Binary Transmission Masking for ISAC

• The paper introduces a rigorous binary masking design that enables half-duplex ISAC, minimizes self-interference, and achieves optimal sensing metrics.
• It employs cyclic difference sets and Fourier spectrum optimization to balance mainlobe uniformity and sidelobe suppression in both 1D and 2D range-Doppler domains.
• The approach also integrates RIS-based privacy masking, ensuring high sensing accuracy and communication throughput while thwarting unauthorized signal interception.

Binary transmission masking in integrated sensing and communication (ISAC) is the use of a rigorously designed, time-varying binary (0/1) transmit mask to modulate when a node is actively transmitting versus receiving, or to select among predefined waveform or beamforming configurations, in order to optimize joint communication and sensing objectives. The binary structure enables robust half-duplex operation, avoids self-interference (SI), enhances privacy, and provides provable optimality in key sensing metrics when masks are properly constructed. This article details the foundational principles, performance analysis, and applications of binary transmission masking approaches for ISAC networks across waveform, ambiguity function, and privacy-preserving system levels.

1. Mathematical Framework for Binary Transmission Masking in Half-Duplex ISAC

The canonical setting for binary transmission masking employs a discrete-time sequence $m[n] \in \{0,1\}$ indicating transmission ("TX", $m[n]=1$) or reception ("RX", $m[n]=0$) at fast time index $n$, over a framelength $N$. The average duty cycle, directly proportional to communication throughput, is $\rho = \frac{1}{N}\sum_{n=0}^{N-1} m[n]$.

The transmitted waveform under this masking is:

$x(t) = \sum_{i} m[i]\,x_i\,\psi(t-iT_c)$

where $x_i$ is the data symbol (zeroed when $m[i]=0$), and $\psi$ is a Nyquist pulse. The receive schedule, $m_r[n] = 1 - m[n]$, ensures strictly alternating half-duplex operation: the receiver is only active in RX slots, absolutely prohibiting SI.

Sensing in this framework is captured by the range-ambiguity matrix:

$$r_{k,\ell} = \sum_{i=0}^{N-1} m_r[i]\,m_t[i-k]\,m_t[i-\ell]\,x_{i-k} x^*_{i-\ell}$$

with indices modulo $N$, enabling a clear linkage between the binary mask and the resultant ambiguity structure for target detection and ranging (Xiong et al., 13 Feb 2025).

2. Performance Metrics: Mainlobe Fluctuation, Sidelobe Structure, and Mask Optimality

Key ISAC sensing performance metrics governed by the mask design include:

• Mainlobe fluctuation (Integrated Range Glint, IRGI):

$$\overline{g} = \frac{1}{N-1}\sum_{k=1}^{N-1}|r_{k,k}|^2 - \left|\frac{1}{N-1}\sum_{\ell=1}^{N-1} r_{\ell,\ell}\right|^2$$

quantifies per-bin uniformity in target response, directly tied to range-blindness.

• Sidelobe levels:
  • Average expected sidelobe level (AESL):

  $${\rm AESL} = \sum_{k=1}^{N-1} \sum_{\ell>0, \ell\neq k} \mathbb{E}|r_{k,\ell}|^2$$ - Peak-expected sidelobe level (PESL):

  $${\rm PESL} = \max_{k>0,\ell>0,\ell\neq k} \mathbb{E}|r_{k,\ell}|^2$$

Optimization is cast as minimizing the $\ell_4$-norm of the Fourier spectrum of $m$, subject to a weight constraint:

$$\min_{m \in \{0,1\}^N,\ 1^T m = \rho N} \quad \| F m \|_4^4$$

where $F$ is the discrete Fourier transform (DFT) matrix (Xiong et al., 13 Feb 2025).

Optimal masks are realized by cyclic difference sets (CDS), most notably Singer CDS for $N, K, \lambda$ parameter sets, yielding two-level periodic autocorrelation, perfect mainlobe flatness (IRGI $=0$), and minimax-optimal sidelobe properties (Xiong et al., 13 Feb 2025, Liu et al., 15 Jan 2026).

3. Binary Masking for 2D Range–Doppler Sensing

Extending the analysis to the full 2D (range–Doppler) ambiguity, the periodic binary mask $m_t[n]$ and its autocorrelation profile $a[k] = \sum_{n=0}^{N-1} m_t[n] m_t[n-k]$ regulate both spatial and Doppler-domain performance.

The core results include:

• Doppler-invariant range sidelobes: For delays $k \neq \ell$, the second moment $\mathbb{E}|r(k,l,\nu)|^2$ is independent of Doppler index $\nu$, preserving range-sidelobe suppressing properties across the Doppler domain (Liu et al., 15 Jan 2026).

• Mainlobe–Doppler trade-offs: For $k=\ell$, mask autocorrelation $a[k]$ controls mainlobe uniformity and Doppler sidelobe floor. In the moderately dynamic regime ($\nu < M$ for $M$ PRI segments), CDS masks maintain minimax-optimal trade-offs, but for highly dynamic scenarios ($\nu \gg M$), a concave trade-off arises: flattening mainlobe fluctuation via higher $a[k]$ increases aggregate Doppler sidelobe energy, and vice versa.

Summary of key analytic formulas includes:

• Range–sidelobe: $M\sum_{n=0}^{N-1} m_r[n] m_t[n-k] m_t[n-l]$

• Mainlobe (zero Doppler): $M^2(\rho N - a[k])^2 + (\mu_4-1)M(\rho N - a[k])$

• High-Doppler sum: $f(a) = (\rho N - a)(N - (\rho N - a))$

CDS-type masks are universally optimal in the constrained moderate Doppler regime, but "comb" masks (polarizing $a[k]$ to $\{0, \rho N\}$) may reduce average Doppler sidelobe energy if some mainlobe fluctuation is acceptable (Liu et al., 15 Jan 2026).

4. Binary Transmission Masking for Privacy in ISAC with RIS

Binary masking principles are also foundational in privacy-preserving ISAC leveraging Reconfigurable Intelligent Surfaces (RIS). Here, each RIS row is assigned two distinct beamforming vectors $(\theta_r^{(1)}, \theta_r^{(2)})$. The system randomly activates one configuration per row in each time slot, forming a binary masking sequence $(b_r[t])$ over time:

• Masking process: Each $b_r[t] \in \{1,2\}$ toggles at $\sim$kHz rates, providing strong temporal entropy.

• Design objectives:

  • Communication direction: Beamformers are nearly identical for robust link throughput: $$|(h_r^{\sf C})^H \theta_r^{(1)}| \approx |(h_r^{\sf C})^H \theta_r^{(2)}|$$, phase-matched.
  • Sensing direction: Beamformers yield large output differences $$|(h_r^{\sf S})^H \theta_r^{(1)} - (h_r^{\sf S})^H \theta_r^{(2)}|$$, masking environment/target features from unauthorized interceptors.

A time-domain masking and demasking strategy aligns configuration indices at the legitimate receiver, enabling static clutter removal, gain normalization, and temporal recombination to yield valid CSI streams (He et al., 8 Jan 2026).

PrivISAC demonstrates that legitimate sensing accuracy ($>$94%) and communication throughput ($>$80%) are retained, while adversarial classification is reduced toward random chance ($\sim$30%)—far outperforming conventional phase-randomization and MIMO-based privacy tools (He et al., 8 Jan 2026).

5. Comparative Perspective: Binary Masking Versus Traditional ISAC Waveforms

Conventional continuous-wave (CW) and OFDM-based ISAC systems require full-duplex operation to enable simultaneous transmission and echo reception, leading to pronounced SI, expensive mitigation hardware, and limited long-range sensitivity. Pulse-based half-duplex approaches, historically used in radar, suffer from very low duty cycles (≤10%), unsuitable for efficient communications.

Binary transmission masking, as realized in MASked Modulation (MASM), supports high duty cycle ($\rho \sim 0.5$), hence high data throughput, while eliminating SI by construction. Sidelobe and mainlobe metrics are controlled rigorously through mathematical mask design, notably using CDS (Xiong et al., 13 Feb 2025).

Compared to co-prime pulse repetition frequency (PRF) staggering, which provides limited and heuristic mainlobe/sidelobe balancing, binary masking achieves systematic, globally optimal ambiguity function shaping in both 1D and 2D domains (Liu et al., 15 Jan 2026).

6. Practical Guidelines and Implementation Considerations

• Mask design: For small $N$, exhaustive enumeration is viable; for practical $N$, branch-and-bound convex relaxations or CDS-based sequence selection is used (Xiong et al., 13 Feb 2025).
• Duty cycle selection: Empirical results indicate that $\rho \simeq 0.5$ achieves balanced sensing–throughput trade-offs, with mainlobe loss of only $\sim$3 dB compared to continuous transmission (Xiong et al., 13 Feb 2025).
• RIS hardware for privacy masking: Low-cost 1-bit RIS arrays suffice, with shift-register upgrades on millisecond timescales. Synchronization overhead is minimal (~6 ms every 0.5 s) relative to indoor channel coherence (He et al., 8 Jan 2026).
• Synchronization: Periodic static configurations, coefficient-of-variation landmarks, and grouping/demasking operations are critical for legitimate user operation in high-entropy masking environments (He et al., 8 Jan 2026).
• Doppler regime adaptation: In moderately dynamic environments ($\nu_{\max}<M$), CDS construction is preferred. In highly dynamic settings, design must carefully balance mainlobe uniformity and Doppler-sidelobe energy depending on application priorities (Liu et al., 15 Jan 2026).

7. Concluding Observations and Research Outlook

Binary transmission masking in ISAC unifies mathematical rigor with systems-level practicality, offering high-throughput, SI-free, and privacy-aware operation. The approach is mathematically governed by binary mask autocorrelation properties, with cyclic difference set sequences providing fundamental performance bounds in mainlobe flatness and sidelobe suppression. Extensions to 2D range-Doppler ambiguity and RIS-mediated privacy illustrate the broad applicability and flexibility of the framework. Ongoing research explores mask design under hardware constraints, joint waveform-beamforming optimization, and robust operations in dynamic wireless environments (Xiong et al., 13 Feb 2025, Liu et al., 15 Jan 2026, He et al., 8 Jan 2026).