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Robust Beamforming for Wireless Information and Power Transmission (1210.5814v1)

Published 22 Oct 2012 in cs.IT and math.IT

Abstract: In this letter, we study the robust beamforming problem for the multi-antenna wireless broadcasting system with simultaneous information and power transmission, under the assumption of imperfect channel state information (CSI) at the transmitter. Following the worst-case deterministic model, our objective is to maximize the worst-case harvested energy for the energy receiver while guaranteeing that the rate for the information receiver is above a threshold for all possible channel realizations. Such problem is nonconvex with infinite number of constraints. Using certain transformation techniques, we convert this problem into a relaxed semidefinite programming problem (SDP) which can be solved efficiently. We further show that the solution of the relaxed SDP problem is always rank-one. This indicates that the relaxation is tight and we can get the optimal solution for the original problem. Simulation results are presented to validate the effectiveness of the proposed algorithm.

Citations (362)

Summary

  • The paper presents a robust beamforming design that optimizes simultaneous wireless information and power transmission under worst-case CSI uncertainties.
  • It reformulates the nonconvex beamforming problem into an SDP through semidefinite relaxation, ensuring a tight, rank-one solution for global optimality.
  • Simulation results demonstrate that the robust design significantly outperforms non-robust methods by maximizing energy efficiency and achieving reliable data rates under channel errors.

Robust Beamforming for Wireless Information and Power Transmission

The paper presented by Xiang and Tao investigates a robust beamforming approach for multi-antenna wireless broadcasting systems that focus on simultaneous information and power transmission. These systems face challenges due to imperfect channel state information (CSI) and the aim is to design a beamforming strategy that maximizes energy harvested by a receiver while maintaining minimal data rate thresholds for information receivers across all potential channel uncertainties.

Problem Context and Formulation

In contemporary wireless networks, extending operational time for energy-constrained devices through energy harvesting while transmitting data is essential. Traditional approaches assume perfect CSI, which is rarely available in practice due to estimation errors and feedback delays. This paper, therefore, adopts a worst-case deterministic model for CSI, treating CSI errors as bounded variations rather than stochastic distributions. Such a model ensures a robust performance across all feasible CSI variations, targeting both energy maximization and quality of service (QoS) reliability.

The system considered is a three-node model comprising a transmitter with multiple antennas and two single-antenna receivers, one for information and the other for energy. The challenge lies in the non-convex nature of the problem, as it involves an infinite number of constraints due to the continuous spectrum of possible CSI deviations.

Methodology and Solution Approach

The authors leverage semidefinite programming (SDP) to reformulate this nonconvex problem into a tractable form. The transformation utilizes semidefinite relaxation (SDR), transforming the beamforming optimization into a solvable SDP problem. The distinct aspect demonstrated here is that the SDR leads to a rank-one solution, a property not always applicable in such relaxations. This indicates that the relaxation is tight, and the globally optimal solution can be derived directly from the SDP framework.

The primary steps include reformulating objective functions and constraints using triangle inequality and Cauchy-Schwarz inequality, ensuring constraints hold for every possible deviation within the CSI error bounds. Consequently, the problem is expressed in terms of quadratic constraints and solved using convex optimization techniques.

Simulation Results

The paper reports simulation results confirming the feasibility and efficiency of the proposed method. For various levels of CSI uncertainty, the robust design consistently outperforms non-robust designs, especially for higher data rate targets. The analysis reveals little performance degradation under small CSI errors, demonstrating the robustness of the beamforming design when channel uncertainties are restrained.

Moreover, the results confirm that using non-robust designs without accommodating channel uncertainties significantly increases the likelihood of failing to meet information rate demands. The computational approach is shown to efficiently handle channel error bounds, maximizing harvested energy without increasing outage rates.

Implications and Future Directions

The research contributes a rigorous solution to the beamforming problem in simultaneous wireless information and power transmission (SWIPT) settings, ensuring robustness against idealized CSI assumptions. The secure fallback of achieving a rank-one solution through SDP solidifies its practical applicability, making it favorable for implementation in wireless protocols where energy harvesting is pivotal.

Future research might explore extensions to more complex network topologies involving multiple information and energy receivers or dynamic channel models. Investigating the integration of these robust models with emerging communication standards like 5G, which inherently seek efficiency and robustness, could also prove beneficial. Additionally, this methodology could be adapted for adaptive networks that dynamically adjust to real-time channel variations and feedback mechanisms, fostering further gains in both efficiency and robustness.

This paper offers insightful contributions to beamforming design, presenting a solution that aligns with the goal of scalable and resilient wireless networks incorporating energy harvesting technologies.