[Paper Review] Joint MOO of Transmit Precoding and Receiver Design in a Downlink Time Switching MISO SWIPT System

Nafiseh Janatian, Ivan Stupia+1 more|arXiv (Cornell University)|Oct 26, 2016

Energy Harvesting in Wireless Networks17 references3 citations

TL;DR

This paper proposes a multi-objective optimization (MOO) framework for joint transmit precoding and time-switching (TS) ratio design in a downlink MISO SWIPT system with multiple multi-armed access points and single-antenna users. By using the weighted Chebyshev method to relax a non-convex rank-constrained problem into a non-convex semidefinite program (SDP), and solving it via majorization-minimization, the approach achieves Pareto-optimal trade-offs between data rate and harvested energy, with theoretical proof that the optimal solution satisfies the rank-one constraint.

ABSTRACT

In this paper, we consider a time-switching (TS) co-located simultaneous wireless information and power transfer (SWIPT) system consisting of multiple multi-antenna access points which serve multiple single antenna users. In this scenario, we propose a multi-objective optimization (MOO) framework to design jointly the Pareto optimal beamforming vector and the TS ratio for each receiver. The objective is to maximize the utility vector including the achieved data rates and the harvested energies of all users simultaneously. This problem is a non-convex rank-constrained MOO problem which is relaxed and transformed into a non-convex semidefinite program (SDP) based on the weighted Chebycheff method. The majorization-minimization algorithm is utilized to solve the nonconvex SDP and the optimal solution is proved to satisfy the rank constraint. We also study the problem of optimizing the beamforming vectors in a fixed TS ratio scenario with the same approach. Numerical results are provided for two coordinated access points with MISO configuration. The results illustrate the trade-off between harvested energy and information data rate objectives and show the effect of optimizing the precoding strategy and TS ratio on this trade-off.

Motivation & Objective

• Address the challenge of balancing information rate and energy harvesting in multi-user downlink MISO SWIPT systems with time-switching receivers.
• Design a joint optimization framework for beamforming vectors and time-switching ratios to maximize both data rates and harvested energy simultaneously.
• Overcome the non-convex, rank-constrained nature of the multi-objective problem through relaxation and transformation into a non-convex SDP.
• Ensure the optimal solution maintains the required rank-one structure for beamformers using theoretical analysis and algorithmic enforcement.
• Evaluate the impact of joint optimization on the trade-off between spectral efficiency and energy harvesting performance.

Proposed method

• Formulate a multi-objective optimization (MOO) problem to maximize the utility vector comprising data rates and harvested energies across all users.
• Apply the weighted Chebyshev method to transform the non-convex, rank-constrained MOO problem into a non-convex semidefinite program (SDP).
• Utilize the majorization-minimization (MM) algorithm to iteratively solve the non-convex SDP, ensuring convergence to a stationary point.
• Prove that the optimal solution of the relaxed problem satisfies the rank-one constraint for beamformers, ensuring physical feasibility.
• Derive Karush-Kuhn-Tucker (KKT) conditions and analyze slackness to identify the active objectives and determine the optimal Lagrange multipliers.
• Establish that the dual variables enforce rank-one solutions via the rank-null space theorem, confirming beamformer structure.

Experimental results

Research questions

• RQ1 How can the Pareto-optimal trade-off between information rate and energy harvesting be achieved in a multi-user MISO SWIPT system with time-switching receivers?
• RQ2 What is the impact of jointly optimizing beamforming vectors and time-switching ratios on the system's performance trade-off?
• RQ3 Can the non-convex, rank-constrained MOO problem in SWIPT be effectively relaxed and solved via semidefinite programming and majorization-minimization?
• RQ4 Under what conditions does the optimal solution of the relaxed problem maintain the required rank-one structure for beamformers?
• RQ5 How does the proposed joint optimization compare to fixed time-switching ratio designs in terms of performance trade-offs?

Key findings

• The proposed MOO framework successfully achieves a Pareto-optimal trade-off between data rate and harvested energy in a downlink MISO SWIPT system.
• The majorization-minimization algorithm converges to a solution that satisfies the rank-one constraint for all beamformers, ensuring physical feasibility.
• Theoretical analysis confirms that the optimal dual variables enforce a rank-one structure on the beamforming matrices, with rank(𝒳ₗⱼ) = 1 for all l, j.
• Numerical results demonstrate that joint optimization of precoding and TS ratio significantly improves the rate-energy trade-off compared to fixed-configuration designs.
• The optimal solution is characterized by a single active objective per user, determined by the minimum of the normalized rate and energy metrics.
• The method achieves a balanced performance improvement across users, with the beamforming design effectively managing interference for both information decoding and energy harvesting.