Weber-Fechner Quality of Experience Model

• Weber-Fechner QoE models are perceptually-inspired metrics that use logarithmic scaling to map system resources to subjective quality perception.
• They are integrated into optimization frameworks like mixed-integer programming and reinforcement learning to enhance resource allocation in VR and vehicular networks.
• Empirical studies demonstrate reduced latency and improved fairness by aligning resource allocation with the non-linear characteristics of human sensation.

The Weber-Fechner Quality of Experience (QoE) Model defines a class of perceptually inspired, mathematically grounded user experience metrics which model human quality perception for networked, interactive, or perceptual computing systems. These models leverage the psychophysical Weber-Fechner law—originally describing the logarithmic scaling between the intensity of a physical stimulus and its perceived strength—to ensure that resource allocation and algorithmic design decisions align with the nonlinearities of human sensation. In modern applications, Weber-Fechner-based QoE models are used as reward signals or optimization objectives in wireless multimedia systems, multi-user virtual reality (VR) platforms, and embodied AI-enhanced vehicular networks, directly influencing reinforcement learning and mixed-integer optimization procedures.

1. Theoretical Foundations: Weber-Fechner Law in Psychophysical Modeling

The classical Weber-Fechner law formalizes the empirically observed relationship that perceived intensity $S$ of a stimulus is proportional to the logarithm of its physical magnitude $I$ relative to a threshold $I_0$:

$S = k \ln\left(\frac{I}{I_0}\right)$

where $k$ is the “Weber fraction” and $I_0$ is the minimal detectable stimulus. This formulation unifies Weber’s law (change detection proportional to stimulus magnitude) and Fechner’s logarithmic law (perceived intensity over orders of magnitude). In the context of QoE models, stimulus $I$ is mapped onto an application-dependent resource (e.g., keyframe rate, transmit power), and $S$ is related to the user’s perceptual satisfaction.

2. Application to VR: Weber-Fechner QoE in Virtual Reality Interaction

In multi-user VR ecosystems, the Weber-Fechner model is instantiated to reflect the perceptual impact of visual fidelity and system latency. The key technical construction is as follows (Zhang et al., 24 Jun 2025):

• Stimulus Definition: For each user $k$, attention level $a$, and time slot $I$0, the stimulus is the normalized number of delivered keyframes,

$I$1

where $I$2 is the keyframes/sec in attention tier $I$3 and $I$4 is the slot duration (with the minimum possible $I$5 per slot serving as threshold $I$6).

• Perceptual Mapping: The perceived fidelity is then

$I$7

• Composite QoE Metric:

$I$8

where $I$9 is total latency, $I_0$0 the allowable latency, $I_0$1 indexes visual attention from blind spot (0) to central vision (3), $I_0$2 the count of salient characters, and $I_0$3 the total in field of view.

The inclusion of latency and attention weights ensures multidimensional fidelity constraints while ensuring the metric is strictly monotonic with critical user-centric parameters.

3. Integrating Weber-Fechner QoE into Optimization Frameworks

The constructed Weber-Fechner QoE metric is embedded directly into resource allocation problems. In VR, the design is formalized as a mixed-integer program (MIP) over bandwidth $I_0$4, CPU frequencies $I_0$5, and integer keyframe rates $I_0$6. The objective is

$I_0$7

subject to system constraints (total bandwidth, server CPU, range/integrity of $I_0$8, and per-slot as well as aggregate fairness/quality lower bounds). Solution methods rely on continuous-discrete action reinforcement learning, notably Partial-State Causal DDPG (PS-CDDPG), where the sum of $I_0$9 acts as the core reward, and fairness/feasibility constraints modulate penalties during agent training (Zhang et al., 24 Jun 2025).

4. Extension to Multi-User Fairness and Horizon-Fair QoE

QoE fairness across multiple users is quantified using the horizon-fair QoE (hfQoE), defined as

$S = k \ln\left(\frac{I}{I_0}\right)$0

where $S = k \ln\left(\frac{I}{I_0}\right)$1 is the standard deviation of users’ average QoE, $S = k \ln\left(\frac{I}{I_0}\right)$2 and $S = k \ln\left(\frac{I}{I_0}\right)$3 the respective maximum and minimum QoE observed over users and time up to $S = k \ln\left(\frac{I}{I_0}\right)$4. This metric penalizes dispersion in subjective experience and is enforced as a hard constraint in optimization, ensuring no user experiences persistent underperformance relative to the group (Zhang et al., 24 Jun 2025).

5. Alternate Instantiations: Weber-Fechner QoE in Vehicular Networks

In vehicular systems, Weber-Fechner-inspired QoE models are adapted to encode semantic communication fidelity and radio resource consumption. The core metric is

$S = k \ln\left(\frac{I}{I_0}\right)$5

where $S = k \ln\left(\frac{I}{I_0}\right)$6 is semantic similarity (cosine between BERT embeddings of transmitted/reconstructed messages), $S = k \ln\left(\frac{I}{I_0}\right)$7 is transmit power, $S = k \ln\left(\frac{I}{I_0}\right)$8 is link/subband assignment, and $S = k \ln\left(\frac{I}{I_0}\right)$9, $k$0 are monotonic normalizations emulating diminishing returns (in practice, $k$1, $k$2). The optimization procedure seeks to maximize QoE subject to power, SINR, and semantic-fidelity constraints, and system-level resource allocation is governed by this perceptual metric (Zhang et al., 2 Jan 2025).

6. Adaptive Resource Control and Empirical Outcomes

Empirical studies demonstrate that Weber-Fechner-based QoE models capture the non-linear, saturating effects of resource increments on perceived quality. In VR, joint optimization using these metrics results in significant reduction in interactive latency and improved fairness and individual experience, outperforming non-perceptually guided alternatives (Zhang et al., 24 Jun 2025). In vehicular networks, adaptation of semantic symbol length and resource allocation guided by Weber-Fechner metrics yields superior performance under dynamic channel conditions and system load, confirming that QoE improves sublinearly with increased resources and semantic fidelity, in accordance with diminishing-returns predicted by the law (Zhang et al., 2 Jan 2025).

7. Assumptions, Scaling, and Generalization

Across both domains, design choices such as the selection of minimum keyframes (defining $k$3), normalization functions ($k$4 versus explicit logarithms), and multi-factor compositionality reflect system-specific trade-offs. Slot-based mapping ($k$5s), attention-weighted summation, and clarity on minimum/maximum latency thresholds ensure practical enforceability and non-negativity of the QoE metric. The paradigm is extensible to other perceptual applications—audio, haptics, or multimodal interfaces—provided that the mapping between stimulus and sensation adheres to the psychophysical principles underlying the Weber-Fechner law.

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Summary Table: Weber-Fechner QoE Metric Realizations in Two Domains

Domain	Formula	Resource Parameterization
Virtual Reality (VR)	$k$6	Keyframe rate, latency, attention levels
Vehicular Networks	$k$7	Transmit power, semantic similarity, link assignment

These models underpin reinforcement learning and constrained optimization procedures, delivering perceptually fair and efficient quality targets in complex, resource-bounded systems.