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.

Collaborative Beamforming (CB) has been introduced in Wireless Sensor Networks (WSNs) context as a long-distance and power-efficient communication scheme. One challenge for CB is the randomness of sensor node locations where different network realizations result in different CB beampatterns. First, we study the effect of sensor node spatial distribution on the CB beampattern. The characteristics of the CB beampattern are derived for circular Gaussian distributed sensor nodes and compared with the case of uniform distributed sensor nodes. It is shown that the mainlobe behavior of the CB beampattern is essentially deterministic. This suggests that the average beampattern characteristics are suitable for describing the mainlobe of a sample beampattern. However, the CB beampattern sidelobes are random and highly depends on the particular sensor node locations. Second, we introduce the multi-link CB and address the problem of random sidelobes where high level sidelobes can cause unacceptable interference to unintended Base Stations or Access Points (BSs/APs). Centralized sidelobe control techniques are impractical for distributed sensor nodes because of the associated communication overhead for each sensor node. Therefore, we propose a node selection scheme as an alternative to the centralized sidelobe control which aims at minimizing the interference at unintended BSs/APs. Our algorithm is based on the use of the inherent randomness of the channels and a low feedback that approves/rejects tested random node combinations. The performance of the proposed algorithm is analyzed in terms of the average number of trials and the achievable interference suppression and transmission rate. Finally, we study CB with power control aiming at prolonging the lifetime of a cluster of sensor nodes in the WSN. The energy available at different sensor nodes may not be the same since different sensor nodes may perform different tasks and not equally frequently. CB with power control can be used to balance the individual sensor nodes' lifetimes. Thus, we propose a distributed algorithm for CB with power control that is based on the Residual Energy Information (REI) at each sensor node while achieving the required average SNR at the BS/AP. The effectiveness of the proposed CB with power control is illustrated by simulations. / Communications

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