Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Power minimization and resource allocation in HetNets with uncertain channel-gains

Gabriel O. Ferreira, Chiara Ravazzi, Fabrizio Dabbene, Giuseppe C. Calafiore

Abstract

We propose an optimization problem to minimize the base stations transmission powers in OFDMA heterogeneous networks, while respecting users' individual throughput demands. The decision variables are the users' working bandwidths, their association, and the base stations transmission powers. To deal with wireless channel uncertainty, the channel gains are treated as random variables respecting a log-normal distribution, leading to a non-convex chance constrained mixed-integer optimization problem, which is then formulated as a mixed-integer Robust Geometric Program. The efficacy of the proposed method is shown in a real-world scenario of a large European city.

Power minimization and resource allocation in HetNets with uncertain channel-gains

Abstract

We propose an optimization problem to minimize the base stations transmission powers in OFDMA heterogeneous networks, while respecting users' individual throughput demands. The decision variables are the users' working bandwidths, their association, and the base stations transmission powers. To deal with wireless channel uncertainty, the channel gains are treated as random variables respecting a log-normal distribution, leading to a non-convex chance constrained mixed-integer optimization problem, which is then formulated as a mixed-integer Robust Geometric Program. The efficacy of the proposed method is shown in a real-world scenario of a large European city.

Paper Structure

This paper contains 17 sections, 2 theorems, 16 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Resource allocation
  4. Stochastic channel-gains
  5. Limitations of literature approaches and our contributions
  6. Problem Formulation
  7. The channel gains as random quantities
  8. Stochastic MIGP
  9. Robust MIGP
  10. Application use cases
  11. Channel gains expected values
  12. Optimization Scenario
  13. On the probability of the chance constrained optimization
  14. Comparison
  15. Robust MIGP and different channel gains distribution
  16. ...and 2 more sections

Key Result

Proposition 1

Let $\rho_{ij}$, $i\in[n]$, $j\in[N]$ be Gaussian random variables with zero mean and unitary standard deviation, as in eq:rho_ij. For each user, compute the quantities $[\underline{\rho}_{ij},\overline{\rho}_{ij}]$ such that Then a robust optimization problem considering the uncertainty box can be derived such that its optimal solution is feasible to the CC-MIGP.

Figures (3)

  • Figure 1: Channel gains (dB) for $\tilde{\sigma} = 3$ and (a) $\tilde{\mu}_{ij}$, (b) $\tilde{\mu}_{ij} - 2 \tilde{\sigma}$, and (c) $\tilde{\mu}_{ij} + 2 \tilde{\sigma}$.
  • Figure 2: The optimal value as a function of (a) $\tilde{\sigma}$ and (b) constraint probability.
  • Figure 3: Percentage of channel gains combination outside box of uncertainties $i\in[n]$ and violated constraints.

Theorems & Definitions (4)

  • Proposition 1: Box uncertainty
  • Theorem 1
  • proof
  • Remark 1