Diagonal Deployment Scheme in SWIPT

• DDS is a pinching-antenna placement strategy in SWIPT that aligns the waveguide along a room's diagonal, exploiting geometric constraints.
• It optimizes the antenna position via the orthogonal projection of the user equipment, yielding closed-form expressions for energy harvesting and rate metrics.
• DDS offers intermediate performance between edge and center deployments, enabling efficient trade-offs through a hybrid time-switching and power-splitting protocol.

Searching arXiv for the specified paper and closely related pinching-antenna SWIPT work. The Diagonal Deployment Scheme (DDS) is a pinching-antenna placement scheme for simultaneous wireless information and power transfer (SWIPT) in which a planar waveguide is aligned along the top-corner–to–corner diagonal of a rectangular service region, and the pinching-antenna is positioned on that diagonal to optimize the energy-rate performance for a randomly located user equipment (UE). In the performance analysis of pinching-antenna-enabled SWIPT systems, DDS is studied alongside the edge deployment scheme (EDS) and the center deployment scheme (CDS), under a hybrid time-switching (TS) and power-splitting (PS) protocol, with closed-form expressions derived for the average harvested energy and average achievable rate of a uniformly distributed UE (Zhang et al., 4 Sep 2025).

1. Geometric definition and system setting

The DDS is formulated in a single-cell SWIPT system in which a base station (BS) equipped with a pinching-antenna serves a single-antenna UE (Zhang et al., 4 Sep 2025). The UE is uniformly distributed over a planar rectangular region of dimensions $D_x \times D_y$ on the ground plane $z=0$, with coordinates

$$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$

The BS is located at

$\psi_{\rm b}=(0,0,h),$

where $h$ is the fixed height of the dielectric waveguide above the ground (Zhang et al., 4 Sep 2025).

Under DDS, the planar waveguide is aligned along the top-corner–to–corner diagonal from $(0,D_y)$ to $(D_x,0)$. The pinching-antenna can be positioned at any point

$\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$

subject to the diagonal constraint

$$y_{\rm p,3}=\frac{D_y}{D_x}\,x_{\rm p,3}, \quad x_{\rm p,3}\in[0,D_x].$$

The notation used in the source identifies this configuration as the third deployment strategy, hence the subscript $3$ in the corresponding distance and performance expressions (Zhang et al., 4 Sep 2025).

The Euclidean distance between the instantaneous pinching-antenna location and the UE is

$z=0$0

Defining the diagonal slope constant

$z=0$1

this can be expanded as

$z=0$2

This geometric construction places DDS between edge-aligned and center-aligned placement schemes in the sense of spatial support: the waveguide is neither constrained to a room edge nor to a central axis, but instead follows a fixed diagonal determined by the room geometry (Zhang et al., 4 Sep 2025).

2. Optimal pinching-antenna positioning on the diagonal

The defining operational feature of DDS is that the pinching-antenna should track the orthogonal projection of the UE onto the diagonal direction (Zhang et al., 4 Sep 2025). By setting $z=0$3, the optimal pinching-antenna position is obtained as

$z=0$4

The minimized distance is then

$z=0$5

Geometrically, the optimization is entirely governed by the fixed diagonal slope $z=0$6. The source emphasizes that there is no further free “angle” parameter, since the diagonal slope is fixed by room geometry (Zhang et al., 4 Sep 2025). The optimization problem is therefore reduced to one-dimensional motion of the pinching-antenna along the diagonal subject to the orthogonal projection rule.

This formulation gives DDS a particularly explicit geometric interpretation. The optimal location is not selected by an unconstrained planar search; it is the point on the installed diagonal waveguide that minimizes the UE-to-antenna distance. A plausible implication is that the computational complexity of antenna-position selection is structurally limited by the diagonal constraint, because the optimal solution is available in closed form rather than through iterative search.

3. Hybrid TS-PS protocol and signal model

The DDS analysis is coupled to a hybrid time-switching and power-splitting protocol in which the total transmission block duration is normalized to $z=0$7 (Zhang et al., 4 Sep 2025). The protocol is parameterized by $z=0$8, the TS factor, and $z=0$9, the PS factor.

During the first fraction $$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$0 of the block, the UE splits the received signal’s power into two streams: a fraction $$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$1 for energy harvesting (EH) and $$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$2 for information decoding (ID). During the remaining fraction $$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$3, all received power is used for ID. Consequently, the effective ID time–power product is

$$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$4

while the EH time–power product is $$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$5 (Zhang et al., 4 Sep 2025).

The small-scale channel between the pinching-antenna and the UE is assumed static over each block, with free-space path-loss. The BS transmits $$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$6 with power $$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$7, with $$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$8. The received signal at the UE is

$$\psi_{\rm u}=(x_{\rm u},\,y_{\rm u},\,0), \quad x_{\rm u}\sim\mathcal U[0,D_x],\;y_{\rm u}\sim\mathcal U[0,D_y].$$9

where $\psi_{\rm b}=(0,0,h),$0 is the free-space gain constant, $\psi_{\rm b}=(0,0,h),$1 is the speed of light, $\psi_{\rm b}=(0,0,h),$2 is the carrier frequency, $\psi_{\rm b}=(0,0,h),$3 is the wavelength, and $\psi_{\rm b}=(0,0,h),$4 is AWGN (Zhang et al., 4 Sep 2025).

Within this protocol, DDS affects both EH and ID only through the distance term $\psi_{\rm b}=(0,0,h),$5, and in optimized operation through $\psi_{\rm b}=(0,0,h),$6. This makes the deployment geometry analytically separable from the TS-PS control variables $\psi_{\rm b}=(0,0,h),$7 and $\psi_{\rm b}=(0,0,h),$8: the former determines the distance statistics, while the latter determines the time-power allocation between EH and ID. This suggests a modular design interpretation in which geometric deployment and resource splitting can be studied jointly but parameterized independently.

4. Closed-form harvested-energy characterization

Under a linear EH model with conversion efficiency $\psi_{\rm b}=(0,0,h),$9, the instantaneous harvested energy per block is

$h$0

Accordingly, the average harvested energy under DDS is

$h$1

To express this in closed form, the analysis defines the diagonal projection length

$h$2

The probability density function of $h$3 is stated to support on $h$4, and a direct integration yields the closed-form result labeled Lemma 4 (Zhang et al., 4 Sep 2025): $h$5

The variables appearing in this expression are explicitly defined in the source: $h$6 is the TS factor, $h$7 is the PS factor, $h$8 is the EH efficiency, $h$9 is the BS transmit power, $(0,D_y)$0 is the waveguide height, and $(0,D_y)$1 are the horizontal room dimensions (Zhang et al., 4 Sep 2025).

The structure of (E1) isolates the deployment-specific effect of DDS in the single geometric term $(0,D_y)$2. Because $(0,D_y)$3, the room aspect ratio directly influences the average harvested energy through the effective diagonal projection length. A plausible implication is that DDS performance is sensitive not only to the absolute room size but also to the anisotropy of the service region.

5. Closed-form achievable-rate characterization

The instantaneous UE SNR under DDS is

$(0,D_y)$4

Since the effective ID fraction is $(0,D_y)$5, the average achievable rate is

$(0,D_y)$6

After a change of variables and integration, the paper gives the closed-form expression labeled Lemma 7 (Zhang et al., 4 Sep 2025): $(0,D_y)$7 with

$(0,D_y)$8

and

$(0,D_y)$9

These expressions make the rate-energy coupling under DDS explicit. The factor $(D_x,0)$0 multiplies the entire rate, while $(D_x,0)$1 multiplies the harvested energy in (E1). In the model as stated, the hybrid TS-PS protocol therefore generates a direct trade-off between $(D_x,0)$2 and $(D_x,0)$3 through the common product $(D_x,0)$4 (Zhang et al., 4 Sep 2025).

The source further reports that average rate versus $(D_x,0)$5 exhibits logarithmic increase with $(D_x,0)$6, and that the PS-rich configuration with $(D_x,0)$7 small yields higher $(D_x,0)$8 (Zhang et al., 4 Sep 2025). This is consistent with the form of (E2), in which reducing $(D_x,0)$9 increases the effective ID fraction.

6. Comparative performance relative to EDS and CDS

The paper compares DDS with EDS and CDS using both analytical curves and Monte–Carlo simulation (Zhang et al., 4 Sep 2025). In a square room with $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$0, exemplified by $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$1 m $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$2 $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$3 m, EDS yields the highest $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$4 and $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$5 due to minimal vertical offset. In the same geometry, DDS outperforms CDS because the diagonal proximity on average is closer than the central line (Zhang et al., 4 Sep 2025).

In a rectangular room with $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$6, exemplified by $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$7 m $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$8 $\psi_{\rm p,3}=(x_{\rm p,3},\,y_{\rm p,3},\,h),$9 m, EDS again leads for both metrics. However, CDS may surpass DDS when the shorter side dominates the UE distribution, making the center line closer on average than the diagonal (Zhang et al., 4 Sep 2025). The overall summary given in the source is that DDS provides a performance between EDS (best) and CDS (worst), and it is superior to CDS in near-square geometries.

The numerical illustrations are based on $$y_{\rm p,3}=\frac{D_y}{D_x}\,x_{\rm p,3}, \quad x_{\rm p,3}\in[0,D_x].$$0 Monte–Carlo trials (Zhang et al., 4 Sep 2025). Three specific observations are reported. First, for average harvested energy versus $$y_{\rm p,3}=\frac{D_y}{D_x}\,x_{\rm p,3}, \quad x_{\rm p,3}\in[0,D_x].$$1, linear growth occurs under the linear model, while saturation occurs under a typical logistic NLM; DDS lies between EDS and CDS in both models, and overtakes CDS in square scenarios. Second, for average rate versus $$y_{\rm p,3}=\frac{D_y}{D_x}\,x_{\rm p,3}, \quad x_{\rm p,3}\in[0,D_x].$$2, DDS again outperforms CDS in square rooms but underperforms in elongated rectangles. Third, for the energy–rate region at $$y_{\rm p,3}=\frac{D_y}{D_x}\,x_{\rm p,3}, \quad x_{\rm p,3}\in[0,D_x].$$3 in an $$y_{\rm p,3}=\frac{D_y}{D_x}\,x_{\rm p,3}, \quad x_{\rm p,3}\in[0,D_x].$$4 room, TS and PS trade-off curves are nearly linear and coalesce for all schemes under the linear model, whereas under NLM the PS curve becomes mildly non-linear and the DDS region strictly contains that of CDS, though EDS remains the best (Zhang et al., 4 Sep 2025).

These comparisons clarify a frequent potential misconception: DDS is not presented as the uniformly best deployment strategy. Its role is explicitly intermediate. The source characterizes it as a flexible compromise between edge and center deployment, not as a replacement for EDS in all geometries (Zhang et al., 4 Sep 2025).

7. Interpretation, constraints, and design implications

The principal optimization insight for DDS is geometric: the pinching-antenna should track the orthogonal projection of the UE onto the diagonal direction (Zhang et al., 4 Sep 2025). This rule completely specifies the optimal deployment point on the installed waveguide: $$y_{\rm p,3}=\frac{D_y}{D_x}\,x_{\rm p,3}, \quad x_{\rm p,3}\in[0,D_x].$$5 Because the diagonal slope is fixed by room geometry, there is no further free “angle” parameter. The source additionally notes that, if one were allowed to tilt the waveguide, the optimal tilt would align with the UE spatial distribution’s principal axis (Zhang et al., 4 Sep 2025). This statement is explicitly conditional and extends beyond the fixed-slope DDS formulation.

From a design perspective, the reported conclusion is that the closed-form performance metrics (E1) and (E2) enable rapid evaluation and optimization in practical SWIPT scenarios (Zhang et al., 4 Sep 2025). The same conclusion states that, in near-square environments, DDS can substantially outperform central placement, especially when diode-saturation effects are moderate, and that its optimal implementation simply requires real-time tracking of the UE’s orthogonal projection onto the pre-installed diagonal waveguide (Zhang et al., 4 Sep 2025).

A plausible implication is that DDS is best understood as a geometry-aware constrained deployment strategy: its effectiveness arises from exploiting a fixed diagonal support that is often closer on average than a center line in near-square rooms, while remaining less favorable than edge deployment when edge proximity dominates. Within the analytical framework of pinching-antenna-enabled SWIPT, DDS thus occupies a distinct position defined by closed-form tractability, explicit geometric optimization, and a deployment-dependent energy–rate trade-off (Zhang et al., 4 Sep 2025).