⚡ electrical engineering

Point Spread Function Optimization for Communication-assisted UAV-borne MIMO TomoSAR

This paper proposes a joint optimization of UAV formation and offloading power allocation, solved via a particle swarm optimization algorithm, to minimize point spread function sidelobes in communication-assisted UAV-borne MIMO TomoSAR systems for high-quality 3D imaging.

Original authors: Pouya Fakharizadeh, Mohamed-Amine Lahmeri, Gerhard Krieger, Robert Schober

Published 2026-05-27

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CC BY 4.0

Original authors: Pouya Fakharizadeh, Mohamed-Amine Lahmeri, Gerhard Krieger, Robert Schober

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ 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 team of drones flying in a specific formation over a city or a forest. Instead of just taking photos, these drones are equipped with special radar eyes that work together to build a detailed 3D map of the terrain, showing exactly how high trees, buildings, or hills are. This technology is called MIMO TomoSAR.

However, building this 3D map is tricky. The radar signal acts like a flashlight beam. If the beam isn't focused perfectly, it creates "ghosts" or blurry spots around the real objects. In radar terms, these unwanted echoes are called sidelobes. If the sidelobes are too strong, they can hide smaller objects or create fake targets, making the 3D image look messy and confusing.

The goal of this paper is to figure out the perfect flight path and power settings for these drones so that the radar image is as sharp and clean as possible, with the weakest possible "ghosts" (sidelobes).

Here is how the authors solved this puzzle, broken down into simple concepts:

1. The Two-Part Challenge

The team had to solve two problems at once, which are usually hard to balance:

The Sensing Problem (The Formation): Where should the drones fly? If they are too close together, the radar can't tell heights apart. If they are too far apart, the image gets blurry. They need to find the perfect spacing and angles.
The Communication Problem (The Data Offload): The drones collect a massive amount of radar data. They can't store it all; they have to beam it down to a ground station in real-time. To do this, they use radio waves. If the drones use too much power to talk to the ground, they might run out of battery. If they use too little, the data gets lost or arrives too slowly.

2. The "Smart Swarm" Solution

The authors didn't try to guess the answer with a simple formula because the math is incredibly complex (like trying to find the lowest point in a mountain range full of hidden valleys). Instead, they used an algorithm called Particle Swarm Optimization (PSO).

Think of PSO like a flock of birds searching for the best feeding spot:

Imagine releasing 500 virtual "birds" (computer simulations) into a digital sky.
Each bird represents a different idea for where the drones should fly and how much power they should use.
The birds fly around, checking their ideas. If a bird finds a spot where the radar image is super sharp (low sidelobes) and the communication is fast enough, it remembers that spot.
The birds then share this good news with the flock. Over time, the whole swarm converges on the single best formation and power setting.

3. The "Cheat Code" (Simplifying the Math)

The researchers realized something clever: The quality of the radar image (the sidelobes) depends only on where the drones fly, not on how much power they use to talk to the ground.

The Trick: They separated the problem. First, they let the "birds" figure out the perfect flight path. Then, for that specific path, they calculated the minimum power needed to send the data.
This made the search much faster and more accurate, allowing them to find a solution that was 11 dB better (a huge improvement in signal clarity) than standard methods.

4. The Results

When they tested their method against other common algorithms (like standard genetic algorithms or regular particle swarms), their "smart swarm" approach won every time.

Sharper Images: They achieved much lower "ghost" levels (sidelobes), ranging from -17 dB to -33 dB, meaning the 3D images were very clean.
Trade-offs: They found that if you demand a larger area to be mapped (a wider height range) or if you demand faster data speeds, the image quality naturally gets a bit worse (the sidelobes get louder). But even in these tough scenarios, their method was still the best at keeping the image clear.

In Summary

This paper is about teaching a swarm of drones how to fly in a "sweet spot" formation and manage their radio power so they can build the clearest possible 3D radar map of the world below them. By using a smart, bird-flock-inspired computer algorithm, they found a way to make the radar images significantly sharper and more reliable than before.

Technical Summary: Point Spread Function Optimization for Communication-assisted UAV-borne MIMO TomoSAR

Problem Statement
This paper addresses the challenge of optimizing the Point Spread Function (PSF) for Unmanned Aerial Vehicle (UAV)-borne Multiple-Input Multiple-Output (MIMO) Synthetic Aperture Radar (SAR) tomography systems. The objective is to generate high-quality three-dimensional (3D) images of a scene by retrieving the vertical distribution of scatterers. A critical performance metric in TomoSAR is the PSF, specifically its sidelobe levels. High sidelobes can mask weaker scatterers, create ghost targets, and degrade image interpretability, particularly in complex environments like urban areas.

While PSF optimization is well-established for Fourier-based tomography under far-field and uniform platform spacing assumptions, its application to UAV-based systems with arbitrary formations remains largely unexplored. Furthermore, these systems face a dual constraint: the UAV swarm must maintain a formation that minimizes PSF sidelobes (sensing constraint) while simultaneously offloading collected radar data to a ground station (GS) in real-time via a Frequency Division Multiple Access (FDMA) link (communication constraint). The paper formulates a joint optimization problem to minimize the Peak Sidelobe Level (PSL) of the PSF by optimizing both the UAV formation and the communication power allocation, subject to sensing quality-of-service (QoS) and communication QoS constraints.

Methodology
The authors formulate the problem as a non-convex, min-max optimization task (Problem P). The objective is to minimize the PSL, defined over a symmetric interval $I = [-h_{max}, h_{max}]$ along the normal axis, while satisfying ten constraints. These constraints include:

Sensing: Ensuring distortion-free target reconstruction, limiting tomographic and slant-range resolutions, maintaining flight altitude and look angle bounds, ensuring minimum inter-UAV separation, guaranteeing minimum radar swath width, and meeting minimum Signal-to-Noise Ratio (SNR) thresholds.
Communication: Limiting maximum transmit power, ensuring minimum data rates for real-time offloading, and capping total energy consumption per UAV.

The problem is identified as difficult to solve due to the complex structure of the PSF expression, the non-convexity of several constraints, and the lack of closed-form expressions for PSF zeros (which makes traditional gradient-based methods intractable).

To address this, the authors propose a modified Particle Swarm Optimization (PSO) algorithm. A key innovation in their approach is the reduction of the problem dimension. They observe that for a given UAV formation, the PSL is independent of the communication power allocation. Consequently, the power allocation sub-problem can be solved analytically by setting transmit powers to their minimum required levels to satisfy communication constraints. This allows the PSO algorithm to search only the UAV formation space (reducing dimensionality from $I(K+2)$ to $2I$ ), while the power allocation is determined separately.

The proposed algorithm employs a reflecting-wall mechanism to handle boundary constraints and utilizes a non-parameterized fitness function that penalizes constraint violations. The fitness function evaluates the PSL for feasible solutions and adds penalty terms for infeasible solutions based on the degree of constraint violation.

Key Contributions

Joint Optimization Framework: The paper presents a novel framework for the joint optimization of UAV formation and communication power allocation to minimize PSF sidelobe levels, explicitly accounting for the coupling between sensing performance and communication offloading requirements.
Dimensionality Reduction Strategy: A specific modification to the PSO algorithm is proposed, which decouples the power allocation from the formation search. This significantly reduces the search space complexity and improves convergence efficiency.
Constraint Handling: The solution incorporates a comprehensive set of practical sensing and communication constraints, including resolution limits, energy budgets, and real-time data rate requirements, within a stochastic optimization framework.

Simulation Results
The proposed solution was evaluated against several benchmark schemes: a Conventional Genetic Algorithm (CGA), Genocop II (a constrained optimization GA), and a standard PSO algorithm that did not utilize the dimensionality reduction.

Performance Gain: The proposed scheme achieved a PSL between -17 dB and -33 dB, significantly outperforming the benchmark schemes. Specifically, it demonstrated an 11 dB improvement in PSL suppression compared to the conventional PSO benchmark.
Comparison with ULA: While a Uniform Linear Array (ULA) achieved a PSL comparable to the proposed scheme, the ULA resulted in a significantly wider mainlobe, leading to reduced height resolution. The proposed scheme maintained high resolution while suppressing sidelobes.
Trade-offs: Simulations revealed that increasing the maximum height ( $h_{max}$ ) or the minimum required data rate ( $R_{min}$ ) leads to higher PSLs, indicating fundamental trade-offs between coverage, communication requirements, and imaging quality. Notably, for $R_{min} > 6.18$ Mb/s, all benchmark schemes failed to find feasible solutions, whereas the proposed approach remained effective.

Significance
The paper claims that its proposed solution significantly improves sidelobe suppression compared to existing benchmark schemes, thereby enhancing the quality of reconstructed 3D TomoSAR images. By successfully integrating communication constraints into the formation optimization, the work demonstrates the feasibility of real-time, communication-assisted UAV-borne MIMO TomoSAR systems. The results suggest that the proposed joint optimization approach is essential for achieving high-fidelity imaging in scenarios where UAVs must simultaneously perform sensing and data offloading under strict resource limitations.

1. The Two-Part Challenge

2. The "Smart Swarm" Solution

3. The "Cheat Code" (Simplifying the Math)

4. The Results

In Summary

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