Digital Twin--Driven Adaptive Wavelet Strategy for Efficient 6G Backbone Network Telemetry

TL;DR

This paper tackles the challenge of compressing backbone network telemetry for 6G digital twins while preserving long-range dependence (LRD) and energy conservation. It presents an exact equivalence between MERA tensor networks and paraunitary two-channel filter banks, enabling adaptive, orthonormal wavelets learned on the Stiefel manifold with polar projection to guarantee perfect reconstruction. Empirically, learned MERA-inspired wavelets achieve up to 3.8 dB PSNR gains over fixed wavelets on MAWI traces and preserve the Hurst exponent within $|\Delta H| \le 0.03$ at high compression, demonstrating robust LRD fidelity for DT synchronization. The framework provides a scalable, energy-conserving, and theoretically sound platform for telemetry compression in 6G DTs, with potential extension to wireless and edge environments. Overall, the work offers a principled bridge between adaptive data-driven representation learning and strict signal-processing guarantees essential for mission-critical network synchronization.

Abstract

Classical orthogonal wavelets guarantee perfect reconstruction but rely on fixed bases optimized for polynomial smoothness, achieving suboptimal compression on signals with fractal spectral signatures. Conversely, learned methods offer adaptivity but typically enforce orthogonality via soft penalties, sacrificing structural guarantees. This work establishes a rigorous equivalence between Multiscale Entanglement Renormalization Ansatz (MERA) tensor networks and paraunitary filter banks. The resulting framework learns adaptive wavelets while enforcing exact orthogonality through manifold-constrained optimization, guaranteeing perfect reconstruction and energy conservation throughout training. Validation on Long-Range Dependent (LRD) network traffic demonstrates that learned filters outperform classical wavelets by 0.5--3.8~dB PSNR on six MAWI backbone traces (2020--2025, 314~Mbps--1.75~Gbps) while preserving the Hurst exponent within estimation uncertainty ($|ΔH| \le 0.03$). These results establish MERA-inspired wavelets as a principled approach for telemetry compression in 6G digital twin synchronization.

Figures (7)

• Figure 1: Layered architecture for NDT synchronization. The telemetry compression layer (highlighted) provides the interface between raw network measurements and the virtual model. This work contributes the adaptive MERA-wavelet codec operating at this layer.
• Figure 2: Multiresolution analysis (MRA) illustrating recursive approximation/detail splitting with decimation by two. The input discrete-time signal $x_n$ is successively filtered by the low-pass filter $g$ (scaling function) and high-pass filter $h$ (wavelet function), followed by downsampling by a factor of two. The approximation stream propagates upward through all levels, while the detail streams are extracted at each corresponding scale. At each stage, the signal length is halved ($N \rightarrow N/2 \rightarrow N/4 \rightarrow N/8$), forming the dyadic tree structure characteristic of the DWT Mallat2009.
• Figure 3: MERA-inspired wavelet circuit with four dyadic levels ($L=4$). The input signal samples $x_1,\dots,x_{16}$ feed the first layer, which consists of parallel $2\times2$ orthogonal blocks $U_1$ acting on disjoint pairs. At each level, the approximation outputs $a^{(\ell)}$ propagate upward through the hierarchy, while the detail outputs $d^{(\ell)}$ are extracted at their respective scales. This hierarchical structure parallels the DWT (Fig. \ref{['fig:mra']}) but employs learnable transformation blocks $U_\ell$, $\ell=1,2,3,4$.
• Figure 4: Two-channel CQF system. (a): Analysis stage splits input $a_{\ell-1}(m)$ via filters $g(-m)$, $h(-m)$ and downsampling by a factor of two ($\downarrow 2$), producing $a_\ell(n)$ and $d_\ell(n)$. (b): Synthesis stage upsamples by a factor of two ($\uparrow 2$), filters via $g(n)$, $h(n)$, and sums to reconstruct $a_{\ell-1}(m)$. PR is characterized in the polyphase domain by a paraunitary matrix, a condition that will be guaranteed by orthogonal $U_\ell$ (Theorem \ref{['thm:circuit_pu']}).
• Figure 5: PSNR gains of MERA-learned wavelets over fixed baselines as a function of retention ratio $\rho$. A retention ratio of $\rho = 0.1$ corresponds to 90% compression (retaining only 10% of coefficients by magnitude). The learned filters consistently outperform classical wavelets across all compression levels and traffic conditions.

Theorems & Definitions (10)

• Definition 1: Unitary Transformation
• Definition 2: Orthogonal Transformation
• Remark 1: Notational Convention
• Definition 3: MERA-Inspired Orthogonal Layer
• Example 1: MERA Layer Computation
• Definition 4: Paraunitary Filter Bank
• Theorem 1: Architectural Equivalence
• Corollary 1: PR QMF as a special case
• proof : Proof of Theorem \ref{['thm:circuit_pu']}
• proof : Proof of Corollary \ref{['cor:qmf']}