⚡ electrical engineering

Joint Channel and Symbol Estimation for RIS-Assisted Fluid Antenna Systems

This paper proposes the NTFAS protocol and a corresponding two-stage semi-blind BALS receiver to achieve joint channel and symbol estimation in RIS-assisted multiuser uplink systems with fluid antennas, demonstrating improved channel estimation accuracy and spectral efficiency compared to existing benchmarks.

Original authors: Josué V. de Araújo, Daniel C. Alcantara, Gilderlan T. de Araújo, André L. F. de Almeida

Published 2026-06-02

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CC BY 4.0

Original authors: Josué V. de Araújo, Daniel C. Alcantara, Gilderlan T. de Araújo, André L. F. de Almeida

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 listen to a choir of singers (the users) in a large, echoey hall. You want to hear them clearly, but there are two problems:

The Walls are Shifty: The hall has a special wall made of smart tiles (the RIS) that can bounce sound around. You can change the angle of these tiles to make the sound better, but you don't know exactly how they are set up right now.
The Microphone is Fluid: Instead of having a fixed microphone, you have a "fluid antenna" (the FA). This is like a microphone that can physically slide its recording tip to different spots on a small plate to find the clearest sound. But, every time you move the tip, the sound you hear changes completely.

The challenge is: How do you figure out exactly how the sound is bouncing off the walls and what the singers are singing, without spending all day shouting test notes (pilots) to calibrate everything?

The Problem: A Moving Target

In the past, researchers tried to solve this by either fixing the microphone or assuming they already knew how the walls were set up. But in this paper, the authors deal with a scenario where everything is moving: the microphone tip jumps around, the wall tiles change angles, and the singers are all talking at once. Trying to map this out is like trying to solve a giant, 3D jigsaw puzzle where the pieces keep changing shape.

The Solution: The "NTFAS" Protocol

The authors propose a new strategy called NTFAS (Nested Tucker for Fluid Antenna Systems). Here is how they make the puzzle solvable using a clever trick:

1. The "Common Song" Trick
Imagine the singers are all singing the same song, but they are wearing different costumes (coding) and the microphone is listening from different spots (port selection) in each round.

The Trick: The actual lyrics (the data symbols) stay exactly the same across all rounds.
The Result: Even though the microphone moves and the wall tiles shift, the core "song" is a constant thread tying all the observations together. This allows the computer to use math to separate the "song" from the "noise" of the changing environment.

2. The Two-Stage Detective Work
The authors built a "semi-blind" receiver (a detective that doesn't need to be told the answer beforehand) that works in two steps:

Stage 1: The Big Picture. First, the detective looks at all the recordings together. Because the "song" is the same in every recording, it can figure out the combined effect of the wall and the microphone movement. It's like figuring out the total echo of the room without knowing which part is the wall and which part is the mic.
Stage 2: The Split. Once it knows the combined echo, it uses a special mathematical pattern (called PARAFAC) to "unmix" the ingredients. It separates the "User-to-Wall" sound from the "Wall-to-Microphone" sound. Now it knows exactly how the sound travels from the singer to the wall, and from the wall to the mic.

The Payoff: Better Listening

After the detective figures out the environment, it can do two smart things:

Pick the Best Spot: It tells the fluid antenna, "Move your tip to this specific spot where the sound is clearest."
Tune the Wall: It tells the smart wall tiles, "Angle yourselves this way to bounce the sound perfectly to the mic."

What the Results Show

The authors tested this against other methods (like a benchmark that tries to do the same thing but less efficiently).

Clarity (Channel Estimation): Their method was better at figuring out the exact path of the sound (lower error) than the competition.
Speed (Spectral Efficiency): Because they knew the path better, they could send more data (higher speed) without making mistakes.
Accuracy (Bit Error Rate): Interestingly, the final "mistake rate" (how often a note is heard wrong) was about the same as the competition. The paper explains that while their method found the path more accurately, the competition was already good enough that the extra accuracy didn't change the final listening experience in the tests they ran.

The Bottom Line

This paper introduces a smart way to listen to multiple users in a complex, shifting environment. By keeping the "song" constant while changing the "microphone position" and "wall angles," they created a mathematical shortcut to figure out the environment quickly. This allows the system to optimize itself for the best possible signal, getting more data through without needing to shout extra test notes to calibrate the system.

Technical Summary: Joint Channel and Symbol Estimation for RIS-Assisted Fluid Antenna Systems

Problem Statement
This paper addresses the challenge of joint channel and symbol estimation in uplink multiuser communication systems that integrate Reconfigurable Intelligent Surfaces (RIS) and Fluid Antenna Systems (FAS). While RISs enhance coverage by passively shaping the propagation environment and FAs provide spatial adaptability by selecting favorable antenna ports within a compact aperture, their combination introduces significant complexity in channel acquisition. Specifically, the effective channel varies dynamically due to RIS phase shifts, FA port selections, and multiuser transmissions. Existing approaches often assume perfect Channel State Information (CSI) or focus on standalone links, failing to account for the coupled nature of RIS phase shifts, FA port selections, user-dependent coding, and unknown symbols in a cascaded RIS-FAS scenario. High training overheads associated with traditional pilot-based estimation make this a critical bottleneck for future 6G networks.

Methodology
The authors propose the Nested Tucker for Fluid Antenna Systems (NTFAS) protocol and a corresponding two-stage semi-blind receiver based on Bilinear Alternating Least Squares (BALS).

System Model and Tensor Formulation:
- The system comprises $K$ single-antenna users, an RIS with $N_r$ elements, and a Base Station (BS) with $M$ RF chains connected to $N$ FA ports.
- The transmission occurs over $I$ blocks. Within each block $i$ , the FA port selection matrix $S_i$ and user-dependent temporal coding matrix $D_i(C)$ are fixed. However, the RIS phase-shift matrix $D_p(\Theta)$ varies at each time slot $p$ . Crucially, the transmitted symbol matrix $X$ remains invariant across all $I$ blocks.
- This structure allows the received signals to be modeled as a set of coupled Tucker models. The noiseless observation tensor is formulated as $Y_i = A_i \times_1 \Phi \times_2 I_M \times_3 X^T$ , where $\Phi$ represents the composite cascaded channel matrix.
Two-Stage Semi-Blind Receiver:
- Stage 1 (Joint Estimation): The receiver exploits the Tucker structure to jointly estimate the global cascaded channel matrix $\Phi$ and the common symbol matrix $X$ . This is achieved by solving Least Squares (LS) problems on the mode-1 and mode-3 unfoldings of the received signal tensors.
- Stage 2 (Channel Separation): Once $\hat{\Phi}$ is obtained, the receiver leverages its embedded PARAFAC structure ( $\Phi^T \approx (G^T \diamond H)\Theta^T$ ) to decouple the individual channel matrices. Specifically, it separates the User-to-RIS channel ( $G$ ) and the RIS-to-BS channel ( $H$ ) using pseudo-inverse operations on concatenated observation matrices.
Optimization:
- Using the estimated CSI, the system performs a joint optimization of FA port selection and RIS phase shifts to maximize Spectral Efficiency (SE). This involves an exhaustive search over valid FA port combinations and an SVD-based design for RIS phase shifts.

Key Contributions

NTFAS Protocol: A novel transmission strategy where FA port selection and user-dependent coding vary across blocks, while the symbol matrix is shared. This creates a coupled Tucker model structure that enhances channel identifiability without requiring dedicated pilots for every configuration.
Coupled Tensor Modeling: The derivation of received signals as coupled Tucker models sharing common symbol and cascaded-channel factors, enabling the separation of spatial and temporal variables.
Two-Stage BALS Receiver: A semi-blind algorithm that first estimates the cascaded channel and symbols jointly, then separates the individual channel components ( $G$ and $H$ ) via the PARAFAC structure.
Joint Optimization Framework: A method to utilize the estimated CSI for simultaneous FA port selection and RIS phase-shift optimization to maximize SE.

Simulation Results
The proposed NTFAS scheme is evaluated against a competing semi-blind benchmark (from prior work [24]) and a Perfect CSI reference.

Bit Error Rate (BER): NTFAS and the benchmark exhibit nearly identical BER performance across the simulated SNR range. The paper notes that the moderate improvement in channel estimation does not translate to a visible BER gain at the tested operating points, as performance is limited by noise and residual estimation errors.
Normalized Mean Square Error (NMSE): NTFAS demonstrates a consistent and moderate improvement in cascaded-channel NMSE compared to the benchmark. This is attributed to the increased number of coupled equations available for estimating $\Phi$ due to the shared symbol matrix across blocks.
Spectral Efficiency (SE): Due to the more accurate channel estimates, NTFAS achieves higher SE after joint FA/RIS optimization compared to the benchmark, though both remain below the Perfect CSI bound.
Parameter Sensitivity: Simulations indicate that increasing the number of RIS phase configurations ( $P$ ) improves estimation robustness, while increasing the number of users ( $K$ ) degrades performance due to the increased complexity of the joint recovery problem.

Significance and Claims
The paper claims that NTFAS offers a favorable performance–complexity trade-off. While it provides moderate but consistent improvements in NMSE and SE over existing semi-blind benchmarks, it maintains comparable BER performance. The authors emphasize that the proposed method reduces dependence on pilot overhead by exploiting the coupled structure of observations. The complexity of the proposed receiver is shown to be lower than the benchmark in terms of channel-update terms, making it a viable solution for low-overhead receiver design in RIS-assisted FAS uplinks. The work concludes that while the gains are moderate, the approach successfully enables joint channel and symbol estimation in a scenario where traditional methods struggle with high training costs. Future work is identified as addressing lower-complexity optimization, hardware impairments, time-varying channels, and multi-antenna users.