Massive wireless energy transfer with statistical CSI beamforming

Wireless energy transfer (WET) is a promising solution to enable massive machine-type communications (mMTC) with low-complexity and low-powered wireless devices. Given the energy restrictions of the devices, instant channel state information at the transmitter (CSIT) is not expected to be available in practical WET-enabled mMTC. However, because it is common that the terminals appear spatially clustered, some degree of spatial correlation between their channels to the base station (BS) is expected to occur. The paper considers a massive antenna array at the BS for WET that only has access to i) the first and second order statistics of the Rician channel component of the multiple-input multiple-output (MIMO) channel and also to ii) the line-of-sight MIMO component. The optimal precoding scheme that maximizes the total energy available to the single-antenna devices is derived considering a continuous alphabet for the precoders, permitting any modulated or deterministic waveform. This may lead to some devices in the clusters being assigned a low fraction of the total available power in the cluster, creating a rather uneven situation among them. Consequently, a fairness criterion is introduced, imposing a minimum amount of power allocated to the terminals. A piece-wise linear harvesting circuit is considered at the terminals, with both saturation and a minimum sensitivity, and a constrained version of the precoder is also proposed by solving a non-linear programming problem. A paramount benefit of the constrained precoder is the encompassment of fairness in the power allocation to the different clusters. Moreover, given the polynomial complexity increase of the proposed unconstrained precoder, and the observed linear gain of the system's available sum-power with an increasing number of antennas at the ULA, the use of massive antenna arrays is desirable.