Power Control of Multi-Layer Repeater Networks (POLARNet)

In this letter we introduce POLARNet – power control of multi-layer repeater networks – for local optimization of SNR given different repeater power constraints. We assume relays or repeaters in groups or layers spatially separated. Under ideal circumstances SISO narrow-band communication and TDD, the system may be viewed as a dual to a deep neural network, where activations, corresponding to repeater amplifications, are optimized and weight matrices, corresponding to channel matrices, are static. Repeater amplifications are locally optimized layer-by-layer in a forward-backward manner over compact sets. The method is applicable for a wide range of constraints on within-layer power/energy utilization, is furthermore gradient-free, step-size-free, and has proven monotonicity in the objective. Numerical simulations show significant improvement compared to upper bounds on the expected SNR. In addition, power distribution over multiple repeaters is shown to be superior to optimal selection of single repeaters in the layers.

💡 Research Summary

The paper introduces “POLARNet” (Power Control of Multi-Layer Repeater Networks), an innovative framework designed for the local optimization of the Signal-to-Noise Ratio (SNR) in multi-layer repeater networks subject to various power constraints. As wireless networks evolve toward more complex, multi-hop architectures to extend coverage, managing power distribution across multiple layers of relays becomes a significant computational challenge.

The fundamental breakthrough of this research lies in establishing a mathematical duality between a multi-layer repeater network and a Deep Neural Network (DNN). Under the assumption of SISO (Single-Input Single-Output) narrowband communication and TDD (Time Division Duplex) operation, the authors demonstrate that the wireless relaying process can be modeled as a neural network. In this analogy, the static channel matrices represent the weights of the network, while the adjustable amplification factors of the repeaters correspond to the activations. This mapping allows the complex task of wireless power control to be treated as a neural network optimization problem.

The proposed POLARNet algorithm utilizes a layer-by-layer forward-backward optimization approach over compact sets. This method is particularly robust because it is “gradient-free,” meaning it does not require the calculation of complex derivatives of the channel matrices, which is often impractical in highly dynamic wireless environments. Furthermore, the algorithm is “step-size-free,” eliminating the need for tedious tuning of learning rates, and it possesses proven monotonicity, ensuring that the objective function (SNR) improves steadily throughout the optimization process. The framework is versatile enough to handle various intra-layer power and energy utilization constraints.

Numerical simulations provide strong evidence of the effectiveness of POLARNet, showing significant improvements in expected SNR compared to established theoretical upper bounds. A key finding of the study is that distributing power across multiple repeaters within a layer is superior to the traditional approach of selecting only a single optimal repeater. This suggests that a coordinated, distributed power allocation strategy is essential for maximizing network performance. Ultimately, POLARNet provides a scalable, stable, and highly efficient methodology for managing the next generation of complex, multi-layered wireless infrastructures, such as those envisioned in 6G technology.