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Simple Bounds for the Symmetric Capacity of the Rayleigh Fading Multiple Access Channel

Elad Domanovitz, Uri Erez

TL;DR

A practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario and a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel.

Abstract

Communication over the i.i.d. Rayleigh slow-fading MAC is considered, where all terminals are equipped with a single antenna. Further, a communication protocol is considered where all users transmit at (just below) the symmetric capacity (per user) of the channel, a rate which is fed back (dictated) to the users by the base station. Tight bounds are established on the distribution of the rate attained by the protocol. In particular, these bounds characterize the probability that the dominant face of the MAC capacity region contains a symmetric rate point, i.e., that the considered protocol strictly attains the sum capacity of the channel. The analysis provides a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel. Finally, a practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario.

Simple Bounds for the Symmetric Capacity of the Rayleigh Fading Multiple Access Channel

TL;DR

A practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario and a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel.

Abstract

Communication over the i.i.d. Rayleigh slow-fading MAC is considered, where all terminals are equipped with a single antenna. Further, a communication protocol is considered where all users transmit at (just below) the symmetric capacity (per user) of the channel, a rate which is fed back (dictated) to the users by the base station. Tight bounds are established on the distribution of the rate attained by the protocol. In particular, these bounds characterize the probability that the dominant face of the MAC capacity region contains a symmetric rate point, i.e., that the considered protocol strictly attains the sum capacity of the channel. The analysis provides a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel. Finally, a practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario.

Paper Structure

This paper contains 9 sections, 6 theorems, 45 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation and Preliminaries
  3. Lessons from the DMT
  4. I.I.D. Rayleigh-fading MAC with Single-Antenna Terminals
  5. Two-user i.i.d. single antenna Rayleigh-fading MAC
  6. Extension to the ${N}$-user i.i.d. scalar Rayleigh-fading MAC
  7. Upper Bound on the Outage Probability for the symmetric $N$-user Rayleigh-fading MIMO MAC
  8. Practical Realization of the Communication Protocol via Precoded Integer Forcing
  9. Conclusions

Key Result

Theorem 1

For a two-user i.i.d. Rayleigh-fading MAC with sum capacity $C$, for any rate $R\leq C$,

Figures (11)

  • Figure 1: DMT curve for a two-user scalar Rayleigh-fading MIMO-MAC where all terminals are equipped with a single antenna.
  • Figure 2: Different capacity regions corresponding to a two-user MAC with sum capacity $C=2$. For the channel depicted with a dashed-dotted line, the dominant face constitutes the bottleneck and $C_{\Sigma-\rm sym}=C$.
  • Figure 3: Probability density function of the symmetric capacity of a two-user i.i.d. Rayleigh-fading MAC given that the sum capacity is $C=2$.
  • Figure 4: Demonstration of the quantities appearing in the bounds appearing in Theorem \ref{['thm:thm2']} for the case of a $4$-user i.i.d. Rayleigh-fading MAC with sum capacity $C=8$.
  • Figure 5: Comparison of empirical evaluation of \ref{['eq:sym_capacity_MAC']} and Theorem 2 (upper and lower bounds for the outage probability) for a $4$-user i.i.d. Rayleigh-fading MAC ($N_t=N_r=1$) with sum capacity $C_{}=8$.
  • ...and 6 more figures

Theorems & Definitions (11)

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