na distância próxima foi maior do que na distância intermediária, que por sua vez foi maior do que na distância oficial, sugerindo que a distância é uma variável crítica quando avaliamos o arremesso. O grupo 1 obteve melhoras durante a intervenção que se mantiveram durante o seguimento e no grupo 2, alguns atletas também obtiveram melhoras durante a intervenção, mas para alguns participantes estes resultados diminuíram no seguimento, sugerindo assim, que a dimensão diâmetro foi mais crítica para estes atletas do que a dimensão altura. O procedimento de fading promoveu melhoras no índice de acertos dos atletas avaliados

This thesis aims at proposing all the possible enhancements for the Multi-Resolution Frequency-Domain ParFlow (MR-FDPF) model. As a deterministic radio propagation model, the MR-FDPF model possesses the property of a high level of accuracy, but it also suffers from some common limitations of deterministic models. For instance, realistic radio channels are not deterministic but a kind of random processes due to, e.g. moving people or moving objects, thus they can not be completely described by a purely deterministic model. In this thesis, a semi-deterministic model is proposed based on the deterministic MR-FDPF model which introduces a stochastic part to take into account the randomness of realistic radio channels. The deterministic part of the semi-deterministic model is the mean path loss, and the stochastic part comes from the shadow fading and the small scale fading. Besides, many radio propagation simulators provide only the mean power predictions. However, only mean power is not enough to fully describe the behavior of radio channels. It has been shown that fading has also an important impact on the radio system performance. Thus, a fine radio propagation simulator should also be able to provide the fading information, and then an accurate Bit Error Rate (BER) prediction can be achieved. In this thesis, the fading information is extracted based on the MR-FDPF model and then a realistic BER is predicted. Finally, the realistic prediction of the BER allows the implementation of the adaptive modulation scheme. This has been done in the thesis for three systems, the Single-Input Single-Output (SISO) systems, the Maximum Ratio Combining (MRC) diversity systems and the wideband Orthogonal Frequency-Division Multiplexing (OFDM) systems.

Οι ραγδαία αυξανόμενες απαιτήσεις για ασύρματες ευρείας ζώνης υπηρεσίες και τα πρόσφατα επιτεύγματα στο σχεδιασμό κι υλοποίηση κινητών τερματικών συσκευών με δυνατότητες παροχής υπηρεσιών διαδικτύου επισπεύδουν την εισαγωγή των ασυρμάτων συστημάτων επικοινωνίας τέταρτης γενεάς στην παγκόσμια αγορά. Βασικό ρόλο στην εκπλήρωση των απαιτήσεων για αυξημένο ρυθμό μετάδοσης δεδομένων και ποιότητα υπηρεσιών που έχουν τεθεί από τα συστήματα αυτά, διαδραματίζουν οι χωροχρονικές τεχνικές επεξεργασίας σήματος που εφαρμόζονται στα ασύρματα συστήματα με πολλαπλές κεραίες στον πομπό ή/και στο δέκτη. Ευρέως διαδεδομένα και συνάμα απλά στην υλοποίηση συστήματα πολλαπλών κεραιών είναι οι δέκτες χωρικού διαφορισμού (ΔΧΔ), οι οποίοι παρέχουν τη δυνατότητα αποδοτικής αντιμετώπισης του φαινομένου των διαλείψεων πολυδιόδευσης που εμφανίζονται στο ασύρματο κανάλι, συνδυάζοντας κατάλληλα τα πολλαπλά ληφθέντα αντίγραφα του εκπεμπόμενου σήματος. Η θεωρητικά αναμενόμενη βελτίωση στις επιδόσεις ασυρμάτων συστημάτων που δύνανται να προσφέρουν οι ΔΧΔ σε σύγκριση με τους συμβατικούς δέκτες μονής κεραίας, προϋποθέτει τη στατιστική ανεξαρτησία των διαλείψεων πολυδιόδευσης που εμφανίζονται στις πολλαπλές κεραίες του δέκτη. Σε πρακτικές υλοποιήσεις, όμως, ποικίλες παράμετροι, όπως για παράδειγμα η μικρή απόσταση μεταξύ των πολλαπλών κεραιών του δέκτη, συντελούν ώστε οι διαλείψεις που εμφανίζονται στους κλάδους των ΔΧΔ να είναι αυθαίρετα συσχετισμένες. Η θεωρητική μελέτη επιδόσεων ΔΧΔ που υπόκεινται σε αυθαίρετα συσχετισμένα κανάλια διαλείψεων πολυδιόδευσης, γνωστών ως διαλείψεις μικρής κλίμακας (ΔΜΙΚ), αποτελεί το αντικείμενο έρευνας της παρούσας διδακτορικής διατριβής. Αν και πολυάριθμες ερευνητικές εργασίες ασχολούνται με τη μοντελοποίηση των συσχετισμένων ΔΜΙΚ και της επίδρασής τους στις επιδόσεις ΔΧΔ, η πλειονότητά τους, χρησιμοποιώντας τις στατιστικές ιδιότητες πολυ-μεταβλητών κατανομών, περιορίζεται σε ειδικές μορφές συσχέτισης των διαλείψεων και σε συμβατικές τεχνικές ΔΧΔ. Το γεγονός αυτό οφείλεται, σε μεγάλο βαθμό, στην απουσία απλών στη χρήση και στον υπολογισμό μαθηματικών εκφράσεων για τις στατιστικές ιδιότητες πολυ-μεταβλητών κατανομών με αυθαίρετα συσχετισμένες τυχαίες μεταβλητές (ΤΜ). Στα πλαίσια της διατριβής αυτής επισκοπούνται, αρχικά, οι προταθείσες μαθηματικές εκφράσεις για τις κυριότερες στατιστικές ιδιότητες των πολυ-μεταβλητών κατανομών Rayleigh, Nakagami-m, Weibull και γενικευμένου Γάμα (ΓG) με διάφορες μορφές συσχέτισης και περιγράφονται οι δυνατότητες χρησιμοποίησής τους στη μελέτη επιδόσεων ΔΧΔ που λειτουργούν σε συσχετισμένες ΔΜΙΚ. Κατόπιν, παρουσιάζοντας μια νέα μεθοδολογία δημιουργίας αυθαίρετα συσχετισμένων και μη απαραιτήτως ταυτόσημα κατανεμημένων (ΤΚ) ΤΜ ΓG, η οποία βασίζεται σε αυθαίρετα συσχετισμένες ΤΜ Gauss και στην ειδική κατηγορία των πινάκων Householder για την τριδιαγωνιοποίηση του πίνακα συσχέτισης (ΠΣ) των ΤΜ Gauss, προέκυψαν μια κλειστής μορφής έκφραση άνω φράγματος για την από κοινού συνάρτηση πυκνότητας πιθανότητας (ΣΠΠ) και μια αναλυτική έκφραση άνω φράγματος σε αναπαράσταση απειροσειρών για την από κοινού αθροιστική συνάρτηση κατανομής (ΑΣΚ) αυθαίρετα συσχετισμένων και μη απαραιτήτως ΤΚ ΤΜ ΓG. Τα προταθέντα άνω φράγματα περιέχουν αρκετές γνωστές μαθηματικές εκφράσεις για τις από κοινού ΣΠΠ κι ΑΣΚ ως ειδικές περιπτώσεις. Στη συνέχεια, προσεγγίζοντας τον ΠΣ αυθαίρετα συσχετισμένων ΤΜ Gauss με έναν ειδικής κατηγορίας πίνακα Green, εξάγεται μια κλειστής μορφής έκφραση προσέγγισης για την από κοινού ΣΠΠ αυθαίρετα συσχετισμένων και μη απαραιτήτως ΤΚ ΤΜ ΓG καθώς και μια αναλυτική έκφραση προσέγγισης σε αναπαράσταση απειροσειρών για την από κοινού ΑΣΚ τους. Επίσης, παρουσιάζονται αναλυτικές εκφράσεις σε αναπαραστάσεις απειροσειρών για τις κυριότερες στατιστικές ιδιότητες της τρι-μεταβλητής κατανομής ΓG με αυθαίρετο ΠΣ και μη απαραιτήτως ΤΚ ΤΜ καθώς και της πολυ-μεταβλητής κατανομής ΓG με σταθερό ΠΣ και μη απαραιτήτως ΤΚ ΤΜ. Όλων των μορφών οι προταθείσες αναλυτικές μαθηματικές εκφράσεις για τις ΣΠΠ κι ΑΣΚ της πολυ-μεταβλητής κατανομής ΓG χρησιμοποιούνται για τη μελέτη επιδόσεων δεκτών διαφορισμού επιλογής (ΔΕ), διαφορισμού μέγιστου λόγου (ΔΜΛ) και διαφορισμού μεταγωγής κι εξέτασης (ΔΜκΕ) που υπόκεινται σε ποικίλα περιβάλλοντα αυθαίρετα συσχετισμένων ΔΜΙΚ. Αρχικά, εξάγονται αναλυτικές εκφράσεις άνω φραγμάτων για την πιθανότητα διακοπής επικοινωνίας (ΠΔΕ), τη μέση πιθανότητα σφάλματος συμβόλου (ΜΠΣΣ) διαφόρων σχημάτων διαμόρφωσης και τη μέση χωρητικότητα καναλιού (ΜΧΚ) κατά Shannon δεκτών ΔΕ που λειτουργούν σε περιβάλλον αυθαίρετα συσχετισμένων και μη απαραιτήτως ΤΚ διαλείψεων ΓG. Επίσης, παρουσιάζονται αναλυτικές εκφράσεις για τα ίδια κριτήρια επίδοσης δεκτών ΔΕ με τρεις κεραίες καθώς κι αναλυτικές εκφράσεις προσεγγίσεων για τα κριτήρια επίδοσης δεκτών ΔΕ οποιουδήποτε πλήθους κεραιών. Κατόπιν, εξάγοντας νέες αναλυτικές μαθηματικές εκφράσεις σε αναπαραστάσεις απειροσειρών για τις κυριότερες στατιστικές ιδιότητες του αθροίσματος οποιουδήποτε αριθμού αυθαίρετα συσχετισμένων και ΤΚ ΤΜ Γάμα, προκύπτουν αναλυτικές εκφράσεις για την ΠΔΕ, τη ΜΠΣΣ διαφόρων σχημάτων διαμόρφωσης και τη ΜΧΚ κατά Shannon δεκτών ΔΜΛ που λειτουργούν σε αυθαίρετα συσχετισμένες και ΤΚ διαλείψεις Nakagami-m. Για το ίδιο περιβάλλον διαλείψεων, παρουσιάζονται αναλυτικές εκφράσεις σε αναπαραστάσεις απειροσειρών για την ΠΔΕ και τη ΜΠΣΣ διαφόρων σχημάτων διαμόρφωσης δεκτών ΔΜκΕ οποιουδήποτε πλήθους κεραιών. Η στενότητα των προταθέντων άνω φραγμάτων για τα κριτήρια επίδοσης των δεκτών ΔΕ, ΔΜΛ και ΔΜκΕ που υπόκεινται σε περιβάλλοντα αυθαίρετα συσχετισμένων ΔΜΙΚ, η ορθότητα των αναλυτικών εκφράσεων για τα ίδια κριτήρια κι η ακρίβεια των προταθέντων προσεγγίσεών τους μελετήθηκαν εκτενώς συγκρίνοντας πολυάριθμα αριθμητικά αποτελέσματα των εκφράσεων αυτών με αντίστοιχα αποτελέσματα που προέκυψαν από προσομοιώσεις σε Η/Υ, οι οποίες υλοποιήθηκαν για το σκοπό αυτό. / The rapidly increasing demands for wireless wideband services and the recent advances in the design and implementation of mobile terminal devices with Internet-based service providing capabilities expedite the introduction of fourth generation (4G) wireless communications systems in the international wireless market. These systems are expected to ensure increased data rates and quality of service in an anytime anywhere basis. Wireless systems that utilize multiple antennas at the transmitter and/or receiver as well as space-time signal processing techniques play a fundamental role in accomplishing the demands imposed by 4G wireless communications systems. Well-known multiple-antenna systems that enable simple implementations are space diversity receivers (SDRs). By properly combining the multiple received replicas of the transmitted signal, SDRs are capable of effectively mitigating the detrimental effects of multipath fading, known as small-scale fading (SSF), that is inherent in wireless channels. SDRs are theoretically known to improve wireless system’s performance compared with conventional single-antenna receivers. This improvement requires that the SSF channels among multiple receiver’s antennas are statistically independent. However, in practical implementations, due to several parameters such as for example the small distance among the receiver’s multiple branches, SSF channels are arbitrarily correlated. This doctoral dissertation presents a theoretical performance study of SDRs operating over arbitrarily correlated SSF channels. Although numerous scientific papers deal with correlated SSF channel modeling and the impact of correlated SSF on the performance of SDRs, their vast majority, which utilizes the statistical properties of multivariate distributions for studying SDRs’ performance, is restricted to special forms of fading correlation and conventional SDR techniques. This happens mainly due the fact that there is a lack of simple mathematical expressions for the statistical properties of multivariate distributions with arbitrarily correlated random variables (RVs) in the literature. Within the framework of this dissertation, firstly, the previously proposed mathematical expressions for the most prevalent statistical properties of the multivariate Rayleigh, Nakagami-m, Weibull and generalized Gamma (ΓG) distributions with various forms of correlation are summarized. Moreover, their capabilities of being utilized for the performance study of SDRs operating over correlated SSF are described. Next, by presenting a new methodology for generating arbitrarily correlated and not necessarily identically distributed (ID) ΓG RVs that is based on arbitrarily correlated Gaussian RVs and the special class of Householder matrices for tridiagonalizing the correlation matrix (CM) of Gaussian RVs, a closed-form upper bound expression for the joint probability density function (PDF) and an analytical upper bound expression in infinite series form for the joint cumulative distribution function (CDF) of arbitrarily correlated and not necessarily ID ΓG RVs are derived. The proposed upper bounds contain several known mathematical expressions for the joint PDF and CDF as special cases. In addition, by approximating the CM of arbitrarily correlated Gaussian RVs with the special class of Green’s matrices, a closed-form approximate expression for the joint PDF and an analytical approximate expression in infinite series form for the joint CDF of arbitrarily correlated and not necessarily ID ΓG RVs are obtained. Furthermore, analytical expressions in infinite series form for the most prevalent statistical properties of the trivariate ΓG distribution with an arbitrary CM and not necessarily ID RVs as well as of the multivariate ΓG distribution with a constant CM and not necessarily ID RVs are presented. The proposed analytic mathematical expressions of all forms for the PDF and CDF of the multivariate ΓG distribution are used for the performance study of selection diversity (SD), maximal-ratio diversity (MRD), and switch-and-examine diversity (SED) receivers over various arbitrarily correlated SSF channels. Firstly, analytical upper bound expressions for the outage probability (OP), average symbol error probability (ASEP) for several modulation formats, and average channel capacity (ACC) in Shannon’s sense of SD receivers operating over arbitrarily correlated and not necessarily ID ΓG fading are derived. Moreover, analytical expressions for the same performance criteria of triple-branch SD receivers as well as analytical approximate expressions for the performance criteria of multibranch SD receivers are presented. Next, by obtaining new analytic mathematical expressions in infinite series form for the most prevalent statistical properties of the sum of any number of arbitrarily correlated and ID Gamma RVs, analytical expressions for the OP, ASEP for several modulation formats, and ACC in Shannon’s sense of multibranch MRD receivers operating over arbitrarily correlated and ID Nakagami-m fading are derived. For the same fading conditions, analytical expressions in infinite series form for the OP and ASEP for several modulation formats of multibranch SED receivers are presented. The tightness of the proposed upper bounds for the performance criteria of multibranch SD, MRD, and SED receivers in various arbitrarily correlated SSF environments, the correctness of the analytical expressions for the same criteria, and the accuracy of the proposed approximations for them are studied in depth through comparisons between numerically evaluated results for the expressions and equivalent results obtained by means of computer simulations that were implemented for this purpose.