Gaussian Process-Based Extended Object Estimation for 6G ISAC at Millimeter-Wave Frequencies

Technical Summary: Gaussian Process-Based Extended Object Estimation for 6G ISAC at Millimeter-Wave Frequencies

Problem Statement
Future sixth-generation (6G) Integrated Sensing and Communication (ISAC) systems aim to enhance environmental awareness by moving beyond the conventional assumption that multipath components originate from single point objects (landmarks). While high-resolution sensing at millimeter-wave (mmWave) frequencies allows for the resolution of multiple incidence points (IPs) from a single physical object—termed an "extended object"—existing literature lacks experimental validation of methods capable of estimating the shapes of these objects in practical scenarios. Specifically, while Gaussian Processes (GPs) have been theoretically proposed for extended object estimation (EOE), their efficacy using real-world, 5G New Radio (NR) compliant measurement data in both mapping and Simultaneous Localization and Mapping (SLAM) contexts remains unexplored.

Methodology
The paper proposes a GP-based framework for EOE, validated through a bistatic sensing setup operating at 60 GHz with a 400 MHz bandwidth, compliant with 5G NR standards. The methodology proceeds in three stages:

1. Incidence Point (IP) Estimation:

   • System Model: The system utilizes beam-based OFDM transmission with Uniform Planar Arrays (UPAs) at both the transmitter (Tx) and receiver (Rx). Channel parameters (Time-of-Arrival, Angle-of-Departure, Angle-of-Arrival) are extracted from Positioning Reference Signals (PRS).
   • Mapping Scenario: Assuming the Rx state (position, heading, clock bias) is known, IPs are estimated by solving a nonlinear optimization problem minimizing the quadratic cost function between measured and geometrically predicted channel parameters.
   • SLAM Scenario: When the Rx state is unknown, a robust snapshot SLAM algorithm based on Random Sample Consensus (RANSAC) and Least Squares (LS) is employed. This partitions measurements into inliers (Line-of-Sight and single-bounce Non-Line-of-Sight) and outliers to jointly estimate the Rx trajectory and IP locations.

2. Data Clustering and Transformation:

   • Estimated IPs are clustered using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm to group points belonging to the same object.
   • For each cluster, the Cartesian coordinates are converted to polar coordinates $(\theta, r)$ relative to the cluster centroid. The angles $\theta$ serve as regressors (inputs), and radial distances $r$ serve as observations (outputs).

3. Gaussian Process Regression:

   • The object shape is modeled as a star-convex function $f(\theta)$ mapping polar angles to radial distances.
   • A GP regression model is trained using a periodic squared exponential covariance function to capture the star-convex nature of the objects.
   • Hyperparameters (magnitude scale $\sigma_f$, length scale $\ell$, and noise variance $\sigma_n^2$) and the mean function are learned by maximizing the log marginal likelihood.
   • The model predicts the full object contour and provides a 95% confidence interval, even when trained on partial contour data.

Key Contributions

• Experimental Validation: The paper provides the first experimental validation of GP-based EOE using practical mmWave data acquired from a 5G NR-compliant setup, bridging the gap between theoretical proposals and real-world implementation.
• Dual-Scenario Evaluation: The method is rigorously tested in two distinct operational modes:
  • mmWave Mapping: Where the receiver trajectory is known.
  • mmWave SLAM: Where the receiver trajectory is unknown and must be estimated simultaneously with the object shapes.
• Partial Contour Handling: The study demonstrates the capability of GPs to reconstruct object shapes (specifically pillars and walls) using only a limited subset of measurement points, reflecting practical constraints where a single Tx-Rx pair cannot capture the full object contour.

Results

• Synthetic Data: Initial tests on synthetic data showed that increasing the number of measurement points improves Root Mean Square Error (RMSE) performance, confirming the robustness of GP-based EOE even with small datasets.
• Experimental Data (Mapping): In the mapping scenario, the GP successfully reconstructed the shapes of pillars (approximating circles) and walls. The results indicated that smooth geometries (pillars) were estimated accurately even with partial data, while complex geometries (walls) required more extensive angular coverage for precise estimation.
• Experimental Data (SLAM): Despite the inherent inaccuracies in IP estimation when the Rx state is unknown (compared to the mapping case), the overall shape estimation performance remained comparable to the mapping scenario.
• Geometric Variations: The study noted that the characteristic length-scale hyperparameter ($\ell$) varied significantly between object types (e.g., $\ell \approx 0.23$ for walls vs. $\ell \approx 1.31$ for pillars), reflecting the rate of variation in the radial function required to model different shapes.

Significance and Claims
The authors claim that combining ISAC systems with GP-based EOE enables improved environmental awareness in future wireless systems. The primary significance lies in the ability to estimate the physical characteristics (shape, size) of extended objects rather than treating them as point scatterers. The paper asserts that:

• GP-based EOE performs reliably in both mmWave mapping and SLAM scenarios under practical measurement conditions.
• The estimated extended objects provide more concrete structural insights than point-scatterer models.
• This enhanced awareness can be leveraged to improve ISAC applications, such as refining clutter cancellation algorithms and enabling more accurate environmental mapping.

The paper maintains a modest stance, acknowledging that the predictive capability is constrained by the number of measurement points and angular coverage. It suggests that while coarse estimates of wall extents are possible with limited data, finer details may require multiple Tx-Rx pairs to capture full contours.