Channel Capacity and Lower Bound for Ambient
Backscatter Communication Systems
Wenjing Zhao
†
, Gongpu Wang
†
, Feifei Gao
‡
, Yulong Zou
, and Saman Atapattu
∗
†
School of Computer and Information Technology, Beijing Jiaotong University, Beijing, China
‡
Department of Automation, Tsinghua University, Beijing, China
Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, China
∗
Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, Australia
Email: 16120460@bjtu.edu.cn, gpwang@bjtu.edu.cn, feifeigao@ieee.org,
yulong.zou@gmail.com, saman.atapattu@unimelb.edu.au
Abstract—Ambient backscatter is an emerging technology that
utilizes the surrounding radio frequency (RF) signals such as
digital digital television (TV) broadcasting, cellular or Wireless-
Fidelity (Wi-Fi) to enable batteryless devices to communicate
with each other. One open problem for ambient backscatter
is channel capacity. In this paper, we investigate the capacity
problem of an ambient backscatter communication system with
a passive tag and a reader. Based on the Gaussian channel
model, we design a method to determine channel capacity for
the ambient backscatter communication system. The channel
capacity is the maximal value of the derived mutual information.
Interestingly, we find that the capacity for the ambient backscat-
ter communication system is obtained when the input signals
are not equiprobable. Finally, numerical results are provided to
corroborate our theoretical analysis.
Index Terms—Ambient backscatter, capacity, Gaussian vari-
able, lower bound, mutual information.
I. INTRODUCTION
Internet of things (IoT) has recently received extensive
attentions from industry and academia [1]. One important com-
ponent of IoT is the Radio Frequency Identification (RFID)
system which typically consists of a reader and a tag.
In a conventional RFID system, the reader first generates
and transmits a carrier signal to the tag, and then the tag
backscatters the signal to the reader. However, the traditional
reader transmits a carrier signal generated by an oscillator,
and it also requires a separate encoding/decoding circuitry.
Both the oscillator and the circuitry are usually powered by
a dedicated power supply. While these modules are essential
for successful communication, such in-built technology may
no longer be promising for small-scale devices. To overcome
such limitations, ambient backscatter prototypes are proposed
in [2]–[4].
Ambient backscatter technology utilizes environmental
wireless signals such as digital television (TV) broadcasting,
cellular or Wireless-Fidelity (Wi-Fi) to harvest energy and
transmit information, which gets rid of the battery and avoids
heavy manual maintenance. The basic principles of ambient
backscatter can be described as follows:
1) the tag indicates bit 1 or bit 0 by reflecting or non-
reflecting the received signals, respectively;
2) the reader can receive the backscattered signals and
decode as bits 1 and 0 with specific signal processing
technologies.
Using ambient backscatter technology, Wi-Fi Backscatter
is presented to connect RF-powered devices to the Internet.
Such system can achieve communication rates up to 1 Kbps
while covering distances up to 2.1 meters [3]. To strengthen
the communication rates and ranges of ambient backscatter
communication systems, a multi-antenna cancellation method
and a coding mechanism can be used which achieve commu-
nication rates up to 1 Mbps with distances up to 24 meters [4].
In addition, signal detection approaches such as a differential
detector, a maximum likelihood (ML) detector, a maximum
a posteriori (MAP) detector and a joint-energy detector are
proposed and their corresponding bit error rate (BER) perfor-
mance is analyzed for ambient backscatter systems [5]–[10].
Channel capacity is an important indicator of system perfor-
mance. Channel ergodic capacity for full-duplex communica-
tion with backscatter modulation is derived in [11]. In ambient
backscatter systems, the unique dual channel is with discrete
input and continuous output, which implies that existing
methods such as Shannon theory and the definition of mutual
information can not be directly used. Therefore, it is necessary
to seek a new method to solve the channel capacity problem
for ambient backscatter systems, which motivates our current
work.
In this work, we suppose that the channel state information
(CSI) is known. Actually, the CSI can be estimated through
some given methods, including least squares (LS) estima-
tor [12], best linear unbiased estimator (BLUE) and linear
minimum mean square error (LMMSE) estimator. Based on
Gaussian channel model for ambient backscatter communica-
tion systems, we consider the received signals as discrete se-
quences and evaluate the mutual information of these discrete
sequences. Subsequently, the channel capacity is obtained
by maximizing the mutual information with respect to the
distribution of input signals. Additionally, through a Markov
chain, a lower bound of the channel capacity is obtained.
978-1-5386-2062-5/17/$31.00 ©2017 IEEE