IEEE Signal Processing - May 2018 - 64

Space

Frequency
f2
S1

Space
Frequency

Frequency

S3
S2

t1
t2

(1, 1)

t1
t2

t3
t4

f2
f1

(1, 2)

Time

(1, 3)

(1, 4)

Time
(1, 1)

(2, 1)

(a)

(3, 1)

(4, 1)

Time
(1, 1)

(b)

(2, 1)

(1, 2)

(2, 2)

(c)

FIGURE 4. An illustration of leveraging frequency and spatial diversities in Wi-Fi to achieve large effective bandwidth: (a) frequency diversity, (b) spatial
diversity, and (c) frequency-spatial diversity.

C is a threshold to strike a balance of the true-positive rate and
r F, ,, H
r F, test) 1 C,
false-positive rate in positioning. When TR (H
the IPS cannot formulate a credible location estimation and thus
returns zero to imply an unrecognized location.

Experimental results
To evaluate the positioning performance in practice, we
deployed two Wi-Fi devices, each equipped with three omnidirectional antennas, in an indoor office environment consisting of a large number of objects-such as chairs, desks,
shelves, and sofas-as well as ceilings and walls. We measured CSI values from 50 locations of interest, with 20 CSI
values for each.
We evenly divided the 20 measured CSI values at each
location into a training set and a testing set. We calculated
the TRRS matrix using the CSIs collected at the 50 candidate
locations. Each element of the matrix represents the TRRS
between the CSI values at the training and testing locations.
Therefore, the block diagonal components of the TRRS matrix
indicate the similarity among CSI values obtained at the same
locations, while the block off-diagonal components indicate
the similarity among CSI values of different locations.
Figure 5 illustrates the TRRS matrices under the effective bandwidths of 10, 40, 120, and 360 MHz. First, we see
from Figure 5 that the block diagonal components of the
matrices are close to 1, meaning high similarities among
CSI values of the same locations, while the off-diagonal
64

components decrease with an increasing effective bandwidth. When the effective bandwidth is small, e.g., 10 MHz,
some off-diagonal components are even greater than the
diagonal ones, which leads to positioning errors. The gap
between the diagonal and off-diagonal components increases
as the effective bandwidth increases, resulting in improved
positioning performance.
There are environmental dynamics in indoor spaces due to
the movement of people and objects, and these dynamics could
severely degrade the positioning performance, since they introduce random perturbations in the CSI fingerprints. However,
since the proposed positioning technique exploits a large effective bandwidth from multiple antennas and/or multiple Wi-Fi
channels and utilizes the entire multipath CSI signature with a
high degree of freedom as a unique feature for positioning, it is
robust against environmental dynamics, which can affect only
a portion of the multipath propagation.
Figure 6(a) shows the receiver operating characteristic
(ROC) curve with human activities, where a person walked
continuously around one Wi-Fi device used for channel sounding. For a fixed false-positive rate of 0.15%, the
true-positive rate increased from 94.17% at a 40-MHz
effective bandwidth up to 99.11% at a 120-MHz effective
bandwidth. When the effective bandwidth reached 240 MHz
and then 360 MHz, the true-positive rate further increased
to 99.61% and 99.89%, respectively. Figure 6(b) shows the ROC
curve with large object movement, where a person operated

IEEE Signal Processing Magazine

May 2018

Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018