Virtual Array Sensing in Wireless Radio

• Virtual Array Sensing is a technique that synthesizes high-resolution virtual sensor arrays from sparse physical elements using frequency, time, or mobility diversity.
• It exploits difference and sum co-array methods to enhance super-resolution DoA estimation and support advanced integrated sensing-and-communication functionalities.
• Hardware–software co-design with reconfigurable RF front-ends and efficient signal processing enables real-time wideband spatial inference with improved power efficiency.

Virtual Array Sensing in Wireless Radio

Virtual array sensing refers to methodologies in wireless radio systems that synthesize high-resolution spatial (or spatio-temporal) apertures using physical arrays, frequency or time diversity, or reconfigurable architectures, to enable spatial inference and environment sensing well beyond conventional array hardware constraints. By exploiting methods such as sparse array geometries, mobility, frequency agility, or signal processing transformations, virtual array sensing leverages mathematical co-array concepts to realize super-resolution, multi-source localization, passive mapping, and integrated sensing-and-communication (ISAC) functionalities. This encompasses both classical co-array theory, SAR-inspired techniques, and hardware–software co-design for real-time wideband spatial inference.

1. Principles of Virtual Array Construction

Core to virtual array sensing is the realization of a virtual co-array—a set of effective sensor positions generated from physical array elements via algebraic manipulations, switching, frequency diversity, or motion. The two main co-array types are:

• Difference co-array: Generated from unique inter-element spacings, where the set $$\mathcal{D}_{\rm virt} = \{d_i - d_j : 1 \leq i < j \leq M\}$$ for sensor positions $\{d_m\}$ forms the virtual array and enables spatial covariance domain expansion (Gupta et al., 2021, Yu et al., 30 Jun 2025).
• Sum co-array: For active sensing (MIMO, radar), combining transmit and receive aperture locations gives $$S_\Sigma = S_{\rm tx} + S_{\rm rx} = \{m+n | m \in S_{\rm tx}, n \in S_{\rm rx}\}$$, enabling virtual transmit–receive arrays with up to $N_{\rm tx}N_{\rm rx}$ elements (Rajamäki et al., 21 Jan 2026, Rajamäki et al., 2024).

Sparse arrays (e.g., nested, co-prime) violate Nyquist sampling in the spatial domain, trading physical element density for a much larger virtual aperture—potentially allowing resolution and identifiability of more sources than array channels. The process involves reconstructing sample covariance or higher-order cumulant matrices, redundancy mapping, and forming virtual steering vectors $$a_v(\theta) = [e^{j\pi \Delta_i\sin\theta}]_{i=1}^L$$ where $\{\Delta_i\}$ are the virtual lags (Yu et al., 30 Jun 2025).

In active scenarios, careful joint design of spatial geometry and waveform rank is critical: for sum co-arrays, the maximum number of resolvable scatterers is governed by Kruskal-rank, minimum required waveform rank, and the redundancy pattern, not just virtual element count (Rajamäki et al., 2024).

2. Hardware–Software Architectures and Realizations

Virtual array concepts are realized via a variety of architectures:

• Reconfigurable RF front-ends: Sparse antenna arrays combined with sub-Nyquist sampling (SNS) and modulated wideband converters (MWC) enable direct acquisition of compressed spatial information. FPGA-based co-processing partitions heavy tasks (covariance, vectorization, subspace decomposition, MUSIC) onto programmable logic for low-latency wideband spatial inference, with on-the-fly partial reconfiguration to adapt to active signal count (Gupta et al., 2021).
• Antenna position mobility: Movable antenna (MA) arrays physically reposition N elements (or a single element sequentially) to synthesize an aperture exceeding that of fixed ULAs. Alternating optimization and closed-form deployment rules maximize Fisher information under CRB constraints in 1D and 2D, achieving "virtual" ULA or planar apertures (Ma et al., 2024).
• Switching-based virtual MIMO: High-dimensional MIMO apertures are emulated using RF switching networks (e.g., in distributed USRP testbeds) where limited RF chains sample many antenna ports in a time-division manner. This allows scaling to hundreds or thousands of virtual channels, facilitating ultra-high-resolution channel sounding and passive/integrated sensing without hardware replication (Sandra et al., 2024).
• Frequency-domain virtual arrays: Frequency-agile mmWave radios with leaky-wave antennas exploit the frequency-to-angle mapping $\theta(f) = \arcsin[\beta(f)/(2\pi f/c)]$, using local oscillator sweeps to scan spatial angles and realize "frequency-as-aperture" (FaA) sensing with a single physical radiator (Ho et al., 29 Jan 2026).
• Single-RF-chain temporal synthesis: Synthetic aperture radar (SAR) principles are applied in mmWave beam alignment via Synthesis of Virtual Array Manifold (SVAM)—time-varying analog combiners select different antenna subsets over sequential snapshots, producing a virtual array manifold for spatial inference even under hardware-constrained conditions (Pote et al., 2024).

3. Signal Models, Inference Workflows, and Algorithmic Techniques

The general workflow for virtual array sensing comprises:

1. Signal acquisition via physical array, frequency, or switching diversity, possibly with sub-Nyquist compression.
2. Co-array mapping, forming sample covariance ($R=\mathbb{E}[yy^H]$), co-array expansion (e.g., vectorization and Khatri–Rao product for difference arrays, Kronecker for sum arrays), and redundancy reduction.
3. Virtual-domain inference:
   • For angular estimation, structure-preserving mapping to Toeplitz or Hankel matrices allows subspace methods (MUSIC, ESPRIT, RIMAX, SAGE) to extract directions of arrival/departure (Gupta et al., 2021, Sandra et al., 2024).
   • Exploiting higher-order cumulants, or attention-based deep architectures, for pilot-free, snapshot-adaptive, permutation-invariant DoA estimation under unknown labels and non-Gaussian symbols (Yu et al., 30 Jun 2025).
   • Beam alignment via Bayesian inference—updating posterior densities over the angular grid per virtual block, optimizing next combiner for maximal spatial information gain (Pote et al., 2024).
4. Performance scaling:
   • The effective number of resolvable sources is dictated by virtual aperture size ($L$ for difference co-array, $N_\Sigma$ for sum co-array), Kruskal-rank bounds, and waveform rank (Rajamäki et al., 2024).
   • Trade-offs center on latency, resource utilization, and SNR scaling. For example, in SNS-based architectures, sampling-rate compression can cut digital power by 80% with only minor NDEE penalty (Gupta et al., 2021).

When the array geometry allows, multi-stage processing—combining synthetic image addition or multi-block transmission—can suppress grating lobes and enhance main lobe resolution (Rajamäki et al., 21 Jan 2026).

4. Performance Characteristics and Analytical Constraints

The following table summarizes key performance metrics observed in leading virtual array sensing implementations:

Metric	Value/Regime	Source
Max number of resolvable sources	Up to $O(M^2)$	(Rajamäki et al., 21 Jan 2026, Yu et al., 30 Jun 2025)
Angular resolution $\Delta\theta$	$O(1/L_{virt})$	(Gupta et al., 2021, Ho et al., 29 Jan 2026)
Range resolution (FaA, $B$ bandwidth)	$\Delta R \approx c/(2B)$	(Ho et al., 29 Jan 2026)
Virtual MIMO elements via switching	Up to $896$ (128×7)	(Sandra et al., 2024)
CRB improvement (SVAM vs. repetition)	Up to $12$ dB	(Pote et al., 2024)
Power consumption (FaA-Single node)	$<1$ W	(Ho et al., 29 Jan 2026)
Positioning error (LIS)	$<6$ cm (active) / $<30$ cm (passive)	(Vaca-Rubio et al., 2021)

Notable analytical results include:

• For difference co-arrays, DoA error (NDEE) scales as $O(1/\sqrt{\mathrm{SNR}})$; virtual aperture size sets identifiability (Gupta et al., 2021).
• For sum co-arrays, maximum scattered identifiability is $$N_{\max} = \lfloor\frac{1}{2}\min(N_sN_r,N_\Sigma)\rfloor$$ where $N_s$ is waveform rank (Rajamäki et al., 2024).
• In XL-MIMO, SNR scaling saturates with array size, dictated by angular span parameters, with diminishing returns in near-field (Wang et al., 2021).
• In frequency-as-aperture architectures, spatial resolution is set by the swept bandwidth and spatial sampling law (Ho et al., 29 Jan 2026).
• Movable antenna arrays can achieve CRB scaling as $1/\mathrm{var}(x)$ (1D) or $1/A^2$ (2D), outperforming conventional fixed arrays (Ma et al., 2024).

5. Applications, Use Cases, and System Integration

Virtual array sensing underpins a broad range of ISAC and beyond-communications applications:

• Wideband spatial sensing: Real-time detection and DoA estimation in multi-band, congested spectrum using sparse array front-ends with SNS (Gupta et al., 2021).
• mmWave beam alignment: SVAM achieves near-CRB performance with a single RF chain, supporting dynamic Bayesian beam adaptation in both fading-known and unknown regimes (Pote et al., 2024).
• Integrated localization and communication (ILAC): Sparse/Nested/Co-prime arrays with virtual aperture processing enable sub-degree localization of dense user populations, streamlined beam management, and sum-rate gains in 5G-NR/6G, provided data and sensing are hybridized appropriately (Min et al., 25 Feb 2025, Yu et al., 30 Jun 2025).
• Embeddable low-cost sensing: FaA architectures permit cost- and power-efficient 2D spatial sensing in IoT and wearables using a single leaky-wave antenna and agile LO (Ho et al., 29 Jan 2026).
• Distributed massive MIMO: Rapid-switching channel sounders perform real-time multifaceted channel and environment mapping, facilitating high-resolution passive tracking and spatial fingerprinting (Sandra et al., 2024).
• Large intelligent surface (LIS) radio sensing: Commodity-device communication signals, processed over LIS as a virtual spatial camera, yield fine-grained radio maps for both active and passive multi-object detection (Vaca-Rubio et al., 2021).

6. Design Limitations, Redundancy Patterns, and Research Challenges

While virtual array synthesis provides expanded DoF, several limitations and structural constraints are observed:

• Redundancy pattern criticality: Arrays with identical sum co-arrays and physical/virtual sensor counts can differ in identifiability performance depending on their redundancy pattern matrix $\Upsilon$, especially at minimal waveform rank. Robust identifiability requires joint optimization of array geometry and waveform design (Rajamäki et al., 2024).
• Resolution–sidelobe trade-offs: Sparse arrays yield narrow main lobes but require synthetic beamforming (e.g., image addition) to suppress grating or ambiguity lobes; more time-multiplexed codes are needed as hardware sparsity increases (Rajamäki et al., 21 Jan 2026).
• Constraints in communication: Virtual array processing is not directly applicable to data communication streams since phase information is lost, SNR is degraded, and inter-user interference exacerbates. Hybrid processing—physical array for communication, virtual array for localization—is mandated in ILAC (Min et al., 25 Feb 2025).
• Calibration and Real-Time Control: Large or distributed virtual apertures demand precise calibration (phase, pattern), synchronization, and low-latency processing. Modular hardware–software co-design is necessary for scalable architectures (Gupta et al., 2021, Sandra et al., 2024).
• Computational Overhead: Covariance and higher-order cumulant expansion, as well as real-time matrix operations, introduce significant computational demands, motivating attention-based or structure-exploiting architectures (Yu et al., 30 Jun 2025).

7. Future Directions and Integration in ISAC

Virtual array sensing is central to the evolving ISAC and 6G wireless ecosystem:

• Pilot-free and standardized integration: Methods that reuse uplink or communication data for localization enable "sensing for free," directly compatible with 3GPP 5G NR and ongoing 6G standards (Yu et al., 30 Jun 2025).
• Scalable and embeddable hardware: Single-chain, frequency-as-aperture architectures, and reconfigurable switching encourage widespread deployment in battery-powered edge and IoT devices (Ho et al., 29 Jan 2026).
• Algorithmic advances: Deep-transformer models and jointly optimized redundancy-aware designs promise further leaps in multi-source identifiability, computational cost, and robustness under practical mismatches (Yu et al., 30 Jun 2025, Rajamäki et al., 2024).
• Integrated channel and environment inference: Unified MIMO and LIS approaches enable passive and active sensing of rich, dynamic environments using seamless software-defined frameworks (Sandra et al., 2024, Vaca-Rubio et al., 2021).
• Theoretical frontiers: Proper characterization of identifiability, DoF scaling, SNR laws under near-field and extreme aperture regimes, and redundancy pattern impact remains vital for predictive, resource-efficient ISAC design (Wang et al., 2021, Rajamäki et al., 2024).

In totality, virtual array sensing provides a mathematically rigorous and hardware-adaptive toolkit for high-dimensional wireless radio sensing, foundational to advanced localization, channel sounding, and multi-modal ISAC applications.