⚡ electrical engineering

LAWNs Meet SWIPT: Beamforming and Power Splitting Optimization for Predictive Control

This paper proposes a two-stage optimization framework combining model predictive control with semidefinite relaxation and successive convex approximation to jointly optimize beamforming and power splitting in SWIPT-enabled low-altitude wireless networks, ensuring energy sustainability and collision-free trajectory tracking for uncrewed aircraft systems navigating mobile no-fly zones.

Original authors: Jun Wu, Wenchao Liu, Weijie Yuan, Nanchi Su

Published 2026-06-23

📖 5 min read🧠 Deep dive

CC0 1.0

Original authors: Jun Wu, Wenchao Liu, Weijie Yuan, Nanchi Su

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a busy, low-altitude sky filled with a fleet of delivery drones (UASs). These drones are like tiny, battery-powered birds that need two things to survive and do their jobs: instructions on where to fly and energy to keep their batteries charged.

Usually, these two needs are handled separately: a ground station sends radio waves to tell the drone where to go, and a separate charger (or a solar panel) gives it power. But this new paper proposes a clever "two-in-one" solution called SWIPT (Simultaneous Wireless Information and Power Transfer). Think of it like a ground station sending out a single, magical radio beam that acts as both a GPS navigator and a wireless charger at the same time.

Here is the breakdown of the paper's ideas using simple analogies:

1. The Problem: A Sky Full of Moving Obstacles

The sky isn't empty. It has "No-Fly Zones" (NFZs)—areas where drones aren't allowed to go. These could be static, like a tall building, or mobile, like a temporary zone created by a police helicopter or an emergency vehicle moving around.

The Challenge: If the drone's battery dies, it crashes. If it gets the wrong instructions or loses the signal, it might fly into a forbidden zone. The drone needs to stay on a perfect path while constantly recharging, all while dodging moving obstacles.
The Trade-off: The radio beam carries both data (instructions) and energy. If the drone uses too much of the signal to charge its battery, it might not have enough "clarity" to hear the instructions. If it uses too much to listen, it won't get enough power. It's like trying to drink from a firehose while also trying to listen to a whisper; you have to split the flow perfectly.

2. The Solution: The "Fluid Flow" Map

To figure out the safest path through a sky with moving obstacles, the authors didn't just draw lines on a map. Instead, they used Stream Function Theory.

The Analogy: Imagine the sky is a giant swimming pool. The "No-Fly Zones" are solid rocks or moving fish in the water. The drone is a leaf floating on the surface.
How it works: The authors created a mathematical "current" (like water flowing around rocks). The leaf (drone) naturally follows the smooth curves of the water, which automatically bend around the rocks (obstacles) without ever hitting them. Even if a rock moves, the water current shifts instantly, guiding the leaf around it safely. This creates a smooth, collision-free "highway" for the drone to follow.

3. The Brain: A Smart Controller (MPC)

Once the path is drawn, the drone needs a brain to actually fly it. The paper uses a method called Model Predictive Control (MPC).

The Analogy: Imagine driving a car. A simple driver just looks at the road right in front of them and steers. But a predictive driver looks 10 seconds ahead. They see a curve coming up, so they start slowing down before they reach the curve.
How it works: The ground station (the brain) constantly predicts where the drone will be in the next few seconds. It calculates the perfect steering and speed adjustments to keep the drone on the "water current" path, even if the wind blows or the obstacles move.

4. The Optimization: Balancing the Beam

The hardest part is the math. The ground station has to decide:

How to aim the antenna (Beamforming): Like using a flashlight to shine a tight beam directly at the drone instead of a floodlight.
How to split the signal (Power Splitting): Deciding what percentage of the signal is for "listening" (instructions) and what percentage is for "charging" (energy).

The authors created a two-step recipe to solve this complex puzzle:

Step 1: First, they figure out the perfect steering commands for the drone (ignoring the radio stuff for a moment).
Step 2: Then, they adjust the radio beam and the split ratio to make sure the drone gets enough energy and enough clear instructions to follow those steering commands. They use advanced math tricks (like "relaxing" the problem to make it easier to solve) to find the best balance.

5. The Results

The paper ran computer simulations to test this idea. They compared their "smart, fluid-flow, two-in-one" system against older, dumber methods (like simple steering or random charging).

The Outcome: Their system was much better. The drones stayed on their paths more accurately (less wobble) and harvested significantly more energy. It proved that by treating the "navigation" and "charging" as one single, coordinated problem, you can make drone fleets safer, more efficient, and capable of flying longer without running out of battery.

In short: This paper teaches us how to guide a fleet of drones through a chaotic, obstacle-filled sky by using a single radio beam that acts as both a map and a charger, guided by a mathematical "water current" that naturally steers them around danger.

Technical Summary: Lawns Meet SWIPT: Beamforming and Power Splitting Optimization for Predictive Control

Problem Statement
This paper addresses the challenge of sustaining and controlling Uncrewed Aircraft Systems (UASs) within Low-Altitude Wireless Networks (LAWNs). Specifically, it investigates a system where a multi-antenna Base Station (BS) must simultaneously deliver control information and wireless energy to a fleet of UASs via Simultaneous Wireless Information and Power Transfer (SWIPT). The system operates under two critical constraints:

Dynamic Safety Constraints: UASs must navigate complex, shared airspace containing multiple mobile No-Fly Zones (NFZs) (e.g., restricted military areas or temporary flight restrictions) while tracking predefined reference trajectories.
Resource and Stability Constraints: The UASs are battery-limited and rely on harvested energy for long-term operation. Furthermore, the control loop is closed over wireless links subject to finite blocklength (FBL) transmission constraints, where communication quality directly impacts closed-loop stability and tracking performance.

The core problem is a joint optimization of transmit beamforming vectors, power splitting (PS) ratios, and control inputs to minimize the trajectory tracking error per unit of harvested energy, while ensuring system stability and collision avoidance.

Methodology
The authors propose a comprehensive framework comprising three main components:

Reference Trajectory Generation via Stream Function Theory:
To ensure safe navigation in dynamic airspace, the paper utilizes ideal fluid flow theory. A stream function is constructed to generate smooth, collision-free reference trajectories.
- Static NFZs: Modeled using doublet flows to create streamlines that naturally bypass circular obstacles.
- Mobile NFZs: Addressed by introducing a vortex flow component centered at the moving obstacle. This induces a rotational flow field that guides UASs to bypass mobile zones (either clockwise or counter-clockwise) based on the relative velocity and direction.
- The resulting stream function provides an analytical guidance field that inherently satisfies collision avoidance constraints with low computational complexity.
System Modeling and Problem Formulation:
- UAS Dynamics: The kinematic model of the UAS is linearized around a local operating point and discretized using the forward Euler method to form a state-space model suitable for Model Predictive Control (MPC).
- SWIPT Model: The received signal is split into an information decoding (ID) stream and an energy harvesting (EH) stream using a PS ratio $\alpha_k$ . The system employs Finite Blocklength (FBL) transmission to characterize the rate-reliability-latency tradeoff for short control packets.
- Optimization Objective: A real-time optimization problem is formulated to minimize the ratio of total control cost (tracking error) to total harvested energy. Constraints include system dynamics, actuator limits, a minimum stabilizing data rate (derived from Theorem 1), maximum transmit power, and minimum harvested power requirements.
Two-Stage Optimization Framework:
The formulated problem is non-convex and intractable. The authors propose a two-stage solution:
- Stage 1 (Control Input Design): The control inputs are optimized independently using a standard Quadratic Programming (QP) approach. An augmented state-space model is introduced to optimize control increments rather than absolute values, ensuring smooth control actions.
- Stage 2 (Beamforming and PS Ratio Design): An Alternating Optimization (AO) framework is employed to jointly optimize the transmit beamforming vectors and PS ratios.
  - Semidefinite Relaxation (SDR): The rank-one constraint on the beamforming covariance matrix is relaxed. The authors prove that the relaxation is tight, guaranteeing a rank-one optimal solution.
  - Successive Convex Approximation (SCA): Non-convex constraints related to the FBL rate and SINR are approximated using convex upper bounds.
  - The algorithm iterates between optimizing beamforming (given fixed PS ratios) and optimizing PS ratios (given fixed beamforming) until convergence.

Key Contributions

Stream Function-Based Navigation: Development of a stream function-based reference path design that provides analytical, smooth guidance fields capable of handling both static and mobile NFZs with low computational complexity, enabling real-time applicability.
Joint Control and Energy Optimization: Formulation of a real-time optimization problem that minimizes tracking error per harvested energy under FBL constraints. This explicitly balances wireless control performance (stability) with energy sustainability.
Efficient Algorithmic Framework: Proposal of a two-step optimization framework combining MPC-based control design with an iterative SDR and SCA-based algorithm for beamforming and power splitting. The paper proves the tightness of the SDR relaxation and the convergence of the proposed algorithm.

Simulation Results
Extensive numerical simulations validate the proposed design against benchmark schemes (PID, LQR, MRT beamforming, random PS ratio, and fairness schemes):

Trajectory Tracking: The proposed MPC-based approach significantly outperforms PID and LQR in terms of Root Mean Square Error (RMSE), particularly in dynamic environments with mobile NFZs. The ability to anticipate future deviations allows for more robust tracking.
Convergence: The proposed iterative algorithm converges rapidly (within 10 iterations).
Energy and Performance Trade-off: The proposed scheme achieves a superior balance between tracking accuracy and harvested energy compared to benchmarks.
- Increasing transmit power and the number of antennas improves harvested energy for all schemes, but the proposed method consistently yields the highest values.
- There is a clear trade-off between the required Spectral Efficiency (SE) threshold and harvested energy; stricter stability requirements (higher SE) reduce available energy for harvesting.
Robustness: The method maintains performance even as UASs move further from the BS or encounter sharp turns required to avoid mobile NFZs.

Significance
The paper claims that its proposed design offers a viable solution for the sustainable implementation of SWIPT-enabled LAWNs. By unifying collision-free path planning for dynamic environments with joint wireless control and energy management, the work addresses the critical limitations of battery-constrained UASs operating in complex, regulated airspace. The results demonstrate that the proposed framework significantly outperforms existing benchmark schemes in both tracking accuracy and energy sustainability, validating its potential for practical deployment in future 6G low-altitude networks.

1. The Problem: A Sky Full of Moving Obstacles

2. The Solution: The "Fluid Flow" Map

3. The Brain: A Smart Controller (MPC)

4. The Optimization: Balancing the Beam

5. The Results

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