Multicast Wirelessly Powered Network With Large Number of Antennas via First-Order Method

To prolong the lifetime of energy constrained devices in Internet of Things, devices can harvest wireless energy from the control signal multicast from the access point. Unfortunately, hampered by the path-loss, the efficiency of such multicast wirelessly powered network is low. While large-scale antennas at access point can be used to improve the efficiency, the beamforming design problem in multicast wirelessly powered network is known to be NP-hard, and the traditional difference of convex programming becomes prohibitively time consuming in large-scale settings. On the other extreme, by using the assumption of infinite number of antennas and applying the law of large numbers, simple beamforming solution is possible. However, when applied to scenarios with finite number of antennas, the performance of such asymptotic solution is far from that of difference of convex programming. To resolve this apparent complexity-performance dilemma, this paper develops an algorithm which reduces the computation time by orders of magnitude, while still guaranteeing the same performance compared with the difference of convex programming. In particular, the proposed algorithm consists of two fast-convergent iterative procedures and is guaranteed to obtain a Karush–Kuhn–Tucker solution. Furthermore, in each iteration, the algorithm only requires the computation of inner products between channel vectors and can be run in parallel for all the users. Thus, the complexity scales linearly with the number of antennas at access point. Finally, numerical results validate the performance and the speed of the proposed scheme.