# Optimal Distributed Channel Assignment in D2D Networks Using Learning in Noisy Potential Games

## TL;DR

This paper introduces a novel distributed learning algorithm for optimal channel assignment in noisy D2D networks, effectively handling estimation noise and ensuring convergence to optimal solutions.

## Contribution

It formulates CAP as a noisy potential game and proposes BLLA, the first distributed algorithm with proven convergence to optimal channel assignments under noise.

## Key findings

- BLLA converges to optimal solutions in noisy environments.
- Sum data rate increases with more channels and users.
- BLLA outperforms better response algorithms in noisy settings.

## Abstract

We present a novel solution for Channel Assignment Problem (CAP) in Device-to-Device (D2D) wireless networks that takes into account the throughput estimation noise. CAP is known to be NP-hard in the literature and there is no practical optimal learning algorithm that takes into account the estimation noise. In this paper, we first formulate the CAP as a stochastic optimization problem to maximize the expected sum data rate. To capture the estimation noise, CAP is modeled as a noisy potential game, a novel notion we introduce in this paper. Then, we propose a distributed Binary Log-linear Learning Algorithm (BLLA) that converges to the optimal channel assignments. Convergence of BLLA is proved for bounded and unbounded noise. Proofs for fixed and decreasing temperature parameter of BLLA are provided. A sufficient number of estimation samples is given that guarantees the convergence to the optimal state. We assess the performance of BLLA by extensive simulations, which show that the sum data rate increases with the number of channels and users. Contrary to the better response algorithm, the proposed algorithm achieves the optimal channel assignments distributively even in presence of estimation noise.