Center Deployment Scheme in SWIPT

• CDS is a geometric deployment strategy for SWIPT where a dielectric waveguide is fixed along the center line (y = D_y/2) and the antenna is adaptively positioned along x to minimize the propagation distance.
• The scheme yields closed-form expressions for average harvested energy and achievable rate, demonstrating a linear energy–rate trade-off parameterized by factors like α, β, P_t, h, and D_y.
• Comparative analysis shows that while CDS is simple and analytically tractable, its performance typically falls between the more optimal EDS and DDS schemes, with effectiveness influenced by room geometry.

In the pinching-antenna-enabled SWIPT literature, the Center Deployment Scheme (CDS) is a deployment strategy in which a dielectric waveguide of length $D_x$ is laid parallel to the $x$-axis at the lateral midpoint $y=D_y/2$, and a flexible pinching antenna moves along that center line to serve a randomly located single-antenna user equipment (UE) in the rectangular ground region $[0,D_x]\times[0,D_y]$. Within this setting, CDS is one of three practical pinching-antenna placement schemes—together with the edge deployment scheme (EDS) and the diagonal deployment scheme (DDS)—introduced to support flexible deployment and to characterize the energy–rate trade-off under simultaneous wireless information and power transfer (SWIPT) with a hybrid time-switching (TS) and power-splitting (PS) protocol (Zhang et al., 4 Sep 2025).

1. Geometric definition and placement rule

CDS is defined by the waveguide trajectory

$$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$

where $h$ is the waveguide height above ground. The UE position is

$\Psi_u=(x_u,\,y_u,\,0),$

with $x_u\sim\mathcal U[0,D_x]$ and $y_u\sim\mathcal U[0,D_y]$.

The placement rule under CDS is distance-minimizing along the admissible center line. Since the UE $x$-coordinate is known to the base station, the optimal pinching-antenna position is

$x$0

so that the three-dimensional propagation distance reduces to

$x$1

This specialization is structurally important. Once the waveguide has been fixed at $x$2, the optimization over antenna position collapses to a single coordinate match in $x$3, and no further free parameter remains. The midpoint choice $x$4 is stated to be symmetric and to minimize the worst-case mid-line distance over $x$5 (Zhang et al., 4 Sep 2025).

2. Propagation model and hybrid TS–PS SWIPT operation

The CDS analysis assumes a deterministic line-of-sight channel with free-space path-loss exponent $x$6 and AWGN. The received baseband signal at the UE is

$x$7

where

$x$8

$x$9 is the transmit power, $y=D_y/2$0 satisfies $y=D_y/2$1, and $y=D_y/2$2.

The instantaneous SNR is therefore

$y=D_y/2$3

SWIPT is implemented through a hybrid TS–PS protocol with normalized block length $y=D_y/2$4. A fraction $y=D_y/2$5 of each block is devoted to energy harvesting (EH), and during that EH phase the received RF power is split so that the fraction $y=D_y/2$6 is sent to the rectifier and $y=D_y/2$7 to information decoding (ID). The remaining $y=D_y/2$8 fraction of time is fully used for ID.

Under a linear EH model with efficiency $y=D_y/2$9, the average harvested energy is

$[0,D_x]\times[0,D_y]$0

The average achievable rate is

$[0,D_x]\times[0,D_y]$1

For non-linear EH, the summary states the Jensen upper bound

$[0,D_x]\times[0,D_y]$2

where $[0,D_x]\times[0,D_y]$3 is the logistic EH curve (Zhang et al., 4 Sep 2025).

3. Distance distribution and closed-form CDS metrics

Because $[0,D_x]\times[0,D_y]$4, one may define

$[0,D_x]\times[0,D_y]$5

with PDF

$[0,D_x]\times[0,D_y]$6

Hence,

$[0,D_x]\times[0,D_y]$7

The CDF and PDF of $[0,D_x]\times[0,D_y]$8 are

$[0,D_x]\times[0,D_y]$9

and

$$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$0

Using this distribution, the average harvested energy under the linear model becomes

$$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$1

Thus,

$$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$2

The average achievable rate is

$$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$3

After the substitution $$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$4, $$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$5, and integration by parts, the closed form is

$$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$6

(Zhang et al., 4 Sep 2025).

These expressions are the CDS specializations of the paper’s general lemmas with $$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$7. They reduce the performance analysis to explicit functions of $$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$8, $$\Psi_{p,2}=(x_{p,2},\,D_y/2,\,h), \qquad 0\le x_{p,2}\le D_x,$$9, $h$0, $h$1, $h$2, $h$3, and the carrier-dependent constant $h$4.

4. Optimality structure and the energy–rate trade-off

The optimal positioning rule under CDS is especially simple: $h$5 The scheme is therefore “centered” only in the $h$6-dimension; along the $h$7-dimension it remains fully adaptive to the UE realization.

The closed forms immediately expose the SWIPT trade-off: $h$8 More precisely,

$h$9

where $\Psi_u=(x_u,\,y_u,\,0),$0 depends only on $\Psi_u=(x_u,\,y_u,\,0),$1, $\Psi_u=(x_u,\,y_u,\,0),$2, and $\Psi_u=(x_u,\,y_u,\,0),$3. At fixed $\Psi_u=(x_u,\,y_u,\,0),$4, the trade-off can be parameterized by $\Psi_u=(x_u,\,y_u,\,0),$5: $\Psi_u=(x_u,\,y_u,\,0),$6 with

$\Psi_u=(x_u,\,y_u,\,0),$7

Within the analyzed model, increasing $\Psi_u=(x_u,\,y_u,\,0),$8 or $\Psi_u=(x_u,\,y_u,\,0),$9 improves EH linearly but reduces rate linearly by the same prefactor in front of the expectation. The summary further states that both $x_u\sim\mathcal U[0,D_x]$0 and $x_u\sim\mathcal U[0,D_x]$1 scale linearly with $x_u\sim\mathcal U[0,D_x]$2, both decline as $x_u\sim\mathcal U[0,D_x]$3 or $x_u\sim\mathcal U[0,D_x]$4, and both improve for smaller path-loss exponent, although only exponent $x_u\sim\mathcal U[0,D_x]$5 is studied (Zhang et al., 4 Sep 2025).

A common overinterpretation would be to equate geometric symmetry with global optimality. The reported formulas do not support that conclusion: symmetry yields analytical tractability and implementation simplicity, but it does not by itself guarantee the best energy or rate outcome.

5. Comparative position relative to EDS and DDS

CDS is introduced together with EDS and DDS, and the paper provides closed-form expressions for all three schemes, enabling direct numerical comparison. The reported qualitative ordering is as follows.

• EDS: yields the largest $x_u\sim\mathcal U[0,D_x]$6 and $x_u\sim\mathcal U[0,D_x]$7, because the antenna moves along $x_u\sim\mathcal U[0,D_x]$8 and can achieve smaller distances on average.
• CDS: exhibits moderate performance, with

$x_u\sim\mathcal U[0,D_x]$9

for most $y_u\sim\mathcal U[0,D_y]$0 combinations.

• DDS: can outperform CDS when the room is “long” in one diagonal direction; for a highly rectangular room with $y_u\sim\mathcal U[0,D_y]$1, CDS can beat DDS.

A concrete numerical ordering is given for

$y_u\sim\mathcal U[0,D_y]$2

$y_u\sim\mathcal U[0,D_y]$3

Under the default settings

$y_u\sim\mathcal U[0,D_y]$4

Monte-Carlo simulation confirms several CDS-specific trends: $y_u\sim\mathcal U[0,D_y]$5 grows nearly linearly with $y_u\sim\mathcal U[0,D_y]$6 under the linear model and saturates under the non-linear model; $y_u\sim\mathcal U[0,D_y]$7 grows logarithmically with $y_u\sim\mathcal U[0,D_y]$8; and the energy–rate locus for CDS is a straight line between $y_u\sim\mathcal U[0,D_y]$9 and $x$0 (Zhang et al., 4 Sep 2025).

Taken together, these results locate CDS as a middle-ground placement rule: symmetric and easy to implement, but generally suboptimal relative to EDS, with performance relative to DDS depending on room geometry.

6. Scope of the term and acronym reuse

The expression “Center Deployment Scheme (CDS)” is not unique to pinching-antenna SWIPT. In a separate medical image classification context, the same acronym denotes a lightweight cross-center deployment framework built around multi-domain imaging shift simulation, a MobileNetV2-based domain-invariant encoder, domain-adversarial training with a Gradient Reversal Layer, a lightweight quantum feature enhancement layer, and Batch-Norm-based test-time adaptation on unseen centers (Xia et al., 25 Jan 2026).

That usage is technically distinct from the antenna-placement CDS of (Zhang et al., 4 Sep 2025). In the medical-imaging setting, the term refers to a deployment pipeline for domain generalization rather than to a geometric placement rule. The reuse of the acronym therefore requires contextual disambiguation when CDS is cited across disciplines.

Within the SWIPT literature, however, CDS has a precise and narrow meaning: the waveguide is fixed on the center line $x$1, the pinching antenna is positioned at $x$2, and the resulting performance is characterized analytically through the induced distance law, the hybrid TS–PS protocol, and the closed-form harvested-energy and achievable-rate expressions (Zhang et al., 4 Sep 2025).