⚡ electrical engineering

Pilot-Free Optimal Control over Wireless Networks: A Control-Aided Channel Prediction Approach

This paper proposes a pilot-free optimal control framework for wireless networked systems that leverages control-aided channel prediction to generate control commands without real-time channel state information, utilizing Kalman filter-based and deep reinforcement learning approaches for linear and nonlinear plants respectively to achieve superior control performance and prediction accuracy.

Original authors: Minjie Tang, Zunqi Li, Photios A. Stavrou, Marios Kountouris

Published 2026-02-26

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CC BY 4.0

Original authors: Minjie Tang, Zunqi Li, Photios A. Stavrou, Marios Kountouris

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 trying to steer a remote-controlled drone (the plant) through a stormy, windy night. You are sitting in a control tower (the remote controller), and you need to send commands to the drone to keep it stable.

The Old Problem: The "Pilot" Bottleneck
In traditional systems, before you could send a command, you had to shout a specific "test phrase" (a pilot signal) across the radio to check how the wind is blowing right now. The drone would listen, figure out the wind speed, and whisper it back to you. Only then could you send your steering command.

This has two big problems:

Wasted Energy: Shouting test phrases takes up time and battery power.
Too Slow: By the time you shout, listen, and calculate, the wind might have already changed.

The New Solution: "Steering as a Flashlight"
This paper proposes a clever new way to do things called "Pilot-Free Control."

Instead of shouting a test phrase, the controller simply sends the steering commands themselves. But here's the magic: the controller uses the way the drone reacts to those commands to figure out what the wind is doing.

Think of it like walking through a dark room with a flashlight.

Old Way: You stop, shine a light on the wall to see where you are, then take a step. (Slow and wasteful).
New Way: You just start walking. As you bump into furniture or feel the air move, you instantly learn where the walls are and adjust your path. The act of walking is the way you see.

In this paper, the "steering commands" act as the flashlight. The controller watches how the plant (the drone) moves in response to the command. If the drone moves slower than expected, the controller knows, "Ah, the channel (wind) is bad right now," and adjusts the next command accordingly.

How It Works (The Two Brains)

The system uses two smart "brains" working together:

1. The Predictor Brain (The Weather Forecaster)

For Simple Systems (Linear): It uses a classic math tool called a Kalman Filter. Imagine a detective who looks at the last few steps the drone took and guesses where the wind is blowing next. It doesn't need a weather report; it just watches the drone's behavior to predict the future.
For Complex Systems (Non-Linear): It uses a Neural Network (a type of AI) called KalmanNet. This is like a super-smart detective that has learned from millions of past storms. It can handle chaotic, unpredictable winds that a simple math formula can't figure out.

2. The Controller Brain (The Pilot)

For Simple Systems: It uses a mathematical rule (based on the Bellman Principle) to decide the perfect move. It's like a chess grandmaster who calculates the best move based on the current board and the predicted weather.
For Complex Systems: It uses Reinforcement Learning (specifically MM-DDPG). This is like a pilot who learns by trial and error in a flight simulator. It learns a policy: "If the wind is gusting from the left and the drone is tilting right, push the stick hard to the left."

Why Is This a Big Deal?

No More "Test Phrases": By reusing the control commands as the way to sense the channel, the system saves a massive amount of energy and bandwidth. It's like getting a free weather report just by driving your car.
It's Robust: Even if the prediction isn't perfect, the system is designed to be "conservative." If the controller thinks the channel is uncertain (like a foggy night), it automatically eases off on the controls to avoid crashing, rather than making a wild guess.
It Works for Everything: The paper shows this works for simple, predictable machines (like a chemical plant) and complex, chaotic ones (like a swarm of drones or a self-driving car).

The Bottom Line

This paper teaches us how to build a control system that doesn't need to stop and ask "How is the connection?" before acting. Instead, it learns the connection while it acts. It turns the control signal into a dual-purpose tool: it steers the machine and simultaneously maps the invisible path it's traveling on.

This makes wireless control systems faster, more efficient, and capable of handling the messy, real-world chaos of wireless networks without needing constant, energy-draining check-ins.

1. Problem Statement

Wireless Networked Control Systems (WNCSs) rely on real-time Channel State Information (CSI) to design optimal control policies that stabilize dynamic plants over fading channels. However, acquiring accurate CSI is notoriously difficult due to:

Time-varying nature: Wireless channels change rapidly, making static estimates obsolete.
Overhead: Conventional methods rely on pilot-aided transmission (sending known sequences to estimate the channel), which consumes significant spectral and energy resources. This overhead is particularly burdensome in massive MIMO systems and can lead to pilot contamination.
Nonlinearity: Existing control designs often assume linear plants or simplified channel models (e.g., i.i.d. fading), failing to capture the temporal correlation and high-dimensional states of practical multipath channels.

Core Question: Can we design an optimal controller for WNCSs without a priori CSI or dedicated pilot transmissions?

2. Methodology

The authors propose a pilot-free framework where control signals serve a dual purpose: regulating the plant and acting as implicit pilots for channel prediction. The framework is developed for both linear and nonlinear systems.

A. System Architecture

Dual Role of Control Signals: The remote controller generates control commands ( $u_k$ ) based on the current plant state ( $x_k$ ) and a predicted channel state ( $\hat{H}$ ). The actuator receives a noisy version of this command, which is then used to infer the channel state.
Implicit Channel Estimation: Instead of sending dedicated pilots, the system uses the history of control inputs and observed state transitions to estimate the channel. The relationship between the control input, the plant dynamics, and the received signal allows the controller to "learn" the channel.

B. Linear Systems (OFDM Architecture)

For linear plants over Orthogonal Frequency-Division Multiplexing (OFDM) channels:

Channel Prediction (Problem 1):
- Modeled as a Minimum Mean Square Error (MMSE) estimation problem.
- Solved using a Kalman Filter (KF). The filter treats the channel gain as a hidden state evolving via a Gauss-Markov process and uses the observed plant state transitions (driven by control inputs) as measurements.
- Stability: The paper proves that the prediction error covariance remains bounded (mean-square stable) under the proposed framework.
Optimal Control (Problem 2):
- Formulated as an infinite-horizon average-cost problem.
- The optimal policy follows the Bellman optimality principle, resulting in a Markov-modulated control law.
- Curse of Dimensionality Mitigation: Since the channel state is continuous, solving the Bellman equation directly is intractable. The authors approximate the solution using a Coupled Algebraic Riccati Equation (CARE).
- Algorithm: A Stochastic Approximation (SA) algorithm is used to compute the CARE solution online, converging to a stabilizing control policy.

C. Nonlinear Systems (General Architectures)

For nonlinear plants and general communication models (e.g., MIMO, OTFS, AFDM):

Channel Prediction:
- Replaces the standard KF with KalmanNet, a model-aware neural network.
- KalmanNet learns the innovation embedding and gain networks, avoiding the need for exact noise statistics or Jacobian computations (unlike Extended/Unscented KFs).
Optimal Control:
- Uses Reinforcement Learning (RL) due to the nonlinearity and non-stationarity of the channel.
- Proposes a Markov-Modulated Deep Deterministic Policy Gradient (MM-DDPG).
- The state space includes both the plant state and the predicted channel state. The algorithm explicitly accounts for the temporal correlation of the channel (Markov modulation) to ensure stable policy learning in time-varying environments.

3. Key Contributions

Pilot-Free Paradigm: First framework to leverage control signals directly as implicit pilots for channel prediction in WNCSs, eliminating the need for dedicated pilot overhead.
Linear System Theory:
- Derivation of an optimal control policy coupled with a Kalman-based channel predictor.
- Proof of stability for both the channel predictor and the closed-loop system.
- Development of a tractable CARE-based approximation and an SA algorithm with convergence guarantees.
Nonlinear Extension:
- Integration of KalmanNet for channel prediction in nonlinear WNCSs (first of its kind).
- Development of MM-DDPG to handle continuous, high-dimensional action spaces with temporally correlated channel states.
Theoretical Guarantees: Established conditions for the existence and uniqueness of stabilizing solutions and proved the almost sure convergence of the proposed learning algorithms.

4. Numerical Results

The framework was evaluated against benchmarks (LS, EKF, UKF, Blind prediction, and Pilot-aided schemes) in two scenarios:

Linear OFDM System:
- Channel Prediction: The proposed method reduced Normalized Mean Square Error (NMSE) by approximately one order of magnitude compared to baselines across all SNR levels.
- Control Performance: Achieved at least 80% reduction in average plant state energy compared to baselines, demonstrating superior stability.
Nonlinear MIMO System:
- Channel Prediction: Achieved at least 60% NMSE reduction compared to baselines (including EKF and UKF).
- Control Performance: Consistently outperformed all benchmarks, maintaining stability even at low SNR where non-adaptive controllers (PID, fixed LQR) failed.
Pilot Overhead: The proposed scheme required zero dedicated pilot power, whereas pilot-aided baselines showed monotonically increasing cumulative transmit power.

5. Significance

Efficiency: By eliminating pilot overhead, the framework significantly improves spectral and energy efficiency, which is critical for massive IoT and 6G applications.
Robustness: The approach handles high-dimensional, time-correlated fading channels and nonlinear dynamics, addressing limitations of previous works that relied on simplified channel models.
Joint Design: It establishes a new paradigm where communication (channel prediction) and control are tightly coupled rather than treated as separate layers, enabling optimal performance in uncertain wireless environments.
Scalability: The use of deep learning (KalmanNet, MM-DDPG) allows the framework to scale to complex, nonlinear systems where analytical solutions are impossible.

In conclusion, this paper provides a rigorous theoretical foundation and practical algorithms for pilot-free optimal control, demonstrating that control signals can effectively replace dedicated pilots to achieve high-precision channel estimation and stable system control.