A dual-hop amplify-and-forward MIMO cooperative beamformer in distributed wireless sensor networks

In this paper, we propose a cooperative beamforming (CB) technique for dual-hop amplify-and-forward communication in WSNs with one source, N -1 interferences, and K relay nodes. First, an optimal beamformer is obtained that maximizes the signal-to-interference-plus-noise ratio at the intended receiver in the far-field subject to the following constraints: 1) The relay nodes total transmit power is bounded; and 2) the received power from the N transmitters at L - 1 unintended receivers in the far-field is zero. It is shown that the optimal beamformer can only be implemented if each relay node knows the locations and the backward channels of all other relay nodes in the network. As this knowledge is not typically available at nodes in WSNs, we use a technique to approximate the optimal beamforming coefficients with quantities that depend only on the locally-available information at each individual relay node. The average beampattern expression of the proposed CB technique is then derived and its properties are analyzed. In particular, it is shown that the average gain of the beamformer linearly increases with K in the direction of the intended receiver while remaining fixed in the directions of the unintended receivers.