Collaborative Null-Steering Beamforming for Uniformly Distributed Wireless Sensor Networks

Null-steering transmit beamformers aim to maximize the received signal power in the direction of the intended receiver while substantially reducing the power impinging on the unintended receivers located in other directions. The existing null-steering beamformers may not be directly applied in wireless sensor networks (WSNs) as they do not conform with the decentralized nature of WSNs and require every node to be aware of the locations of all other nodes in the network. This manuscript presents a novel collaborative null-steering beamformer that can be implemented in uniformly distributed WSNs in which each node is oblivious of other nodes' locations. The average beampattern expression of the proposed beamformer is derived and it is shown that the beampattern associated with any arbitrary realization of the nodes' locations converges with probability one to the so-obtained average beampattern as the number of collaborating nodes grows large. Properties of the average beampattern are analytically studied. In particular, it is proven that the average gain of the proposed beamformer is inversely proportional to the number of collaborating nodes in the directions of unintended receivers and further, if a mild condition is satisfied, it is approximately equal to that of the collaborative conventional beamformer in the directions with far angular distance from any unintended receiver. It is argued that if virtual unintended receivers are assumed at proper directions, then the proposed collaborative null-steering beamformer can form an average beampattern with sidelobe peaks substantially smaller than those of the average beampattern of the collaborative conventional beamformer. To substantiate this argument, the optimal direction of a virtual unintended receiver is obtained such that its associated collaborative null-steering beamformer forms an average beam-pattern with minimal largest side-lobe peak. Depending on the number of collaborating nodes, it is further shown that the largest average sidelobe peak of the latter beamformer is up to 6.6 (dB) less than that of the collaborative conventional beamformer.