Random Array Theory and Collaborative Beamforming

In wireless sensor networks, the sensor nodes are often randomly situated, and each node is likely to be equipped with a single antenna. If these sensor nodes are able to synchronize, it is possible to beamform by considering sensor nodes as a random array of antennas. Using probabilistic arguments, it can be shown that random arrays formed by dispersive sensors can form nice beampatterns with a sharp main lobe and low sidelobe levels. This chapter reviews the probabilistic analysis of linear random arrays, which dates back to the early work of Y. T. Lo (1964), and then discusses recent work on the statistical analysis of two-dimensional random arrays originally derived in the framework of wireless sensor networks.