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Tri-Hybrid SWIPT with Reconfigurable Parasitic Antennas

Thien Duc Hua, Mohammadali Mohammadi, Hien Quoc Ngo, Michail Matthaiou

arXiv:2610.13402v1eess.SPcs.IT

TL;DR

Existing tri-hybrid work often assumes uncoupled elements, while multiuser SWIPT with parasitic antennas calls for a coupling-aware antenna-domain model. The paper develops a tri-hybrid design incorporating that model and reports improved SE and harvested energy over hybrid precoding. Its evaluation is for single-carrier SWIPT.

  • Problem

    Prior tri-hybrid studies tend to neglect mutual coupling by spacing adjacent antennas beyond half a wavelength and assuming uncoupled elements.

    Source: §I · p. 1

  • Method

    The paper models coupling-aware multiuser SWIPT with a parasitic-assisted EM precoder and uses a fully connected analog precoder with coordinate-descent-optimized parasitic elements.

    Source: §I · p. 1, §IV · p. 5

  • Results

    The proposed tri-hybrid scheme achieves higher min SE than the active-only hybrid baseline, while tri-hybrid-BD reaches approximately 5.0 mW saturated sum-NLHE.

    Source: §IV · p. 6

  • Takeaways & Limitations

    The results support coupling-aware EM-layer design for physically consistent and energy-efficient SWIPT systems.

    Source: §V · p. 6

    The proposed framework addresses single-carrier SWIPT; the conclusion identifies wideband OFDM SWIPT as future work.

    Source: §V · p. 6

Abstract

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We propose a coupling-aware tri-hybrid precoding architecture for simultaneous wireless information and power transfer (SWIPT) using reconfigurable parasitic antennas. By integrating multiport network theory and information theory, we develop a third precoding layer that explicitly accounts for mutual coupling and reactive energy storage within the antenna domain. To efficiently optimize this architecture, we propose a low-complexity tri-hybrid solution comprising coordinate descent (CD) for parasitic reactive load optimization, a singular value decomposition (SVD)-based analog precoder, and a protective partial zero-forcing (PPZF) digital precoder. Numerical results demonstrate that the transmit array introduces impedance mismatch that reduces the real power accepted by the antenna array. Moreover, the proposed tri-hybrid architecture significantly outperforms hybrid precoding by constructively exploiting the coupling effects, yielding substantial gains in spectral efficiency (SE) and sum non-linear harvested energy (NLHE) at a fraction of the hardware cost.

I. INTRODUCTION

The introduction motivates a coupling-aware tri-hybrid design for multiuser SWIPT, addressing the uncoupled-element assumption in prior tri-hybrid studies. It reports gains over conventional hybrid precoding in a dense-array setup.

I. INTRODUCTION

  • Existing tri-hybrid studies tend to neglect mutual coupling by spacing adjacent antennas farther than half a wavelength and assuming uncoupled elements.The proposed setting instead considers coupling-aware parasitic-assisted tri-hybrid precoding for multiuser SWIPT with separate IRs and ERs.Source: §I · p. 1
  • The architecture connects antenna-domain current distribution with analog and digital precoding through a multiport circuit model and evaluates the fraction of source power accepted by the antenna structure.The evaluation incorporates the source-to-array PTE metric.Source: §I · p. 1
  • The proposed low-complexity solution uses coordinate descent for parasitic loads, SVD-based analog precoding, and PPZF digital precoding.Source: §I · p. 1
  • With spacing below half a wavelength, the coupled tri-hybrid architecture yields over a two-fold improvement in min SE and a three-fold increase in sum NLHE versus hybrid precoding.The comparison is for a dense array setup.Source: §I · p. 1

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system model represents multiuser SWIPT through digital, analog, and parasitic-assisted EM precoding layers. A multiport antenna model relates their signals to antenna currents and mutual impedances.

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The transmitter serves K information receivers and J energy receivers with N = A + P antennas and fewer RF chains than antennas for cost efficiency.The stream vector contains information-bearing symbols for the first K users and energy-bearing symbols for the remaining J.Source: §II · p. 2
  • Digital precoding combines user streams, the unit-modulus analog RF precoder maps RF chains to active antennas, and the EM precoder represents parasitic-assisted antenna-domain control.Source: §II · p. 2
  • The antenna-domain current is formed by cascading the EM, RF, and baseband precoders on the symbol vector, bridging signal processing to antenna-port currents and radiated fields.Source: §II · p. 2
  • The multiport model distinguishes self and mutual impedances within the active and parasitic arrays and mutual coupling between the two arrays, assuming identical dipole properties for dissipation-loss computation.Source: §II · p. 2

ZR,1, . . . , ZR,P

The antenna-domain formulation derives equivalent active and parasitic circuit relations, then accounts for impedance mismatch in the current excitation and precoder. The mismatch reduces current entering the array, while the precoder encodes power delivery and matching.

ZR,1, . . . , ZR,P

  • Kirchhoff’s voltage law and the parasitic-loop relationship yield equivalent voltage-current relations for the active antenna and parasitic circuits.These equivalents are used in further derivations.Source: ZR,1, . . . , ZR,P · p. 2
  • The active-array current is reduced because the source impedance is not conjugate-matched to the array input impedance matrix.Equation (7) expresses the current through the factor (ZS + Zin)−1 ZS.Source: ZR,1, . . . , ZR,P · p. 2
  • The precoder FEM maps baseband excitation to antenna ports, while its current-divider matrix captures excitation-dependent source-power delivery to the terminated array.Matching is assessed as accepted real power relative to available source power.Source: ZR,1, . . . , ZR,P · p. 2

A. Channel Model, Circuit-Power, and SWIPT metrics

The section models a coupled transmitter and receiver channels, then defines source-to-array power transfer and SWIPT performance metrics. It also specifies the PPZF interference treatment and the nonlinear harvested-power measure.

Array and channel model

  • The transmitter uses active and parasitic elements arranged in a planar array, with the active elements in the central column and parasitic elements in symmetric columns.Adjacent-column and adjacent-row spacings are denoted by dx and dy.Source: A. Channel Model, Circuit-Power, and… · pp. 2–3
  • The model maps peak-current excitation to received power using a current-to-received-power channel coefficient under a far-field plane-wave approximation.The channel formulation assumes matched isotropic receive antennas and aligned polarization.Source: A. Channel Model, Circuit-Power, and… · p. 3

Circuit-power metrics

  • The PTE ratio is accepted real power divided by available source power, with accepted power comprising radiation and conductor dissipation.The available source power is defined for the specified sources under conjugate matching, while the actual antenna configuration need not be matched.Source: A. Channel Model, Circuit-Power, and… · p. 3

SWIPT metrics

  • PPZF places energy-directed beams in the effective information-receiver channel's null space, while SE and sum-NLHE quantify information and harvested-energy performance.The harvested output power uses a parameterized nonlinear energy-harvesting model with receiver-specific saturation and circuit parameters.Source: A. Channel Model, Circuit-Power, and… · p. 3

B. Problem Formulation

The design uses a log-determinant surrogate for the effective channel to promote aggregate gain, spatial rank, and conditioning. Its formulation includes hardware and load constraints and adopts a line-of-sight specialization.

Surrogate objective

  • The log-determinant of the effective channel is used as a surrogate that promotes aggregate channel gain, spatial rank, and conditioning for subsequent digital precoding.The effective propagation matrix combines the receiver channels with the EM-layer, RF, and baseband precoders.Source: B. Problem Formulation · p. 3

Model scope

  • The study adopts a line-of-sight specialization to isolate coupling, impedance mismatch, and parasitic-load optimization, leaving joint robust treatment of multipath fading and imperfect CSI beyond scope.The system model does not prohibit multipath fading or imperfect CSI.Source: B. Problem Formulation · p. 3

Constraints

  • The parasitic reactances are bounded by [Xmin, Xmax], alongside a circuit-aware source-power budget and a unit-modulus analog-precoder constraint.The formulation identifies the reactance interval as the feasible load range.Source: B. Problem Formulation · p. 4

III. PARASITIC-ASSISTED TRI-HYBRID PRECODING DESIGN

The proposed coupling-aware tri-hybrid optimization strategy separates a non-convex design into EM-layer, analog, and digital precoding stages.

III. PARASITIC-ASSISTED TRI-HYBRID PRECODING DESIGN

  • The strategy addresses non-convex coupling among EM-layer reactances, analog phase shifters, and the digital precoder by dividing the design into three stages.The formulation also includes unit-modulus and hardware constraints.Source: §III · p. 4
  • The EM layer is optimized with coordinate descent, followed by SVD-based analog optimization.These are the first two stages of the proposed low-complexity strategy.Source: §III · p. 4
  • PPZF baseband precoding is the final stage and manages multi-user interference.It follows the EM-layer and analog optimization stages.Source: §III · p. 4

A. EM-Layer Design

The EM-layer design searches parasitic reactances to maximize a log-determinant objective for the coupling-aware effective channel. Coordinate descent tests grid values one reactance at a time and stops at a tolerance or sweep limit.

A. EM-Layer Design

  • The parasitic load vector is optimized to maximize the log-determinant of the coupling-aware effective channel.The resulting EM-layer precoder is formed from the optimized loads.Source: A. EM-Layer Design · p. 4
  • Each parasitic reactance is searched over a uniform grid spanning the feasible interval [Xmin, Xmax].The grid contains NG points.Source: A. EM-Layer Design · p. 4
  • The search begins with independently and uniformly drawn initial reactances, then updates one reactance at a time while holding the others fixed.At each coordinate update, candidate grid values are evaluated and the value maximizing the objective is selected.Source: A. EM-Layer Design · p. 4
  • The iterative procedure ends when consecutive outer iterations improve by less than the tolerance or when it reaches TCD sweeps.The objective value is tracked across iterations.Source: A. EM-Layer Design · p. 4

B. Analog Precoder Design

The analog precoder aligns the RF chains with the dominant spatial subspace of the effective channel, using an SVD-based construction followed by a constant-modulus adjustment.

B. Analog Precoder Design

  • The analog precoder aligns the RF chains with the dominant spatial subspace of the effective channel.The design uses the effective channel matrix.Source: B. Analog Precoder Design · p. 4
  • The SVD selects the first NRF right singular vectors to form the RF precoder, completing the columns orthonormally when needed.The singular values are ordered in descending order.Source: B. Analog Precoder Design · p. 4
  • A constant-modulus analog precoder is obtained by applying the specified operations elementwise to the SVD-based construction.Source: B. Analog Precoder Design · p. 4

C. Digital Precoder Design

The digital layer uses PPZF beamforming to manage interference among information receivers while protecting them from energy-directed interference, subject to stated rank and channel conditions.

C. Digital Precoder Design

  • PPZF manages interference among information receivers while providing complete spatial protection from energy-directed interference intended for energy receivers.The protection maintains the information receivers' SINR.Source: C. Digital Precoder Design · p. 4
  • The PMRT precoders lie in the null space of the effective information-receiver channel, inducing zero interference at each information receiver.The null-space projection matrix satisfies H_IR B_IR = 0.Source: C. Digital Precoder Design · pp. 4–5
  • The SVD–PPZF construction requires K < NRF ≤ min{U, A}, a full-row-rank effective information-receiver channel, and nonzero projected energy-receiver channels.The digital precoder is scaled to satisfy the transmit-power budget and uses equal weighting of normalized directions.Source: C. Digital Precoder Design · pp. 4–5
  • The baseband precoder applies PPZF toward information receivers and PMRT toward energy receivers after partitioning the effective channels.Source: C. Digital Precoder Design · p. 4

IV. NUMERICAL RESULTS

The numerical evaluation compares tri-hybrid and hybrid precoding under shared active-element and RF-chain budgets, while examining how antenna spacing and power affect performance. The proposed design improves minimum SE and harvested energy, with the reported PTE depending on the coupling regime.

IV. NUMERICAL RESULTS

  • The reference setup uses 20 active antennas and 40 parasitic elements, with 10 RF chains serving four information receivers and four energy receivers.The evaluation uses a single-frequency approximation at 2.4 GHz and averages performance over 100 realizations.Source: §IV · pp. 5–6
  • The benchmarks include active-only block-diagonal and fully connected hybrid precoders, plus tri-hybrid counterparts with block-diagonal or fully connected analog precoding.The proposed tri-hybrid-BD combines a fully connected analog precoder with CD-optimized parasitic elements.Source: §IV · p. 5
  • At d = 0.4λ, the proposed scheme achieves 83.41% PTE, exceeding TB1, TB2, and TB3 by 35.91, 36.17, and 23.26 percentage points, respectively.At 0.3λ, stronger coupling may increase mismatch and reduce accepted real power; at 0.5λ, weaker coupling reduces the loads' ability to compensate.Source: Table I · p. 5, §IV · p. 5
  • Figure 1 plots CD-algorithm convergence with TCD = 20, tolerance 0.0001, 0.4λ spacing, and Pn = 20 dBm.Source: Figure 1 · p. 6
  • The tri-hybrid scheme achieves higher min SE than the active-only hybrid baseline, while tri-hybrid-BD reaches about 5.0 mW sum-NLHE and outperforms the listed alternatives.The sum-NLHE advantage appears as power rises above 10 dBm; at or below 10 dBm, all schemes harvest negligible NLHE.Source: Figure 2 · p. 6, §IV · p. 6

V. CONCLUSION

The paper concludes that coupling-aware tri-hybrid precoding can improve SE and sum-NLHE over conventional hybrid precoding under identical RF-chain constraints. Its evaluated framework is single-carrier, with wider-band design and antenna Q-factor constraints left for future work.

V. CONCLUSION

  • The proposed single-carrier SWIPT architecture uses reconfigurable parasitic antennas and an EM-layer precoder that accounts for mutual coupling and impedance mismatch.The antenna-domain, analog, and digital layers are optimized sequentially.Source: §V · p. 6
  • Numerical results show substantial SE and sum-NLHE gains over conventional hybrid precoding under identical RF-chain constraints.Source: §V · p. 6
  • Future work will extend the framework to wideband OFDM SWIPT and incorporate antenna Q-factor constraints for reactive-energy storage and frequency-dependent matching.Source: §V · p. 6
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