Sensor-Guided CHM Modulation

• Sensor-guided CHM modulation is a framework using sensor data to adjust modulation processes in anomaly detection, imaging, and communications.
• It integrates low-dimensional sensor inputs with high-dimensional data, ensuring causal, context-driven feature scaling and signal optimization.
• Applications include adaptive phase modulation in lensless imaging, energy-efficient UAV communications, and robust delay-Doppler automotive radar.

Sensor-guided CHM modulation encompasses a class of frameworks, techniques, and architectures in which sensor signals directly inform or adapt modulation processes—either for feature extraction in machine learning (e.g., anomaly detection), physical-layer communication, or optical imaging. Recent work demonstrates this paradigm across industrial machine vision, lensless microscopy, resource-constrained wireless data collection, and integrated sensing-communication radar systems. The “CHM” abbreviation refers to Causal Heterogeneous Modulation in anomaly detection (Liu et al., 25 Dec 2025), Continuous Height Modulation in computational imaging (Jiang et al., 2021), Combined Height-and-Modulation in UAV communications (Chen, 2022), and Chirp-guided Delay-Doppler Modulation in automotive radar (Li et al., 22 May 2025), with each instantiation ultimately using sensor-derived context to guide modulation of critical feature streams.

1. Fundamental Principles and Roles

Sensor-guided CHM modulation arises from the need to balance, exploit, and physically link disparate information streams in scenarios characterized by strong heterogeneity or causal relationships. In robotic welding UAD, low-dimensional, high-frequency sensor data (current, voltage) encode causal process context, whereas high-dimensional modalities (video, audio) are susceptible to drowning out subtle process cues (Liu et al., 25 Dec 2025). The key principle is to use sensor signals as a governing prior, such that they can scale and shift downstream features in neural encoders. In lensless imaging, sensor placement and movement directly modulate the diversity of phase information available for computational phase retrieval (Jiang et al., 2021). In UAV wireless harvesting and mmWave radar ISAC, dynamic modulation jointly controlled by sensor feedback (height, channel state, environmental maps) optimizes power, rate, and robustness (Chen, 2022, Li et al., 22 May 2025).

2. Architectural Implementations and Data Flows

The architectural details depend on domain and signal type. In “Causal-HM,” raw process signals—$X_v$ (video), $X_a$ (audio), $X_s$ (sensor time series)—are fed to feature extraction backbones (V-JEPA2, AST) and to a Mamba state-space sensor encoder (Liu et al., 25 Dec 2025). The sensor encoder outputs a context vector $h_s$, projected into affine parameters $[\gamma,\beta]$ that modulate every activation in the backbones via

$$f_{\rm CHM}(F,h_s) = F\odot(1+\gamma(h_s)) + \beta(h_s)$$

for feature matrix $F$ in video or audio tokens.

In lensless imaging, the tilted sensor physically induces a location-dependent object-to-detector height $z(x) = x\sin\theta$, which produces a controlled phase modulation $\phi(x) = \frac{2\pi}{\lambda}x\sin\theta$ for each scan (Jiang et al., 2021). By laterally scanning the specimen and recording frames, one builds a dataset with rich defocus diversity for multi-height phase retrieval.

UAV-sensor data harvesting uses a constrained Markov decision process, with system state $s_t = (D_t, H_t, B_t)$ and joint adaptive actions $a_t = (M_t, U_t)$—modulation index and height change—selected using backward induction to minimize expected sensor transmit energy under BER, volume, and height constraints (Chen, 2022).

In mmWave vehicular radar, cognitive sensing by dedicated chirps identifies idle time-frequency bars. Data is then modulated (delay, Doppler, amplitude) within those blocks via TDM or DDM schemes, adapting to sensor feedback on the environment and system state (Li et al., 22 May 2025).

3. Mathematical Formalisms and Core Algorithms

Central to sensor-guided CHM are parameterized modulation equations, policy optimization, and phase retrieval algorithms.

In Causal-HM (Liu et al., 25 Dec 2025):

• $h_s = \mathrm{Mamba}(X_s)\in\mathbb{R}^{d_s}$
• $$[\gamma,\beta]=\mathrm{LinearProj}(h_s)\in\mathbb{R}^{2D}$$
• CHM modulation: $$f_{\rm CHM}(F,h_s) = F\odot(1+\gamma(h_s))+\beta(h_s)$$ for both $F_v$ and $F_a$

Pseudo-code excerpt:

h_s = MambaEncoder(X_s) gamma, beta = LinearProj(h_s) F_v_mod = F_v * (1 + gamma) + beta F_a_mod = F_a * (1 + gamma) + beta

In lensless continuous height modulation (Jiang et al., 2021):

• The lateral scan at $x_j$ induces defocus $d_j=\tan\theta x_j$
• The iterative phase retrieval engine uses forward/backward propagation and intensity constraints.

For UAV communication (Chen, 2022):

• The transmit power to meet BER constraint:

$$p_t = -\frac{\sigma^2(M_t-1)}{1.6g_t}\ln\left(\frac{\gamma}{0.2}\right)$$

• Bellman recursion for optimal policy:

$$V_t(s_t) = \min_{(M_t,U_t)} \left\{C(s_t,a_t) + \sum_{s_{t+1}}P(s_{t+1}|s_t,a_t)V_{t+1}(s_{t+1})\right\}$$

In automotive radar (Li et al., 22 May 2025):

• Delay-Doppler domain modulation of chirp signals, using FFT-based transformations and matched filtering for symbol recovery in the Range-Doppler Map.

4. Addressing Heterogeneity and Enforcing Causality

A core challenge addressed by CHM mechanisms is the heterogeneity gap: low-dimensional, context-rich sensor data can be overwhelmed by high-dimensional modalities in naive fusion. Sensor-guided modulation acts as a soft gating (affine transform), ensuring that sensor events modulate all downstream features proportionally (Liu et al., 25 Dec 2025). This residual-style modulation guarantees unidirectional process-to-result causal flow; sensor signals modulate process features upstream, prior to encoding and mapping to result features. In lensless imaging, the sensor’s physical geometry imposes phase diversity essential for robust phase retrieval, with continuous, spatially indexed modulation derived automatically from sensor position (Jiang et al., 2021). In UAV communications and radar ISAC, adaptive policies based on sensor-derived state optimize energy efficiency and sensing-communication coexistence (Chen, 2022, Li et al., 22 May 2025).

5. Performance Metrics and Experimental Outcomes

Reported metrics and outcomes are domain specific:

• “Causal-HM” achieves a state-of-the-art I-AUROC of 90.7% on Weld-4M benchmark across four modalities, demonstrating robust anomaly detection (Liu et al., 25 Dec 2025).
• Lensless continuous height modulation resolves 690 nm linewidth targets and acquires 120 mm² blood-smear mosaics with match-to-manual WBC counting in 18 s (Jiang et al., 2021).
• UAV CHM data harvesting saves up to 48.23% energy over modulation-only baselines, with non-monotonic savings as height steps increase (Chen, 2022).
• Automotive radar DDM achieves $\mathcal{O}(10^3)$ bps rates and maintains sub-DFT-limit range/velocity/angle estimation errors, with robust BER vs. SNR scaling (Li et al., 22 May 2025).

Paper ID	Domain	Key Metric / Outcome
(Liu et al., 25 Dec 2025)	Mfg UAD	I-AUROC 90.7% (Weld-4M); robust causality
(Jiang et al., 2021)	Optical Im.	690 nm res; WBC count = manual; 18s mosaic
(Chen, 2022)	UAV Data	48.23% energy saved vs modulation-only
(Li et al., 22 May 2025)	Auto Radar	DDM $\sim 10^3$ bps; sub-DFT param errors

6. Practical Considerations and Tuning

Implementation details impact robustness and reproducibility. In Causal-HM (Liu et al., 25 Dec 2025):

• Mamba SSM: 2 layers, $d_s=128$
• CHM modulation head: $128 \rightarrow 2 \times 512$, bias included, zero initialization
• Training: AdamW, lr = $10^{-4}$, batch = 16, 300 epochs, cosine annealing

In lensless imaging (Jiang et al., 2021):

• Sensor tilt $\theta \sim 5^\circ$; pixel pitch 1.67 µm
• Lateral stage precision $<0.1$ µm; super-resolution factor $M=3$

In UAV and radar systems (Chen, 2022, Li et al., 22 May 2025):

• CMDP parameters for dynamic policy optimization (height steps, modulation sets, noise PSD)
• FFT and matched filtering complexity scaling for real-time processing.

7. Challenges, Extensions, and Future Directions

Ongoing research highlights the extension of sensor-guided CHM to multimodal domains, leveraging AI-driven semantic extraction, multi-agent networking, and security-resilient implementations (Li et al., 22 May 2025). In anomaly detection, enforcing strict $Process \to Result$ mapping may inspire more causal architectures for UAD across manufacturing processes. In imaging, the methodology generalizes to 3D phase tomography and multi-wavelength setups (Jiang et al., 2021). UAV and radar systems benefit from joint constellation optimization balancing BER and sensing resolution; dynamic allocation and pairing can maximize aggregate utility and coverage (Chen, 2022, Li et al., 22 May 2025).

This suggests that sensor-guided CHM will continue to shape multimodal fusion, context-driven modulation, and cross-domain sensing-communication frameworks, underpinned by principled causal guidance and adaptive resource management.