A Distributed Amplify-and-Forward Beamforming Technique in Wireless Sensor Networks

We consider L far-field terminals with one source and L-1 interferences that transmit to a wireless sensor network (WSN) with K uniformly distributed relaying nodes. Each relaying node receives a signal mixture from the L transmitters in the first phase, multiplies it with a properly selected beamforming weight and retransmits the resultant signal to a single receiving terminal in the second phase. The decentralized nature of the WSN dictates every node to compute its beamforming weight based only on its limited locally available information and without the knowledge of the locations and the channels of any other node in the network. Unfortunately, the optimal beamforming weights that maximize the signal-to-interference-plus-noise ratio (SINR) at the receiver cannot be computed locally. To circumvent this problem, we derive accurate local approximates of the SINR-optimal beamforming weights. Our proposed beamforming technique uses the so-obtained locally computable weights and, hence, can be implemented in a distributed fashion. The performance of the proposed distributed beamformer is analyzed both when the directions of the interferences are perfectly known and when they are imperfectly estimated. The advantages of the proposed distributed beamformer in comparison with a conventional distributed beamformer are analytically proved and are further verified by various simulation results.