Maximizing Uplink and Downlink Transmissions in Wirelessly Powered IoT Networks

This paper proposes a Mixed Integer Linear Program and a learning-based approach to optimize mode scheduling, transmit power, power splitting, and decoding order in wirelessly powered IoT networks using RSMA, achieving near-optimal packet transmission counts and significantly outperforming competing methods.

The Gist

Imagine a busy coffee shop called the IoT Network. In this shop, there is one main barista (the Hybrid Access Point or HAP) and a bunch of customers (the IoT devices) who are trying to do two things at once:

1. Get a refill (harvest energy from radio waves).
2. Order a drink (send or receive data).

The problem is that the customers have empty cups (no battery). They can only order a drink if they have enough energy to pay for it. The barista has a magic machine that can shoot energy beams (like a laser pointer) to refill their cups, but the machine also needs to talk to them.

The paper by Song and Chin is about figuring out the perfect schedule for this coffee shop to get the most transactions done without anyone running out of energy.

The Old Way vs. The New Way

The Old Way (TDD - Time Division Duplex):
Imagine the barista has a strict rule: "First 5 minutes, I only refill cups. Next 5 minutes, I only take orders."

• The Flaw: What if the energy beam is blocked by a wall during the "refill" time? The customers stay empty. What if the customers are too tired to shout their orders during the "order" time? The barista misses out. The schedule is rigid, regardless of how the day is actually going.

The New Way (Mode-Based Structure):
The authors propose a smarter barista. Instead of a fixed schedule, the barista looks at the situation every single minute and asks: "Is it better to refill cups right now, or take orders?"

• If the energy beam is strong, the barista spends the minute refilling cups.
• If the customers are full of energy and the connection is clear, the barista spends the minute taking orders.
• The Goal: Maximize the total number of drinks served and refills given.

The Secret Sauce: "Splitting the Beam" (RSMA & Power Splitting)

This isn't just about timing; it's about how the barista talks to the customers.

1. The "Common Message" (RSMA):
   Imagine the barista shouts a general announcement that everyone can hear (like "We are out of oat milk!"). Then, the barista whispers a secret order to one specific customer.

   • How it works: The customer listens to the loud announcement first, understands it, and then "cancels it out" in their brain. Once the noise is gone, they can clearly hear their own secret whisper. This allows the barista to talk to everyone at once without the messages getting mixed up.

2. The "Split Cup" (Power Splitting):
   When the barista shoots an energy beam at a customer, the customer doesn't just drink the energy. They use a special cup that splits the liquid.

   • Part A goes into the battery (Energy Harvesting).
   • Part B goes to the brain to decode the message (Data Decoding).
   • The paper figures out the perfect ratio for this split. If you split it 50/50, you might not get enough energy. If you split it 90/10, you get a full message but a half-empty battery. The math finds the sweet spot.

The Two Solutions Proposed

The authors came up with two ways to run this coffee shop:

1. The "Crystal Ball" Method (MILP - The Perfect Planner)
This is a super-smart computer algorithm that knows the future. It knows exactly how strong the energy beam will be and how clear the air will be for the next hour.

• How it works: It calculates the absolute perfect schedule. It knows, "At 10:05, the sun will be in the way, so let's take orders then. At 10:06, the sun is gone, so let's refill."
• The Catch: In real life, we don't have crystal balls. We can't see the future. This method is the "Gold Standard" to measure how good other methods are, but it's too slow and complex to run on a real-time phone.

2. The "Smart Learner" Method (Reinforcement Learning)
Since we can't see the future, the authors built a "Smart Barista" that learns by doing.

• How it works: The barista tries different strategies. "If I refill now, do I get more orders later?" If yes, it remembers that. If no, it tries something else. Over time, it learns a pattern.
• The Result: This "Smart Barista" doesn't know the future, but it learns from the past and present so well that it achieves 90% of the efficiency of the "Crystal Ball" method. It's almost as good as knowing the future, but it works in real-time!

Why This Matters

The paper shows that by being flexible (switching between refilling and ordering based on real-time conditions) and using smart math (splitting signals and energy), we can:

• Send 25% more data than current methods.
• Keep devices running longer without needing to plug them in.
• Make the whole network much more efficient.

In a nutshell: The paper teaches us how to run a wireless network like a savvy shop owner who knows exactly when to charge the customers' phones and when to let them talk, using a little bit of magic math to split the signal and energy perfectly.

Technical Summary

1. Problem Statement

The paper addresses the challenge of optimizing resource allocation in Wirelessly Powered Internet of Things (IoT) networks. Specifically, it focuses on a network comprising a Hybrid Access Point (HAP) and multiple RF-energy harvesting devices.

The core problem involves maximizing the total number of successfully decoded packets (both uplink and downlink) over a planning horizon. The system faces several constraints and complexities:

• Energy Constraints: Devices rely on Radio Frequency (RF) signals for both energy harvesting and data reception (Simultaneous Wireless Information and Power Transfer - SWIPT). They use Power Splitting (PS) to divide received power between energy harvesting and information decoding.
• Multiple Access: The network utilizes Rate Splitting Multiple Access (RSMA), where messages are split into common and private parts, decoded via Successive Interference Cancellation (SIC).
• Dynamic Channel Conditions: Channel gains vary over time. The HAP must decide whether a specific time slot is better suited for Downlink (HAP to devices) or Uplink (devices to HAP) transmission based on current and future channel states.
• Coupling: There is a fundamental coupling between the HAP's transmission strategy, the energy harvested by devices, and the subsequent ability of devices to transmit uplink data.
• Information Availability: The optimal solution requires non-causal Channel State Information (CSI) (knowing future channels), which is often unavailable in real-time. The paper also seeks a solution using only causal CSI (current and past channels).

2. Methodology

The authors propose a two-pronged approach: an optimal mathematical formulation and a learning-based heuristic.

A. System Model

• Time Structure: Unlike conventional Time-Division Duplex (TDD) where downlink and uplink phases are fixed, the paper uses a mode-based time structure. Each time slot is dynamically assigned as either Downlink or Uplink.
• Downlink (RSMA): The HAP transmits a superposition of a common message (for all devices) and private messages. Devices use power splitting to harvest energy while decoding the common message, then use SIC to decode their private message.
• Uplink (RSMA): Devices split their messages into sub-messages and transmit with different power levels. The HAP uses SIC to decode them based on a specific decoding order.
• Energy Dynamics: Devices have a non-linear energy harvesting model. Their residual energy evolves based on harvested energy (from downlink slots) minus energy consumed (for uplink transmission).

B. Optimization Formulation (MILP)

To find the theoretical optimum, the authors formulate a Mixed Integer Linear Program (MILP).

• Objective: Maximize the weighted sum-throughput (total packets decoded) over $T$ time slots.
• Decision Variables:
  1. Mode of each slot (Downlink/Uplink).
  2. Transmit power allocation for common/private messages.
  3. Power splitting ratio ($\rho$) for devices in downlink slots.
  4. Decoding order for uplink slots.
• Linearization: The original problem is a Mixed Integer Non-Linear Program (MINLP) due to non-linear energy harvesting functions and SINR constraints involving products of variables. The authors linearize these using:
  • Piecewise linear approximation for the non-linear energy harvesting function.
  • McCormick envelopes to linearize the product of power coefficients and power splitting ratios.
• Reduced Order Set: To mitigate the factorial complexity of decoding orders ($2N!$), they propose a reduced set of orders by eliminating permutations that only swap messages from the same device, creating a more tractable MILP-Re.

C. Learning-Based Approach (Reinforcement Learning)

Since the MILP requires non-causal CSI (future knowledge), the authors propose a Q-Learning approach for real-time operation using only causal CSI.

• MDP Formulation:
  • State ($S$): Defined by the residual energy and channel gain of all devices (quantized into power levels).
  • Action ($A$): Binary choice: Select Downlink ($0$) or Uplink ($1$) mode for the current slot.
  • Reward ($R$): The weighted sum-throughput achieved in that slot.
• Hybrid Execution:
  • The Q-learning agent decides the mode of the slot.
  • Once the mode is selected, the HAP solves a Linear Program (LP) to optimize the internal parameters (power splitting, power coefficients, or decoding order) for that specific mode.
  • This separates the discrete mode selection (handled by RL) from the continuous resource optimization (handled by LP).

3. Key Contributions

1. Novel Network Architecture: First study to combine RSMA and SWIPT in a wireless-powered IoT network with a flexible mode-based time structure (dynamic switching between uplink/downlink).
2. Optimal MILP Formulation: Developed the first MILP that jointly optimizes slot modes, transmit powers, power splitting ratios, and decoding orders. It provides a performance upper bound given non-causal CSI.
3. Learning-Based Scheduler: Introduced a Q-learning framework that achieves near-optimal performance using only causal CSI, coupled with LP solvers for intra-slot optimization.
4. Comprehensive Evaluation: Provided the first comparative analysis of these solutions against benchmarks like TDD, Random selection, and Round Robin.

4. Results

The authors evaluated their solutions using simulations (Python/Gurobi) with parameters based on real-world hardware (e.g., Powercast receivers).

• Performance vs. Optimal (MILP): The Q-learning approach achieves approximately 90% of the optimal number of packet transmissions provided by the non-causal MILP.
• Comparison with Benchmarks:
  • The Q-learning approach yields 25% more transmitted packets compared to a Random approach.
  • It yields 15% more packets compared to a Round Robin approach.
  • It significantly outperforms conventional TDD structures, which cannot adapt slot modes to channel conditions.
• Impact of Parameters:
  • Distance: As distance increases, throughput decreases for all methods, but Q-learning adapts better than TDD by selecting more downlink slots to recharge devices.
  • Transmit Power: Higher HAP power increases throughput. The gap between Q-learning and MILP is largest at moderate power levels (0.9W) where the decision to save energy for future uplinks is most critical.
  • SIC Threshold: Higher decoding thresholds reduce throughput for all methods due to higher energy consumption, but Q-learning maintains a significant lead over random/TDD.
  • Device Count: Throughput increases with more devices, though the computational complexity of the Uplink LP grows.

5. Significance

This paper is significant because it bridges the gap between theoretical optimization and practical implementation in energy-constrained IoT networks.

• Efficiency: It demonstrates that dynamic mode selection (adapting to channel conditions) is far superior to static TDD frames, especially in environments where energy harvesting is critical.
• Practicality: By showing that a learning-based approach can achieve 90% of the "oracle" (non-causal) performance, it validates the feasibility of deploying such intelligent schedulers in real-world IoT systems where future channel states are unknown.
• RSMA Integration: It pioneers the application of RSMA in the context of simultaneous energy and information transfer, showing that RSMA can effectively manage interference while supporting energy harvesting constraints.