The use of wireless communication techniques and network centric topologies for portable communication networks and platforms makes it important to investigate new distributed beamforming techniques. Platforms such as micro air vehicles (MAVs), unattended ground sensors (UGSs), and unpiloted aerial vehicles (UAVs) can all benefit from advances in this area by enabling advantages in stealth, enhanced survivability, and maximum maneuverability. Collaborative beamforming is an example of a new technique to utilize these systems which uses a randomly distributed antenna array with a fitting phase coefficient for the elements. In this example, the radiated signal power of each element is coherently added in the far-field region of a specified target direction with net destructive interference occurring in all other regions to suppress sidelobe behavior. A wide variety of topologies can be used to confine geometrically these mobile random arrays for analysis. The distribution function for these topologies must be able to generalize the randomness within the geometry. Gaussian and Uniform distributions are investigated in this analysis, since they provide a way to calculate the statistically averaged beampattern for linear, planar (square and circular), and volumetric (cubical, cylindrical, and spherical) geometries. They are also of practical interest since the impact of array topology on the beampattern can typically be described in closed form. A rigorous analysis is presented first for disc-shaped topologies to motivate the discussion on random array properties and provide several new insights into their behavior. The analyses of volumetric geometries which are of interest to this work are drawn from this planar topology to provide a tractable and coherent discussion on the properties of more complex geometries. This analysis considers Normal and Gaussian distributed array element populations to derive the average beampattern, sidelobe behavior, beamwidth, and directivity. The beampattern is also examined in a similar manor for circular and spherical arrays with a truncated Gaussian distribution. A summary of the random array analysis and its results concludes this thesis.

The concept of cooperation in communications has drawn a lot of research attention in recent years due to its potential to improve the efficiency of wireless networks. This new form of communications allows some users to act as relays and assist the transmission of other users' information signals. The aim of this thesis is to apply optimization techniques in the design of multi-relay wireless networks employing cooperative communications. In general, the thesis is organized into two parts: ``Distributed space-time coding' (DSTC) and ``Distributed beamforming', which cover two main approaches in cooperative communications over multi-relay networks. <br><br> In Part I of the thesis, various aspects of distributed implementation of space-time coding in a wireless relay network are treated. First, the thesis proposes a new fully-diverse distributed code which allows noncoherent reception at the destination. Second, the problem of coordinating the power allocation (PA) between source and relays to achieve the optimal performance of DSTC is studied and a novel PA scheme is developed. It is shown that the proposed PA scheme can obtain the maximum diversity order of DSTC and significantly outperform other suboptimal PA schemes. Third, the thesis presents the optimal PA scheme to minimize the mean-square error (MSE) in channel estimation during training phase of DSTC. The effect of imperfect channel estimation to the performance of DSTC is also thoroughly studied. <br><br> In Part II of the thesis, optimal distributed beamforming designs are developed for a wireless multiuser multi-relay network. Two design criteria for the optimal distributed beamforming at the relays are considered: (i) minimizing the total relay power subject to a guaranteed Quality of Service (QoS) measured in terms of signal-to-noise-ratio (SNR) at the destinations, and (ii) jointly maximizing the SNR margin at the destinations subject to power constraints at the relays. Based on convex optimization techniques, it is shown that these problems can be formulated and solved via second-order conic programming (SOCP). In addition, this part also proposes simple and fast iterative algorithms to directly solve these optimization problems.

The concept of cooperation in communications has drawn a lot of research attention in recent years due to its potential to improve the efficiency of wireless networks. This new form of communications allows some users to act as relays and assist the transmission of other users' information signals. The aim of this thesis is to apply optimization techniques in the design of multi-relay wireless networks employing cooperative communications. In general, the thesis is organized into two parts: ``Distributed space-time coding' (DSTC) and ``Distributed beamforming', which cover two main approaches in cooperative communications over multi-relay networks. <br><br> In Part I of the thesis, various aspects of distributed implementation of space-time coding in a wireless relay network are treated. First, the thesis proposes a new fully-diverse distributed code which allows noncoherent reception at the destination. Second, the problem of coordinating the power allocation (PA) between source and relays to achieve the optimal performance of DSTC is studied and a novel PA scheme is developed. It is shown that the proposed PA scheme can obtain the maximum diversity order of DSTC and significantly outperform other suboptimal PA schemes. Third, the thesis presents the optimal PA scheme to minimize the mean-square error (MSE) in channel estimation during training phase of DSTC. The effect of imperfect channel estimation to the performance of DSTC is also thoroughly studied. <br><br> In Part II of the thesis, optimal distributed beamforming designs are developed for a wireless multiuser multi-relay network. Two design criteria for the optimal distributed beamforming at the relays are considered: (i) minimizing the total relay power subject to a guaranteed Quality of Service (QoS) measured in terms of signal-to-noise-ratio (SNR) at the destinations, and (ii) jointly maximizing the SNR margin at the destinations subject to power constraints at the relays. Based on convex optimization techniques, it is shown that these problems can be formulated and solved via second-order conic programming (SOCP). In addition, this part also proposes simple and fast iterative algorithms to directly solve these optimization problems.

This dissertation focuses on an efficient cooperative communication method for wireless ad hoc networks. Typically, performance enhancement via cooperative communications can be achieved at the cost of other system resources such as additional bandwidth, transmit power, or more complex synchronization methods between cooperating signals. However, the proposed ooperative transmission scheme in this research utilizes system resources more efficiently by reducing the redundant and wasteful cooperating signals typically required, while maintaining the desired performance improvement. There are four main results in this dissertation. First, an efficient cooperative retransmission scheme is introduced to increase bandwidth efficiency by reducing wasteful cooperating signals. The proposed cooperative transmission method does not require any additional information for cooperation. Furthermore, we ensure good quality for the cooperating signals through a simple yet effective selection procedure. Multiple cooperating nodes can be involved in the cooperation without prior planning via distributed beamforming. The proposed cooperative retransmission scheme outperforms traditional retransmission by the source as well as other cooperative methods in terms of delay and packet error rate (PER). Secondly, the outage probabilities of the cooperative retransmission scheme are analyzed for both the perfect synchronization case and when offset estimation is performed for distributed beamforming. The performance with offset estimation is close to the perfect synchronization case, especially for short data packets. A low-rate feedback channel is introduced to adjust the phase shift due to channel variation and the residual frequency offset. It is shown that substantial gain can be achieved with a low-rate feedback channel, even for long data packets. Third, the throughput efficiency and average packet delay of the proposed cooperative retransmission scheme are analyzed using a two-state Markov model for both a simple automatic repeat request (ARQ) and a hybrid ARQ technique. The benefits of the cooperative ARQ approach are also verified in a multihop network with random configurations when there are concurrent packet transmissions. The average transmit power for the cooperating signals is also investigated in the proposed cooperative transmission scheme with various power control approaches. Finally, cooperative multiple input multiple output (MIMO) systems are examined, mainly focusing on power allocation methods to increase overall channel capacity. An efficient and simple power allocation method at the cooperating node is proposed which can be used for an arbitrary number of antennas without any additional information. / Ph. D.

Σκοπός αυτής της εργασίας είναι η μελέτη τεχνικών κατανεμημένου προσανατολισμού σε πραγματικές συνθήκες. Πιο συγκεκριμένα σε αυτά στα συστήματα θεωρείται ότι ο κόμβος-πομπός δεν έχει καλή σύνδεση με το δέκτη και κατά συνέπεια δεν μπορεί να επικοινωνήσει απευθείας με τον κόμβο-δέκτη χωρίς δραματική αύξηση της ενέργειας μετάδοσης. Παρόλα αυτά η χρήση κατανεμημένου προσανατολισμού δίνει τη δυνατότητα να βελτιωθεί σημαντικά η κατανάλωση ενέργειας. Το σχήμα που θα χρησιμοποιηθεί είναι ενίσχυση και προώθηση (AF) 2 βημάτων, με το οποίο οι συνεργατικοί κόμβοι απλώς ενισχύουν και στην συνέχεια επαναμεταδίδουν το μήνυμα. Συνεπώς, ζητούμενο είναι η εύρεση των μιγαδικών βαρών με τα οποία πρέπει ο κάθε συνεργαζόμενος κόμβος χωριστά να ενισχύσει το σήμα. Οι τεχνικές που θα χρησιμοποιηθούν έχουν ως κριτήρια την ελαχιστοποίηση της ενέργειας μετάδοσης με ταυτόχρονη ικανοποίηση του SNR, μεγιστοποίηση του SNR με περιορισμένη ολική ενέργεια μετάδοσης και μεγιστοποίηση του SNR με περιορισμένη ενέργεια μετάδοσης ανά συνεργαζόμενο κόμβο. Το πρώτο κριτήριο θα εξεταστεί, επίσης, και σε συστήματα με πολλαπλούς πομπούς και δέκτες. Λόγω της φύσης του προβλήματος, ο κατανεμημένος προσανατολισμός αναμένεται να έχει μεγάλη απήχηση σε συστήματα με πολλούς διασκορπιστές και εμπόδια, όπως σε ένα αστικό περιβάλλον, και, επομένως, είναι λογικό να θεωρηθεί ότι τα κανάλια του συστήματος είναι Rayleigh, δηλαδή ασυσχέτιστα χωρίς οπτική επαφή (LOS). Για να προσομοιωθεί το σύστημα σε πραγματικές συνθήκες οι μέθοδοι που θα υλοποιήσουμε στην εργασία χρησιμοποιούν τα στατιστικά του καναλιού. Επιπλέον, η εκτίμηση καναλιού εφόσον θεωρούμε ότι έχουμε Gaussian λευκό θόρυβο θα γίνει με την χρήση του βέλτιστου γραμμικού εκτιμητή (BLUE). Η επίδραση της εκτίμησης του καναλιού θα μελετηθεί για δύο περιπτώσεις: με αμοιβαία και χωρίς αμοιβαία κανάλια. / The purpose of this thesis is the study of methods of distributed beamforming under real circumstances. More specifically, these systems are considered that the transmitter must increase tremendously the required transmit energy to communicate with the receiver. However the use of the distributed beamforming allows the system to improve the energy consumption. The scheme that is used from relays is amplify and forward of two steps, where the relays only amplify and then forward the message to the destination. That is, the purpose is to find the complex weights to be used by the corresponding relay so as to amplify the message of the transmitter. The methods that are implemented have as criterions the minimization of transmit energy while satisfying the SNR, maximization of SNR while limiting the system's transmit energy and maximization of SNR while limiting transmit energy of each relay individually. The first criterion is also studied at systems with more than one pair transmitter-receiver. Due to the nature of the problem, distributed beamforming is expected to be used at environments with many obstacles and scatterers, like urban environment, and so it is rationale to suppose that the channels should be Rayleigh, meaning uncorrelated without line of sight. To simulate the system under real circumstances the methods that we will implement shall use the second order statistics of the channels. Moreover, due to Gaussian white noise, channels are estimated using the Best Linear Unbiased Estimator. The impact of channel estimation is studied in two cases: "reciprocal" and "not reciprocal".