PCRPA: Polarization-Coding Reconfigurable Array

• PCRPA is a phased array technology that codes polarization along with amplitude and phase, reducing RF channel requirements while enabling flexible beam synthesis.
• It employs real-time RF switching and coded element excitations to generate arbitrarily polarized and dual-polarized beams across diverse frequency bands.
• PCRPA design involves trade-offs between hardware savings and potential power or directivity loss, necessitating advanced synthesis, calibration, and learning techniques.

Searching arXiv for the cited PCRPA and related polarization-reconfigurable phased-array papers. Polarization-Coding Reconfigurable Phased Array (PCRPA) denotes a phased-array class in which polarization state is treated as a controllable aperture variable together with the usual amplitude and phase controls. In the most explicit formulation, each PCRPA element connects to a single T/R channel and incorporates two-level RF switches for real-time control of polarization states and waveforms; by adjusting element codes and excitation weights, the array can generate arbitrarily polarized and dual-polarized beams (Wang et al., 27 Aug 2025). Closely related work realizes the same principle through adjustable-phase multi-port antennas, dual-circular-polarization reflectarrays, shared-aperture phased arrays, and dynamic polarization control in the near field, so PCRPA is best understood as a general electromagnetic-and-signal-processing paradigm rather than a single hardware topology (Yang et al., 2023, Liu et al., 2023, Räsänen et al., 18 Jun 2026, Myers et al., 2022, Liu et al., 20 Oct 2025).

1. Conceptual basis and architectural scope

In a conventional polarimetric phased array, each element is a dual-polarized antenna with two orthogonal ports, typically horizontal and vertical, and each port is connected to an independent transmit/receive channel. For an $N$-element array, the number of RF and digital channels is therefore $2N$. PCRPA reduces this hardware burden by keeping dual-polarized or polarization-reconfigurable elements while connecting each element to only one T/R channel, then using RF switching or element-state control to decide whether that element contributes through the H port, the V port, or a reconfigurable polarization state (Wang et al., 27 Aug 2025).

This channel reduction is the defining economic motivation. The direct PCRPA formulation targets polarimetric phased arrays for radar, where dual transmit/receive channels otherwise dominate system cost and complexity. In that setting, PCRPA preserves beam and polarization agility while halving the number of RF channels per element, at the price of coding constraints and some loss in power or directivity (Wang et al., 27 Aug 2025).

A broader literature reaches the same operating principle through different front ends. Reconfigurable antenna arrays expose element electromagnetic modes, RF-domain analog beamforming, and baseband digital beamforming as joint design variables; polarization-reconfigurable arrays, dual-CP reflectarrays, orthogonally polarized RISs, and shared-aperture SATCOM arrays all instantiate that multi-domain control, even when the feed architecture is not a conventional corporate-fed phased array (Liu et al., 20 Oct 2025, Liu et al., 2023, Wang et al., 24 May 2026, Räsänen et al., 18 Jun 2026). This suggests that PCRPA is a unifying description of apertures in which element polarization states are explicitly coded and combined with array-factor control.

2. Element-level polarization coding mechanisms

One canonical PCRPA element is the adjustable-phase four-port antenna. In that design, the current density on the radiating patch is reshaped by controlled port phases, so element pattern and polarization are both functions of port selection and phase state. For dual-port excitation with equal amplitudes and phase difference $\Delta$,

$$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$

and the radiation pattern is expressed as a function of $\Delta$. For four-port excitation, circular polarization is obtained by exciting two orthogonal modes with a phase difference $\beta \approx \pm 90^\circ$, with $\beta=+90^\circ$ for RHCP and $\beta=-90^\circ$ for LHCP. The corresponding element “codebook” is

$$\text{code} = \{\text{ports on/off}, \Delta, \beta\},$$

which directly encodes both pattern and polarization state (Yang et al., 2023).

The reported four-port element operates from 4.0 to 5.0 GHz, maintains element efficiency of about $75\%$ across band, and has realized gain of about $2N$0–$2N$1 dBi to preserve very wide beams. In dual-port mode it supports linear polarization with wide-beam, dual-beam, and tilted-beam states; in four-port mode it supports RHCP and LHCP with axial ratio below $2N$2 dB across 4–5.0 GHz, broadside wide beams, and tilted circularly polarized beams (Yang et al., 2023).

At the signal-model level, polarforming expresses the polarization state of a reconfigurable polarized antenna as

$2N$3

so linear, circular, and general elliptical states are realized through the amplitude ratio and phase difference of two orthogonal ports. In the SISO case the effective channel is

$2N$4

and optimal polarizations are the dominant left and right singular vectors of the $2N$5 polarization channel $2N$6 (Zhou et al., 2024).

Near-field dynamic polarization control extends this idea from a single element to an aperture-wide spatial code. With two orthogonal dipoles per antenna and per-element weights $2N$7, $2N$8, the received SNR is

$2N$9

and the optimal solution is antenna-wise normalized conjugate matching. In the reported 300 GHz circular uniform planar array example, the optimal polarization angle varies significantly over the aperture in the near field and becomes almost constant only toward the far field (Myers et al., 2022). This is the continuous-valued limit of PCRPA element coding.

3. Array-level coding and synthesis algebra

At array level, PCRPA combines conventional steering phases with polarization codes. In the direct polarimetric phased-array formulation, let $\Delta$0 denote binary H/V coding vectors, with $\Delta$1, and $\Delta$2, $\Delta$3. Using active element patterns $\Delta$4, the PCRPA field components are

$\Delta$5

with steering weights

$\Delta$6

The aperture is therefore a polarization-coded thinned array whose beam pattern is determined jointly by complex excitations and binary H/V assignments (Wang et al., 27 Aug 2025).

For arbitrarily polarized beams, the desired co-polarization unit vector is parameterized as

$\Delta$7

where $\Delta$8 is the auxiliary polarization angle and $\Delta$9 is the polarization phase difference. PCRPA then decomposes $$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$0 into the embedded H- and V-port basis of the active element pattern, computes the desired H/V ratio $$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$1, maps the magnitudes into element counts $$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$2, and applies a compensation phase

$$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$3

to all V-coded elements (Wang et al., 27 Aug 2025).

A reflectarray version of the same algebra uses dual circular-polarization channels. If the reflected LCP and RCP fields are

$$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$4

then, for $$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$5 and $$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$6,

$$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$7

which is a pure linear polarization whose angle is

$$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$8

Thus element-wise LCP/RCP phase coding and array-level phase constants jointly realize beam steering and arbitrary linear-polarization synthesis (Liu et al., 2023).

4. Representative realizations and quantitative performance

Several reported apertures illustrate how PCRPA principles are realized in practice.

Work	Architecture	Reported capability
Adjustable-phase four-port array (Yang et al., 2023)	Compact four-port element and $$\mathbf{J}(\Delta) = J_0 \left( 1 + e^{j\Delta} \right) = 2J_0 \cos\left(\frac{\Delta}{2}\right) e^{j\left(\phi_1+\frac{\Delta}{2}\right)},$$9 passive planar array	4.0–5.0 GHz; linear, RHCP, and LHCP; $\Delta$0 scan for dual linear polarization; $\Delta$1 scan for RHCP/LHCP; dual- and triple-beam modes
Dual-CP 1-bit reflectarray (Liu et al., 2023)	$\Delta$2 dual-CP reconfigurable reflectarray at 16.8 GHz	LP(0°), LP(45°), LP(90°), LP(135°); beam steering up to $\Delta$3 in xoz; at least $\Delta$4 two-dimensional scanning; measured RMSE $\Delta$5 for LCP and $\Delta$6 for RCP beam phase vs phase constant
Shared-aperture SAPAA (Räsänen et al., 18 Jun 2026)	Modular S-/X-band shared-aperture phased array	S-band 2.2–2.29 GHz and X-band 8.025–8.4 GHz; LP/RHCP/LHCP synthesis; axial ratios below 0.1 dB over a $\Delta$7 scan range
Orthogonally polarized subarray RIS (Wang et al., 24 May 2026)	100 GHz PCB-based RIS with six $\Delta$8 subarrays in a $\Delta$9 aperture	Cross-polarized reflection magnitude $\beta \approx \pm 90^\circ$0 dB over 90.9–109.6 GHz; co-polarization $\beta \approx \pm 90^\circ$1 dB over 92.2–104.7 GHz; gain enhancement about 10 dB from 86 to 100 GHz and about 5 dB from 100 to 106 GHz; 0.165 W
Varactor multifunctional metasurface (Yang et al., 2023)	Four-layer $\beta \approx \pm 90^\circ$2 reflective metasurface	X/Y and circular polarization switching with more than 10 dB cross polarization isolation; $\beta \approx \pm 90^\circ$3 steering; $\beta \approx \pm 90^\circ$4 phase offset
Low-cost PCRPA prototype (Wang et al., 27 Aug 2025)	$\beta \approx \pm 90^\circ$5 X-band polarimetric phased-array testbed	Experiments validate low cross-polarization and sidelobe levels comparable to conventional architectures within the scan range, with measurable power and directivity loss

These realizations cover passive planar arrays, reflectarrays, shared-aperture SATCOM arrays, RISs, and metasurfaces. A plausible implication is that PCRPA should be regarded as an aperture-synthesis principle that spans transmit, receive, reflective, and hybrid implementations, provided the aperture can independently manipulate polarization basis components and spatial phase.

5. Pattern synthesis, calibration, and learning

Pattern synthesis in PCRPA differs from conventional phased-array synthesis because the optimization variables are mixed discrete-continuous. In the direct PCRPA architecture, single-beam arbitrarily polarized synthesis uses active element patterns, desired polarization parameters $\beta \approx \pm 90^\circ$6, element-count constraints $\beta \approx \pm 90^\circ$7, and the compensation phase $\beta \approx \pm 90^\circ$8. The reported methods include constrained random generation of polarization codes and a binary genetic algorithm; for dual-polarized beams the synthesis introduces a central symmetry constraint,

$\beta \approx \pm 90^\circ$9

and reduces the dual-beam design to a minimax nonlinear integer program over a single binary vector $\beta=+90^\circ$0 (Wang et al., 27 Aug 2025).

In fairness-aware polarimetric ISAC, optimization is carried out directly on the product manifold formed by the beamformer power sphere and the unit-norm polarization vectors of the polarization-reconfigurable antennas. The problem maximizes a weighted combination of the minimum user SINR and the minimum sensing SCNR, and the reported exact-penalty product Riemannian manifold gradient descent (EP-PRMGD) algorithm combines exact penalty, log-sum-exp smoothing, Riemannian gradient projection, and retraction to guarantee convergence to a Karush-Kuhn-Tucker point (Xiong et al., 18 Mar 2026).

In integrated polarimetric sensing and communication, waveform covariance and polarization are alternately optimized under communication QoS constraints. For depolarization-parameter estimation, the MSE objective is handled with semi-definite relaxation and majorization-minimization; for target SINR maximization, the paper modifies the same framework using Charnes–Cooper and Dinkelbach-style fractional programming steps (Lee et al., 29 Jun 2025). These formulations explicitly treat the block-diagonal polarization matrices $\beta=+90^\circ$1 and $\beta=+90^\circ$2 as design variables in the sensing and communication channel models.

Pilot-efficient learning is an additional control layer. In a PR-MISO system with a uniform linear array of $\beta=+90^\circ$3 polarization-reconfigurable elements at the transmitter and a single polarization-reconfigurable element at the receiver, deep neural networks are trained on double-side pilots to output both polarization vectors and beamforming vectors without explicit channel estimation. The reported method achieves a maximum of 20% improvement in beamforming gain over a first-estimate-then-optimize scheme (Oh et al., 2024). This suggests that learned control is particularly attractive when PCRPA channel estimation would otherwise scale with the full polarimetric state dimension.

6. Applications, trade-offs, and open problems

The application space is broad. The direct PCRPA work is motivated by radar target detection and anti-jamming in polarimetric phased arrays (Wang et al., 27 Aug 2025). Reflectarray-based polarization coding is proposed for beam alignment and polarization synchronization in satellite communication and mobile communication (Liu et al., 2023). Shared-aperture polarization-reconfigurable arrays target SATCOM ground-station reception with multi-mission operation (Räsänen et al., 18 Jun 2026). Near-field dynamic polarization control improves received SNR relative to switched- or dual-polarization phased arrays when the optimal polarization varies spatially across the aperture (Myers et al., 2022). Orthogonally polarized sub-terahertz RISs address coverage enhancement around 100 GHz (Wang et al., 24 May 2026). IPSAC formulations exploit polarization diversity for target characterization, rainfall forecasting, vegetation identification, and target classification while maintaining communication QoS (Lee et al., 29 Jun 2025).

The trade-offs are equally consistent across the literature. Channel reduction in PCRPA “inevitably incurs power and directivity loss,” and experiments on the $\beta=+90^\circ$4 X-band prototype confirm that behavior (Wang et al., 27 Aug 2025). Varactor and switch implementations introduce insertion loss, parasitics, and control-routing complexity; at 100 GHz, bondwire and switch loss account for much of the gap between ideal and measured gain, and subarray partitioning is used specifically to mitigate those effects (Wang et al., 24 May 2026). In 1-bit dual-CP reflectarrays, phase quantization and amplitude variation perturb polarization purity and gain, even though measured RMSE remains only $\beta=+90^\circ$5 for LCP and $\beta=+90^\circ$6 for RCP beam phase tracking (Liu et al., 2023). In shared-aperture SATCOM arrays, axial-ratio values below 0.1 dB are near the practical limit of polarimetric far-field measurement accuracy, so calibration burden remains substantial (Räsänen et al., 18 Jun 2026).

Near-field results add another caution: dynamic polarization control yields median SNR improvement of about 1.9 dB over switched-polarization arrays but only about 0.4 dB over dual-polarization arrays in the strong near field (Myers et al., 2022). This suggests that the strongest case for full element-wise polarization coding arises when spatially varying polarization is intrinsic to the channel or when hardware savings are as important as absolute RF performance.

Open problems follow the same trajectory identified in the broader reconfigurable-array literature: theoretical modeling, hardware reliability, channel estimation techniques, intelligent optimization methods, and innovative network architectures (Liu et al., 20 Oct 2025). For PCRPA specifically, recurring unresolved issues are accurate wide-angle calibration, discrete-versus-continuous polarization code design, switch-aware loss modeling, large-array bias/control distribution, and joint space-polarization optimization under realistic mutual coupling and bandwidth constraints.