Optimizing the Size of an Antenna Array

We analyze the optimal number of sensor nodes that should participate in a beamforming process in order to minimize the energy expended by nodes in a sensor network. As we increase the number of sensor nodes involved in beamforming (for a fixed energy per bit to noise power spectral density required at the receiver), the transmit power of each node is significantly reduced, but the overhead in implementing even a simple collaborative algorithm increases. We specify the optimal number of nodes to use to minimize the total energy expended, and thus extend the lifetime of a sensor network.