Robust beamforming and power splitting design in MISO SWIPT downlink system

• Published in: IET communications Vol. 10; no. 6; pp. 691 - 698
• Main Authors: Chu, Zheng, Zhu, Zhengyu, Xiang, Weichen, Hussein, Jamal
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 14.04.2016
• Subjects: array signal processing; Beamforming; Bernstein‐type inequality; channel state information; Channels; concave programming; conditional value‐at‐risk functional; convex problem; convex programming; covariance matrices; covariance matrix; Design engineering; energy harvesting; energy harvesting constraint; Error functions; error mean matrix; error statistics; Gaussian; Gaussian channel uncertainty model; Gaussian channels; Gaussian distribution; Gaussian error function; Inequalities; minimisation; MISO SWIPT downlink system; multiple‐input‐single‐output downlink system; nonconvex problem; Optimization; probability constraint; radio transmitters; radiofrequency power transmission; random distribution; random processes; robust beamforming design; robust power minimisation problem; robust power splitting design; semidefinite relaxation; signal‐to‐inference‐plus‐noise ratio; simultaneous wireless information and power transfer; SINR constraint; telecommunication power management; Uncertainty; wireless channels; simultaneous wireless information and power transfer; Bernstein-type inequality; Gaussian error function; Gaussian channel uncertainty model; Gaussian distribution; channel state information; robust power splitting design; radiofrequency power transmission; covariance matrix; multiple-input-single-output downlink system; semidefinite relaxation; SINR constraint; robust beamforming design; random distribution; wireless channels; MISO SWIPT downlink system; robust power minimisation problem; concave programming; Gaussian channels; array signal processing; error statistics; error mean matrix; covariance matrices; telecommunication power management; signal-to-inference-plus-noise ratio; random processes; energy harvesting; convex programming; probability constraint; nonconvex problem; conditional value-at-risk functional; energy harvesting constraint; convex problem; radio transmitters; minimisation
• ISSN: 1751-8628; 1751-8636; 1751-8636
• DOI: 10.1049/iet-com.2015.0475

In this study, the authors consider simultaneous wireless information and power transfer (SWIPT) in a multiple-input-single-output (MISO) downlink system, where power splitting scheme is considered for each user of this system. Since channel state information of each user cannot be available at the transmitter, robust beamforming for SWIPT in the MISO downlink system is presented by incorporating with different types of channel uncertainty models. The authors first formulate the robust power minimisation problem subject to the signal-to-inference-plus-noise ratio (SINR) and energy harvesting (EH) constraints by incorporating two Gaussian channel uncertainties. The original problem is not convex in terms of channel uncertainties, and cannot be solved efficiently. The authors employ the well-known Bernstein-type inequality and Gaussian error function to make probability based constraints tractable, respectively, in order to recast the original problem as the convex form. Moreover, the robust power minimisation problem with the probability based SINR and EH constraints is formulated by incorporating random distribution with known error mean and covariance matrix. By exploiting conditional value-at-risk functional and semi-definite relaxation, this optimisation problem is relaxed as the convex form. Finally, numerical results are provided to validate the performance of these proposed robust schemes.