  The performance of collaborative beamforming is analyzed using the theory of
random arrays. The statistical average and distribution of the beampattern of
randomly generated phased arrays is derived in the framework of wireless ad hoc
sensor networks. Each sensor node is assumed to have a single isotropic antenna
and nodes in the cluster collaboratively transmit the signal such that the
signal in the target direction is coherently added in the far- eld region. It
is shown that with N sensor nodes uniformly distributed over a disk, the
directivity can approach N, provided that the nodes are located sparsely
enough. The distribution of the maximum sidelobe peak is also studied. With the
application to ad hoc networks in mind, two scenarios, closed-loop and
open-loop, are considered. Associated with these scenarios, the effects of
phase jitter and location estimation errors on the average beampattern are also
analyzed.
