Sensing Data Protocol (SDP) Overview

• Sensing Data Protocol (SDP) is a framework that standardizes sensing data acquisition, preprocessing, and benchmarking across wireless sensor networks and cloud environments.
• It employs deterministic sanitization, canonical frequency projection, and tensor construction along with CP factorization for efficient, hardware-agnostic data representation.
• SDP integrates advanced security measures like JSON Web Encryption and signature protocols, and uses rigorous evaluation metrics to enhance reproducibility and performance.

The Sensing Data Protocol (SDP) is a class of protocol-level specifications, middleware layers, and benchmark frameworks developed for acquiring, representing, securing, and benchmarking sensing data across wireless sensor networks and cloud-enabled environments. Modern SDP variants address challenges of data heterogeneity, fairness, reproducibility, and statistical rigor in learning-based wireless sensing. Distinct SDP instantiations exist for efficient data forwarding, hardware-agnostic tensor canonicalization, unified benchmarking, and cloud security. The SDP concept harmonizes physical-layer data preprocessing, canonical tensor construction, standardized evaluation, and, in some designs, cryptographically rigorous object security and key management.

1. Formal SDP Abstraction and Canonicalization

A contemporary SDP is formally specified as a quadruple

$\mathrm{SDP} = (f_s,\, \mathcal{F},\, T,\, \Pi)$

where:

• $f_s(\cdot)$ is a deterministic physical-layer sanitization function that removes device- and channel-induced artifacts (e.g., sampling time offset (STO) and carrier frequency offset (CFO)) from raw channel state information (CSI), through phase corrections:

$$\tilde{h}_{r,t}^{(k)}(t) = \hat{h}_{r,t}^{(k)}(t) \exp\big(j\,2\pi(\hat{\delta} f_k + \hat{\epsilon} t)\big)$$

where $f_k$ is subcarrier frequency, and $\hat{\delta}, \hat{\epsilon}$ are estimates of STO and CFO.

• $\mathcal{F}$ performs canonical frequency projection by interpolating device-specific raw subcarrier measurements onto a fixed grid of size $K$, resulting in device-agnostic representations:

$$\mathcal{F}(\mathbf{h}_{r,t}(\cdot); K)_k = \mathrm{interp}\big(\{h_{r,t}^{(k')}\}_{k'=1}^{K_{\rm raw}}\big)$$

• $T$ denotes canonical tensor construction. Sanitized and projected CSI is organized into tensors $\mathcal{X} \in \mathbb{C}^{A \times K \times T}$, with $A=N_rN_t$ antenna pairs, $K$ canonical subcarriers, and window length $T$.
• $\Pi$ prescribes fully specified and deterministic training and evaluation protocols: fixed data splits (e.g., cross-user), locked random seeds, optimizer settings, and evaluation metrics (Zhang et al., 13 Jan 2026, Huang et al., 13 Dec 2025).

This layered abstraction allows pipeline-agnostic learning over wireless sensing data, supporting reproducibility, interoperability, and hardware-agnosticism.

2. Unified Data-Block Schemas and Synchronization

SDP mandates a device- and modality-agnostic data schema for representing multi-modal wireless signals. The canonical frame- and sequence-level structure is as follows (Huang et al., 13 Dec 2025, Zhang et al., 13 Jan 2026):

• Frame-level:
  • timestamp: real-valued
  • subcarrier list $\mathcal{K} = \{k_1, ..., k_K\}$
  • channel matrices $\{H_k(t)\}_{k \in \mathcal{K}}$, $H_k(t) \in \mathbb{C}^{N_r \times N_t}$
  • validity mask $$M_{\rm frame}(t) \in \{0,1\}^{N_r \times N_t \times K}$$
• Sequence-level:
  • Stack $W$ consecutive frames for sliding windows into tensors $X \in \mathbb{C}^{A \times K \times T}$, with $A=N_rN_t$ and $T=W$.

Non-OFDM modalities (e.g., FMCW radar) are resampled and interpolated to this canonical layout. Temporal and frequency alignment is handled by:

• Timestamp correction using linear model fitting: $$t_{i,n}^{\rm corrected} = \alpha_i t_{i,n} + \beta_i$$
• Frequency alignment by mapping raw $\mathcal{K}_i$ to canonical $\mathcal{K}$
• Linear interpolation for time resampling
• Validity masking for sequences outside valid capture intervals

These steps ensure cross-device and cross-modality comparability.

3. Pooling, Factorization, and Benchmark Protocols

A signature feature is the canonical pooling stage, typically realized via Canonical Polyadic (CP) factorization using Alternating Least Squares (ALS). For a windowed tensor $X \in \mathbb{C}^{A \times K \times T}$, SDP computes a rank-$R$ CP decomposition: $$X \approx \sum_{r=1}^R \mathbf{a}_r \circ \mathbf{b}_r \circ \mathbf{c}_r = [\![A, B, C]\!]$$ with factors $A \in \mathbb{C}^{A \times R}$, $B \in \mathbb{C}^{K \times R}$, $C \in \mathbb{C}^{T \times R}$. The ALS update equations optimize

$$\min_{A, B, C} \left\| X - [\![A,B,C]\!] \right\|_F^2 + \epsilon (\|A\|_F^2 + \|B\|_F^2 + \|C\|_F^2)$$

and employ mode-$n$ unfolding and Khatri–Rao products for efficient updates. The pooled descriptor $h$ concatenates per-factor norms, centroids, and mode-wise spreads.

Downstream learning models share a standardized architecture: ResNet-style 2D stems plus temporal Transformer backbones, locked at $\approx$4.3M parameters and 0.42 GFLOPs. Task heads include:

• Detection: binary sigmoid+threshold
• Recognition: softmax+cross-entropy
• Regression: linear+$\ell_2$ loss

The protocol prescribes cross-user data splits, fixed preprocessing, and explicit loss weighting by learned task uncertainties.

4. Security, Confidentiality, and Key Management in Sensing Data Protocols

Some SDP instances focus on secure sensor data outsourcing, as realized in the SensorCloud Protocol (Henze et al., 2016). The data representation is based on SenML-style JSON records with a common envelope, supporting both cleartext and encrypted payloads. Security is provided through per-record object security:

• Confidentiality: JSON Web Encryption (JWE; RFC 7516) for field-level symmetric-key encryption (AES-GCM-256).
• Integrity and Authenticity: JSON Web Signature (JWS; RFC 7515) with ECDSA-P256 signatures.
• Key Management: Asymmetric distribution of public keys (gateway/cloud), symmetric data-keys for per-sensor encryption, and explicit key upload/download message types (typ=400/401/402/403). All cryptographic mechanisms adhere strictly to IETF standards.

The protocol supports fine-grained access control and multi-tenant isolation, with end-to-end flows encompassing data capture, encryption, signing, HTTPS/MQTT transmission, cloud ingestion, and controlled service-side decryption.

5. Statistical Measures, Experimental Validation, and Benchmarking

SDP frameworks deploy rigorous and standardized metrics to ensure robust and reproducible evaluation:

• Classification: Top-1 accuracy and macro-F1 score
• Regression: Mean Absolute Error (MAE)
• Stability: Inter-seed variance/standard deviation across fixed random seeds
• Confidence Intervals: 95% Student-$t$ intervals
• Efficiency: Parameter count, GFLOPs, GPU latency

Extensive experiments across canonical datasets (Widar3.0, GaitID, XRF55, ElderAL-CSI) demonstrate that SDP pipelines achieve competitive or improved accuracy while reducing inter-seed variance by up to an order of magnitude (e.g., Widar3.0: $91.8\%\pm0.3\%$ with SDP vs. $90.3\%\pm1.2\%$ baseline (Zhang et al., 13 Jan 2026)). Performance is hardware-agnostic; cross-device deployments yield stable, transferable results with modest computational overhead ($\approx$2.9% GFLOPs reduction in some settings).

6. Protocol Trade-Offs, Reproducibility, and Scalability

SDP’s deterministic design mandates no data augmentation, fixed random seeds, and invariant preprocessing pipelines, significantly enhancing reproducibility and comparability. The cost is a modest potential reduction in absolute accuracy for highly specialized tasks, but gains in protocol- and algorithm-level interpretability greatly outweigh this constraint for benchmarking purposes. Pooling on a canonical frequency grid ($K=30$) ensures both expressiveness and insensitivity to high-dimensional device noise.

For secure SDPs, strict object security, standardized JSON semantics, and key management assure per-tenant data protection and compliance with modern cryptographic requirements.

Scalability analyses indicate protocol overheads scale with $O(M\,\#\text{forwarded packets})$, with fundamental efficiency gains obtained via compressed superpositions, compressed sensing, and factorization-based reductions (Kaneko et al., 2012, Huang et al., 13 Dec 2025, Henze et al., 2016).

7. Related Protocols and Extensions

Compressed-sensing-based SDP variants enable energy-efficient, routing-free forwarding in multi-hop wireless sensor networks by leveraging in-network sparse recovery. Nodes forward superimposed event signatures, recover original messages via iterative $\ell_1$-regularized minimization (e.g., ISTA), and achieve overhead/energy reductions of $80$-$90\%$ versus AODV+MAC or CDMA flooding approaches (Kaneko et al., 2012).

Secure SDP instantiations such as SensorCloud specify extensible, fine-grained message schemas scalable for RESTful or MQTT-based delivery in both private and public cloud contexts (Henze et al., 2016).

A plausible implication is that SDP offers a foundation for the unification of sensing data acquisition, heterogeneous device integration, standardized learning-based benchmarking, and cloud-native security, accelerating the field’s transition toward reproducible, interoperable, and statistically rigorous wireless sensing research.