⚡ electrical engineering

Energy-Constrained Joint Power and Hierarchical Beam Optimization for mmWave IoT Networks

This paper proposes a tractable joint optimization framework for transmit power and hierarchical beam resolution in mmWave IoT networks that, under a total energy constraint, utilizes a calibrated analytical model and a lightweight Newton-Lagrange solver to achieve significant energy savings and improved alignment reliability compared to fixed or heuristic strategies.

Original authors: Muhutasim Billah, Irfan Md Huma

Published 2026-09-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Muhutasim Billah, Irfan Md Huma

Original paper licensed under CC BY 4.0 (https://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

In the invisible landscape of modern wireless communication, data travels as invisible waves that must be precisely aimed to reach their destination. For the next generation of Internet of Things devices—sensors and small computers that monitor everything from city traffic to factory machines—this aiming process is becoming increasingly difficult. To handle the massive amounts of data these devices will generate, engineers are turning to millimeter-wave signals. These signals are incredibly fast but behave like light: they travel in straight lines and are easily blocked by walls or even rain. To make them work, devices must use directional antennas that focus the signal into a tight beam, much like a flashlight, rather than broadcasting it in all directions. However, finding the exact direction to point this flashlight is a complex puzzle. The device must scan through many possible angles to find the path to the receiver, a process that consumes time and, crucially, battery power. For devices that run on harvested energy—squeezing power from sunlight, vibrations, or radio waves—this scanning process can drain their entire energy budget before they even begin to send a single message.

Researchers Muhutasim Billah and Irfan Md Humayun from the International Islamic University Chittagong have tackled this specific dilemma. They investigated how to make the beam-finding process as efficient as possible for these energy-harvesting devices. Their work focuses on a method called hierarchical beam alignment, where the device first searches broadly to find the general direction and then narrows down to a precise angle. The core challenge they addressed is how to split a limited amount of available energy between these two stages of searching. If a device spends too much energy on the initial broad search, it may not have enough power left to refine the direction accurately. If it saves too much for the final step, it might fail to find the correct general area in the first place. The researchers developed a new mathematical framework to determine the perfect balance, ensuring the device finds its connection without wasting a single joule of its precious, harvested power.

To solve this, the team created a model that simulates the real-world behavior of these signals as they bounce off surfaces and fade in strength. They recognized that the exact math for predicting whether a beam alignment will succeed is too complex for a small device to calculate in real-time. Instead, they designed a simplified, smooth mathematical function that acts as a reliable guide. This function captures the essential relationship between the power used, the number of angles searched, and the likelihood of success, without requiring heavy computational resources. Using this guide, they built a lightweight algorithm that can run on the small microchips found in IoT devices. This algorithm acts as a decision-maker, constantly adjusting how much power to use for the initial search versus the final refinement, and deciding exactly how many fine-tuned angles to check, all based on the total energy currently available in the device's battery.

The researchers tested their method through extensive computer simulations, running half a million different scenarios to see how the system performed under various conditions. They compared their adaptive approach against traditional methods that use fixed power settings or simple rules of thumb. The results showed that their method significantly improved the chances of a successful connection, especially when energy was scarce. In situations where power was very limited, the traditional methods often failed to align the beams correctly, leading to dropped connections. In contrast, the new framework intelligently allocated more power to the initial broad search to ensure a reliable start, only shifting focus to the finer details once a secure path was established. As the available energy increased, the system naturally adjusted to allow for more detailed searches, eventually matching the performance of much more expensive and power-hungry exhaustive search methods.

A key finding of the study is that the optimal strategy changes depending on how much energy the device has. When energy is tight, the system prioritizes reliability in the first stage of the search, using a coarser, less detailed scan to guarantee it finds the right general direction. As more energy becomes available, the system becomes more ambitious, increasing the number of precise angles it checks to lock onto the connection with greater accuracy. This dynamic adjustment prevents the device from wasting energy on unnecessary precision when a simple connection is all that is needed, or from failing to connect because it was too conservative. The study demonstrates that by treating the beam alignment process as a flexible resource management problem rather than a fixed procedure, engineers can build more robust and longer-lasting networks for the future of connected devices.

The work also highlights the importance of the environment in which these devices operate. The simulations accounted for a specific type of signal behavior known as Rician fading, which describes how signals behave when there is a clear direct path between the transmitter and receiver, but also some scattered reflections. The researchers found that their optimization method remained effective even with these complex signal conditions. By avoiding the need for heavy, complex calculations, their approach offers a practical path forward for real-world deployment. It suggests that future smart sensors and industrial devices can maintain high-speed connections without the need for large batteries or frequent recharging, simply by being smarter about how they use the energy they harvest. The study concludes that the key to unlocking the potential of millimeter-wave technology for the Internet of Things lies not just in building faster signals, but in managing the energy required to find them.

Technical Summary: Energy-Constrained Joint Power and Hierarchical Beam Optimization for mmWave IoT Networks

Problem Statement
Millimeter-wave (mmWave) Internet of Things (IoT) networks require precise Beam Alignment (BA) to overcome severe path loss, typically employing hierarchical search strategies to reduce overhead. However, these strategies incur significant energy costs, creating a critical conflict for energy-harvesting (EH) IoT devices that operate under strict, stochastic energy budgets. Existing literature largely treats these challenges in isolation: hierarchical BA schemes assume fixed, unconstrained power, while energy-aware resource allocation focuses on data transmission post-alignment, neglecting the costly BA phase. Consequently, there is a lack of frameworks that jointly optimize the beam alignment strategy and power allocation under the energy causality constraints intrinsic to EH-powered devices. Misallocating energy during BA—either by probing too sparsely or too wastefully—can lead to link outages before communication begins.

Methodology
The paper proposes a joint optimization framework for a two-stage hierarchical BA process (coarse search followed by fine search) in a mmWave IoT link powered by harvested energy. The system model assumes a static node communicating with a fixed access point under Rician block fading (dominant Line-of-Sight with non-line-of-sight components).

The core of the methodology involves three components:

Analytical Surrogate Modeling: Since the exact alignment success probability under hierarchical search and Rician fading involves intractable order statistics of correlated non-central chi-square variables, the authors develop a calibrated, differentiable surrogate model. This model approximates the stage-wise success probability as a function of transmit power, beam resolution, and the Rician K-factor. It is designed to be smooth and numerically stable to facilitate gradient-based optimization.
Mixed-Integer Optimization Formulation: The problem is formulated as a Mixed-Integer Non-Linear Program (MINLP). The objective is to maximize the overall alignment success probability by jointly optimizing:
- Continuous variables: Transmit power allocation ( $p_1, p_2$ ) for the coarse and fine stages, subject to a total energy constraint ( $p_1 + p_2 = P_{total}$ ).
- Discrete variable: The number of beams to probe in the fine-search stage ( $T_2$ ), selected from a predefined codebook.
Lightweight Solver: To ensure feasibility on resource-constrained IoT microcontrollers, the authors design a custom Newton–Lagrange solver. The solution strategy decomposes the problem into an outer loop that iterates over discrete candidates for $T_2$ and an inner loop that solves the continuous equality-constrained subproblem for optimal power split using finite-difference gradients and Hessians. This approach avoids reliance on heavy external optimization toolboxes or matrix inversions.

Key Contributions
The paper claims four primary contributions:

Joint Optimization Framework: Development of a novel framework that simultaneously selects the optimal fine-stage beam count and allocates transmit power across two hierarchical stages to maximize alignment success probability under a strict total energy constraint.
Differentiable Surrogate Model: Derivation of a smooth, calibrated model for stage-wise BA success probability under Rician fading. This model captures the interplay between Signal-to-Noise Ratio (SNR), beamwidth, and search granularity, enabling efficient gradient-based optimization without requiring complex order-statistics formulations.
Embedded-Ready Solver: Design of a lightweight Newton–Lagrange solver tailored for IoT hardware. It addresses the resulting equality-constrained problem without external dependencies, ensuring computational feasibility for real-time operation on low-power nodes.
Comprehensive Validation: Extensive Monte Carlo simulations (500,000 trials) validating the framework. The results demonstrate that the proposed method captures essential performance trends and achieves substantial energy savings and improved alignment reliability compared to fixed or heuristic allocation strategies.

Results
Simulation results across a total energy budget ranging from 0.1 mW to 100 mW indicate:

Adaptive Beam Selection: The optimal number of fine-search beams ( $T_2$ ) increases monotonically with the available energy budget. In low-energy regimes, the optimizer prefers coarse searches to maintain Stage-1 reliability, shifting to higher-resolution searches only when sufficient energy is available.
Non-Linear Power Allocation: The optimal power split is non-linear. At low energy levels, the majority of power is allocated to Stage-1 to ensure sector identification reliability. As the budget increases, power allocation shifts toward Stage-2 to enhance fine-search precision, eventually stabilizing.
Performance Gains: The proposed scheme consistently maintains high beamforming gain and alignment success probability, particularly in low-energy regimes (< 0 dBm). In these scenarios, it significantly outperforms a heuristic baseline (Conv2), which suffers from Stage-1 failures due to insufficient power. At higher energy levels, the proposed method converges to the performance of an exhaustive search baseline (Conv1) but with significantly lower computational and energy overhead.
Model Accuracy: While the analytical surrogate model exhibits a deliberate numerical offset from empirical Monte Carlo results to ensure numerical stability and differentiability, it successfully captures the critical performance trends (monotonic increase with energy, saturation at high levels) required to guide the optimizer to the correct optimal configuration.

Significance and Claims
The authors position this work as the first to integrate energy constraints, analytical alignment modeling, and joint mixed-variable optimization specifically for the mmWave IoT beam alignment stage. The paper claims that by treating BA energy not as a fixed cost but as a limited resource to be optimally distributed, the proposed framework addresses a critical gap in current literature. The significance lies in providing a practical design tool that enables robust mmWave connectivity for energy-harvesting IoT devices, offering fundamental insights into the trade-offs between energy consumption, beam resolution, and alignment reliability. The work is presented as a practical solution for real-time execution on constrained hardware rather than a closed-form theoretical solution, with future work suggested for multi-stage hierarchies and hardware impairments.

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