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Multilevel Topological Interference Management: A TIM-TIN Perspective

Chunhua Geng, Hua Sun, Syed A. Jafar

TL;DR

An analytical baseline approach is proposed, which decomposes a network into TIN and TIM components, and a distributed numerical algorithm called ZEST is developed, leading to the duality of the TIM-TIN problem in terms of generalized degrees-of-freedom (GDoF).

Abstract

The robust principles of treating interference as noise (TIN) when it is sufficiently weak, and avoiding it when it is not, form the background of this work. Combining TIN with the topological interference management (TIM) framework that identifies optimal interference avoidance schemes, we formulate a TIM-TIN problem for multilevel topological interference management, wherein only a coarse knowledge of channel strengths and no knowledge of channel phases is available to transmitters. To address the TIM-TIN problem, we first propose an analytical baseline approach, which decomposes a network into TIN and TIM components, allocates the signal power levels to each user in the TIN component, allocates signal vector space dimensions to each user in the TIM component, and guarantees that the product of the two is an achievable number of signal dimensions available to each user in the original network. Next, a distributed numerical algorithm called ZEST is developed. The convergence of the algorithm is demonstrated, leading to the duality of the TIM-TIN problem (in terms of GDoF). Numerical results are also provided to demonstrate the superior sum-rate performance and fast convergence of ZEST.

Multilevel Topological Interference Management: A TIM-TIN Perspective

TL;DR

An analytical baseline approach is proposed, which decomposes a network into TIN and TIM components, and a distributed numerical algorithm called ZEST is developed, leading to the duality of the TIM-TIN problem in terms of generalized degrees-of-freedom (GDoF).

Abstract

The robust principles of treating interference as noise (TIN) when it is sufficiently weak, and avoiding it when it is not, form the background of this work. Combining TIN with the topological interference management (TIM) framework that identifies optimal interference avoidance schemes, we formulate a TIM-TIN problem for multilevel topological interference management, wherein only a coarse knowledge of channel strengths and no knowledge of channel phases is available to transmitters. To address the TIM-TIN problem, we first propose an analytical baseline approach, which decomposes a network into TIN and TIM components, allocates the signal power levels to each user in the TIN component, allocates signal vector space dimensions to each user in the TIM component, and guarantees that the product of the two is an achievable number of signal dimensions available to each user in the original network. Next, a distributed numerical algorithm called ZEST is developed. The convergence of the algorithm is demonstrated, leading to the duality of the TIM-TIN problem (in terms of GDoF). Numerical results are also provided to demonstrate the superior sum-rate performance and fast convergence of ZEST.

Paper Structure

This paper contains 11 sections, 9 theorems, 21 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Robust principles of interference management: Ignore, avoid
  3. TIM-TIN: Joint view of signal vector spaces and signal power levels
  4. Overview of results
  5. System Model
  6. TIM-TIN Problem Formulation
  7. An Analytical Decomposition Approach
  8. A Distributed Numerical Approach
  9. Numerical Validations
  10. Discussions
  11. Conclusion

Key Result

Lemma 1

Suppose that $\mathbf{v}_i$, $i\in[m]$ are $n\times 1$ vectors, and $\kappa_1\geq\kappa_2\geq...\geq\kappa_m\geq0$. We have

Figures (9)

  • Figure 1: The received signal at Receiver 1, where the length of the vector represents the received power of the carried symbol. Here the number of channel uses $n$ is 2.
  • Figure 2: \ref{['5user']} A 5-user interference channel. The red solid lines and dashed blue lines represent strong and medium interfering links, respectively. The weak interfering links are omitted to avoid cluttering the graph. \ref{['5user_M1']} The TIN component with all medium interfering links. \ref{['5user_S1']} The TIM component with all strong interfering links. \ref{['sol2']} The achievable scheme to achieve the symmetric GDoF value 0.3 in the original network.
  • Figure 3: The symmetric multilevel neighboring interference channel with an infinite number of users. To avoid cluttering the figure, only the direct links for users with indexes $\{K-S-M-1,...,K+S+M+1\}$ and the interring links for Receiver $k$ are shown. The red solid lines and blue dashed lines represent strong and medium interfering links, respectively.
  • Figure 4: Applying ZEST to a 5-user interference channel, where the solid blue and dash black links represent direct and cross links, respectively. In this channel, all the direct and interfering links are with channel strength level $1$, and all the other links are with channel strength level $0$ and thus omitted to avoid cluttering the graph. \ref{['n1_ori']} The transmission scheme in the original channel in step 1), \ref{['n1_rec']} the transmission scheme in the reciprocal channel in step 3), \ref{['n2_ori']} the transmission scheme in the original channel in step 5).
  • Figure 5: Sum-rate performance of ZEST, Max-SINR, TDMA, SAPC, and the full power transmission, when \ref{['30_10_seeds_200sims_peak']}$x=0.5$, and \ref{['30_10_seeds_200sims_peak_set2']}$x=0.75$, where the latter models the settings with more diverse channel strengths between strong and weak interfering links.
  • ...and 4 more figures

Theorems & Definitions (15)

  • Lemma 1
  • Lemma 2
  • Example 1
  • Theorem 1
  • Example 2
  • Theorem 2
  • Remark 1
  • Example 3
  • Theorem 3
  • Remark 2
  • ...and 5 more