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Backscatter Multiplicative Multiple-Access Systems: Fundamental Limits and Practical Design

Wanchun Liu, Ying-Chang Liang, Yonghui Li, Branka Vucetic

TL;DR

The achievable rate region of the BM-MAC is analyzed and it is proved that its region is strictly larger than that of the conventional time-division multiple-access scheme in many cases, including, e.g., the high SNR regime and the case when the direct channel is much stronger than the backscatter channel.

Abstract

In this paper, we consider a novel ambient backscatter multiple-access system, where a receiver (Rx) simultaneously detects the signals transmitted from an active transmitter (Tx) and a backscatter Tag. Specifically, the information-carrying signal sent by the Tx arrives at the Rx through two wireless channels: the direct channel from the Tx to the Rx, and the backscatter channel from the Tx to the Tag and then to the Rx. The received signal from the backscatter channel also carries the Tag's information because of the multiplicative backscatter operation at the Tag. This multiple-access system introduces a new channel model, referred to as multiplicative multiple-access channel (M-MAC). We analyze the achievable rate region of the M-MAC, and prove that its region is strictly larger than that of the conventional time-division multiple-access scheme in many cases, including, e.g., the high SNR regime and the case when the direct channel is much stronger than the backscatter channel. Hence, the multiplicative multiple-access scheme is an attractive technique to improve the throughput for ambient backscatter communication systems. Moreover, we analyze the detection error rates for coherent and noncoherent modulation schemes adopted by the Tx and the Tag, respectively, in both synchronous and asynchronous scenarios, which further bring interesting insights for practical system design.

Backscatter Multiplicative Multiple-Access Systems: Fundamental Limits and Practical Design

TL;DR

The achievable rate region of the BM-MAC is analyzed and it is proved that its region is strictly larger than that of the conventional time-division multiple-access scheme in many cases, including, e.g., the high SNR regime and the case when the direct channel is much stronger than the backscatter channel.

Abstract

In this paper, we consider a novel ambient backscatter multiple-access system, where a receiver (Rx) simultaneously detects the signals transmitted from an active transmitter (Tx) and a backscatter Tag. Specifically, the information-carrying signal sent by the Tx arrives at the Rx through two wireless channels: the direct channel from the Tx to the Rx, and the backscatter channel from the Tx to the Tag and then to the Rx. The received signal from the backscatter channel also carries the Tag's information because of the multiplicative backscatter operation at the Tag. This multiple-access system introduces a new channel model, referred to as multiplicative multiple-access channel (M-MAC). We analyze the achievable rate region of the M-MAC, and prove that its region is strictly larger than that of the conventional time-division multiple-access scheme in many cases, including, e.g., the high SNR regime and the case when the direct channel is much stronger than the backscatter channel. Hence, the multiplicative multiple-access scheme is an attractive technique to improve the throughput for ambient backscatter communication systems. Moreover, we analyze the detection error rates for coherent and noncoherent modulation schemes adopted by the Tx and the Tag, respectively, in both synchronous and asynchronous scenarios, which further bring interesting insights for practical system design.

Paper Structure

This paper contains 32 sections, 17 theorems, 78 equations, 14 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Achievable Rate Region of M-MAC
  4. Maximum Achievable Rate of $\bm X_1$
  5. Maximum Achievable Rate of $X_2$
  6. Maximum Achievable Sum Rate
  7. Time-Division Multiple Access vs. Multiplicative Multiple Access
  8. The Rate Region of the Conventional TDMA Backscatter Channel
  9. Strict Convexity of the Achievable Rate Region of the M-MAC
  10. The High SNR Scenario
  11. The Weak Backscatter Channel Scenario
  12. The BPSK Scenario
  13. Numerical Results
  14. Detection Design and Analysis of Multiplicative Multiple-Access Systems
  15. Joint Detection Method
  16. ...and 17 more sections

Key Result

Proposition 1

The maximum rate of $\bm X_1$, $R^{\max}_1$, is achieved when the Tag transmits a constant symbol which makes the received signal power largest at the Rx, and $R^{\max}_1$ is given by where $h_1$ and $h_0$ are defined in hnew.

Figures (14)

  • Figure 1: An ambient BackCom system.
  • Figure 2: Illustration of $\bm X_1$ and $X_2$ when $N=5$.
  • Figure 3: An illustration of the achievable rate region of the M-MAC. The red-solid-line region, $o-A_1-C-D$, is contained by the achievable rate region of the M-MAC. The black-solid-line region, $o-B_1-C-B_2$, is the region of interest for the analysis.
  • Figure 4: Achievable rate region with different $\vert g \vert^2$.
  • Figure 5: Achievable rate region with different $\theta$.
  • ...and 9 more figures

Theorems & Definitions (31)

  • Remark 1
  • Proposition 1
  • Proposition 2
  • proof
  • Lemma 1
  • Lemma 2
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • ...and 21 more