⚡ electrical engineering

PAPR-Aware Waveform Design for Energy-Efficient MIMO-OFDM SWIPT

This paper proposes a unified analytical framework and a frequency-domain resource allocation strategy for MIMO-OFDM SWIPT systems that optimizes waveform design to balance the conflicting requirements of low peak-to-average power ratio for power amplifier efficiency and high peak-to-average power ratio for rectifier energy harvesting, thereby significantly enhancing overall energy transfer performance.

Original authors: Chongda Huang, Yue Xiao, Qianzhen Zhang, Lilin Dan, Xianfu Lei, Kai-Kit Wong

Published 2026-03-20

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Chongda Huang, Yue Xiao, Qianzhen Zhang, Lilin Dan, Xianfu Lei, Kai-Kit Wong

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to send a package to a friend using a delivery truck. This package has two jobs:

Deliver a letter (Information/Data).
Power the friend's house (Energy/Harvesting).

In the world of wireless technology, this is called SWIPT (Simultaneous Wireless Information and Power Transfer). Usually, engineers have to choose between sending a clear letter or sending a lot of power, but rarely both at the same time efficiently.

This paper introduces a clever new way to design the "truck" (the radio signal) so it does both jobs perfectly, even when the road is bumpy and the truck engine is finicky.

Here is the breakdown using simple analogies:

1. The Problem: The "Bumpy Ride" Dilemma

The authors focus on a specific type of signal called OFDM (used in 4G and 5G). Think of OFDM as a truck carrying many small crates (subcarriers) at once.

The Transmitter (The Sender): The truck has an engine (Power Amplifier). If the crates are stacked unevenly, the truck hits a huge bump (a "Peak"). To avoid breaking the engine, the driver must drive very slowly and carefully (low power) to ensure the bump doesn't crush the engine. This wastes fuel (energy).
- The Goal: We want the crates to be stacked evenly (Low Peak-to-Average Power Ratio, or Low PAPR) so the engine can run hot and efficient.
The Receiver (The Friend): The friend has a special solar panel (Rectifier) to catch the energy. Surprisingly, this solar panel works better when the signal hits it with a massive, sudden jolt (a High Peak). A gentle, steady breeze doesn't charge it well; it needs a lightning bolt.
- The Goal: We want the signal to have huge spikes (High PAPR) when it arrives so the solar panel charges fast.

The Conflict: The sender wants a smooth, flat signal to save fuel, but the receiver wants a spiky, bumpy signal to charge up. It's like trying to drive a car smoothly to save gas, but the passenger needs the car to hit speed bumps to wake up.

2. The Solution: The "Magic Partition"

The authors propose a smart way to split the signal into three different zones, like dividing a highway into three lanes:

Lane 1: The "Smooth Lane" (Tone Reservation)
- What it does: This lane is reserved for "calming" the signal. The sender uses these frequencies to cancel out the big bumps before the signal leaves the transmitter.
- Result: The truck leaves the garage with a smooth load, saving the engine (Power Amplifier) from stress and saving fuel.
Lane 2: The "Shock Lane" (Index Modulation)
- What it does: This lane is designed to create a massive, synchronized spike at the receiver. The sender arranges the signal so that all the waves line up perfectly at the exact moment they hit the friend's solar panel.
- Result: Even though the truck left the garage smoothly, the signal "rebuilds" itself into a giant spike just as it arrives, waking up the solar panel and charging it super fast.
Lane 3: The "Letter Lane" (Standard Data)
- What it does: This is the normal lane for sending the actual text messages (data).
- Result: The friend still gets their letter clearly, just like before.

3. The "Magic Metric" (The Scorecard)

The authors created a simple score called $\Xi$ (Xi).

Think of it as a ratio: How much "spike" the receiver gets divided by how much "spike" the transmitter has to deal with.
If you can make the receiver's spike huge while keeping the transmitter's spike small, your score goes up, and the whole system becomes incredibly efficient.

4. The Results: A Win-Win

By using this "Magic Partition" strategy:

The Engine (Transmitter): Runs much more efficiently because it doesn't have to slow down for bumps. It saves about 10% more energy.
The Solar Panel (Receiver): Charges about 3 times faster because it gets those perfect, synchronized spikes it loves.
The Letter: Still arrives safely and clearly.

The Big Picture

Imagine you are a chef.

Old Way: You have to cook a meal that is either very spicy (good for the hungry guest) or very mild (good for your delicate stove). You can't do both.
New Way: You cook the food mild (saving your stove), but just before serving it, you sprinkle a special "magic spice" on top that only the guest can taste. The stove is happy, the guest is thrilled, and the meal is perfect.

This paper proves that by carefully designing where and how we send our signals, we can solve the conflict between saving energy at the source and harvesting energy at the destination, making future wireless networks (like 6G) much greener and more powerful.

1. Problem Statement

Simultaneous Wireless Information and Power Transfer (SWIPT) faces a fundamental design dilemma regarding the Peak-to-Average Power Ratio (PAPR) of the transmitted waveform:

Transmitter Side (Power Amplifier - PA): High PAPR signals force the PA to operate with a large Output Back-Off (OBO) to maintain linearity and avoid distortion. This significantly reduces PA efficiency and increases power consumption. Low PAPR is preferred here.
Receiver Side (Rectifier): Energy harvesting relies on the non-linear switching behavior of diode-based rectifiers. High PAPR signals create large instantaneous peaks that drive the diode into its non-linear region more effectively, thereby boosting RF-to-DC conversion efficiency. High PAPR is preferred here.

Existing solutions often address these issues separately or avoid OFDM (which inherently has high PAPR) for SWIPT, sacrificing spectral efficiency and compatibility with modern communication standards (like 5G/6G). There is a lack of a unified framework that jointly optimizes MIMO-OFDM waveforms to balance these conflicting requirements.

2. Methodology

The authors propose a unified analytical framework and a novel system architecture for MIMO-OFDM SWIPT.

A. Unified Analytical Framework

The paper establishes a mathematical model linking PAPR to end-to-end efficiency ( $\eta$ ):

PA Modeling: Drain efficiency ( $\eta_{PA}$ ) decreases as the required OBO increases, which is positively correlated with the expected transmit PAPR ( $E[\text{PAPR}_{TX}]$ ).
Rectifier Modeling: RF-to-DC conversion efficiency ( $\eta_{R}$ ) increases with the exponential moment of the received signal envelope, which is positively correlated with the expected receive PAPR ( $E[\text{PAPR}_{RX}]$ ).
Proposed Metric: A dimensionless metric $\Xi$ is introduced to capture the trade-off:
$\Xi = \frac{E[\text{PAPR}_{RX}]}{E[\text{PAPR}_{TX}]}$
Maximizing $\Xi$ implies reducing transmit PAPR (for PA efficiency) while increasing receive PAPR (for rectifier efficiency).

B. System Architecture: Frequency-Domain Resource Allocation

The proposed system partitions the available spectrum into three functional blocks within a Power-Splitting (PS) receiver architecture:

Tone Reservation (TR) Block ( $K_{TR}$ ): Used to suppress the transmit-side PAPR.
Index Modulation (IM) Block ( $K_{IM}$ ): Used to shape the waveform to create coherent peaks at the receiver, enhancing rectifier efficiency.
QAM Block ( $K_{QAM}$ ): Used for standard high-rate data transmission.

Key Mechanisms:

Receive-Side Peak Enhancement (IM): The IM subcarriers are mapped such that non-zero symbols are phase-aligned. Through Fourier transform properties, these symbols coherently superimpose at a specific time-domain sample (e.g., the first sample), creating a dominant peak at the energy harvesting branch without increasing the average power significantly.
Transmit-Side PAPR Reduction (TR): Reserved subcarriers are optimized using a Gradient Descent-based Tone Reservation algorithm. These tones generate a cancellation signal that opposes the peaks created by the IM and QAM components at the transmitter, effectively lowering the transmit PAPR.
Optimization Strategy: The problem is formulated as a Rate-Energy (R-E) maximization task. The authors use Successive Convex Approximation (SCA) to solve the non-convex subcarrier allocation problem ( $K_{TR}, K_{IM}$ ), iteratively updating local affine surrogate models for PA and rectifier efficiencies.

3. Key Contributions

Unified Modeling: Established a rigorous analytical framework characterizing the dual, conflicting roles of PAPR on PA efficiency and rectifier performance in MIMO-OFDM systems.
Novel Waveform Design: Proposed a frequency-domain resource allocation strategy that simultaneously employs Tone Reservation (to lower TX-PAPR) and Index Modulation (to boost RX-PAPR). This allows the system to exploit the non-linearities of the rectifier while protecting the PA.
Metric Introduction: Defined the $\Xi$ metric as a design-oriented indicator for optimizing the trade-off between information throughput and energy harvesting.
Scalability: Demonstrated that this approach is viable for large-scale MIMO-OFDM configurations, a scenario often avoided in SWIPT literature due to PAPR concerns.

4. Simulation Results

Extensive simulations using LDMOS PA models and Schottky diode rectifier models (HSMS-285x) validated the approach:

PA Efficiency: The proposed scheme reduced transmit PAPR to ~5 dB (compared to higher values in conventional OFDM), allowing the PA to operate closer to saturation. This resulted in a >10% improvement in PA efficiency.
Rectifier Performance: By creating coherent peaks via IM, the receive-side PAPR was significantly enhanced. This led to a nearly 3x increase in rectification efficiency and output voltage compared to conventional OFDM.
End-to-End Gain: The overall harvested energy increased by several times. The system achieved a substantial expansion of the Rate-Energy (R-E) region.
Trade-off: The authors demonstrated that sacrificing only 25–35% of spectral efficiency (by allocating subcarriers to TR and IM) yields multiplicative gains in energy transfer, making it highly efficient for SWIPT.
Metric Validation: A strong monotonic correlation was observed between the proposed metric $\Xi$ and the end-to-end energy efficiency, confirming its utility as a design guide.

5. Significance

This paper bridges a critical gap in SWIPT research by moving away from the "low PAPR only" paradigm. It proves that MIMO-OFDM, the backbone of modern wireless communications, can be adapted for efficient simultaneous power and information transfer.

Practical Impact: The solution is compatible with existing OFDM standards (like 5G) by utilizing resource allocation rather than changing the fundamental modulation scheme.
Energy Efficiency: It offers a viable path to powering battery-constrained IoT devices and sensor networks by maximizing the energy harvested from the same signal used for data transmission.
Future Direction: The framework sets a foundation for future research in multi-user scenarios and machine learning-based real-time optimization of energy-information trade-offs.