Simultaneous Source Separation, Synchronization, Localization and Mapping for 6G Systems

TL;DR

This work tackles MP-SLAM in 6G by handling simultaneous source separation, synchronization, and environment mapping when base stations are unsynchronized and introduce inter-BS interference. It proposes a BS-dependent data association model within a joint Bayesian framework and solves the inference via sequential sum-product message passing on a factor graph, jointly estimating MT states, BS biases, and PVAs (including VA/PVA states) over time. The results show no significant performance loss compared to fully synchronized, orthogonal baselines, demonstrating robust localization and mapping under interference, while enabling principled feature classification by persistent properties. The framework is flexible and scalable, with potential to integrate additional sensing modalities and to extend to real-world PRS data and dynamic network scenarios, contributing to robust ISAC-enabled 6G deployments.

Abstract

Multipath-based simultaneous localization and mapping (MP-SLAM) is a promising approach for future 6G networks to jointly estimate the positions of transmitters and receivers together with the propagation environment. In cooperative MP-SLAM, information collected by multiple mobile-terminals (MTs) is fused to enhance accuracy and robustness. Existing methods, however, typically assume perfectly synchronized base stations (BSs) and orthogonal transmission sequences, rendering inter-BS interference at the MT negligible. In this work, we relax these assumptions and address simultaneous source separation, synchronization, and mapping. A relevant example arises in modern 5G systems, where BSs employ muting patterns to mitigate interference, yet localization performance still degrades. We propose a novel BS-dependent data association and synchronization bias model, integrated into a joint Bayesian framework and inferred via the sum-product algorithm on a factor graph. The impact of joint synchronization and source separation is analyzed under various system configurations. Compared with state-of-the-art cooperative MP-SLAM assuming orthogonal and synchronized BSs, our statistical analysis shows no significant performance degradation. The proposed BS-dependent data association model constitutes a principled approach for classifying features by arbitrary properties that persist over time, such as reflection order or feature type (scatter points versus walls).

Figures (6)

• Figure 1: Figure (a) shows an exemplary environment consisting of three walls including a single mt that receives radio signals via multipath propagation from two unsynchronized, interferingbs that transmit using identical frequency bands/symbols. Figure (b) shows the received signal at the center of gravity of MT1 at time $n$. The signals from BS1 and BS2 are delayed with respect to time $0$ by the apparent synchronization biases $\Delta b_{1}^{(1)} = b_{\mathrm{bs},n}^{(1)} - b_{\mathrm{mt},n}^{(1)}$ and $\Delta b_{1}^{(2)} = b_{\mathrm{bs},n}^{(2)} - b_{\mathrm{mt},n}^{(1)}$, which arise from the differences between the corresponding BS and MT clock biases.
• Figure 2: Simulation environment for time $n=1$ after the first MT update (a), the last MT update (b) and for time $n=2$ after the last MT update. The colors represent the true (box) and the estimated (+ and dot) association of map features (pva) to bs.
• Figure 3: Exemplary indoor environment with one bs at position $\bm{p}^{(j)}_\text{bs}$ and two MTs at position $\bm{p}_{n}^{(i)}$ and $\bm{p}_{n}^{(i')}\space\space$, jointly observing a va at $\bm{p}^{(j)}_{\text{va},l}$. The figure also illustrates the array geometry of the agents and pa, assuming $o^{(j)}_{n}=0$.
• Figure 4: Factor graph corresponding to the factorization shown in \ref{['eq:jointpostpdf']}. Dashed arrows represent messages that are only passed in one direction. The detailed graph in (a) represents the green subgraphs of the overall factor graph in (b). The following short notation is used. Variables and variable nodes: $\bm{x}_i \triangleq \bm{x}^{(i)}_{n}$, $\underline{\bm{y}}^{i}_k \triangleq \underline{\bm{y}}^{(i)}_{k,n}$, $\overline{\bm{y}}^{j}_m \triangleq \overline{\bm{y}}^{(j,i)}_{m,n}$, $\underline{a}_k \triangleq \underline{a}^{(i)}_k$, $\overline{a}_m \triangleq \overline{a}^{(i)}_m$, $b_{\text{bs}}^{j} \triangleq b_{\text{bs},n}^{(j)}$, $\overline{j}_m \triangleq \overline{j}^{(i)}_{m,n}$, $K^- \triangleq K_{n-1}$, $K \triangleq K^{(i)}_{n}$$\tilde{K} = J+ K^{(i)}_{n}$, and $K^+ \triangleq K_{n}$. Factor node: $f_{i} \triangleq f(\bm{x}^{(i)}_{n}|\bm{x}^{(i)}_{n-1})$, $f_{y,k} \triangleq f(\underline{\bm{y}}_{k,n} | \bm{y}_{k,n-1})$ for $i = 1$, $f_{y,k} \triangleq f(\underline{\bm{y}}^{(i)}_{k,n} | \bm{y}^{(i-1)}_{k,n-1})$ for $i > 1$, $f^{j}_{\text{b}} \triangleq f^{(i)}(b_{\text{bs},n}^{(j,i)}| b_{\text{bs},n}^{(j,i-1)})$, and $\psi_{ k,m} \triangleq \Psi(\underline{a}^{(i)}_{k,n},\overline{a}^{(i)}_{m,n})$. Messages: $\tilde{f}_\text{x}^{i} \triangleq f(\bm{x}^{(i)}_{n}|\bm{z}_{1:n})$, $\tilde{f}_\text{b}^{j} \triangleq f(b_{\text{bs},n}^{(j)}|\bm{z}_{1:n})$, and $\tilde{f}_k \triangleq f(\bm{y}_{k}|\bm{z}_{1:n})$, where $\bm{y}_{k}$ represents an entry of $\bm{ \mathsfbr{y} }_{n} \!=\space [\underline{\bm{ \mathsfbr{y} }}^{(I)\space \text{T}}_{n} \space\space \overline{\bm{ \mathsfbr{y} }}^{(I) \text{T}}_{n} ]^\text{T}$. The dashed arrows indicate messages representing MT and PVA beliefs of time $n-1$ and $n+1$, which are only propagated forward in time and the minus sign "$-$" indicates beliefs from the previous time $n-1$.
• Figure 5: Performance of mt and bs biases in terms of mean error per time $n$.