Dynamic Power Splitting (DPS) in SWIPT

• Dynamic power splitting (DPS) is a technique in SWIPT that adaptively allocates received RF power between energy harvesting and information decoding based on real-time channel state information.
• It optimizes rate-energy trade-offs by dynamically adjusting the splitting ratio, outperforming static approaches in diverse network settings including cooperative relays and multiuser systems.
• DPS is implemented in various architectures, addressing practical concerns such as nonlinear energy harvesting, hardware constraints, and CSI acquisition through threshold-based and convex optimization methodologies.

Dynamic power splitting (DPS) is a signal processing strategy in simultaneous wireless information and power transfer (SWIPT) systems where the received radio frequency (RF) signal is adaptively split, in real time, between information decoding (ID) and energy harvesting (EH) paths according to current channel state information (CSI), network objectives, or system constraints. Unlike static power splitting (SPS), DPS dynamically adjusts the power splitting factor to optimize trade-offs between communication and energy delivery, and subsumes several classical SWIPT receiver architectures as special cases. DPS is central to a wide range of network topologies, including point-to-point, multi-antenna, cooperative relay, random-access, and multiuser systems, and is robust to circuit nonidealities such as nonlinear EH models and hardware switching overhead.

1. Principles and Formal Definition

The DPS operation at the receiver is defined as follows: given an instantaneous received RF power $|y(t)|^2$ (or per symbol/block analog), the receiver splits this into two branches via a tunable power splitter. The splitting ratio is a time-varying function, $\rho(t)\in[0,1]$, yielding:

• $\rho(t)|y(t)|^2$ for EH
• $(1-\rho(t))|y(t)|^2$ for ID

with $\rho(t)$ chosen adaptively. This generic DPS model generalizes time switching (TS; all-EH or all-ID in slots), static power splitting (SPS; constant $\rho$), and on-off power splitting (OPS; hybrid TS/SPS with blockwise or per-symbol patterns) (Zhou et al., 2012).

The essence of DPS is to achieve a system-level trade-off between harvested energy and information throughput, tailored to system-specific rate-energy (R-E) or outage constraints. This is achieved by optimally adapting $\rho$ with respect to instantaneous or statistical CSI, nodal roles (e.g., relay, user), channel nonidealities, and network operating conditions.

2. Optimality Criteria and Analytical Structures

The design of the optimal DPS policy depends on system objectives and CSI availability. Standard problem formulations include:

• Rate-energy region boundary tracing: maximize $R(\rho)$ under $Q(\rho)\geq Q_0$, or dual problems, for example, maximize harvested energy subject to a minimum ergodic capacity.
• Outage minimization: minimize $P_{\text{out}} = \Pr\{ R(\rho) < R_\text{th} \}$ by optimizing $\rho$ over the space of realizable CSI and noise (Liu et al., 2019, Shi et al., 2018, Hu et al., 2015).
• Joint transceiver optimization: with transmitter CSI, jointly optimize power allocation and receiver splitting per channel block (Liu et al., 2013, Kang et al., 2018).

Analytically, the optimal solution is frequently characterized by piecewise threshold-based structures. For instance, in ergodic fading SISO channels, (Liu et al., 2013) demonstrates the optimal DPS is given by

$$\alpha^*(h)= \begin{cases} 1, & h < h_\text{th}, \ \left[1/(\lambda h P) - \sigma^2/(h P)\right]_0^1, & h \geq h_\text{th}, \end{cases}$$

where $\alpha = 1-\rho$ and $h$ is the current channel power gain. In relay networks, the optimal $\rho^*$ is determined by solving for equality in critical SNR or energy-harvesting constraints, resulting in explicit formulas, e.g., $$\rho^* = \max\left\{1 - \frac{\gamma_\text{th} d^\alpha \sigma^2}{P h^2},\,0\right\}$$ in non-linear EH relays (Shi et al., 2018).

The basic mechanism is that DPS dedicates as much power as possible to EH in favorable channel conditions, subject to maintaining reliability or rate guarantees.

3. System Architectures and Implementation Considerations

DPS can be realized in both separated and integrated receiver architectures (Zhou et al., 2012):

• Separated Receiver: RF domain splitting precedes conversion and baseband processing. Allows fine-grained $\rho(t)$ control with independent EH and ID paths.
• Integrated Receiver: Splitting after rectification; supports energy modulation, but the achievable rate is limited by the nonlinear envelope-detection channel.

Hardware feasibility requires low-latency control of variable splitters, often at the symbol or block level, and the acquisition of accurate, low-overhead CSI (amplitude squared of all relevant fading links). For relay-based SWIPT, the relay must obtain or be fed back the instantaneous channel gains (which may impose pilot and feedback overhead) (Liu et al., 2019).

With non-negligible circuit power or quantization errors in CSI, DPS designs must be robustified, and practical algorithms often use precomputed look-up tables or quantized $\rho$ adaptation to mitigate hardware constraints (Shi et al., 2018, Zhou et al., 2012). For high-speed systems (block-fading), blockwise adaptation is often sufficient, as the time-scale of fading matches DPS update feasibility.

4. DPS in Cooperative and Multiuser Relay Networks

DPS is essential in SWIPT relay system design, under both amplify-and-forward (AF) (Hu et al., 2015) and decode-and-forward (DF) (Liu et al., 2019, Shi et al., 2018) protocols. In DF cooperative schemes with direct source-destination (DL) links, the optimal splitting factor at the relay is

$$\rho^* = \begin{cases} 0, & |h_1|^2 < |h_0|^2, \ \frac{|h_1|^2 - |h_0|^2}{|h_1|^2(1+\eta|h_2|^2)}, & \text{otherwise} \end{cases}$$

where $h_0, h_1, h_2$ are channel gains S$\to$D, S$\to$R, R$\to$D, and $\eta$ is the EH efficiency (Liu et al., 2019). The key insight is that DPS exploits the direct link's diversity, dynamically shifting from EH to ID as the relative channel strengths change.

In two-way and full-duplex relays with nonlinear (piecewise linear/logistic) EH models, DPS further adapts to the nonlinearity, maximizing capacity or minimizing outage by leveraging the convexity/concavity of the end-to-end rate as a function of $\rho$ (Shi et al., 2018, Hu et al., 2015, Liu et al., 2015).

For random access and IoT-like uplinks with unpredictable interference and multi-user activity, DPS is combined with CSI prediction and scheduling mechanisms, where $\rho(t)$ optimally balances harvested power and symbol-detection reliability in each slot, often using machine-predicted activity patterns (Kisseleff et al., 2020).

5. Rate-Energy Trade-off and Nonlinear Energy Harvesting

The explicit rate-energy (R-E) region boundaries achievable by DPS have been characterized under both idealized (linear) and realistic (nonlinear/saturating) EH models. Under ideal circumstances, the optimal DPS converges to static power splitting or on-off strategies, depending on the presence of circuit power constraints (Zhou et al., 2012). With nonlinear EH (sigmoidal/logistic harvesting function), the optimality conditions are more intricate, but the following principles hold (Kang et al., 2018):

• For any required average harvested energy $Q$, the R-E boundary is traced by solving

$$\max_{\{\rho_\nu\}}\,\,\mathbb{E}[R_\nu(P,\rho_\nu)]\quad \text{s.t.}\quad \mathbb{E}[Q_\nu^{\rm NL}(P,\rho_\nu)]\geq Q,$$

where $Q_\nu^{\rm NL}$ is the nonlinear harvested energy in fading block $\nu$.

• The optimal policy is typically piecewise, with closed-form or root-finding solutions for $\rho_\nu$ per-fading block.

Numerical and analytical results have consistently shown that DPS dramatically outperforms time switching and fixed splitting in enlarging the R-E region, particularly under practical nonlinear circuit constraints.

6. Advanced SWIPT Network Applications

In emerging architectures, such as dynamic metasurface antenna (DMA)-aided multiuser MISO SWIPT systems, DPS variables are integrated as part of a large-scale semidefinite-programming-based joint beamforming and resources optimization framework (Altinoklu et al., 11 Nov 2025). Here, $\{\rho_k\}$ (per-user splits) are optimized along with digital precoders and DMA weights under Lorentzian-constrained holography subject to users' SINR and EH requirements, both for linear and nonlinear EH models. Alternating optimization schemes with convex relaxations are deployed, and the gains in transmit-power reduction relative to static splitting are substantial and robust even as circuit noise and analog tuning constraints are imposed.

7. Performance Insights, Limitations, and Future Directions

Key findings and practical guidelines established across the literature include:

• Diversity and Capacity: DPS achieves full diversity and maximizes ergodic capacity in cooperative relay networks versus static or random power splitting (Liu et al., 2019).
• CSI Acquisition: The theoretical performance presumes perfect instantaneous CSI, but practical systems must contend with quantization, estimation errors, and pilot overhead. DPS remains robust but may require lookup-lists and coarser adaptation.
• Hardware Complexity: Fine-grained real-time control of $\rho$ must be supported by the analog front-end. For block-fading channels or limited mode-switch time, blockwise DPS suffices.
• Nonlinearities: Realistic nonlinear EH functions necessitate policy adaptation that directly incorporates sigmoidal or piecewise-linear characteristics. Simple linear-DPS approximations can be suboptimal and overly conservative (Kang et al., 2018, Shi et al., 2018).
• Scalability: Low-complexity heuristics, convex relaxations, and precomputed policy tables are effective for large-scale, multiuser, or high-mobility systems (Zhou et al., 2012, Altinoklu et al., 11 Nov 2025).
• Broader Applicability: DPS principles generalize across relaying (DF, AF, full-duplex), random access, multi-antenna (SIMO/MISO), and massive MIMO/DMA architectures, showing flexibility and superior R-E tradeoff under diverse operating conditions.

Open directions include robust DPS design under imperfect/imperfectly-quantized CSI, hardware-limited splitter dynamics, joint time/power/resource allocation strategies in full-network SWIPT deployments, and integration with intelligent reflecting surfaces and metasurfaces for fine-grained spatial energy/information beamforming. The theoretical and numerical consensus is that DPS, by adapting to both channel conditions and transceiver/circuit realities, forms the fundamental backbone for capacity- and reliability-optimal SWIPT system design.