High-Frequency Cross-Layer Compensation

• High-frequency cross-layer compensation enhancement is a strategy that restores or leverages high-frequency information across system layers to reduce artifacts and improve signal integrity.
• It employs advanced interpolation techniques and layered parametric architectures to mitigate phase noise, quantization loss, and hardware impairments in wireless and multimedia applications.
• The approach combines spatial and frequency-domain methods using adaptive algorithms, achieving up to 3 dB SNR gains and state-of-the-art performance in both communication and video restoration.

High-frequency cross-layer compensation enhancement refers to a set of principled strategies, algorithmic frameworks, and architectural designs that restore or leverage high-frequency information across the boundaries of inference layers or physical/algorithmic domains. In modern signal processing and neural enhancement pipelines, especially those targeting extreme-frequency wireless communications and high-fidelity multimedia delivery, this paradigm has emerged as central for mitigating artifacts, combating distortion, and achieving statistical near-optimality under challenging conditions.

1. High-frequency Distortions in Cross-layer Systems

High-frequency distortions, typically arising from phase noise in sub-THz wireless links, quantization loss in transform-based compression, or front-end hardware impairments (e.g., IQ imbalance, sampling jitter), degrade the effective SNR and lead to significant performance loss in both physical and algorithmic layers. In DFT-s-OFDM systems used for sub-THz transmission, oscillator-induced phase noise (PN) possesses high temporal correlation and disperses signal energy among subcarriers, generating both common-phase error and inter-carrier interference (ICI) (Bello et al., 2022). In multimedia systems, high-frequency coefficients are the most susceptible to quantization, leading to perceptually significant artifacts in reconstructed images or video (Zhang et al., 18 Mar 2024).

2. Interpolation-based Enhancement in Wireless Receivers

The interpolation filter (IF) framework for DFT-s-OFDM sub-THz receivers exemplifies high-frequency cross-layer compensation. The receiver first extracts PTRS (Phase-Tracking Reference Signal) observations $\underline{\mathbf a}_p$ using pilot subcarriers embedded according to 3GPP protocols, then solves for the minimum mean-squared error (MMSE) estimator of the exponential phase-noise vector $\underline{\mathbf\Phi'}$ via

$$\mathbf Z = (\mathcal R_{\Phi'}\,\mathbf M_p^H)\left[\mathbf M_p\,\mathcal R_{\Phi'}\,\mathbf M_p^H + \mathbf M_p\,\mathcal R_{\beta}\,\mathbf M_p^H\odot(\underline{s_p}\,\underline{s_p}^H) + \mathbf M_p\,\sigma_n^2\,\mathbf M_p^H \odot (\underline{s_p}\,\underline{s_p}^H)\right]^{\dagger}$$

where $\mathcal R_{\Phi'},\mathcal R_{\beta}$, and $\sigma_n^2$ are the covariances of the phase noise, ICI, and AWGN respectively, and $\mathbf M_p$ is a binary sampling matrix. The estimator reconstructs phase rotations at all active subcarriers, allowing full-resolution derotation—even in the presence of sparse pilot allocation and rapidly-varying phase noise. This enables substantial BER and TBLER gains over linear or DCT-based interpolators, especially at low pilot density (up to 3 dB SNR improvement at 16-QAM; 0.8 dB for 64-QAM at 300 GHz) (Bello et al., 2022). Notably, the algorithm's construction is agnostic to specific pilot patterns and seamlessly integrates with existing 5G-NR standards.

3. Multi-layer Parametric Architectures for Joint Impairments

In the context of high-frequency broadband links, layered compensation engines such as the PhyCOM network generalize cross-layer enhancement to arbitrary constellations of intertwined linear impairments (Choqueuse et al., 2022). PhyCOM models the channel and all front-end distortion sources as a succession of widely linear parametric layers, each invertible via a compact trainable mapping. Physical layers—representing IQ imbalance, carrier frequency offset (CFO), phase noise (via block-diagonal or Wiener models), and sparse FIR multipath—are jointly inverted via a feedforward network, culminating in maximum a posteriori symbol projection.

Training leverages a Levenberg–Marquardt (LM) or Gauss–Newton optimizer, balancing pilot allocation and computational cost to achieve near-clairvoyant symbol error rates at mmWave/microwave frequencies with only tens of pilots even under rapidly-evolving high-frequency channel statistics. This approach eliminates the error floors typical of concatenated DSP blocks by enforcing global compensation across layers, directly targeting high-frequency nonidealities that manifest differently in each parametric block.

4. High-frequency Enhancement in Neural Upsampling Networks

In transform-based video (or image) enhancement, high-frequency cross-layer compensation is operationalized by combining frequency-domain priors with spatial-domain refinement modules. The Hierarchical Frequency-based Upsampling and Refining (HFUR) network exemplifies this approach (Zhang et al., 18 Mar 2024). HFUR’s Implicit Frequency Upsampling (ImpFreqUp) module first synthesizes missing high-frequency DCT coefficients via a quantization-aware convolutional branch, injecting learned estimates of quantization loss directly in the latent frequency space. This process is implemented via a learned implicit IDCT, with kernel weights initialized from the DCT matrix, enabling coarse-to-fine recovery at fractional spatial resolutions.

Subsequently, the Hierarchical and Iterative Refinement (HIR) module splits features into high and low-frequency branches. Detail refinement is performed via self-attentive residual blocks, while non-local contextual refinement suppresses artifacts in low-frequency content. Inter-branch cross-compensation iteratively shares information, compensating both missing high-frequency detail and filtered-out contextual cues. The overall pipeline is jointly supervised by spatial and DCT-domain losses to ensure both artifact suppression and edge integrity.

5. Design Principles and Implementation Options

Across domains, certain principles for high-frequency cross-layer compensation enhancement emerge:

• Leverage exact or affine-learned transform-domain quantization tables to target restoration at high-frequency bins most affected by channel or compression operations (Zhang et al., 18 Mar 2024).
• Exploit stochastic models of high-frequency impairment (e.g., phase noise covariance) to construct LMMSE/Wiener-optimal compensation matrices (Bello et al., 2022).
• Build modular, layer-wise parametric networks, allowing insertion or exclusion of compensation layers as dictated by dominant hardware or channel effects (e.g., adding PN layers or block-FIR updates at higher carrier frequencies) (Choqueuse et al., 2022).
• Fuse information across spatial and frequency scales, employing iterative cross-compensation to enhance restoration robustness and avoid over-suppression of valid high-frequency content (Zhang et al., 18 Mar 2024).
• Integrate compensation and detection (or enhancement) in a joint optimization, rather than concatenating single-effect modules. This elevates performance beyond what is feasible with isolated linear or non-blind restoration blocks.

Table: Comparison of Selected Cross-layer Enhancement Approaches

Approach/Domain	Core Mechanism	High-frequency Effectiveness
IF for DFT-s-OFDM (Bello et al., 2022)	LMMSE phase-noise interpolation	3 dB SNR BER gain at low pilot density
PhyCOM (Choqueuse et al., 2022)	Layered ZF network, all impairments	Sub-1% SER floor with minimal pilots
HFUR (Zhang et al., 18 Mar 2024)	DCT upsampling + dual-pass refinement	State-of-the-art video artifact suppression

6. Performance Characterization and Limitations

Performance benchmarks consistently show that high-frequency cross-layer compensation enhancement leads to marked improvements in both uncoded and coded communication error rates, as well as in perceptual quality and objective error for multimedia post-processing. For instance, IF filtering at 64-QAM and 300 GHz yields 0.8 dB SNR gain over linear approaches at coded block error rates ≈0.1 (Bello et al., 2022). PhyCOM closes the gap to clairvoyant joint compensation with semisupervised refinement and moderate computational requirements, outperforming traditional DSP in both MSE and SER (Choqueuse et al., 2022). HFUR achieves state-of-the-art visual quality metrics by explicitly targeting frequency-domain artifacts (Zhang et al., 18 Mar 2024).

However, real-time cross-layer signaling, blocklength limitations, and pilot overhead introduce trade-offs. Notably, higher-layer MAC/RRC adaptation (e.g., for dynamic pilot density or filter complexity) is not addressed in current IF or PhyCOM work. Algorithmic extensions to generalized transforms (e.g., non-DCT basis, multiantenna scaling) and cross-domain transfer remain open for future research.

7. Future Directions and Recommendations

For future system evolution, the available literature suggests several actionable directions:

• Integrate cross-layer compensation with adaptive, real-time control signaling once standard support matures.
• Generalize compensation networks to non-orthogonal or overcomplete transform domains, including wavelets and learned bases.
• Extend modular compensation to multi-dimensional/multi-antenna physical layers, including frequency-dependent impairments.
• Codify iterative, cross-compensating refinement as a general pattern for cascaded physical-digital systems and for neural restoration pipelines.
• Leverage joint frequency-spatial objective functions to guarantee no compromise between artifact removal and high-frequency fidelity.

By formalizing high-frequency cross-layer compensation enhancement—across wireless physical layers, algorithmic enhancement nets, and their interaction with protocol design—researchers and engineers can achieve robust, spectrally efficient, and high-fidelity systems well-matched to the requirements of next-generation communications and multimedia applications (Bello et al., 2022, Choqueuse et al., 2022, Zhang et al., 18 Mar 2024).