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Power Control of Multi-Layer Repeater Networks (POLARNet)

Johan Siwerson, Johan Thunberg

TL;DR

The paper addresses end-to-end SNR optimization in a multi-layer repeater network under per-layer power constraints. It introduces POLARNet, a gradient-free, gradient-free, forward-backward layer-wise method that updates repeater gains within predefined activation sets to monotonically improve the end-to-end channel gain |h_tot|^2. It provides algorithmic details, convergence proofs, and multiple activation-set choices, along with complexity analysis and SNR bounds. Numerical experiments under Rician fading and IID channels demonstrate substantial SNR gains and show that distributing power across repeaters yields better performance than selecting a single repeater, highlighting the practical appeal of the approach for RA-MIMO-like scenarios.

Abstract

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.

Power Control of Multi-Layer Repeater Networks (POLARNet)

TL;DR

The paper addresses end-to-end SNR optimization in a multi-layer repeater network under per-layer power constraints. It introduces POLARNet, a gradient-free, gradient-free, forward-backward layer-wise method that updates repeater gains within predefined activation sets to monotonically improve the end-to-end channel gain |h_tot|^2. It provides algorithmic details, convergence proofs, and multiple activation-set choices, along with complexity analysis and SNR bounds. Numerical experiments under Rician fading and IID channels demonstrate substantial SNR gains and show that distributing power across repeaters yields better performance than selecting a single repeater, highlighting the practical appeal of the approach for RA-MIMO-like scenarios.

Abstract

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.

Paper Structure

This paper contains 17 sections, 19 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal-to-noise ratio (SNR)
  4. Problem Formulation
  5. The proposed method -- POLARNet
  6. Algorithm
  7. Monotone convergence of the objective
  8. Activation sets
  9. The non-negative $2$-ball
  10. The non-negative $\infty$-ball
  11. Select at most K policy
  12. The non-negative $1$-ball or select one policy
  13. Forward-backward-traversing layers
  14. Computational complexity
  15. SNR bounds
  16. ...and 2 more sections

Figures (3)

  • Figure 1: System model of a multi-layer repeater network with a single base station (green), three repeater layers (purple) and a single user (red).
  • Figure 2: Convergence performance for the considered scenario and comparison to the optimal solution in Section \ref{['subsubsec:select1']}.
  • Figure 3: Convergence performance for the scenario in Section \ref{['sec:snr_bounds']} and comparison to the bounds on SNR in \ref{['eq:SNR_upper:2']}, \ref{['eq:SNR_upper:3']}.