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Fairness and Sum-Rate Maximization via Joint Channel and Power Allocation in Uplink SCMA Networks

Joao V. C. Evangelista, Zeeshan Sattar, Georges Kaddoum, Anas Chaaban

TL;DR

This work employs a variant of the block successive upper-bound minimization (BSUM) framework, obtaining polynomial-time approximation algorithms to the original problem, and evaluates the algorithms’ robustness against outdated channel state information (CSI).

Abstract

In this work, we consider a sparse code multiple access uplink system, where $J$ users simultaneously transmit data over $K$ subcarriers, such that $J > K$, with a constraint on the power transmitted by each user. To jointly optimize the subcarrier assignment and the transmitted power per subcarrier, two new iterative algorithms are proposed, the first one aims to maximize the sum-rate (Max-SR) of the network, while the second aims to maximize the fairness (Max-Min). In both cases, the optimization problem is of the mixed-integer nonlinear programming (MINLP) type, with non-convex objective functions, which are generally not tractable. We prove that both joint allocation problems are NP-hard. To address these issues, we employ a variant of the block successive upper-bound minimization (BSUM) \cite{razaviyayn.2013} framework, obtaining polynomial-time approximation algorithms to the original problem. Moreover, we evaluate the algorithms' robustness against outdated channel state information (CSI), present an analysis of the convergence of the algorithms, and a comparison of the sum-rate and Jain's fairness index of the novel algorithms with three other algorithms proposed in the literature. The Max-SR algorithm outperforms the others in the sum-rate sense, while the Max-Min outperforms them in the fairness sense.

Fairness and Sum-Rate Maximization via Joint Channel and Power Allocation in Uplink SCMA Networks

TL;DR

This work employs a variant of the block successive upper-bound minimization (BSUM) framework, obtaining polynomial-time approximation algorithms to the original problem, and evaluates the algorithms’ robustness against outdated channel state information (CSI).

Abstract

In this work, we consider a sparse code multiple access uplink system, where users simultaneously transmit data over subcarriers, such that , with a constraint on the power transmitted by each user. To jointly optimize the subcarrier assignment and the transmitted power per subcarrier, two new iterative algorithms are proposed, the first one aims to maximize the sum-rate (Max-SR) of the network, while the second aims to maximize the fairness (Max-Min). In both cases, the optimization problem is of the mixed-integer nonlinear programming (MINLP) type, with non-convex objective functions, which are generally not tractable. We prove that both joint allocation problems are NP-hard. To address these issues, we employ a variant of the block successive upper-bound minimization (BSUM) \cite{razaviyayn.2013} framework, obtaining polynomial-time approximation algorithms to the original problem. Moreover, we evaluate the algorithms' robustness against outdated channel state information (CSI), present an analysis of the convergence of the algorithms, and a comparison of the sum-rate and Jain's fairness index of the novel algorithms with three other algorithms proposed in the literature. The Max-SR algorithm outperforms the others in the sum-rate sense, while the Max-Min outperforms them in the fairness sense.

Paper Structure

This paper contains 15 sections, 7 theorems, 41 equations, 9 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. Notation
  5. System Model
  6. SCMA Overview
  7. Joint Subcarrier and Power Allocation
  8. Solving $\mathbf{P_{\text{Max-SR}}}$
  9. Solving $\mathbf{P}_{\textbf{Max-Min}}$
  10. Numerical Results
  11. Performance with Outdated CSI
  12. Convergence Analysis and Algorithm Complexity
  13. Algorithm Complexity
  14. Conclusions
  15. Proof of Theorem \ref{['th:np_hard']}

Key Result

Theorem 1

Both the $\mathbf{P_{\text{Max-SR}}}$ and the $\mathbf{P_{\text{Max-Min}}}$ problems are NP-hard.

Figures (9)

  • Figure 1: Example of an SCMA uplink system with $J = 6$, $K = 4$, $N = 2$ and $d_f = 3$. The square arrays demonstrate the codebook of each user and each square represent the available resource elements (RE). An empty square indicates that no signal is transmitted in the RE and different filling patterns indicate a different complex value.
  • Figure 2: Example factor graph with $J = 6$, $K = 4$, $N = 2$ and $d_f = 3$. The circles denote user nodes and the squares denote resource nodes.
  • Figure 3: Sum-rate comparison for $J=6$, $K=4$, $d_f=3$ and $N=2$.
  • Figure 4: Jain's fairness index comparison for $J=6$, $K=4$, $d_f=3$ and $N=2$.
  • Figure 5: BER comparison for $J=6$, $K=4$, $d_f=3$ and $N=2$.
  • ...and 4 more figures

Theorems & Definitions (15)

  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 2
  • proof
  • Lemma 3
  • proof
  • ...and 5 more