Model-based Implicit Neural Representation for sub-wavelength Radio Localization

TL;DR

This work addresses high-precision radio localization in challenging NLoS environments by learning a location-to-channel mapping via a model-based neural network $f_{\boldsymbol{\theta}}: \mathbb{R}^2 \to \mathbb{C}^{N_a\times N_s}$, which serves as a generative channel model to augment the fingerprinting dictionary. The approach enables data augmentation and on-the-fly synthesis of channel realizations, then localizes by minimizing the Frobenius distance $\|\mathbf{H}(\mathbf{x})-f_{\boldsymbol{\theta}}(\tilde{\mathbf{x}})\|_F$ over locations, with an off-grid gradient refinement and a bi-level grid to control complexity. Theoretical injectivity analyses show that, in rich-multipath, multi-antenna settings, the channel function is effectively injective with respect to the similarity measure, while practical ambiguities are mitigated by the gradient-based refinement and circle-based searches. Experiments on realistic outdoor and indoor scenarios demonstrate sub-wavelength median localization (e.g., $\sim 0.01$ cm to $0.06$ cm) and memory savings of roughly an order of magnitude relative to storing a large fingerprinting dictionary, highlighting the method’s potential for scalable, high-precision localization in integrated sensing and communication systems.

Abstract

The increasing deployment of large antenna arrays at base stations has significantly improved the spatial resolution and localization accuracy of radio-localization methods. However, traditional signal processing techniques struggle in complex radio environments, particularly in scenarios dominated by non line of sight (NLoS) propagation paths, resulting in degraded localization accuracy. Recent developments in machine learning have facilitated the development of machine learning-assisted localization techniques, enhancing localization accuracy in complex radio environments. However, these methods often involve substantial computational complexity during both the training and inference phases. This work extends the well-established fingerprinting-based localization framework by simultaneously reducing its memory requirements and improving its accuracy. Specifically, a model-based neural network is used to learn the location-to-channel mapping, and then serves as a generative neural channel model. This generative model augments the fingerprinting comparison dictionary while reducing the memory requirements. The proposed method outperforms fingerprinting baselines by achieving sub-wavelength localization accuracy, even in complex static NLoS environments. Remarkably, it offers an improvement by several orders of magnitude in localization accuracy, while simultaneously reducing memory requirements by an order of magnitude compared to classical fingerprinting methods.

Figures (11)

• Figure 1: Overview of the proposed method: the left-hand side illustrates the classical $k$-NN/MLP approaches using a fixed database (DB), whereas the right-hand side depicts the proposed scheme, in which a neural network learning the location-to-channel mapping serves as a neural database.
• Figure 2: Memory-performance trade-off comparison. The memory requirements of the proposed method originates from the used neural network learnable parameters: further explanations are provided in Section \ref{['sec:experiments']}.
• Figure 3: Architecture of the neural model $f_{\boldsymbol{\theta}}$ proposed in chatelier_loc2chan24. The Fourier Feature (FF) embedding projects the input location $\mathbf{x}$ into a subspace that captures high frequency variations.
• Figure 4: Illustration of Theorem \ref{['thm:minima_frob']} in a vector space whose origin is $\mathbf{x}$: minimum circles for $N_a = 4$ antennas, $N_s = 3$ frequencies (color-coded as gray/red/green), and $k \in \llbracket 0, 2\rrbracket$. For $k=0$, circles originating from all frequencies coincide, as observed in Eq \ref{['eq:thm_condition_global_min']}.
• Figure 5: Illustration of the proposed localization scheme steps. $\mathrm{a}$: a grid-search is performed on the global grid $\mathbb{G}_{\mathsf{G}}$. $\mathrm{b}$: a second grid-search is performed on the local grid $\mathbb{G}_{\mathsf{L}}$, constructed from the obtained location at the previous step. $\mathrm{c}$: a first gradient-descent procedure is performed, and a local-minima is reached. $\mathrm{d}$: locations are sampled on circles of center $\tilde{\mathbf{x}}_{\mathrm{gd}}$ and radii $k \lambda_0$. $\mathrm{e}$: a second gradient-descent procedure is performed from the best location in the sampled circle locations, from a PS distance perspective. The bottom row illustrates the steps and loss functions involved in the proposed method (Off-Grid (PI/PS)) and its variants, which are presented in details in Section \ref{['sec:experiments']}.

Theorems & Definitions (21)

• Remark 2.1
• Definition 1
• Remark 3.1
• Remark 3.2
• Definition 2
• Remark 3.3
• Definition 3
• Remark 3.4
• Theorem 1
• proof