⚡ electrical engineering

Phase-Only Positioning in Distributed MIMO Under Phase Impairments: AP Selection Using Deep Learning

This paper proposes a deep learning-based framework for antenna point selection in distributed MIMO systems that maintains high-precision carrier phase positioning accuracy under phase synchronization errors while reducing inference complexity by approximately 19.7%.

Original authors: Fatih Ayten, Musa Furkan Keskin, Akshay Jain, Mehmet C. Ilter, Ossi Kaltiokallio, Jukka Talvitie, Elena Simona Lohan, Mikko Valkama

Published 2026-02-06

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Fatih Ayten, Musa Furkan Keskin, Akshay Jain, Mehmet C. Ilter, Ossi Kaltiokallio, Jukka Talvitie, Elena Simona Lohan, Mikko Valkama

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 find a lost friend in a massive, foggy city using only the sound of their voice. You have a team of microphones (Antenna Points, or APs) scattered around the city. Instead of measuring how long the sound takes to reach you (which is like standard GPS), you are trying to locate them by listening to the exact "wobble" or phase of the sound waves. This is called "Carrier Phase Positioning." It's incredibly precise—like finding someone within the width of a coin—but it's also very fragile.

Here is the story of the paper, broken down into simple concepts:

1. The Problem: The "Out-of-Tune" Orchestra

In a perfect world, all your microphones would be perfectly synchronized, like an orchestra playing in perfect time. But in the real world, the microphones are spread out, and they get slightly out of sync. This is called a phase synchronization error.

Think of it like a choir where one singer is slightly off-key. If you try to figure out where the sound is coming from based on that singer's voice, you might get the wrong answer. The paper acknowledges that these "off-key" errors usually ruin the accuracy of these high-tech positioning systems.

2. The Solution: A Smart "Spotter" (Deep Learning)

The researchers built a system with two main parts:

The Calculator (Hyperbola Intersection): This is the math engine that tries to figure out the location. It draws invisible hyperbolic curves (like the shape of a guitar pick) based on the sound differences between microphones. Where the curves cross is where the person is.
The Spotter (Deep Learning): This is the new, smart part. Imagine you have a team of 9 microphones. If you try to use all of them at once to draw curves, it's like trying to solve a puzzle with 100 pieces at once—it takes a long time and the "off-key" singers might mess it up.

The Deep Learning Spotter acts like a smart manager. It looks at the current situation (how loud the signal is, where the microphones are standing) and instantly picks the best two microphones to use for the calculation. It ignores the noisy or poorly positioned ones.

3. How It Works: The "Best Pair" Strategy

The paper explains that you don't need all 9 microphones to get a great answer; you just need the right two.

The Old Way: Try to use every possible combination of microphones. This is slow and gets confused by the "off-key" errors.
The New Way: The AI looks at the data and says, "Hey, Microphone #3 and Microphone #7 are the clearest right now. Let's just use those two."

By picking the best pair, the system becomes faster (because it does less math) and more accurate (because it avoids the noisy data).

4. The Results: Faster and Sharper

The researchers tested this in a simulated city with 9 microphones. Here is what they found:

Accuracy: Even with the "off-key" synchronization errors, the system could still find the location with centimeter-level precision. It's like finding a needle in a haystack without losing your balance.
Speed: By only using the two best microphones selected by the AI, the system became about 20% faster (using less computing power) compared to trying to use all the data.
Robustness: When they trained the AI specifically to expect "off-key" errors, it learned to ignore them. It stayed accurate even when the conditions were messy.

5. What They Didn't Say (Important Boundaries)

The paper is very specific about what it tested:

It only works in Line-of-Sight situations (where the microphones can "see" the user directly, without walls blocking the signal).
It only works in 2D (flat ground, not 3D space like a tall building).
It is a simulation, not a real-world field test yet.
They did not test it on medical devices, self-driving cars, or specific future 6G products yet; they only proved the math and logic work in a computer simulation.

The Big Picture

Think of this paper as teaching a GPS system how to be a smart filter. Instead of drowning in too much data and getting confused by noise, the system learns to pick the "golden" pieces of information to solve the puzzle quickly and accurately, even when the equipment isn't perfect. This is a step toward making future wireless networks (like 6G) able to pinpoint locations with incredible precision.

Technical Summary: Phase-Only Positioning in Distributed MIMO Under Phase Impairments

1. Problem Statement

Carrier phase positioning (CPP) offers the potential for centimeter-level accuracy in next-generation wireless systems by utilizing carrier phase observations exclusively, without relying on time-of-arrival (ToA) or time-difference-of-arrival (TDoA) measurements. While recent literature suggests high accuracy is achievable in distributed multiple-input multiple-output (D-MIMO) networks using phase-only measurements, practical deployments face significant challenges. Specifically, phase synchronization errors across distributed antenna points (APs) inherently degrade performance. Furthermore, next-generation networks require strict latency compliance, necessitating reduced model complexity. Existing methods often fail to adequately address the combined impact of phase synchronization errors and the computational burden of processing all available ambiguity combinations in D-MIMO systems.

2. Methodology

The paper proposes a learning-based Location Management Function (LMF) framework, termed Distributed LMF (DLMF), which integrates deep learning (DL) with a hyperbola intersection method to achieve robust, high-precision positioning under phase impairments. The methodology consists of three primary components:

2.1 System Model and Differential Measurements

The system assumes an uplink configuration with $I$ spatially distributed APs and a User Equipment (UE) at an unknown position $x_{ue}$ . The phase of the received signal at the $i$ -th AP is modeled to include wavelength-dependent distance, phase perturbations between the DLMF and APs, UE-DLMF phase offsets, integer ambiguity, and measurement noise.
To mitigate common phase offsets, the system utilizes differential measurements between a reference AP ( $i=0$ ) and other APs ( $m \in \{1, \dots, I-1\}$ ). These differential measurements correspond geometrically to sets of hyperbolas parameterized by integer ambiguity differences ( $\Delta z_m$ ).

2.2 Hyperbola Intersection with Ambiguity Estimation

The core localization model adopts the hyperbola intersection method, comprising:

Differential Ambiguity Estimator: A Multi-Layer Perceptron (MLP) that estimates the vector of differential ambiguities ( $\Delta \hat{z}$ ) from the differential phase measurements.
Gradient Descent (GD) Solver: An iterative solver that refines the UE position estimate using the estimated differential distances. It minimizes a quadratic cost function over $T$ iterations.

2.3 Deep Learning-Based AP Selection

To address computational complexity and optimize accuracy, the paper introduces a neural network (NN) for Adaptive AP Selection. Instead of estimating all possible ambiguity pairs, the system selects an optimal pair of two ambiguities ( $\Delta z_a, \Delta z_b$ ) to minimize positioning error.

Input Features: The NN utilizes a feature vector $F \in \mathbb{R}^{8I}$ $F \in R^{8 I}$ , concatenating:
- Measurement-based features: Differential phase measurements ( $\delta$ ) and Signal-to-Noise Ratio (SNR) values at each AP.
- Geometry-based features: Distances and angles relative to the reference AP, closest neighbor, and farthest AP.
Network Architecture: An MLP with an input layer of size $8I$ , five hidden layers (sizes $A, 2A, 4A, 2A, A$ ), and an output layer of size $\binom{I-1}{2}$ . The network predicts the positioning error for every possible ambiguity pair.
Selection Strategy: The pair $(a^*, b^*)$ corresponding to the minimum predicted error is selected for the GD solver.

3. Key Contributions

Robustness to Phase Synchronization Errors: The study demonstrates that training the ambiguity estimator on data reflecting phase perturbations allows the hyperbola intersection method to maintain high accuracy even in the presence of synchronization errors.
DL-Driven AP Selection: The paper introduces a novel framework that uses a deep neural network to select the optimal pair of antenna points for ambiguity estimation. This approach leverages both signal measurements and deployment geometry to avoid suboptimal pair choices.
Complexity Reduction: By restricting the localization process to only two selected ambiguities (rather than all available ones) and using the DL model to guide this selection, the framework significantly reduces computational load without sacrificing precision.

4. Simulation Results

Simulations were conducted in a $100 \text{ m}^2$ area with $I=9$ distributed APs, emulating a D-MIMO topology.

Accuracy under Perturbation: When trained on data with phase perturbations (standard deviation $\sigma$ ), the model maintained an overall ambiguity estimation accuracy above 99% and a 95th-percentile positioning error below 0.5 cm, even when tested on datasets with varying perturbation levels.
AP Selection Performance: The proposed DL-based selection method significantly outperformed benchmarks including Random selection, Max-SNR selection, and using all ambiguities (No selection).
- The Max-SNR and Random benchmarks resulted in severe accuracy degradation (95th percentile errors of ~509 cm and ~551 cm, respectively).
- The Proposed method achieved a 95th percentile error of 0.26 cm, closely approaching the "Best achievable" ground-truth subset (0.14 cm).
Complexity: The proposed framework reduced the overall inference complexity by approximately 19.7% compared to using all ambiguities, while maintaining superior accuracy compared to methods that do not use selection or use naive selection strategies.

5. Significance and Claims

The paper claims that carrier phase-only positioning, when augmented with deep learning solutions, is a viable enabler for reliable, high-precision localization in realistic 6G D-MIMO deployments. The significance of the work lies in:

Practical Robustness: Explicitly addressing and mitigating phase synchronization errors, a critical practical impairment often overlooked in theoretical CPP studies.
Efficiency: Demonstrating that adaptive AP selection can reduce computational complexity (FLOPs) while simultaneously improving positioning accuracy by avoiding poor ambiguity pair choices.
Future Enabler: Positioning this learning-driven approach as a key component for future 6G systems, with the authors noting that future work will extend the framework to multipath and three-dimensional scenarios.

The authors remain modest regarding the current scope, acknowledging that the study focuses on line-of-sight (LoS) propagation and that the impact of AP position uncertainties requires further investigation.