# Beamforming Optimization for Full-Duplex Wireless-powered MIMO Systems

## TL;DR

This paper develops optimized beamforming techniques for full-duplex wireless-powered MIMO systems, enhancing energy harvesting and communication efficiency under various CSI availability scenarios.

## Contribution

It introduces a joint optimization method for beamforming and energy harvesting parameters, including a semidefinite relaxation approach and a closed-form zero-forcing solution.

## Key findings

- Proposed methods outperform sub-optimum and half-duplex systems.
- Efficient optimization algorithms achieve near-optimal rate regions.
- The approach adapts to different CSI availability scenarios.

## Abstract

We propose techniques for optimizing transmit beamforming in a full-duplex multiple-input-multiple-output (MIMO) wireless-powered communication system, which consists of two phases. In the first phase, the wireless-powered mobile station (MS) harvests energy using signals from the base station (BS), whereas in the second phase, both MS and BS communicate to each other in a full-duplex mode. When complete instantaneous channel state information (CSI) is available, the BS beamformer and the time-splitting (TS) parameter of energy harvesting are jointly optimized in order to obtain the BS-MS rate region. The joint optimization problem is non-convex, however, a computationally efficient optimum technique, based upon semidefinite relaxation and line-search, is proposed to solve the problem. A sub-optimum zero-forcing approach is also proposed, in which a closed-form solution of TS parameter is obtained. When only second-order statistics of transmit CSI is available, we propose to maximize the ergodic information rate at the MS, while maintaining the outage probability at the BS below a certain threshold. An upper bound for the outage probability is also derived and an approximate convex optimization framework is proposed for efficiently solving the underlying non-convex problem. Simulations demonstrate the advantages of the proposed methods over the sub-optimum and half-duplex ones.