  For multi-user transmissions over MIMO interference channels, each user
designs the transmit covariance matrix to maximize its information rate. When
passive radio-frequency (RF) energy harvesters are present in the network, the
transmissions are constrained by both the transmit power limits and the energy
harvesting requirements. A passive RF energy harvester collects the radiated
energy from nearby wireless information transmitters instead of using a
dedicated wireless power source. It needs multiple transmitters to concentrate
their RF radiation on it because typical electric field strengths are weak. In
this paper, strategic games are proposed for the multi-user transmissions.
First, in a non-cooperative game, each transmitter has a best-response strategy
for the transmit covariance matrix that follows a multi-level water-filling
solution. A pure-strategy Nash equilibrium exists. Secondly, in a cooperative
game, there is no need to estimate the proportion of the harvested energy from
each transmitter. Rather, the transmitters bargain over the unit-reward of the
energy contribution. An approximation of the information rate is used in
constructing the individual utility such that the problem of network utility
maximization can be decomposed and the bargaining process can be implemented
distributively. The bargaining solution gives a point of rates that is superior
to the Nash equilibria and close to the Pareto front. Simulation results verify
the algorithms that provide good communication performance while satisfying the
RF energy-harvesting requirements.
