⚡ electrical engineering

On the Value of Base Station Motion Knowledge for Goal-Oriented Remote Monitoring with Energy-Harvesting Sensors

This paper formulates goal-oriented remote monitoring with energy-harvesting sensors and mobile receivers as a partially observable Markov decision process, demonstrating that incorporating base station motion knowledge into optimal sampling and transmission policies significantly reduces estimation distortion compared to stationary or constant-channel assumptions.

Original authors: Sehani Siriwardana, Jean Michel de Souza Sant'Ana, Richard Demo Souza, Abolfazl Zakeri, Onel Luis Alcaraz López

Published 2026-02-20

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CC BY 4.0

Original authors: Sehani Siriwardana, Jean Michel de Souza Sant'Ana, Richard Demo Souza, Abolfazl Zakeri, Onel Luis Alcaraz López

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 you are a farmer living in a remote valley, far from any cell towers or power lines. You have a special sensor on your crops that needs to send updates about the weather and soil health to a "monitor" (like a satellite or a drone) flying overhead. However, your sensor runs on a tiny battery that only charges when the sun shines (energy harvesting).

This paper is about how to make that sensor smarter so it doesn't waste its precious energy sending useless messages, especially when the "monitor" flying overhead is moving fast and the connection quality changes constantly.

Here is the breakdown of the problem and the solution, using simple analogies:

1. The Problem: The "Moving Target" and the "Fragile Battery"

In most old systems, we assume the receiver (the satellite or drone) is sitting still, like a lighthouse on a cliff. The signal is always the same.

But in this paper, the receiver is moving. Think of it like trying to throw a ball to a friend who is running around a track.

The Challenge: Sometimes your friend is close and you can throw hard (Good Channel). Sometimes they are far away or behind a tree (Bad Channel).
The Constraint: Your arm (the sensor) gets tired. You only have a few throws left before you need to rest and recharge (Energy Harvesting).
The Mistake: If you don't know where your friend is running, you might throw the ball when they are far away (wasting energy and the ball gets lost) or when they are right next to you but you are too tired to throw.

2. The Solution: "Knowing the Dance Steps"

The researchers asked: What if the sensor knew exactly how the satellite/drones moves?

Instead of guessing, the sensor learns the "dance steps" of the receiver. It knows that the satellite will be in a "bad spot" for 10 seconds, then a "great spot" for 5 seconds, then "bad" again.

They created a smart decision-maker (an algorithm) that acts like a chess player. It doesn't just look at the current move; it looks ahead.

If the channel is bad: The sensor says, "I'll hold my breath and wait. I won't waste my battery."
If the channel is good: The sensor says, "Now is the perfect time! I'll grab the data and send it immediately."

3. The Two Ways to Guess the Answer

Since the sensor can't always send data, the receiver (the satellite) has to guess what the weather is like based on the last message it got. The paper tested two ways of guessing:

The "Most Likely" Guess (ML): "The last time I heard from you, it was sunny. It's probably still sunny."
The "Best Average" Guess (MMD): "It's been sunny for a while, but statistically, rain is more likely at this time of day, so I'll guess rain to be safe."
The Result: The "Best Average" guess (MMD) was slightly better at keeping the picture clear.

4. The Big Win: Saving Distortion

In the world of data, "distortion" is like a blurry photo. If the data is old or lost, the photo is blurry. The goal is to keep the photo sharp.

The researchers ran simulations with two types of moving receivers:

Simple Movement: Like a drone hovering back and forth.
Complex Movement: Like a real Low Earth Orbit (LEO) satellite that rises, gets high overhead, and then sets.

The Results:

When the sensor ignored the movement and just sent data whenever it had battery, the "photo" was very blurry (high distortion).
When the sensor knew the movement and waited for the perfect moment to send, the "photo" became 10% to 42% sharper.

The Takeaway

Think of this like waiting for the perfect moment to shout across a canyon.

The Old Way: Shout whenever you feel like it. Sometimes the wind carries your voice; sometimes it doesn't. You get tired and run out of breath.
The New Way: You listen to the wind. You know the wind dies down every 5 minutes. You stay silent, save your breath, and then shout only when the wind is blowing perfectly toward the other side.

In short: By teaching energy-harvesting sensors to "watch" where the receiver is moving, we can send much clearer information using the same amount of energy. It turns a chaotic, blurry conversation into a crisp, clear one.

1. Problem Statement

The paper addresses the challenge of goal-oriented remote monitoring for unobservable Markov sources in remote areas (e.g., beyond cellular coverage) using Energy-Harvesting (EH) sensors.

Context: Unlike traditional systems with stationary base stations, this work focuses on scenarios where the receiver (monitor) is mobile, such as Low Earth Orbit (LEO) satellites or Unmanned Aerial Vehicles (UAVs).
The Core Issue: The mobility of the receiver induces time-varying channel characteristics (specifically, a varying Reception Success Rate or RSR). Conventional optimization strategies often assume a stationary receiver with a constant channel or ignore channel dynamics entirely.
Objective: To formulate and solve an optimization problem that determines the optimal sampling and transmission policies for an EH sensor. The goal is to minimize the average distortion (estimation error) of the source state at the monitor, subject to strict energy constraints, while explicitly accounting for the receiver's motion and the resulting channel variations.

2. Methodology

The authors propose a framework that models the system dynamics and solves the resulting optimization problem using stochastic control theory.

System Model

Components: An information source (Markov chain with $M$ states), a sensor (with sampler, buffer, controller, and transmitter), and a mobile monitor.
Energy: The sensor is powered by an energy harvester with a finite battery capacity ( $E$ ). Energy arrives via a Bernoulli process. Costs are incurred for sampling ( $\kappa$ ) and transmitting ( $\tau$ ).
Channel Dynamics: The channel is modeled as a finite-state Markov process with $K$ states. The state transition matrix ( $Q$ ) represents the motion of the base station (e.g., satellite rise, culmination, set), and each state has an associated RSR ( $q_s$ ).
Actions: At each time slot, the controller decides on a binary action pair $(\alpha_t, \beta_t)$ $(α_{t}, β_{t})$ :
- $\alpha_t=1$ : Sample the source.
- $\beta_t=1$ : Transmit the buffered sample.
- This creates four possible actions: Idle, Transmit only, Sample only, or Sample + Transmit.

Mathematical Formulation

POMDP Formulation: Since the controller cannot directly observe the source state (only the buffer state and transmission outcomes), the problem is initially formulated as a Partially Observable Markov Decision Process (POMDP).
MDP Transformation: To make the problem tractable, the POMDP is transformed into an equivalent Markov Decision Process (MDP) using a belief state approach. The belief state represents the probability distribution of the source state given the history of observations and actions.
- The authors leverage the property that the belief state converges to a steady-state distribution based on the "Age of Information" (AoI) at the transmitter and monitor. This allows the infinite continuous belief space to be reduced to a finite-state MDP.
Optimization Algorithm: The resulting finite-state MDP is solved using Relative Value Iteration (RVI) to derive the optimal policy ( $\pi^*$ ) that minimizes the long-term average distortion.
Estimation Strategies: Two estimation techniques at the monitor are evaluated:
1. Maximum Likelihood (ML): Estimates the source state based on the most recent received sample.
2. Minimum Mean Distortion (MMD): Uses knowledge of the source's distortion matrix and transition probabilities to minimize expected error.

3. Key Contributions

Explicit Modeling of Receiver Mobility: The paper extends existing goal-oriented monitoring frameworks by incorporating the motion dynamics of the receiver (LEO/UAV) as a time-varying Markov channel, rather than assuming a static or constant average channel.
Optimal Policy Derivation: The authors derive optimal sampling and transmission policies that adapt to both the battery level and the instantaneous channel state (motion state), utilizing the RVI algorithm.
Quantification of Motion Knowledge Value: The study rigorously quantifies the performance gain of knowing the receiver's motion pattern compared to strategies that assume a constant average channel or lack motion knowledge.
Comparative Analysis: The work compares the proposed optimal policy against a "baseline" greedy policy (transmit if energy permits) and evaluates the impact of different motion models (simple 2-state vs. complex LEO-like 6-state).

4. Numerical Results

The authors simulated the system with a 5-state source and varying energy arrival rates ( $\mu$ ).

Distortion Reduction: Incorporating receiver motion knowledge into the optimization significantly reduces the average distortion.
- For a simple 2-state motion model (Good/Bad channel), the optimal policy reduced distortion by 38% to 42% compared to policies without channel knowledge.
- For a complex 6-state LEO-like motion model, the reduction was 10% to 11%. The smaller gain in the complex model is attributed to the system spending more time in suboptimal states, forcing the controller to transmit in non-ideal conditions more often.
Estimation Performance: The MMD estimation strategy consistently outperformed the ML strategy, particularly in scenarios with lower energy availability, as it better utilizes source statistics to minimize error.
Policy Behavior:
- The Optimal (RVIA) policy intelligently delays transmission during "bad" channel states (low RSR) even if energy is available, waiting for better conditions.
- The Baseline policy transmits whenever energy is available, leading to frequent failures in bad channel states and higher overall distortion.
Energy Efficiency: The results demonstrate that "smart" transmission (waiting for good channel states) is more effective than "greedy" transmission, even with limited energy.

5. Significance and Conclusion

This paper highlights a critical insight for the design of 6G and IoT networks involving mobile receivers (satellites, drones): Channel dynamics caused by mobility must be explicitly modeled in the control policy.

Practical Impact: Ignoring receiver motion leads to suboptimal resource usage. By knowing the motion pattern (e.g., satellite ephemeris), sensors can schedule transmissions to coincide with high-probability reception windows, drastically improving data reliability without increasing energy consumption.
Future Directions: The authors suggest extending the framework to scenarios with imperfect Channel State Information (CSI) and multi-sensor networks, which are more realistic for large-scale remote monitoring deployments.

In summary, the work proves that for energy-constrained remote monitoring, the "value" of knowing the base station's motion is substantial, offering up to a 42% improvement in estimation accuracy by enabling the sensor to make context-aware decisions.