This paper focuses on the problem of joint beamforming control and power allocation in the ad-hoc mmWave network. Over the shared spectrum, a number of multi-input-multi-output links attempt to minimize their supply power by simultaneously finding the locally optimal power allocation and beamformers in a self-interested manner. Our design considers a category of non-convex quality-of-service constraints, which are a function of the coupled strategies adopted by the mutually interfering ad-hoc links. We propose a two-stage, decentralized searching scheme, where the adaptation of power-levels and beamformer filters are performed in two separated sub-stages iteratively at each link. By introducing the analysis based on the generalized Nash equilibrium, we provide the theoretical proof of the convergence of our proposed power adaptation algorithm based on the local best response together with an iterative minimum mean square error receiver. Several transmit beamforming schemes requiring different levels of information exchange are compared. Our simulation results show that with a minimum-level requirement on the channel state information acquisition, a locally optimal transmit filter design based on the optimization of the local signal-to-interference-plus-noise ratio is able to achieve an acceptable tradeoff between link performance and the need for decentralization.
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