Signal Processing - November 2016 - 130

To clearly illustrate the impact of
bandwidth on localization performance,
we have conducted experiments to collect CSIs under different bandwidths in
a typical indoor environment. Two channel sounders are placed in an NLOS setting, where one of them is placed on a
customized experiment structure with
5-mm resolution.
To characterize the similarity between
CSIs collected at the same or different locations, the TRRS is calculated, given by
c [ H, H l ] = c

K Kl

m ,

(1)

with
h = max
z

/ H k H kl * e -jk

k=1

/ | H k | 2, Kl = / | H kl | 2 ,

(2)

where H and Hl represent two fingerprints, K is the total number of usable
subcarriers, H k and H kl are the CSIs on
subcarrier k, h is the modified crosscorrelation between H and Hl with
synchronization error compensated, and
K, Kl are the channel energies of H and
Hl , respectively. Realizing that the Wi-Fi
receiver may not be fully synchronous
with the Wi-Fi transmitter due to mismatches in their radio-frequency frontend components [9], an additional phase
rotation of e -jkz is employed to counteract the phase distortions incurred by the
synchronization errors in the calculation
of h, where z can be estimated and compensated using Algorithm 1 shown later
in the section "Calculating Time-Reversal
Resonating Strength by Diversity Exploitation." Equation (1) implies that TRRS
ranges from 0 to 1. More specifically, a
larger TRRS indicates a higher similarity
between two fingerprints and thus the two
associated locations.
The corresponding TRRS between
the target location and nearby locations are illustrated in Figure 2 under
different bandwidth settings. It is
shown in Figure 2(a) that with 40 MHz
bandwidth, a large region of nearby
locations is ambiguous with the target location in terms of the TRRS.
Enlarging the bandwidth shrinks
the area of ambiguous regions. As
130

demonstrated in Figure 2(c), when
the bandwidth increases to 360-MHz,
the ambiguous region is reduced to a ball
of 1 cm radius, which implies centimeter accuracy in localization.
The experiment results motivate us
to formulate a large effective bandwidth by exploiting diversities on Wi-Fi
devices to facilitate centimeter accuracy
indoor localization.

Increasing effective bandwidth
via diversity exploitation
Two different diversities exist in the
current Wi-Fi system, i.e., frequency
diversity and spatial diversity. According to IEEE 802.11n, 35 Wi-Fi channels
are dedicated to Wi-Fi transmission in
2.4- and 5-GHz-frequency bands with
a maximum bandwidth of 40 MHz.
The multitude of Wi-Fi channels leads
to frequency diversity in that they provide opportunities for Wi-Fi devices to
perform frequency hopping when experiencing deep fading or severe interference. On the other hand, spatial diversity
can be exploited on multiple-input, multiple-out (MIMO) Wi-Fi devices, which
is a mature technique that greatly boosts
the spectral efficiency. MIMO has not
only become an essential component of
IEEE 802.11n/ac but also been ubiquitously deployed on numerous commercial Wi-Fi devices. For Wi-Fi systems,
both types of diversity can be harvested
to provide fingerprints with much finer
granularity and thus lead to less ambiguity in comparison with the fingerprint
measured with a bandwidth of only
40 MHz.
Figure 3 shows the general principle
of creating a large effective bandwidth
by exploiting the frequency and spatial diversities either independently or
jointly. Since Wi-Fi devices can work
on multiple Wi-Fi channels, one can
exploit the frequency diversity by performing frequency hopping to obtain
CSIs on different Wi-Fi channels.
A s demon st r at e d i n Figure 3(a),
CSIs on four different Wi-Fi channels
are concatenated together to formulate a fingerprint of a large effective
bandwidth. Despite the fact that the
frequency diversity can be exploited
on a single-antenna Wi-Fi device, it is
IEEE Signal Processing Magazine

November 2016

time-consuming to perform frequency
hopping. For time efficiency, spatial
diversity can be exploited on multiantenna Wi-Fi devices. For a Wi-Fi
receiver with four antennas, e.g., in
Figure 3(b), CSIs on the four receiving
antennas can be combined together to
formulate the fingerprint with a large
effective bandwidth. Figure 3(c) shows
an example of utilizing both the frequency and spatial diversities, where
CSIs on two Wi-Fi channels and from
two receiving antennas are combined
into the fingerprint.
For a Wi-Fi system, the spatial diversity is determined by the number of
antenna links, while the frequency diversity is dependent on the number of
available Wi-Fi channels. Denote the
maximum spatial diversity by S, the
maximum frequency diversity by F, and
the bandwidth for each Wi-Fi channel by
W, the effective bandwidth is calculated
as S # F # W.

Achieving centimeter accuracy
via TRRS
As discussed in the section "Increasing Effective Bandwidth via Diversity
Exploitation," a fine-grained fingerprint
associated with a large effective bandwidth can be generated through diversity exploitation on Wi-Fi devices. In this
section, we first introduce the calculation of TRRS when both of the frequency and spatial diversities are available.
Then, we present the algorithm for
indoor localization.

Calculating TRRS by
diversity exploitation
As discussed in the sections "How Does
Bandwidth Affect the Localization
Performance?" and "Increasing Effective Bandwidth via Diversity Exploitation," to achieve centimeter localization
accuracy, a large effective bandwidth
beyond 40 MHz is required, which can
be obtained by diversity exploitation. For
Wi-Fi devices with a spatial diversity of
S and a frequency diversity of F, the
CSI measurements can be written as
f = 1, 2, f, F
H = {H s, f } s = 1, 2, f, S , where H s, f stands
for the CSI measured with the sth
antenna link on the f th Wi-Fi channel, denoted as the virtual link (s, f).

Table of Contents for the Digital Edition of Signal Processing - November 2016