MASked Modulation: Techniques & Applications

• MASked Modulation is a set of techniques that apply structured masking in signal sequences to control energy, suppress interference, and enforce data priors.
• It spans waveform-level design in ISAC, self-supervised masked autoencoding for denoising and classification, and spatial modulation in VLC, demonstrating diverse applications.
• Optimal mask designs such as cyclic difference sets and comb masks balance throughput, sidelobe suppression, and ambiguity control, advancing performance in communications and beam physics.

MASked Modulation (MASM) refers to a suite of methodologies and systems, spanning both waveform-level signal processing for integrated sensing and communications (ISAC) and representation learning via masked autoencoders, in which structured masking is applied to a modulation or signal sequence. Masking is applied either physically—via periodic transmission masks in waveform design and beam shaping—or virtually—by stochastically occluding samples or patches in the data domain for feature learning. Across these contexts, MASked Modulation is employed to control energy usage, suppress self-interference, impose desired ambiguity structures, or force learning of data priors. Key research directions encompass binary mask design for high-throughput ISAC systems (Xiong et al., 13 Feb 2025), masked autoencoding for denoising/classification (Liu et al., 1 Aug 2025, Faysal et al., 20 Jan 2025), spatial and multi-active-index modulation (Naser et al., 2021), and physical microbunching of particle beams using slit masks (Zhu et al., 2015).

1. Binary Transmission Masking for ISAC Waveform Design

In half-duplex ISAC, MASked Modulation (MASM) employs periodic binary transmit masks to allocate each symbol slot within a pulse repetition interval (PRI) to either transmission or reception. The transmitter multiplies its information-bearing symbol sequence by a mask $m_t(i)\in\{0,1\}$ of period $N$, activating transmission when $m_t(i)=1$ and switching to receive mode when $m_t(i)=0$. The continuous-time transmit signal is expressed as: $x(t)=\sum_{i} m_t(i)\,x_i\,\psi(t-iT_c),$ with $\psi(\cdot)$ a Nyquist pulse and $T_c$ the symbol period. The received slots are indexed by $m_r(i)=1-m_t(i)$, ensuring transmit/receive orthogonality in each slot (Xiong et al., 13 Feb 2025, Liu et al., 15 Jan 2026).

The primary advantage is elimination of self-interference (SI), making MASM suitable for SI-free long-range sensing. A key metric, the duty cycle $\rho=(1/N)\sum_{i=0}^{N-1}m_t(i)$, determines the average communication throughput, while the mainlobe fluctuation and range glint induced by the half-duplex operation are analytically controlled by mask design (Xiong et al., 13 Feb 2025).

2. Mask Design: Objectives, Trade-Offs, and Optimality

The critical mask design problem is to minimize range mainlobe fluctuation (quantified by the integrated range-glint index, IRGI) and sidelobe levels, subject to a throughput (duty cycle) constraint. For constant-modulus signals, IRGI is minimized by flattening the transmit mask's power spectrum, equivalently enforcing two-level periodic autocorrelation. Cyclic difference sets (CDS) and, in particular, Singer CDSs realize this optimal structure for specific $(N,\rho)$ pairs (Xiong et al., 13 Feb 2025, Liu et al., 15 Jan 2026).

The mask optimization problem is: $$\min_{m_t} \|F m_t\|_4^4 \quad \text{subject to } m_t\in\{0,1\}^N,\,\mathbf{1}_N^\top m_t=\rho N,$$ where $F$ is the $N\times N$ unitary DFT matrix. For arbitrary $N$, suboptimal or near-optimal masks are found using heuristic or branch-and-bound searches. In the two-dimensional range-Doppler domain, range sidelobes induced by the mask are proven to be Doppler-invariant, and minimax-optimality of CDS masks extends to both range and Doppler ambiguity suppression in the moderately dynamic regime (Doppler shifts less than the number of PRIs) (Liu et al., 15 Jan 2026).

Aggregate grating-lobe energy in highly dynamic regimes becomes a concave function of the mask autocorrelation, introducing a nontrivial trade-off between mainlobe fluctuation and total sidelobe energy. CDS masks minimize the worst-case grating-lobe energy, while comb masks minimize aggregate energy at the cost of high mainlobe fluctuation.

3. Frame-Level and Practical MASM Variants

Hardware constraints may render symbol-level duplex switching infeasible. To alleviate this, slow-time MASM divides the PRI into $L$ contiguous “slow-time” slots, each comprising $T$ symbol-length “fast-time” bins, and applies the binary mask at slot granularity, $m_t = \tilde{m}_t\otimes\mathbf{1}_T$. This approach expands the unobservable "blind" range bins but significantly eases implementation requirements, permitting the direct reuse of optimally designed CDS masks at the slow-time level (Xiong et al., 13 Feb 2025).

MASM-based ISAC can achieve energy-accumulation efficiency up to $25\%$ of full-duplex continuous-wave operation at $\rho=0.5$, with spectral efficiency $T_\mathrm{comm} = \rho\log_2|\mathcal{S}|$ for constellation $\mathcal{S}$. Sidelobe suppression and range ambiguity are controlled via mask structure, and compared to PRF-staggering, MASM yields lower range glint and lower sidelobes at equivalent throughput (Xiong et al., 13 Feb 2025).

4. Masked Modulation in Deep Learning: Representation and Denoising

Masking strategies are also integral to self-supervised learning for modulation classification and denoising. In the raw-IQ domain, architectures such as RIS-MAE apply random masking to non-overlapping signal patches, compelling a masked autoencoder to reconstruct withheld sections. The approach preserves raw amplitude and phase continuity, enabling the model to learn robust, modulation-aware representations from unlabeled data, which transfer efficiently to few-shot downstream classification (Liu et al., 1 Aug 2025). The masking process is formulated as: $X_\mathrm{masked} = M \odot X,$ where $M$ is a binary mask (mask ratio $r\approx0.75$), $X$ is a 2$\times$1024 real IQ tensor, and only masked patches are reconstructed via mean-squared-error loss.

Denoising Masked Autoencoders (DenoMAE) extend this methodology, leveraging masking across multiple modalities (noisy/clean signals and constellation diagrams, plus explicit noise) to enforce reconstruction from partial context. By including the noise itself as a modality, the model learns cross-domain priors for denoising at very low SNR, enhancing both classification accuracy and data efficiency (Faysal et al., 20 Jan 2025).

5. Multiple Active Index Masked Modulation Schemes

In visible light communications (VLC), MASM describes "multiple active spatial modulation," wherein multiple LEDs (transwriters) are simultaneously active in transmitting distinct symbols. This increases nominal spectral efficiency: $$\eta_\mathrm{MASM}= N_a\,\log_2 M + \log_2\Big\lfloor \binom{N_t}{N_a}\Big\rfloor_{2^p},$$ with $N_a$ active LEDs, $N_t$ total LEDs, and $M$-ary PAM per active transmitter (Naser et al., 2021). The information bits per channel use are split between spatial indices and per-LED signal values.

While MASM in this context yields high raw throughput, bit error rates degrade rapidly with increasing $N_a$ or $M$, due to poor error performance at high spectral loads. Space-time block coding (STBC-SM) and quasi-orthogonal codes alleviate this at cost of decreased raw spectral efficiency but achieve much lower BER and higher net "goodput" in practical systems (Naser et al., 2021).

6. Physical Masked Modulation in Beam Physics

A physically distinct MASM instance leverages slit-masked chicanes to create density-modulated microbunch trains in accelerator physics. A correlated-energy (chirped) electron beam is longitudinally compressed and dispersed in a magnetic chicane; a transverse slit mask imposes a periodic density modulation, which is projected back into the longitudinal domain to generate femtosecond-scale microbunches. Key parameters and results include:

• Chicane: $\theta=18^\circ$, $\rho=0.95$ m, $R_{56}\approx-0.19$ m, $\eta_x\approx-0.34$ m.
• Mask: period $p=900\,\mu$m, width $w=300\,\mu$m.
• Achieved modulation spacing: $\sim100\,\mu$m ($\sim3$ THz), microbunch length $\sim100$ fs (Zhu et al., 2015).

PIC and track code simulations confirm that space-charge and CSR effects minimally perturb the imposed modulation at the nominal parameters.

7. Comparative Perspectives and Limitations

MASked Modulation enables high-throughput, SI-free, half-duplex operation in ISAC; supports interpretable, transferable representations in deep learning for modulation classification; and can implement precise spatiotemporal structuring in particle beams. The trade-off space includes energy efficiency (max $\sim25\%$ in half-duplex ISAC), intrinsic range/Doppler blind zones, additional implementation complexity (mask switching or slow-time slots), and spectral efficiency versus BER depending on code structure and application regime (Xiong et al., 13 Feb 2025, Liu et al., 15 Jan 2026, Naser et al., 2021).

Optimal mask design is often constrained by combinatorial existence (CDS or Singer sets exist only for certain lengths and densities), while in learning contexts, elevated masking ratios ($\approx75\%$) induce strong regularization but may limit representational specificity at extreme noise or SNR boundaries (Liu et al., 1 Aug 2025, Faysal et al., 20 Jan 2025).

Table: Major MASked Modulation Contexts

Domain	Principle	Key Reference
ISAC waveform design	Periodic binary mask, half-duplex, CDS	(Xiong et al., 13 Feb 2025, Liu et al., 15 Jan 2026)
Self-supervised representation learning	Random patch masking (MAE), cross-modal, denoising	(Liu et al., 1 Aug 2025, Faysal et al., 20 Jan 2025)
Visible light comms (VLC)	Multiple active index modulation	(Naser et al., 2021)
Beam microbunching	Slit-mask chicane, physical periodicity	(Zhu et al., 2015)

Comprehensive understanding of MASked Modulation requires attention to context, as identical terminology encodes distinct technical paradigms across waveform engineering, machine learning, channel coding, and accelerator physics.