  Extremely large-scale array (XL-array) has emerged as a promising technology
to enhance the spectrum efficiency and spatial resolution in future wireless
networks by exploiting massive number of antennas for generating pencil-like
beamforming. This also leads to a fundamental paradigm shift from conventional
far-field communications towards the new near-field communications. In contrast
to the existing works that mostly considered simultaneous wireless information
and power transfer (SWIPT) in the far field, we consider in this paper a new
and practical scenario, called mixed near- and far-field SWIPT, where energy
harvesting (EH) and information decoding (ID) receivers are located in the
near- and far-field regions of the XL-array base station (BS), respectively.
Specifically, we formulate an optimization problem to maximize the weighted
sum-power harvested at all EH receivers by jointly designing the BS beam
scheduling and power allocation, under the constraints on the maximum sum-rate
and BS transmit power. First, for the general case with multiple EH and ID
receivers, we propose an efficient algorithm to obtain a suboptimal solution by
utilizing the binary variable elimination and successive convex approximation
methods. To obtain useful insights, we then study the joint design for special
cases. In particular, we show that when there are multiple EH receivers and one
ID receiver, in most cases, the optimal design is allocating a portion of power
to the ID receiver for satisfying the rate constraint, while the remaining
power is allocated to one EH receiver with the highest EH capability. This is
in sharp contrast to the conventional far-field SWIPT case, for which all
powers should be allocated to ID receivers. Numerical results show that our
proposed joint design significantly outperforms other benchmark schemes without
the optimization of beam scheduling and/or power allocation.
