IEEE Signal Processing - May 2018 - 61

environment is demonstrated in Figure 2. When the bandwidth
is 20 MHz (as in LTE), only five multipaths can be resolved;
when it increases to 40 MHz (as in Wi-Fi) approximately ten
multipaths can be resolved. When it rises further, to 125 MHz,
around 30 multipaths with clear details of differences can be
resolved, which shows that the number of multipaths increases
as the bandwidth expands.
To utilize the multipaths as virtual antennas and/or sensors,
we find that a good starting point is to resort to the physics of
TR and its focusing effect. In TR, with two transceivers A and
B, transceiver B first sends a channel-probing signal (e.g., an

period Tsample will merge into a single tap (more details are
discussed in the section "Mapping-Free Indoor Tracking with
Decimeter Accuracy"). Thus, as noted in Figure 1(a), the resolution to separate radio paths with different lengths in a multipath propagation is limited to cTsample = c/B, with c being
the speed of light and B the bandwidth. Therefore, the larger
the bandwidth, the better the spatial resolution and thus the
more multipaths that can be resolved. An example of multipath
channel profiles captured under different bandwidths from
LTE, Wi-Fi, and the entire industrial, scientific, and medical
(ISM) 5-GHz band at the same location in a rich-scattering

y

y

c
B
G (ω )
S
k

Tx
Rx

x

LO

LOS

ω = (r, θ )

S
R

d

S

A

x

S
R0
Tx
Tx/Rx
Virtual Antennas
(Scatterers)

(a)

(b)

FIGURE 1. The concept of multipath propagation. (a) An illustration of a multipath as a virtual antenna. (b) A detailed illustration with each multipath repre-

0.8

0

50

100
150
Time (ns)
(a)

200

0.6

0.7

Normalized Amplitude

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Normalized Amplitude

Normalized Amplitude

sented by its total travel distance, direction of arrival, and power gain. Tx: transmitter; Rx: receiver.

0.6
0.5
0.4
0.3
0.2
0.1
0

0

50

100
150
Time (ns)
(b)

0.5
0.4
0.3
0.2
0.1
0

200

0

50

100 150
Time (ns)
(c)

200

250

FIGURE 2. An illustration of multipath channel versus bandwidth. (a) The measured channel under a 20-MHz bandwidth (LTE standard). (b) The measured
channel under a 40-MHz bandwidth (the IEEE 802.11n standard). (c) The measured channel under a 125-MHz bandwidth (the entire ISM 5-GHz band)
[50]. We first measure a sample channel impulse response (CIR) in a typical indoor environment using a TR prototype [35] with a bandwidth of 125 MHz
in the ISM 5-GHz band, and then different filters with bandwidths of 20 MHz, 40 MHz, and 125 MHz, respectively, are applied to the measured channel
profile. For a linear time-invariant system, the filtering operation on the receiver side is equivalent to that on the transmitter side. Therefore, the filtered
CIR is equivalent to that measured with the same bandwidth as the filter.

IEEE Signal Processing Magazine

|

May 2018

|

61



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

Contents
IEEE Signal Processing - May 2018 - Cover1
IEEE Signal Processing - May 2018 - Cover2
IEEE Signal Processing - May 2018 - Contents
IEEE Signal Processing - May 2018 - 2
IEEE Signal Processing - May 2018 - 3
IEEE Signal Processing - May 2018 - 4
IEEE Signal Processing - May 2018 - 5
IEEE Signal Processing - May 2018 - 6
IEEE Signal Processing - May 2018 - 7
IEEE Signal Processing - May 2018 - 8
IEEE Signal Processing - May 2018 - 9
IEEE Signal Processing - May 2018 - 10
IEEE Signal Processing - May 2018 - 11
IEEE Signal Processing - May 2018 - 12
IEEE Signal Processing - May 2018 - 13
IEEE Signal Processing - May 2018 - 14
IEEE Signal Processing - May 2018 - 15
IEEE Signal Processing - May 2018 - 16
IEEE Signal Processing - May 2018 - 17
IEEE Signal Processing - May 2018 - 18
IEEE Signal Processing - May 2018 - 19
IEEE Signal Processing - May 2018 - 20
IEEE Signal Processing - May 2018 - 21
IEEE Signal Processing - May 2018 - 22
IEEE Signal Processing - May 2018 - 23
IEEE Signal Processing - May 2018 - 24
IEEE Signal Processing - May 2018 - 25
IEEE Signal Processing - May 2018 - 26
IEEE Signal Processing - May 2018 - 27
IEEE Signal Processing - May 2018 - 28
IEEE Signal Processing - May 2018 - 29
IEEE Signal Processing - May 2018 - 30
IEEE Signal Processing - May 2018 - 31
IEEE Signal Processing - May 2018 - 32
IEEE Signal Processing - May 2018 - 33
IEEE Signal Processing - May 2018 - 34
IEEE Signal Processing - May 2018 - 35
IEEE Signal Processing - May 2018 - 36
IEEE Signal Processing - May 2018 - 37
IEEE Signal Processing - May 2018 - 38
IEEE Signal Processing - May 2018 - 39
IEEE Signal Processing - May 2018 - 40
IEEE Signal Processing - May 2018 - 41
IEEE Signal Processing - May 2018 - 42
IEEE Signal Processing - May 2018 - 43
IEEE Signal Processing - May 2018 - 44
IEEE Signal Processing - May 2018 - 45
IEEE Signal Processing - May 2018 - 46
IEEE Signal Processing - May 2018 - 47
IEEE Signal Processing - May 2018 - 48
IEEE Signal Processing - May 2018 - 49
IEEE Signal Processing - May 2018 - 50
IEEE Signal Processing - May 2018 - 51
IEEE Signal Processing - May 2018 - 52
IEEE Signal Processing - May 2018 - 53
IEEE Signal Processing - May 2018 - 54
IEEE Signal Processing - May 2018 - 55
IEEE Signal Processing - May 2018 - 56
IEEE Signal Processing - May 2018 - 57
IEEE Signal Processing - May 2018 - 58
IEEE Signal Processing - May 2018 - 59
IEEE Signal Processing - May 2018 - 60
IEEE Signal Processing - May 2018 - 61
IEEE Signal Processing - May 2018 - 62
IEEE Signal Processing - May 2018 - 63
IEEE Signal Processing - May 2018 - 64
IEEE Signal Processing - May 2018 - 65
IEEE Signal Processing - May 2018 - 66
IEEE Signal Processing - May 2018 - 67
IEEE Signal Processing - May 2018 - 68
IEEE Signal Processing - May 2018 - 69
IEEE Signal Processing - May 2018 - 70
IEEE Signal Processing - May 2018 - 71
IEEE Signal Processing - May 2018 - 72
IEEE Signal Processing - May 2018 - 73
IEEE Signal Processing - May 2018 - 74
IEEE Signal Processing - May 2018 - 75
IEEE Signal Processing - May 2018 - 76
IEEE Signal Processing - May 2018 - 77
IEEE Signal Processing - May 2018 - 78
IEEE Signal Processing - May 2018 - 79
IEEE Signal Processing - May 2018 - 80
IEEE Signal Processing - May 2018 - 81
IEEE Signal Processing - May 2018 - 82
IEEE Signal Processing - May 2018 - 83
IEEE Signal Processing - May 2018 - 84
IEEE Signal Processing - May 2018 - 85
IEEE Signal Processing - May 2018 - 86
IEEE Signal Processing - May 2018 - 87
IEEE Signal Processing - May 2018 - 88
IEEE Signal Processing - May 2018 - 89
IEEE Signal Processing - May 2018 - 90
IEEE Signal Processing - May 2018 - 91
IEEE Signal Processing - May 2018 - 92
IEEE Signal Processing - May 2018 - 93
IEEE Signal Processing - May 2018 - 94
IEEE Signal Processing - May 2018 - 95
IEEE Signal Processing - May 2018 - 96
IEEE Signal Processing - May 2018 - 97
IEEE Signal Processing - May 2018 - 98
IEEE Signal Processing - May 2018 - 99
IEEE Signal Processing - May 2018 - 100
IEEE Signal Processing - May 2018 - 101
IEEE Signal Processing - May 2018 - 102
IEEE Signal Processing - May 2018 - 103
IEEE Signal Processing - May 2018 - 104
IEEE Signal Processing - May 2018 - 105
IEEE Signal Processing - May 2018 - 106
IEEE Signal Processing - May 2018 - 107
IEEE Signal Processing - May 2018 - 108
IEEE Signal Processing - May 2018 - 109
IEEE Signal Processing - May 2018 - 110
IEEE Signal Processing - May 2018 - 111
IEEE Signal Processing - May 2018 - 112
IEEE Signal Processing - May 2018 - 113
IEEE Signal Processing - May 2018 - 114
IEEE Signal Processing - May 2018 - 115
IEEE Signal Processing - May 2018 - 116
IEEE Signal Processing - May 2018 - 117
IEEE Signal Processing - May 2018 - 118
IEEE Signal Processing - May 2018 - 119
IEEE Signal Processing - May 2018 - 120
IEEE Signal Processing - May 2018 - 121
IEEE Signal Processing - May 2018 - 122
IEEE Signal Processing - May 2018 - 123
IEEE Signal Processing - May 2018 - 124
IEEE Signal Processing - May 2018 - 125
IEEE Signal Processing - May 2018 - 126
IEEE Signal Processing - May 2018 - 127
IEEE Signal Processing - May 2018 - 128
IEEE Signal Processing - May 2018 - 129
IEEE Signal Processing - May 2018 - 130
IEEE Signal Processing - May 2018 - 131
IEEE Signal Processing - May 2018 - 132
IEEE Signal Processing - May 2018 - Cover3
IEEE Signal Processing - May 2018 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201809
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201807
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201805
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201803
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201801
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0917
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0717
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0517
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0317
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0916
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0716
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0516
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0316
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0915
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0715
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0515
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0315
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0914
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0714
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0514
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0314
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0913
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0713
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0513
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0313
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0912
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0712
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0512
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0312
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0911
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0711
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0511
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0311
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0910
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0710
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0510
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0310
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0909
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0709
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0509
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0309
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1108
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0908
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0708
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0508
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0308
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0108
https://www.nxtbookmedia.com