Coherent Distributed Phased Array

• Coherent distributed phased arrays are networks of spatially separated antennas synchronized in time, frequency, and phase for constructive signal combining.
• They enable precise beamforming, null steering, and secure spatial communications through advanced consensus algorithms and multidimensional localization.
• Scaling these arrays requires managing synchronization latency, environmental challenges, and complex network topologies to maintain near-ideal coherent gain.

A coherent distributed phased array is a network of spatially separated antenna or transceiver elements operated with synchronized frequency, phase, time, and (if required) amplitude control, such that the radiated or received signals combine constructively in desired spatiotemporal directions at a remote location. This architecture enables beamforming, nulling, and high-SNR communications or sensing, but requires ultra-precise multi-node synchronization and localization. Achieving and maintaining coherence—sub-wavelength electric phase alignment at radio, microwave, millimeter-wave, or optical frequencies—demands advanced coordination protocols, scalable consensus algorithms, and high-accuracy ranging methods. The field combines distributed systems, signal processing, time/frequency metrology, and array electromagnetics, and is the physical-layer substrate for distributed MIMO, distributed radar, secure spatial communications, and emerging applications in OAC and networked sensing.

1. Physical Principles and Architectural Foundations

A coherent distributed phased array consists of antenna elements whose transmit/receive signals are coordinated such that their electromagnetic contributions arrive at a destination in a prescribed phase relationship. For perfect constructive combining (full coherent gain), all signals must be aligned to within a small fraction of the carrier period, typically $\le \lambda/15$ in range and $<0.1$ rad in phase error per element to limit array gain loss to less than 1 dB (Ellison et al., 2020, Dula et al., 16 Nov 2024, Shandi et al., 19 May 2025).

Key theoretical constructs:

• Array Factor and Coherent Gain: For $N$ nodes, ideal beamforming with perfect phase alignment yields $N^2$ power gain at the main lobe ($G(N) = N^2$), while incoherent transmission yields $G(N) = N$ (Silbernagel et al., 17 Sep 2025). Any phase variance decreases gain per $G_c = N^2 e^{-\sigma_\phi^2}$ for standard deviation $\sigma_\phi$.
• Far-Field vs. Near-Field Steering: Classical beamforming applies geometric phase delays per element for far-field targets; near-field operation requires precise localization and distance-dependent phase weights.
• Spatial Decoupling: Elements may be hundreds of wavelengths apart and need not be physically connected, but must be coordinated electrically to operate coherently.

Filled-aperture architectures, such as those demonstrated by Klenke et al., employ segmented-mirror splitters, phase-actuated inputs, and sequential phase-locking to permit coherent superposition in optical or RF domains (Klenke et al., 2021).

2. Synchronization and Localization Methodologies

Synchronization in coherent distributed phased arrays implies much more than frequency lock; time, frequency, phase, and node position must be disciplined precisely.

Two-Way Time Transfer and Ranging

• Protocol: Nodes exchange known time-stamped pulses (e.g., spectrally-sparse two-tone or pulsed-LFM waveforms) in a two-way protocol; offset and range are computed by averaging round-trip timestamps, canceling out static clock biases (Bhattacharyya et al., 22 Jul 2024, Dula et al., 16 Nov 2024, Shandi et al., 19 May 2025).

$$\tau_{ij} = \frac{(t_{\text{RX},j}-t_{\text{TX},i}) + (t_{\text{RX},i}-t_{\text{TX},j})}{2}$$

• Precision: Experimental systems report time synchronization error $\leq 36$ ps (Shandi et al., 19 May 2025), range error $<1$ mm (Dula et al., 16 Nov 2024), supporting coherence at up to 24 GHz.

Frequency Syntonization

• Techniques: Syntonization is often achieved by transmitting a two-tone frequency reference (e.g. $f_c \pm \Delta f/2$) from a primary node which peers use in a self-mixing circuit to recover the carrier and discipline their local oscillators via PLL (Mghabghab et al., 2020, Shandi et al., 19 May 2025, Schlegel et al., 9 Dec 2025).
• Wireless Decentralized Methods: Decentralized syntonization can be achieved via consensus averaging protocols (see below), eliminating the need for wired or optical clocks (Ouassal et al., 2019, Rashid et al., 2022, Rashid et al., 2022).

Localization for Array Geometry

• Classical MDS and Evolutionary Optimization: Pairwise ranges are assembled into an EDM; multidimensional scaling (MDS) recovers node positions up to global translation/rotation. If some ranging links are missing, differential evolution fills in missing distances for robust geometry (Dula et al., 16 Nov 2024).
• Achievable Error Budgets: Localization error $<0.82$ mm suffices for coherence windows up to 24 GHz (Dula et al., 16 Nov 2024).

3. Distributed Consensus and Synchronization Algorithms

Maintaining phase and frequency alignment in a scalable, fully distributed array is a prominent challenge. Several classes of algorithm are now foundational:

Average Consensus and Message-Passing

• Average-Consensus Protocols (DFAC, DFPC, PsFPC): Each node iteratively exchanges its frequency/phase estimates with neighbors (over undirected or directed graphs). Under broad connectivity, all nodes converge to the network average; residual phase error is minimized below the required 18° rms threshold for $>90\%$ gain, a result validated up to $N\sim 1000$ nodes (Ouassal et al., 2019, Rashid et al., 2022, Rashid et al., 2022).
• Message Passing Average Consensus (MPAC): Replaces simple averaging with a message-passing structure, yielding sub-picosecond convergence and phase error below $10^{-11}$ degrees in $N=20$ node arrays (Rashid et al., 2022).

Kalman Filtering Integration

• Distributed Kalman Filtering (HA-DKF, KF-DFPC, KF-PsFPC): Nodes model oscillator drift and phase noise as stochastic state processes; each runs a local Kalman filter and fuses innovations or estimates via consensus. HA-DKF integrates consensus on measurements, predicted innovations, and error covariances to outpace classical diffusion KFs by 2–3×, reaching residual phase errors well below 0.1° (Rashid et al., 2023, Rashid et al., 2022). Online EM learning can further estimate oscillator parameters in unknown or time-varying regimes (Rashid et al., 2022).

Algorithmic Properties and Scaling

• Convergence and Robustness: Message-passing and push-sum consensus converge in $2$–$5$ iterations for moderate connectivity; consensus time scales as $O(\log N)$ for well-connected graphs (Rashid et al., 2022, Ouassal et al., 2019).
• Directed/Time-Varying Networks: Push-sum consensus and MPAC maintain synchronization under dynamic or incomplete connectivity, essential for mobility and wireless networking (Rashid et al., 2022).

4. Open-Loop Beamforming, Null Steering, and Applications

Once time, frequency, phase, and array element positions are aligned, distributed arrays perform a variety of spatial processing tasks.

Open-Loop Beamforming

• Principle: With all array electrical states known, each node transmits with a phase shift matched to its distance and the desired beam direction; no feedback from the receiver is required (Ellison et al., 2020, Merlo et al., 16 Jun 2025, Silbernagel et al., 17 Sep 2025).
• Weights: For angle $\theta$ and element at $d_n$:

$w_n = e^{-j2\pi f_c(d_n \sin \theta)/c}$

• Performance: Experiments show $>98\%$ of ideal coherent gain for up to $N=6$ in outdoor beamsteering demonstrations (Shandi et al., 19 May 2025), maintaining $>90\%$ gain with dynamic node movement and simultaneous null formation (Bhattacharyya et al., 22 Jul 2024, Silbernagel et al., 17 Sep 2025).

Synchronization Latency and Dynamic Operation

• Latency: For real-time beam-steering, ranging and update cycles of $10$–$100$ ms are demonstrated, enabling mobility (Bhattacharyya et al., 22 Jul 2024).
• Dynamic Nulling and Multi-Objective Patterns: LCMP (linear-constrained minimum power) algorithms support multi-beam transmission, focus-plus-null patterns, and multi-user spatial multiplexing using per-target constraints (Bhattacharyya et al., 22 Jul 2024, Silbernagel et al., 17 Sep 2025).

Security and Information Decomposition

• Spatial Signal Decomposition: Distributed coherent arrays can spatially confine the recoverable information region via symbol decomposition—each node transmits a pseudo-random subvector; only at the main-lobe does superposition reconstruct the intended symbol, achieving physical-layer confidentiality (Schlegel et al., 9 Dec 2025). SER of $<0.01$ is attained only within the desired region, with $>0.25$ everywhere else, in both simulation and experiment using a $2$-node array with $\approx 50\lambda$ baseline.

Imaging and Sensing

• Code-Modulated Interferometric Imaging (CMI): Hardware-coded orthogonal phase shifts per element, summed in the RF domain, allow a single analog chain per array to reconstruct all $N(N-1)/2$ baselines. Arrays using this technique reach up to $N=16$ elements and $>100$ image pixels, with imaging noise performance within a factor $N$ of traditional architectures, but at far lower hardware cost (Chauhan, 2021).

5. System Implementation, Antenna Engineering, and Experimental Results

Calibration, CWTT, and TWTT Implementations

• Calibration Approaches: Systems deploy fully-digital TWTT time/frequency estimation using pulsed two-tone waveforms, achieving $60$–$70$ ps timing and $<10^\circ$ phase errors (Merlo et al., 8 Jun 2025, Merlo et al., 16 Jun 2025). Analog CW two-tone methods are also used, but are susceptible to phase wander in motion or multipath (Merlo et al., 8 Jun 2025).
• SDR-Based Prototyping: Experiments commonly employ SDRs (e.g., Ettus X310) and commercial phased arrays, with real-time processing in LabVIEW, GNU Radio, or Python. Femtosecond-level phase coherence at 60 GHz is enabled via optical time standards (Silbernagel et al., 17 Sep 2025).

Antenna Design for Ranging and Coherence

• Dual/Triple-Band Antennas: For co-located transmit and ranging hardware, multi-band patch antennas are engineered such that the phase centers of the high-frequency (ranging) and action-signal (array) ports are aligned to within $<\lambda/10$ (e.g., $<14$ mm at $1.88$ GHz), ensuring that ranging directly maps to action path with sub-radian phase error (Doroshewitz et al., 2019).

Coherence Assurance and Error Budgets

Aspect	Typical Value Achieved	Reference
Time synchronization	< 36 ps RMS	(Shandi et al., 19 May 2025, Merlo et al., 8 Jun 2025)
Phase alignment (per node)	< 0.1 rad (6°)	(Rashid et al., 2023, Rashid et al., 2022)
Range localization error	< 1 mm	(Dula et al., 16 Nov 2024)
Achievable max frequency (24G)	with 0.82 mm loc. error	(Dula et al., 16 Nov 2024)
Coherent gain (normalized)	0.92–1.00 (mean 0.98)	(Shandi et al., 19 May 2025, Merlo et al., 16 Jun 2025)

Residual time/phase errors directly impact coherent gain via $G_c \sim e^{-\sigma_\phi^2}N$; limits and tradeoffs are system-specific.

6. Scalability, Limitations, and Practical Considerations

• Bandwidth and Hardware Constraints: Piezoelectric phase actuators with 3 dB bandwidths below $10$ kHz suffice for optical/RF implementations with phase-dithering schemes like sequential phase locking (Klenke et al., 2021).
• Network Topology and Communication Load: Distributed consensus protocols scale in communication as $O(DN)$, where $D$ is average node degree; message-passing and push-sum variants are robust to asynchrony and dynamic connections (Rashid et al., 2022, Rashid et al., 2022).
• Scaling to High $N$: Fully-connected TWTT pairs scale quadratically; sparse topologies and hierarchical protocols mitigate $O(N^2)$ bottlenecks (Shandi et al., 19 May 2025, Rashid et al., 2022). Optical synchronization networks scale linearly in physical connections; practical arrays have demonstrated $N \sim 6$ for full experimental wireless beam-steering (Shandi et al., 19 May 2025).
• Environmental Impairments: Multipath and mobility are mitigated via dual-LFM or hybrid waveform designs, Doppler-tolerant ranging, and rapid synchronization cycles (Bhattacharyya et al., 22 Jul 2024, Ellison et al., 2020, Merlo et al., 8 Jun 2025).
• Security Implications: Coherently decomposed arrays can confine data reconstruction to a spatial region, providing physical-layer security unattainable by traditional single-node or non-coherent systems (Schlegel et al., 9 Dec 2025).

7. Outlook and Research Directions

Future research on coherent distributed phased arrays targets:

• High-$N$, real-time arrays with decentralized time/frequency/phase consensus robust to RF impairments and node mobility.
• Millimeter-wave ($\geq$60 GHz) and optical systems leveraging ultra-precise femtosecond optically-derived clocks for distributed sensing (Silbernagel et al., 17 Sep 2025).
• Integrated localization, beamforming, and OAC architectures for distributed wireless inference and ultra-secure communications (Sahin, 27 Jun 2025).
• Hardware-efficient consensus and synchronization for low-SNR and highly dynamic environments, facilitating rapid networked adaptation.
• Advanced antenna engineering for bandwidth-agnostic co-located phase centers, supporting high-precision multi-band ranging and action operation (Doroshewitz et al., 2019).

The domain establishes the foundational layer for distributed MIMO, reconfigurable intelligent surfaces, low-latency edge computation, networked radar, and future secure multi-static communications. All advances are predicated on precise, scalable, and robust mutual coherence across distributed network nodes.