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The Pennsylvania State University
The Graduate School
College of Engineering
MODIFIED TRANSMITTED REFERENCE TECHNIQUE
FOR WIRELESS BEACONING
A Thesis in
Electrical Engineering
by
Jason Randall Young
© 2017 Jason Randall Young
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science
December 2017
ii
The thesis of Jason Randall Young was reviewed and approved* by the following:
Ram M. Narayanan
Professor of Electrical Engineering
Thesis Adviser
David M. Jenkins
Research Associate
Kultegin Aydin
Professor of Electrical Engineering
Head of the Department of Electrical Engineering
*Signatures are on file in the Graduate School.
iii
ABSTRACT
Transmitted reference defines a signal processing technique that has interested researchers and
found applicability in a number of engineering areas. In this approach, the information required to
decipher the received signal is transmitted in addition to the message signal. With its unique signaling
scheme, transmitted reference allows communications systems to employ simple receiver architectures
and utilize arbitrary waveforms to convey information. Thus, transmitted reference enables
communications while maintaining low transmit power and operating in challenging environments.
Despite its fundamental advantages, transmitted reference may suffer prohibitive performance
degradation in communications channels that support considerable multipath propagation. Transmitted
reference communications systems may face difficulty in distinguishing between the characteristic
transmitted reference signals and multipath energy occurring naturally in the ambient environment.
One application in which transmitted reference processing may add value is wireless
beaconing, which has evolved from its discovery in the 1880s into a suite of technologies that define
commercial and military systems employed for a plethora of purposes. Wireless beaconing provides
positioning information in scenarios as varied as search and rescue, identification and mitigation of
radio frequency emitters, radar, sonar, and air traffic control. Additionally, wireless beaconing has been
proposed for fifth-generation (5G) cellular base station discovery and ad-hoc networking.
This thesis documents research into a novel signal processing technique that, when integrated
into a wireless beaconing system, enables robust performance in adverse communications channels and
simultaneously affords low transmit power signal characteristics. Extending the state of the art in
transmitted reference radar, this thesis develops a theoretical framework for a modified transmitted
reference signaling scheme that facilitates node detection and beaconing via innovative signal
processing. This thesis also implements MATLAB® software simulations and hardware experiments
that confirm the utility of the technique when integrated into a functional beaconing system.
iv
The modified transmitted reference signal processing technique enables the same features as
conventional transmitted reference signaling, and uses time scale supplements to enhance performance
relative to traditional transmitted reference. The modified transmitted reference algorithm creates two
copies of the same signal, the reference signal and the modulated offset copy. Like standard transmitted
reference, the modified technique encodes information by time delaying the offset copy relative to the
reference signal. The modified transmitted reference technique supplements the encoding process by
applying a time scale – dilation or compression – to the offset copy. The modified transmitted reference
signaling scheme benefits from time scale, as it differentiates the transmitter-encoded offset copy from
naturally-occurring multipath energy that arises in a practical signaling environment. The modified
transmitted reference technique utilizes time scale to achieve reliable transfer of information in
communications channels that present significant challenges for traditional transmitted reference.
Modified transmitted reference wireless beaconing employs spatially distributed, coordinated
signal transceivers that broadcast and collect wide-bandwidth data. Each transceiver coordinates with
all other nodes to broadcast a cooperative waveform that defines a modified transmitted reference
beaconing transmission. At signal reception, modified transmitted reference receivers processes the
signals reflected from objects in the environment using the approach presented herein. Modified
transmitted reference beaconing systems enable discovery and localization of objects of interest, and
may find utility in a broad range of applications.
v
TABLE OF CONTENTS
List of Figures ....................................................................................................................................... vi
List of Tables ....................................................................................................................................... viii
List of Acronyms ................................................................................................................................... ix
Acknowledgements ................................................................................................................................ x
1. Introduction ................................................................................................................................ 1
2. Background ................................................................................................................................ 3
A. Transmitted Reference ................................................................................................................ 3
B. Beaconing ................................................................................................................................. 10
3. Modified Transmitted Reference Technique ............................................................................ 18
A. Modified Transmitted Reference Overview ............................................................................. 19
B. Modified Transmitted Reference Parameterization .................................................................. 22
C. Performance Characteristics of MTR Parameterization ........................................................... 24
4. Modified Transmitted Reference Technique for Beaconing .................................................... 28
A. Angular Resolution and Beaconing System Baseline .............................................................. 33
5. MTR Beaconing Simulation ..................................................................................................... 36
A. Analytic Results ....................................................................................................................... 37
B. Incorporation of Experimental Data ......................................................................................... 48
6. MTR Beaconing Experimentation ............................................................................................ 54
7. Conclusion ................................................................................................................................ 64
MATLAB® Source Code ...................................................................................................................... 66
References ............................................................................................................................................ 71
vi
LIST OF FIGURES
Fig. 2-1. Transmitted reference transmitter and receiver block diagrams. ............................................ 4
Fig. 2-2. Example transmitted reference receiver correlation surface. .................................................. 7
Fig. 2-3. Errant correlation peaks in transmitted reference reception due to multipath. ....................... 9
Fig. 2-4. Illustration of marker beacons for aircraft instrument landing systems. ............................... 10
Fig. 2-5. Typical four-element circular antenna array for direction finding........................................ 14
Fig. 2-6. Receiver position ambiguity with two-sensor two-dimensional beaconing system. ............ 16
Fig. 2-7. Receiver position resolved with three-sensor two-dimensional beaconing system. ............. 17
Fig. 3-1. Modified transmitted reference block diagrams. .................................................................. 18
Fig. 3-2. Example modified transmitted reference receiver correlation surface (𝑠 = 1.001). .............. 21
Fig. 3-3. Impulse response of a reverberant underwater acoustic communication channel. ............... 26
Fig. 3-4. MTR correlation surface with propagation through reverberant channel (𝑠 = 1.01). ........... 27
Fig. 3-5. MTR correlation surface with propagation through reverberant channel (𝑠 = 1.0001). ....... 27
Fig. 4-1. Time difference of arrival geometric approximations. ......................................................... 28
Fig. 4-2. Comparison of time delay values at MTR beaconing transmitters and receiver. ................. 31
Fig. 4-3. Illustration of MTR beaconing receiver mapping delay to angular information. ................. 32
Fig. 4-4. Modified transmitted reference beaconing receiver block diagram. ..................................... 33
Fig. 4-5. MTR beaconing system angular bin centers with 𝐿 = 25 m and 𝐵 = 100 MHz. .................. 35
Fig. 4-6. MTR beaconing system angular bin centers with 𝐿 = 25 m and 𝐵 = 25 MHz. .................... 35
Fig. 5-1. Simulation results for Wi-Fi parameterization and 10 m aperture. ....................................... 39
Fig. 5-2. Simulation results for Wi-Fi parameterization and 50 m aperture. ....................................... 40
Fig. 5-3. Simulation results for Wi-Fi parameterization and 100 m aperture. ..................................... 41
Fig. 5-4. Simulation results for 915 MHz ISM parameterization and 100 m aperture. ....................... 42
Fig. 5-5. Simulation results for acoustic parameterization and 10 m aperture. ................................... 44
Fig. 5-6. Simulation results for acoustic parameterization and 5 m aperture. ..................................... 45
vii
Fig. 5-7. Simulation results for acoustic parameterization and 5 m aperture (direct path only). ........ 46
Fig. 5-8. Simulation results for acoustic parameterization and 5 m aperture (close multipaths). ....... 46
Fig. 5-9. Simulation results for acoustic parameterization and 5 m aperture (spread multipaths). ..... 47
Fig. 5-10. Acoustic data channel impulse response. ............................................................................ 48
Fig. 5-11. MTR correlation surface following signal interaction with WOSS channel. ..................... 50
Fig. 5-12. Simulation results using WOSS environment data with coarse MTR time scales. ............. 51
Fig. 5-13. Simulation results using WOSS environment data with fine MTR time scales. ................ 52
Fig. 6-1. Modified transmitted reference acoustic hardware testbed. .................................................. 55
Fig. 6-2. MTR audio hardware experiment results graphic vs simplified geometry model. ............... 58
Fig. 6-3. Alternate MTR audio hardware testbed configuration. ........................................................ 59
Fig. 6-4. MTR audio hardware angle estimation vs. authentic angle. ................................................. 60
Fig. 6-5. MTR audio hardware angle estimation error vs. authentic angle. ........................................ 60
Fig. 6-6. Wide-baseline MTR audio hardware angle estimation error vs. authentic angle. ................ 62
Fig. 6-7. Wide-baseline MTR audio hardware angle estimation error vs. authentic angle. ................ 63
viii
LIST OF TABLES
Table 3-1. Modified transmitted reference parameters. ...................................................................... 22
Table 5-1. Simulation parameters employed during MTR beaconing software simulations. ............. 38
Table 5-2. Simulation parameters common to all MTR software simulations. ................................... 38
Table 5-3. Simulation parameters employed during WOSS software simulation #1. ......................... 49
Table 6-1. MTR hardware testbed trial parameters. ............................................................................ 55
Table 6-2. MTR audio hardware experiment results summary. .......................................................... 57
ix
LIST OF ACRONYMS
AWGN Additive White Gaussian Noise
DF Direction Finding
FCC Federal Communications Commission
FDOA Frequency Difference of Arrival
HF/DF High Frequency/Direction Finding
ISM Industrial, Scientific and Medical
MTR Modified Transmitted Reference
RF Radio Frequency
SNR Signal-to-Noise Ratio
SWaP Size, Weight, and Power
TDOA Time Difference of Arrival
TR Transmitted Reference
UWB Ultra-Wideband
WOSS World Ocean Simulation System
x
ACKNOWLEDGEMENTS
The author foremost thanks his family for their invaluable contributions to the development of
the research found in this thesis, and to the development of the author himself.
The author acknowledges Dr. Ram Narayanan and Dr. David Jenkins for their erudite advice
and supportive guidance during the development of this thesis.
The author additionally thanks the Applied Research Laboratory at the Pennsylvania State
University for supporting the formulation of this research and document with funding and technical
knowledge.
1
1. INTRODUCTION
For several decades, researchers have studied the transmitted reference (TR) signal processing
technique for an array of applications, primarily focusing on wireless communications [1]. Transmitted
reference enables transfer of necessary information from the transmitter to the receiver, thereby
avoiding the complex receive signal processing required by many communications and radar systems.
Transmitted reference embeds timing, information, and channel equalization into the transmitted signal,
and thus the TR receiver must perform only rudimentary operations, such as integration and
thresholding, to decode the transmitted information. With the development of ultra-wideband (UWB)
signaling, transmitted reference initially served as the physical layer protocol for node discovery,
synchronization and data transfer [2]. Ultra-wideband transmitted reference systems broadcast a
sequence of pulses in time, with reference pulses at periodic intervals, and modulated pulses occupying
time bins corresponding to encoded data between the reference bursts [3]. Due to its ability to perform
self-equalization across a wide bandwidth without processing-intensive traditional techniques (such as
a rake receiver or training data), transmitted reference proved beneficial in wideband applications [4].
Despite its valuable features, transmitted reference was ultimately surpassed in UWB
applications due to its inherent disadvantages [5]. Principally, transmitted reference suffers from the
utilization of pulsed signals, which demands stringent constraints on TR system hardware, particularly
transmit amplifiers [6]. Additionally, pulsed transmitted reference systems broadcast for short
durations, limiting their ability to withstand high noise or interference in low transmit power
applications, and increasing the potential for co-channel interference. Finally, transmitted reference
systems suffer from severe performance degradation in multipath communication channels [4]. In such
environments, the TR receiver may be unable to differentiate between the transmitted TR signal and
multipath signals arising from alternate paths. As such, the TR receiver copes with prohibitive error
and/or false alarm rates, and the utility of transmitted reference technique declines. This thesis provides
a more comprehensive treatment of transmitted reference signaling in Chapter 2.
2
In parallel to the development of transmitted reference, research has focused on wireless
beaconing via a variety of methods. Wireless beaconing is the process of communicating and sharing
awareness of nodes in a communications or sensor network. Beaconing enables the discovery of new
nodes entering a network, and the determination of their location. Wireless beaconing employs multiple
spatially separated timing- and phase-locked receivers. The receivers perform correlation-based signal
processing to determine the near-simultaneous presence of a signal at multiple receivers, and compute
differences (in time, frequency, and/or other dimensions) in the signals received by disparate sensors
[7]. The differences provide information regarding the direction between the beaconing system and the
receiver of interest. Chapter 2 of this thesis reviews the principles of beaconing.
While transmitted reference signaling is infrequently referenced in the context of beaconing,
the TR technique finds applicability in some radar systems. Transmitted reference radars have been
proposed for use as automotive radars [8]. Ultra-wideband transmitted reference enables precise
ranging with minimal receive processing, and thus appeals to automotive radar designers with rigorous
size, weight and power (SWaP) constraints. However, transmitted reference cannot maintain optimal
functionality in cluttered environments, and vehicular settings often present a multitude of multipaths
that hamper TR performance. UWB transmitted reference systems remain the subject of research for
automotive applications, but have largely been abandoned in favor of alternative techniques [8].
This thesis presents a modified transmitted reference signal processing technology that enables
reliable and robust beaconing in communications channels with significant multipath. First, the thesis
reviews the development and deployment of the transmitted reference signal processing technique for
communications and sensing, including beaconing. The thesis then introduces the modified transmitted
reference technique, and outlines the inherent utility of the method. The thesis next summarizes the
basic principles of beaconing, with an emphasis on time-difference of arrival. Finally, the thesis
explores the performance of the modified transmitted reference technology for beaconing. The thesis
details the results of theoretical analysis, software simulation, and hardware experimentation.
3
2. BACKGROUND
A. Transmitted Reference
Transmitted reference (TR) signal processing has existed for several decades, but its practical
utility has been limited by its inherent disadvantages, particularly in multipath communication channels
[6]. Nonetheless, transmitted reference maintains several advantages relative to traditional algorithms.
By broadcasting the reference signal and the time-delay modulated copy close together in time,
transmitted reference achieves a simple correlation-based receiver architecture with minimal, and in
many cases no, equalization. Transmitted reference thereby reduces or eliminates processing-intensive
time- or frequency-domain equalization required by conventional modulation techniques, such as rake
receivers employed in direct-sequence spread spectrum [4]. Additionally, as transmitted reference
encodes information via relative offsets rather than absolute modulations, the signaling scheme can
theoretically employ arbitrary waveforms to transmit information while avoiding potentially
exploitable cyclic and tonal signals. Furthermore, the transmitted reference receiver does not require
much information regarding the transmitted waveform. Therefore, transmitted reference signaling
affords potential advantages in low transmit power communications and radar applications.
Fig. 2-1 depicts the block diagrams for the transmitter and receiver of a transmitted reference
communications system. The transmitted reference signal encompasses a reference signal, 𝑏(𝑡), and a
modulated version of the reference waveform. In transmitted reference processing, modulation occurs
by adding a time delayed replica of the reference waveform to the original signal [9]. Hence, the TR
broadcast assumes the form:
𝑡𝑇𝑅(𝑡) = 𝑏(𝑡) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎) (1)
After the TR transmitter generates and broadcasts the signal, it undergoes distortion while
propagating through a communications channel, and experiences additive noise, often assumed to be
additive white Gaussian noise (AWGN). Additionally, the transmitted signal may propagate with a
direct line-of-sight to the receiver, or it may reflect from various objects between the transmitter and
4
receiver, with indirect energy scattered between the two endpoints. The received signal often includes
some energy from line-of-sight propagation, and additional contributions from indirect paths. Signal
energy deriving from multiple disparate indirect paths constitutes “multipath” propagation, in which
multiple time-delayed and potentially phase- and frequency-shifted copies of the transmitted signal
arrive nearly simultaneously at the receiver. Without proper mitigation, multipath propagation can
significantly impact receiver performance relative to accurate data demodulation [4].
Fig. 2-1. Transmitted reference transmitter and receiver block diagrams.
The transmitted reference receiver need not have any foreknowledge regarding the transmitted
waveform, and thus, TR processing may leverage arbitrary reference waveforms [9]. Due to practical
constraints, including ease of signal generation and transmission, signal duty cycle and required peak
power, transmitted reference systems most frequently employ short time-domain pulses (“impulses”)
[10]. Nonetheless, transmitted reference systems have employed reference signals as diverse as
5
pseudorandom noise (PN) and linear frequency modulated (LFM) waveforms. Regardless of the
transmitted waveform, the receiver simply correlates the received signal with a time offset copy of itself
to generate a correlation surface [9]. Assuming a channel that imparts no signal distortion and no noise,
the transmitted reference receiver generates a correlation surface, 𝛸(𝜏), with the following structure:
𝛸(𝜏) = ∫ 𝑡𝑇𝑅(𝑡)𝑡𝑇𝑅∗(𝑡 − 𝜏)𝑑𝑡
𝑡0+𝑇
𝑡0
(2)
For the transmitted reference signal defined in Equation (1), the TR correlation surface results
from the correlation between the received signal and a time-shifted, complex-conjugated version:
𝛸(𝜏) = ∫ [𝑏(𝑡) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎)][𝑏(𝑡 − 𝜏) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝜏)]∗𝑑𝑡𝑇
0
(3)
Expanding and rearranging the terms using the linearity of the correlation integral, the
transmitted reference correlation surface becomes:
𝛸(𝜏) = ∫ 𝑏(𝑡)𝑏∗(𝑡 − 𝜏)𝑑𝑡𝑡0+𝑇
𝑡0
+ ∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝜏)𝑑𝑡𝑡0+𝑇
𝑡0
+ ∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎)𝑏∗(𝑡 − 𝜏)𝑑𝑡𝑡0+𝑇
𝑡0
+ ∫ 𝑏(𝑡)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝜏)𝑑𝑡𝑡0+𝑇
𝑡0
(4)
The transmitted reference correlation receiver generates four distinct terms:
1. The autocorrelation of the reference signal 𝑏(𝑡)
− This term generates a maximum correlation peak when 𝜏 = 0
2. The autocorrelation of the time-delayed signal 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎)
− This term generates a maximum correlation peak when 𝜏 = 0
3. The correlation between the reference signal and the time-delayed reference signal
− This term generates a maximum correlation peak when 𝜏 = 𝜏𝑑𝑎𝑡𝑎
4. The correlation between the time-delayed reference signal and the reference signal
− This term generates a maximum correlation peak when 𝜏 = −𝜏𝑑𝑎𝑡𝑎
6
The transmitted reference correlation surface consists of four peaks, two of which overlap at
zero lag. The remaining peaks appear at lags symmetric about zero – specifically, at ±𝜏𝑑𝑎𝑡𝑎. The
autocorrelation of 𝑏(𝑡) and the autocorrelation of 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎) each contribute substantial correlation
energy at lag 𝜏 = 0 and minimal energy at nonzero lags (𝜏 ≠ 0). These autocorrelation terms invariably
produce the most prominent peak of the magnitude of the correlation surface, and this autocorrelation
peak arises at zero lag (𝜏 = 0). Transmitted reference systems must not modulate time delay values too
near zero to avoid confusing the transmitter-encoded data delay with the autocorrelation artifact.
Fig. 2-2 depicts a segment of the normalized correlation surface produced by a transmitted
reference correlation receiver. In the figure, the receiver decodes an analytic (no signal distortion or
noise) transmitted reference signal whose modulated copy features a 200-sample time delay (𝜏𝑑𝑎𝑡𝑎 =
200) relative to the reference signal. As expected, the correlation surface includes a peak at zero lag,
and two symmetric peaks at ±𝜏𝑑𝑎𝑡𝑎 whose linear amplitudes are half that of the zero-lag peak.
The TR receiver searches the subset of the correlation lags in which the transmitter encodes
data-bearing time delays [4]. The receiver thresholds the correlation surface to determine the presence
or absence of data (in the case of a TR communications system) or a receiver (in the case of a TR radar
system). Additionally, the receiver decodes data by extracting the time delay, 𝜏𝑑𝑎𝑡𝑎, between the
reference signal and the modulated copy.
The transmitted reference technique provides diverse benefits, including a simple signaling
architecture for both transmitter and receiver, the ability to employ arbitrary waveforms to convey
information, and robustness to a variety of signal distortions imparted by communications channels.
Despite these benefits, transmitted reference modulation suffers from drawbacks inherent to the
technique. For instance, transmitted reference broadcasts its reference signal, in the form of 𝑏(𝑡), rather
than using a reference generated locally at the receiver, as do traditional signaling schemes. The TR
technique thus reduces the received signal-to-noise ratio for a given noise level by expending a portion
(typically half) of the fixed transmit power broadcasting two signals as opposed to one. The TR receiver
7
must cope with this noisy template that generates self-interference. Therefore, transmitted reference
systems typically require greater receive signal-to-noise ratios than traditional modulation techniques
to achieve equivalent communications error rate or radar detection performance [11].
Fig. 2-2. Example transmitted reference receiver correlation surface.
i. Transmitted Reference Performance in Multipath Channels
Transmitted reference signal processing also suffers from a precipitous decline in functionality
due to multipath propagation [4], whether the multipaths comprise TR signal energy, or simply ambient
energy present in the communications channel [5]. To exemplify the impact of multipath propagation
on TR performance, an example is conceived in which a signal – potentially a deliberate broadcast from
a TR transmitter, or possibly a spurious emission of ambient environmental noise in the TR frequency
band – arrives at a receiver following propagation through a two-path channel, one direct path and one
significant multipath. In this example, the TR transmitter encodes a time delay 𝜏𝑑𝑎𝑡𝑎, and the multipath
components arrive at the receiver separated by M samples in time. Hence, the received signal is:
𝑟(𝑡) = 𝑡𝑇𝑅(𝑡) + 𝑡𝑇𝑅(𝑡 − 𝑀) = 𝑏(𝑡) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎) + 𝑏(𝑡 − 𝑀) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀) (5)
8
The transmitted reference receiver then performs correlation processing on the received signal:
𝛸(𝜏) = ∫[𝑏(𝑡) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎) + 𝑏(𝑡 − 𝑀) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀)]
[𝑏(𝑡 − 𝜏) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝜏) + 𝑏(𝑡 − 𝑀 − 𝜏) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀 − 𝜏)]∗𝑑𝑡
𝑡0+𝑇
𝑡0
(6)
Reorganizing terms, the received correlation surface includes 16 terms that generate correlation
peaks at seven unique correlation lags. In Equation (7), the terms are color-coded to correspond to the
lag at which the term contributes its maximum peak.
𝛸(𝜏) = ∫ 𝑏(𝑡)𝑏∗(𝑡 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎)𝑏∗(𝑡 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡)𝑏∗(𝑡 − 𝑀 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝑀)𝑏∗(𝑡 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎)𝑏∗(𝑡 − 𝑀 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝑀)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀)𝑏∗(𝑡 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝑀)𝑏∗(𝑡 − 𝑀 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝑀)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀)𝑏∗(𝑡 − 𝑀 − 𝜏)𝑑𝑡 +𝑡0+𝑇
𝑡0
∫ 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀)𝑏∗(𝑡 − 𝜏𝑑𝑎𝑡𝑎 − 𝑀 − 𝜏)𝑑𝑡𝑡0+𝑇
𝑡0
(7)
To visualize the example, Fig. 2-3 depicts the T receiver correlation surface for demodulation
of the TR signal received at high signal-to-noise ratio following propagation through the
aforementioned two-path channel. The correlation surface in the figure features color coding to match
the lag coding in Equation (7).
Consistent with the result displayed in Fig. 2-2, the direct path generates the desired correlation
peak that corresponds to the transmitter-encoded time delay between the reference and modulated
signals (coded with purple coloration). The direct path also produces two correlation peaks at zero lag
(green) and one peak at the negative of the encoded time delay (orange). The multipath also generates
9
the transmitter-encoded peak due to the correlation between its reference and offset signals.
Additionally, the reference signal of the direct path reception correlates to the reference and modulated
signals of the multipath, generating unwanted correlation peaks. Correlations between direct-path and
multipath reference and offset signals generate more correlation peaks, resulting in twelve peaks at
seven unique correlation lags. The multipath-induced peaks may cause false positives, in which the
receiver selects the wrong correlation peak as the proper time delay (the wrong peak could become the
maximum in a noisy channel). The errant peaks may also result in a false rejection, in which the receiver
views the errant peaks as interference and rejects the true peak as insufficiently above the noise.
Fig. 2-3. Errant correlation peaks in transmitted reference reception due to multipath.
As illustrated by the preceding example and reviewed in [5], transmitted reference suffers potential
performance-inhibiting ambiguities due to multipath channels. The TR technique may generate errant
detections due to multipaths of a signal broadcast by a TR transmitter. Of even greater concern, the
transmitted reference receiver may confuse multipaths of ambient signals, such as environmental noise,
for TR broadcasts, and generate correlation peaks despite the absence of TR transmissions.
10
B. Beaconing
Beaconing aims to detect the presence of an object, and determine the bearing and/or position
of the object relative to the beaconing system. Using one of a number of potential transmitter and
receiver configurations, a beaconing system enables a receiver to generate position information [12].
Amongst a plethora of current and future applications, beaconing frequently supports air traffic control
and positioning of commercial aircraft during runway approach and landing. Beaconing systems for
aircraft landing, denoted as Instrument Landing Systems and Distance Measuring Equipment, emplace
radio frequency marker beacons near the runway and position transceivers on the aircraft body [13].
The aircraft interrogates the ground transponders with a sequence of pulses, and awaits a reply from
the beacons. The aircraft interprets the time delay between its transmissions and the beacon responses
to determine its position and angle relative to the runway [14]. This aircraft navigation beaconing
system mandates stringent time synchronization requirements, but provides accurate measurements for
aircraft approaches without requiring satellite-based navigation. Fig. 2-4 illustrates an aircraft marker
beaconing system.
Fig. 2-4. Illustration of marker beacons for aircraft instrument landing systems.
11
Beaconing systems originated around 1888, when Heinrich Hertz conducted experiments using
a loop antenna and discovered its directional nature. Beaconing systems that mechanically swept a
single directional antenna developed in the years following this initial innovation. Single-antenna
beaconing systems remain abundant due to their simplicity of construction and operation, and their high
portability and flexibility [12]. Nonetheless, early mechanically swept systems focused on longwave
radio frequency signals for radionavigation, and thus required large antennas. These systems proved
impractical due to the constraint of rotating or moving an outsized antenna, so beaconing systems
demanded additional research prior to their widespread deployment.
In 1909, Bellini and Tosi patented a two-antenna direction finding system that vastly
outperformed previous single-sensor designs [15]. The dual-antenna beaconing system allowed for near
arbitrary antenna placement and the use of smaller antennas to collect and process longwave RF signals.
The Bellini and Tosi approach revolutionized beaconing and enabled practical deployment of direction
finding systems [16]. Like prior beaconing systems, the Bellini and Tosi approach required manual
tuning of the antennas in frequency and angle, thus necessitating several minutes of tedious labor to
detect and lock to a receiver. This beaconing technique remained widely popular until World War II,
when American and British systems surpassed the performance in angular resolution and angle estimate
convergence time, as well as the size, weight and power (SWaP) limitations of the Bellini and Tosi
design [16].
Beaconing systems advanced rapidly and gained widespread use during World War II, when
competing militaries attempted to detect and defeat adversary land, sea and aerial platforms prior to
their own discovery. Notable beaconing innovations including the British High Frequency/Direction
Finding (HF/DF, or “huff-duff”) system, which used a set of spatially separated antennas and mixed
the received signals for display on an oscilloscope [16]. The HF/DF system processed the relative phase
of the signals received at the various antennas into a beaconing display. By connecting appropriate
antennas, the HF/DF system could detect and localize radio frequency emitters operating at various
12
frequencies. The HF/DF system coherently observed the signals collected at multiple antennas,
employing an interferometric procedure to obtain receiver direction. The pioneering HF/DF system
enabled tracking of Nazi maritime assets, and is widely credited with aiding the Allied decimation of
the Nazi U-boat fleet in the English Channel and Atlantic Ocean [16].
Presently, beaconing finds civilian applications in search and rescue, navigation and tracking
of ships and aircraft, and bearing/heading detection and analysis [17]. Beaconing allows ships and
aircraft to track navigation stations and remain on course. Beaconing also supports rescue missions
performed by the United States Coast Guard and law enforcement agencies by directing emergency
responders to beacons placed on flotation devices or carried by individuals. Several commercial
beaconing systems provide such capabilities [12]. Additionally, the Federal Communications
Commission employs beaconing systems to search for illegal users of licensed radio frequency
spectrum and aiding in law enforcement. Beaconing also supports military signals intelligence and
electronic warfare operations in detecting and tracking both adversary and friendly assets [17]. In the
near future, wireless beaconing will likely play a crucial role in fifth-generation (5G) cellular systems.
The 5G cellular architecture will require ad-hoc networking, including dynamic discovery of, and
coordination between, wireless nodes.
i. General Theory
The original beaconing technique, single-sensor direction finding systems remain widespread
due to their simplicity and mobility. One-antenna beaconing systems support amateur direction finding
applications, and some commercial uses [17]. Single-antenna systems require rotation of the directional
sensor, and manual or automatic processing of the received signal as a function of azimuth and/or
elevation angle. The processor, in the form of a computer or human, detects the angle combination that
generates the maximum received level of the signal of interest, and adjusts the positioning and pointing
angle of the direction finding system to converge toward the emitter. While they leverage simple
hardware, single-antenna beaconing systems typically require a skilled operator to manually analyze
13
the received signal and thus demand complexity in operation [16]. Additionally, one-sensor systems
face performance degradation in high-multipath environments, such as dense urban settings. In urban
environments, single-sensor direction finding systems may detect a multipath as the strongest received
signal and errantly direct the user toward a point of signal reflection rather than toward the true emitter
position.
To overcome potential ambiguities and enhance performance, most beaconing systems utilize
multiple antennas and simultaneously process the received signal arriving at the various sensors [12].
These beaconing systems measure the properties of the signal of interest at each antenna element in the
array, and compute the differences (in time, frequency, phase and/or other dimensions) between the
signals collected at the dispersed sensors. Beaconing systems map the measured signal disparities into
receiver position information. Multiple-angle beaconing systems may position the antennas in
orthogonal planes (azimuth and elevation, for example) and process the signals arriving at pairs of
antennas. Using this architecture, multi-antenna beaconing systems gather sets of independent
information, and combine the orthogonal data to estimate position in multiple dimensions
simultaneously.
Fig. 2-5 depicts a typical circular antenna array, analogous to a standard sectorized cellular
antenna array, which can perform beaconing. In the figure, the numbered components constitute the
four array antennas, while the central post, labeled “Optional”, illustrates a fifth antenna that can resolve
ambiguities that may arise from antenna spacing. The array receives a signal from an emitter, and each
antenna collects a version of the signal offset slightly in time from the signal received at the remaining
elements. The array spacing converts this timing disparity into a measureable relative phase shift in the
signal received at each antenna. To address potential ambiguities from multipath propagation and other
phenomena, beaconing antenna arrays sometimes use directional elements, such as sector antennas, that
limit the field of view of each sensor and of the composite array, and therefore restrict the angle-of-
arrival of signals arriving at the array following reflection.
14
Fig. 2-5. Typical four-element circular antenna array for direction finding.
Beaconing may occur passively, in which the beaconing system does not transmit but instead
collects emissions from a transmitter of interest. Beaconing may also be active, in which the system
broadcasts a waveform that reflects from a receiver, and returns to sensors that may or may not be co-
located with the beaconing system transmitter [16]. Beaconing systems may additionally employ non-
cooperative ambient signals, such as local Wi-Fi broadcasts or cellular network traffic, and monitor
perturbations from reflections of these signals at an array of receivers. Beaconing systems that leverage
“third party” signals must first generate a comprehensive map of the ambient radio frequency
environment. Using this baseline, the beaconing systems then detect the existence and position of
objects of interest via anomalies, including unnatural modulations of signal properties like amplitude,
frequency and phase.
15
ii. Time-Difference of Arrival (TDOA)
Beaconing systems may employ time difference of arrival (TDOA) to determine the position
of a receiver relative to the beaconing system. Systems using TDOA processing employ multiple
spatially dispersed sensors that collect signals in a timing- and phase-coherent manner [7]. Upon the
detection of an emission of interest, the beaconing system utilizes a correlation receiver to compute the
time difference between the arrivals of the same signal at each of the antennas. The system then maps
these to distances by multiplying the time difference by the propagation speed of the signal [16].
In general, an 𝑁-sensor system can determine the position of an object in (𝑁 − 1) dimensions.
The beaconing system must utilize parameters, such as center frequency and bandwidth, which
effectively illuminate the object and enable the object to reflect energy back to the system, rather than
absorb, refract or transmit that energy, thus directing it away from the beaconing system. For simplicity,
a two-sensor system is initially analyzed to locate an object as a function of one dimension, the angle
between the center of the beaconing system baseline and the receiver. Each of the two beaconing
receivers collects a radio frequency signal reflected by the object. The receivers provide the received
signal information to a processor, which may be located at one of the receivers, or may be remote. This
processor uses correlation processing to compute the time difference of arrival between the receiver
reflections received at the two receivers, and derives the receiver angle from the TDOA. Using two
receivers, the beaconing system determines that the receiver occupies a position on a hyperbola defined
by the TDOA, but the two-antenna system cannot resolve receiver position any further.
Fig. 2-6 presents the receiver tracks for various TDOA values using a radio frequency systems
with 200-meter receiver separation and an acoustic system center frequency of 11 kHz. The receiver
separation, also known as the receiver baseline, is typically defined as a function of the wavelength, λ,
of the transmitted signal. In the Fig. 2-6 example, the receiver baseline comprises approximately 6400
wavelengths. In the figure, black stars represent the beaconing receivers, while the colored lines depict
the hyperbola of receiver locations as a function of TDOA. The figure clearly portrays the receiver
16
position ambiguity, as each TDOA defines a hyperbola on which the receiver lies, but does not
determine the exact receiver position. The figure also portrays the symmetry of the TDOA geometry,
as time differences define a hyperbola symmetric to the curve defined by the time difference equal in
absolute value but opposite in sign.
Fig. 2-6. Receiver position ambiguity with two-sensor two-dimensional beaconing system.
In two dimensions, a beaconing system must employ no fewer than three sensors to estimate
the location of the receiver. Fig. 2-7 depicts a three-receiver beaconing system. This system employs a
“corner” configuration, with pairs of receivers occupying orthogonal axes. The TDOA between signal
arrivals at the receivers along the x-axis generates the blue curve. Analogously, the TDOA between
arrivals at the receivers along the y-axis produces the green curve. The receiver at position (−100, 0)
performs beaconing in both the x and y dimensions using only the energy from the receiver reflection
it receives – no receiver duplication is required and only two correlation results must be generated. The
three-receiver beaconing system creates two initially ambiguous measurements: the receiver can lie
17
along any point on the blue curve, and along any point on the green curve. However, the receiver can
only occupy both curves simultaneously at a single point in space: the unambiguous and authentic
receiver position estimate. The result shown in Fig. 2-7 extends to arbitrarily many dimensions.
Fig. 2-7. Receiver position resolved with three-sensor two-dimensional beaconing system.
Beaconing systems monitor divergent signal properties depending upon their system
bandwidth and mode of operation. Narrowband beaconing systems employ signals whose fractional
bandwidth (the ratio between the signal bandwidth and the center frequency) is small – typically less
than ten percent. Narrowband beaconing systems monitor the phase difference, measured at the system
center frequency, between signals arriving at distributed receivers, and translate the phase differences
to positioning information. Wideband beaconing systems use signals with larger fractional bandwidths,
and measure the time difference of arrival at various receivers to calculate the location of nodes. Thus,
in wideband beaconing systems, time difference substitutes for phase difference in computing
positional information.
18
3. MODIFIED TRANSMITTED REFERENCE TECHNIQUE
To utilize the advantageous characteristics of transmitted reference while simultaneously
mitigating the multipath-induced performance degradation, a modified transmitted reference (MTR)
architecture is proposed. The modified transmitted reference signaling scheme incorporates time scale
(compression or dilation) in addition to time delay. While time scale can be modulated to encode
information orthogonal to time delay, the proposed system does not employ scale in this manner.
Instead, the beaconing system discussed in this thesis utilizes time scale to reliably differentiate the
desired signal from multipath-induced clutter, and to provide additional unique properties. Fig. 3-1
illustrates the modified transmitted reference transmitter and receiver block diagrams, highlighting the
supplements as red blocks, when compared to Fig. 2-1.
Fig. 3-1. Modified transmitted reference block diagrams.
19
A. Modified Transmitted Reference Overview
The traditional transmitted reference signal, 𝑡𝑇𝑅(𝑡), comprises a reference waveform, 𝑏(𝑡), and
a time-delayed offset copy of the reference signal, as illustrated in Equation (8):
𝑡𝑇𝑅(𝑡) = 𝑏(𝑡) + 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎) (8)
The modified transmitted reference technique follows a similar form, but modulates the offset copy
both in time delay and time scale:
𝑡𝑀𝑇𝑅(𝑡) = 𝑏(𝑡) + 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎)) (9)
Analogous to the transmitted reference architecture reviewed in Chapter 2, the MTR receiver
correlates the received signal with a copy of itself to generate a correlation surface. The MTR receiver
applies the same time scale, 𝑠, employed by the transmitter, to the copy signal prior to correlation.
Mathematically, the MTR receiver performs the following operation to generate the MTR correlation
surface:
𝛸(𝜏, 𝑠) = ∫ 𝑡𝑀𝑇𝑅(𝑡)𝑡∗𝑀𝑇𝑅(𝑠(𝑡 − 𝜏))𝑑𝑡
𝑡0+𝑇
𝑡0
(10)
The MTR correlation surface comprises a sequence of time delay bins, each of which results
from a portion of the time series signal 1
|𝑠−1| samples long. Each time delay bin associates a complex
correlation amplitude to a hypothesized relative time delay between the reference signal and the
modulated copy waveform. The MTR receiver selects the hypothesized delay that generates the
maximum correlation amplitude as the likeliest delay between the reference and modulated waveforms.
Employing the definition of 𝑡𝑀𝑇𝑅(𝑡), the received correlation surface becomes:
𝛸(𝜏, 𝑠) = ∫ [𝑏(𝑡) + 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎))][𝑏(𝑠(𝑡 − 𝜏)) + 𝑏(𝑠(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎) − 𝜏))]∗𝑑𝑡𝑡0+𝑇
𝑡0
(11)
Expanding and rearranging terms yields the following result, comprising four terms:
20
𝛸(𝜏, 𝑠) = ∫ 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎))𝑏∗(𝑠(𝑡 − 𝜏))𝑑𝑡𝑡0+𝑇
𝑡0
+ ∫ 𝑏(𝑡)𝑏∗(𝑠(𝑡 − 𝜏))𝑑𝑡𝑡0+𝑇
𝑡0
+ ∫ 𝑏(𝑡)𝑏∗(𝑠(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎) − 𝜏))𝑑𝑡𝑡0+𝑇
𝑡0
+ ∫ 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎))𝑏∗(𝑠(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎) − 𝜏))𝑑𝑡𝑡0+𝑇
𝑡0
(12)
The four terms that define the modified transmitted reference correlation surface each produce
a unique characteristic:
1. The first term represents the correlation between two identically time-scaled copies of the
reference waveform. These signals arise from the modulated copy emitted by the transmitter,
and the reference signal received and time scaled by the receiver. This term generates a
maximum correlation peak when the transmitter and receiver each apply time scale 𝑠 and 𝜏 =
𝜏𝑑𝑎𝑡𝑎.
2. The second term results from the correlation between the reference signal broadcast by the
transmitter and the reference signal received and time scaled by the receiver. This term does
not generate a significant correlation peak when the transmitter and receiver each apply time
scale 𝑠.
3. The third term is the correlation between the transmitted reference signal and the modulated
copy received and time scaled by the receiver. This term correlates a signal that has not been
time scaled with a waveform that has been scaled twice. This term does not produce a
significant correlation peak when the transmitter and receiver each apply time scale 𝑠.
4. The fourth term is the correlation between the transmitted modulated copy and the same
modulated copy following reception and time scale at the receiver. This term results in the
correlation of a signal time scaled once with a signal scaled twice. This term does not produce
a significant correlation peak when the transmitter and receiver each apply time scale 𝑠.
21
Only the first term generates a significant correlation peak when the transmitter and receiver
each apply a time scale 𝑠. The other terms generate nonzero energy on the modified transmitted
reference correlation surface, resulting in increased “interference” on the surface. Nonetheless, the final
three terms do not produce significant peaks on the MTR correlation surface.
Fig. 3-2 permits visualization of the modified transmitted reference correlation surface for the
aforementioned scenario. In this scenario, the modified transmitted reference system employs a
Gaussian white noise reference signal of duration 32,768 samples, and modulates a time scale of 1.001
and a time delay of 200 samples.
Fig. 3-2. Example modified transmitted reference receiver correlation surface (𝑠 = 1.001).
The MTR correlation surface presents a strong peak at the transmitter-encoded time delay, and
features very little energy at other lags. Between lags −40 and zero, the correlation surface displays a
small perturbation. This structure arises from sidelobe energy generated by the second through fourth
22
terms at time scale 𝑠, and its exact characteristic depends upon the properties of the reference signal.
Although the aforementioned terms produce the majority of their energy at time scales other than the
scale of interest, they do contribute spurious energy at the desired scale. The sidelobe energy alters in
characteristic as a function of time scale and time delay parameterization, so careful selection of settings
must occur. However, as the sidelobe energy typically impacts MTR receiver data demodulation less
significantly than do environmental noise and other communications channel phenomena, the sidelobe
energy will be ignored in this thesis and proper parameterization will be assumed.
B. Modified Transmitted Reference Parameterization
The modified transmitted reference technique is defined by a parameter set that dictates the
performance properties of the MTR system. Table 3-1 lists the core properties associated with MTR
signal processing, and provides comments on the performance consequence of the parameters.
Table 3-1. Modified transmitted reference parameters.
MTR
Parameter
Parameter
Units
Parameter
Performance Consequences
Symbol Length (𝑁) samples Integration time; received
output signal-to-noise ratio
Signal Bandwidth (𝐵) Hertz Time resolution; time delay
constellation
Time Scale (𝑠) – Time resolution; multipath
resistance/integration
Time Delay (𝜏) samples Received output
signal-to-noise ratio
As with any communications technique, the modified transmitted reference scheme achieves
improved signal-to-noise ratio by integrating additional signal samples (employing a larger 𝑁
parameter). Naturally, MTR systems employing longer symbol lengths achieve improved error rate
and/or angular estimation accuracy performance as a function of signal-to-noise ratio. Conversely, these
systems produce lower communications data rates and/or lower angle estimate refresh rates relative to
systems using shorter symbols. The modified transmitted reference technique experiences the same
compromises between operable SNR and throughput (defined for a beaconing system as the rate of
position and identification updates, and/or data and information) faced by all communications systems.
23
Unlike traditional modulations, by employing time scale, the MTR technique redefines SNR by
utilizing multipath energy as useful signal energy rather than treating echoes as interference.
The modified transmitted reference technique employs time scale to differentiate the time-
delay modulated signal copy from naturally occurring signal copies that arise from multipath
propagation. The time scale parameter defines several consequential system properties. Most critically,
time scale produces a tunable compromise between time resolution and multipath resilience through
recombination. Time scale constitutes a time-varying difference between the reference signal, 𝑏(𝑡), and
the modulated offset waveform. Time scaling causes the offset signal to be more different than the
reference signal and time progresses within a data symbol. Coarser time scales, or scales farther in
absolute value from unity, generate a more rapid change as a function of time, resulting in consequential
alterations occurring over shorter time intervals. Thus, coarser time scales permit finer time resolution
and improved angular resolution. While they improve resolution, coarser time scales provide less
resistance to multipath than do finer scales. The MTR correlation surface comprises time delay bins of
width 1
𝐵|𝑠−1| seconds in time. Coarser scales generate time delay bins consisting of fewer samples in
time, and hence improved time resolution. MTR systems combine signal energy arriving within 1
𝐵|𝑠−1|
seconds in time into the same time delay bin, thereby withstanding, and using, multipath energy.
For beaconing applications, signal bandwidth – particularly the bandwidth of the signal when
it reaches the receiver – plays a critical role in system performance. Modified transmitted reference
beaconing systems detect angular variations by decoding time delay information. The MTR technique
resolves time delays separated by resolvable cells, with each cell comprising a time interval of
approximately the inverse of the received bandwidth. Therefore, MTR systems employing larger
bandwidths provide enhanced angular resolution, enabling them to perform more precise direction
finding and resolve multiple receivers separated by small angles relative to the MTR beaconing system.
In order to realize the full gain of increased bandwidth, the MTR system must operate in a
communications channel that supports the range of spectrum used by the system. Wideband
24
communications and sensing systems are prone to frequency-selective fading, narrowband interference,
and other phenomena that limit the useable spectrum.
C. Performance Characteristics of MTR Parameterization
The modified transmitted reference scheme benefits from the use of time scale. In classical
transmitted reference signaling, multipath propagation presents a difficult challenge to successful signal
detection and demodulation, and also to beaconing. A transmitted reference system sometimes cannot
differentiate its deliberately-injected multipath, the modulated copy signal 𝑏(𝑡 − 𝜏𝑑𝑎𝑡𝑎), from naturally
occurring multipaths of similar form, i.e. 𝑏(𝑡– 𝑀). By encoding the offset copy with a time scale, 𝑠,
that cannot occur naturally within the environment in which the system operates, the modified
transmitted reference technique differentiates its offset copy from other multipaths and achieves reliable
detection and demodulation, even in channels with significant multipath energy.
The following example illustrates the resistance of the modified transmitted reference
technique to multipath. The MTR receiver collects the signal:
𝑟(𝑡) = 𝑏(𝑡) + 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎)) + 𝑏(𝑡 − 𝑀) + 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎) − 𝑀) (13)
The MTR receiver performs correlation processing on the signal, generating 16 correlation
terms as in the conventional transmitted reference processing (refer to Equation (7)). These terms
include the following four terms that potentially produce significant energy in the correlation surface
at time scale 𝑠:
𝛸(𝜏, 𝑠) = ∫ 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎))𝑏∗(𝑠(𝑡 − 𝜏))𝑑𝑡𝑡0+𝑇
𝑡0
+ ∫ 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎))𝑏∗(𝑠(𝑡 − 𝜏) − 𝑀)𝑑𝑡𝑡0+𝑇
𝑡0
+ ∫ 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎) − 𝑀)𝑏∗(𝑠(𝑡 − 𝜏))𝑑𝑡𝑡0+𝑇
𝑡0
+ ∫ 𝑏(𝑠(𝑡 − 𝜏𝑑𝑎𝑡𝑎) − 𝑀)𝑏∗(𝑠(𝑡 − 𝜏) − 𝑀)𝑑𝑡𝑡0+𝑇
𝑡0
(14)
25
Each of the four terms above yields a maximum correlation peak at time scale s and time delay
𝜏𝑑𝑎𝑡𝑎, assuming that 𝑀 is sufficiently small. As each time delay bin on the MTR correlation surface
comprises 1
𝐵|𝑠−1| seconds in time, the modified transmitted reference technique combines multipaths
with 𝑀 values less than that interval into a single resolvable time delay bin. In traditional transmitted
reference systems, the receiver time resolution is the inverse of the signal duration. These classic TR
receivers must employ short-duration signals to achieve sufficient timing resolution. Due to this rigid
and required architecture, multipaths arriving at any delay 𝑀 will contribute significant energy to bins
other than the transmitter-encoded delay between the reference signal and modulated offset waveform.
In contrast, the MTR receiver combines multipath energy into the desired time delay bin as long as the
multipath arrives within the aforementioned time interval.
As discussed previously, a modified transmitted reference system cannot use and arbitrarily
select its time scale, but must instead balance multipath performance with timing resolution. MTR
systems that employ coarser time scales better resist multipath-induced performance degradation, but
also provide coarser time synchronization and less precise receiver angle measurements. The optimal
MTR parameterization depends upon the communications channel in which the MTR system operates,
as well as the system and receiver geometry, and receiver properties.
Fig. 3-3 depicts the impulse response of an underwater acoustic communications channel
featuring significant reverberation. The communications channel supports three high-energy multipath
arrivals and several lower-amplitude multipaths. The acoustic environment includes multipaths of
significant energy that arrive 104.3, 215.9 and 251.7 milliseconds from the start of the observation.
Thus, the channel defines multipaths that arrive separated by approximately 150, 100 and 50
milliseconds. This environment represents a challenging communications channel that may prove
problematic for conventional transmitted reference systems. Recalling the Fig. 2-3 result of transmitted
reference reception in a single-multipath channel, the highly reverberant environment shown in Fig.
3-3 may prove prohibitive for conventional transmitted reference signaling.
26
Fig. 3-3. Impulse response of a reverberant underwater acoustic communication channel.
The modified transmitted reference technique utilizes its time scale signal processing to
combine multipath arrivals. The MTR scheme enables a tunable integration time defined by the time
scale and signal bandwidth. For instance, Fig. 3-4 depicts the correlation surface produced by a
modified transmitted reference receiver following signal propagation from an MTR transmitter,
through the channel defined by the Fig. 3-3 impulse response, to the receiver. The MTR receiver used
to generate the Fig. 3-4 result employed a 44.1 kHz bandwidth AWGN reference signal and a time scale
of 1.01. Using these parameters, the MTR receiver integrates multipaths arriving within 1
𝐵|𝑠−1|=
1
44.1𝑒3∗|1.01−1|= 2.39 milliseconds into a single correlation bin. As the multipaths in the acoustic
environment arrive at separations exceeding this threshold, the MTR receiver generates a prominent
correlation peak for each of the three significant multipaths.
Conversely, Fig. 3-5 illustrates the correlation surface generated by an MTR receiver using a
time scale of 1.0001. This receiver integrates multipaths arriving within 227 milliseconds into a single
correlation bin. Using a finer time scale (closer to unity), the MTR receiver yields a single, higher-
energy correlation peak despite enduring the same three-multipath channel.
27
Fig. 3-4. MTR correlation surface with propagation through reverberant channel (𝑠 = 1.01).
Fig. 3-5. MTR correlation surface with propagation through reverberant channel (𝑠 = 1.0001).
The modified transmitted reference algorithm may have applicability in various fields, including
digital communications, sensing and navigation. This thesis focuses on developing the theory of one
specific application, and confirming the theoretical results via software simulation and hardware-in-
the-loop experimentation. The thesis utilizes the modified transmitted reference scheme to supplement
direction-finding via interferometric processing.
28
4. MODIFIED TRANSMITTED REFERENCE TECHNIQUE FOR BEACONING
Amongst a diverse array of potential uses, the modified transmitted reference technique can
perform beaconing via time difference of arrival, applying its unique features to direction finding using
arbitrary waveforms, and operating in communications channels with significant multipath. As
described in Chapter 2, the time difference of arrival at a receiver defines a hyperbola along which the
receiver lies [16]. Under certain geometric assumptions, including signal propagation into the far field,
TDOA approximately describes a straight line path between the beaconing transmitters and the receiver.
Fig. 4-1 illustrates a two-transmitter, single-receiver TDOA configuration, with the transmitters
occupying a plane in space. The figure denotes the Euclidean distance between transmitters as 𝐿. This
line will henceforth be referenced as the transmitter baseline. Fig. 4-1 denotes the distance between the
center of the baseline and the receiver as “𝑟”. The MTR beaconing system aims to use the TDOA at
the receiver to compute the angle, 𝜃, between the center of the baseline and the receiver. As displayed
on the figure, when the transmitter-to-receiver distance exceeds the baseline length by orders of
magnitude, the far-field condition is met, and the hyperbola converges to a straight line estimate. The
following discussion invokes the aforementioned constraint, and the receiver will be assumed to occupy
a point on a line extending from the center of the baseline to the receiver at an angle of arrival defined
by the TDOA measurement at the receiver.
Fig. 4-1. Time difference of arrival geometric approximations.
29
The two-transmitter MTR beaconing system actively broadcasts an MTR waveform designed
specifically for direction finding. The MTR system utilizes two spatially separated transmitters, each
of which broadcasts a portion of the MTR beaconing waveform. This MTR system may collocate a
receiver at one of the transmit sites, or it may emplace a remote receiver at another location. For
navigation applications, such as civilian aircraft positioning, the receiver may be collocated with the
object so as to provide the object with information regarding its location. The first transmitter emits a
signal of the form shown in Equation (15):
𝑚1(𝑡) = 𝑏(𝑡) + 𝑏(𝑠1(𝑡 − 𝜏1)) (15)
The transmitter 1 reference signal, 𝑏(𝑡), may be an arbitrary waveform, though the signal
should possess desirable characteristics relative to the communications channel in which the MTR
localizer operates. Likewise, the transmitter should parameterize its time scale, 𝑠1, and time delay, 𝜏1,
for optimal performance in the environment of operation.
Because the reference waveform and the transmitter 1 modulated offset copy originate from
the same transmitter, the two signals arrive at the receiver simultaneously. Upon collection at the
beaconing system receiver, the reference and modulated copy 1 provide timing synchronization to the
beaconing system. The receiver performs correlation processing at time scale 𝑠1 and attempts to detect
the presence of the 𝑚1(𝑡) composite waveform. Upon detection, the receiver decodes the time delay,
defined as 𝜏𝑑. The receiver may or may not demodulate the time delay encoded by the transmitter (𝜏𝑑 ≠
𝜏1) due to the segmented nature of the finite-duration MTR data frames. The receiver aligns itself to
the transmitted data frames through its knowledge of the 𝜏1 value and its decoding of 𝜏𝑑. Because each
MTR receiver time delay bin comprises 1
|𝑠1−1| samples, the MTR receiver performs the following
calculation to align with the transmitted data frames:
∆𝑇 =𝜏𝑑 − 𝜏1
|𝑠1 − 1| samples =
𝜏𝑑 − 𝜏1
𝐵|𝑠1 − 1| seconds (16)
30
Clearly, time scales 𝑠1 farther from unity provide finer timing resolution by decreasing the step
size of 𝛥𝑇 for a one-bin shift in decoded time delay 𝜏𝑑. As discussed in Chapter 3, time scales farther
from unity integrate less multipath, making systems employing these coarse time scales more
susceptible to performance degradation in communications channels that support considerable
multipath. Depending upon the radio frequency environment and the receiver configuration, MTR
systems may optimize their parameters via selection of time scale and other settings.
The second MTR beaconing transmitter broadcasts a signal of the form:
𝑚2(𝑡) = 𝑏(𝑠2(𝑡 − 𝜏1)) (17)
The transmitter 2 waveform constitutes only a modulated offset copy that the MTR receiver
cannot use by itself to demodulate data. However, when the receiver correlates signals containing
𝑚1(𝑡) and 𝑚2(𝑡) with one another, the reference signal 𝑏(𝑡) contained in 𝑚1(𝑡) correlates to both
modulated offset copies, 𝑏(𝑠1(𝑡 − 𝜏1)) and 𝑏(𝑠2(𝑡 − 𝜏1)). By performing correlation at time scale 𝑠1
and time scale 𝑠2, the receiver produces two correlation peaks, one at each scale. After the receiver
detects a valid signal and performs data frame alignment using time scale s1, it then decodes the time
delay associated with time scale 𝑠2.
Due to the spatial separation between the MTR transmitters, the signals 𝑚1(𝑡) and 𝑚2(𝑡) arrive
at the receiver at different times. The reference signal, 𝑏(𝑡), contained in 𝑚1(𝑡), and the modulated
offset copy, contained in 𝑚2(𝑡), correlate at a time delay corresponding to, and resulting from, the
spatial separation. The MTR receiver decodes a time delay, 𝜏2, which comprises two components: the
transmitter-encoded time delay, 𝜏1, and an additional delay, 𝜏𝑠𝑝𝑎𝑡𝑖𝑎𝑙, caused by the time difference of
arrival between the reference (𝑚1(𝑡)) and modulated (𝑚2(𝑡)) signal components. Depending upon
receiver position relative to transmitters 1 and 2, 𝜏𝑠𝑝𝑎𝑡𝑖𝑎𝑙 may assume a positive or negative value. The
MTR receiver essentially discards the 𝜏1 delay, and maps the 𝜏𝑠𝑝𝑎𝑡𝑖𝑎𝑙 delay to the corresponding time
difference of arrival.
31
Fig. 4-2 portrays the time delays at the transmitters and the receiver. The figure depicts that,
although the transmitters encode equal time delay values, the receiver demodulates two distinct delays
that depend upon transmitter encoding and transmitter-to-receiver geometry.
Fig. 4-2. Comparison of time delay values at MTR beaconing transmitters and receiver.
After it decodes the time delay value for each time scale, the modified transmitted reference
receiver maps the delays to a receiver bearing. Recalling the geometry of Fig. 4-1, the MTR receiver
computes the time difference of arrival between the transmitters and receiver:
TDOA = 𝜏𝑠𝑝𝑎𝑡𝑖𝑎𝑙 = 𝜏2 − 𝜏1 (18)
The receiver then converts the TDOA to a differential distance (the difference between the
distance from the receiver to transmitter 1 and the distance from the receiver to transmitter 2). In
Equation (19), the variable “𝑐” denotes the propagation speed of the MTR signal, while “𝐵” represents
the bandwidth of the signal used by the beaconing system.
∆𝑑 =𝑐 ∗ TDOA
𝐵 (19)
Using the approximations described earlier in this chapter, including in Fig. 4-1, the MTR
receiver employs the distance difference and the known MTR system geometry to compute the bearing
between the center of the transmitter baseline and the receiver:
𝜃 = arccos (∆𝑑
𝐿) (20)
32
Fig. 4-3 presents a graphical overview of the concept of operations of the modified transmitted
reference system. The spatially-separated MTR transmitters broadcast the signal as previously
described. In addition to noise and other ambient signals, the receiver collects the signal that originates
from the transmitters, merges at the receiver, and propagates from the receiver to the receiver.
Following combination at the receiver, the signals (a blend of energy from transmitter 1 and transmitter
2) propagate together from the receiver to the receiver, and this receiver-to-receiver path introduces no
additional relative time delay between 𝑚1(𝑡) and 𝑚2(𝑡). The receiver-to-receiver propagation may
generate multipaths not found at the receiver, but present at the receiver. However, the MTR
parameterization – particularly the time scale setting – may enable combination of these multipaths into
a single time delay bin, thus avoiding performance degradation (refer to Chapter 3).
Fig. 4-3. Illustration of MTR beaconing receiver mapping delay to angular information.
Fig. 4-4 illustrates the MTR beaconing block diagram, providing a summary of the steps
required to convert the transmitted signal components into a receiver bearing estimate.
33
Fig. 4-4. Modified transmitted reference beaconing receiver block diagram.
A. Angular Resolution and Beaconing System Baseline
The modified transmitted reference beaconing system achieves finite angular resolution limited by
the reference waveform, 𝑏(𝑡), and the system parameterization and geometry. The MTR beaconing
system employs wideband reference waveforms whose fractional bandwidths exceed those typically
utilized by narrowband systems. Accordingly, the MTR system derives its performance from
parameters such as signal bandwidth and time delay resolution as opposed to wavelength and phasing.
The modified transmitted reference beaconing system uses time-difference of arrival (TDOA) to
compute receiver angle estimates. The beaconing system must experience a resolvable change in the
time difference of arrival, provoked by an alteration in the position of the MTR receiver relative to a
static transmitter configuration, in order to compute a new transmitter-to-receiver angle. The MTR
beaconing system achieves a time delay resolution of the inverse of its signal bandwidth, 1
𝐵 and resolves
34
changes in distance of 𝑐
𝐵. Combining the aforementioned results with the outcome of Equation (20), the
angular resolution of the beaconing system depends upon the signal propagation speed, the reference
signal bandwidth, and the transmitter aperture. The beaconing system attains finer angular resolution
with increasing bandwidth relative to propagation speed, and increased aperture. As evidenced by
Equation (20), beaconing systems utilizing a longer baseline require the receiver to change position
(𝛥𝑑) by a greater amount to effect the same change in time difference of arrival. Thus, larger baselines
improve spatial resolution for beaconing systems.
The baseline is bounded by practical constraints relative to sensor interconnections. Beaconing
systems must synchronize their receivers, and distribute information from each sensor to a site that
performs the correlation processing. A large baseline complicates the essential process of sharing
information between the sensors in a beaconing system. Within the limitations imposed by these
synchronization constraints, beaconing systems typically endeavor to achieve a maximal baseline.
The following figures illustrate the finite resolution of the MTR beaconing system. Each figure
depicts the angle bin centers for the MTR beaconing system as black lines. In Fig. 4-5, the beaconing
system utilizes a transmitter baseline of 25 meters, and a transmitter-to-receiver radius of 10 kilometers,
thus satisfying the Fig. 4-1 approximation. The Fig. 4-5 beaconing system employs a radio frequency
reference signal with a 100 MHz bandwidth, providing a time delay resolution of 10 nanoseconds. The
beaconing system thus employs a baseline comprising a distance of approximately 8.33 time delays.
Fig. 4-5 also depicts the non-uniformity of the beaconing system angular bins: bins at angles closer to
boresight are narrower than those at angles closer to the edge of the field of view.
Fig. 4-6 depicts the results for a beaconing system using the 25-meter baseline and 10-kilometer
radius. In Fig. 4-6, the beaconing system employs a reference signal with a 25-MHz bandwidth. The
limited bandwidth elongates the beaconing system time delay bins, resulting in reduced angular
35
resolution. In Fig. 4-5, the beaconing system resolves 18 angular bins, while in Fig. 4-6, the system
resolves only six bins.
Fig. 4-5. MTR beaconing system angular bin centers with 𝐿 = 25 m and 𝐵 = 100 MHz.
Fig. 4-6. MTR beaconing system angular bin centers with 𝐿 = 25 m and 𝐵 = 25 MHz.
36
5. MTR BEACONING SIMULATION
A software simulation was developed to assess the performance of the modified transmitted
reference beaconing system relative to receiver position accuracy, and to evaluate the validity of the
theoretical development described in Chapters 3 and 4. The software simulation comprises a suite of
functional modules written in the MATLAB® programming language. The software instantiates a two-
transmitter and one-receiver beaconing system, and analyzes the one-dimensional (angle) performance
of this beaconing configuration. The software thus simulates a beaconing configuration such as a
navigation radar, in which a commercial aircraft receives information regarding its position from
ground stations. The simulation permits user definition of the two-dimensional beaconing system as
illustrated in Fig. 4-3. The simulation then performs the signal conditioning and processing defined by
the user-entered parameters.
The simulation computes and stores the ground truth angle information (the angle between the
center of the transmitter baseline and the receiver; this angle is depicted as 𝜃 in Fig. 4-3) based upon
the user-defined geometry. The simulation then synthesizes the components of the modified transmitted
reference signal, 𝑚1(𝑡) and 𝑚2(𝑡), and utilizes the specified geometry (receiver position relative to the
transmitter baseline) to time delay one of the transmit signal components relative to the other. The
software applies amplitude scaling to each signal component based upon free-space path loss, and adds
multipath replicas to the transmitted signal as desired. The simulation also applies additive white
Gaussian noise (AWGN) at the user-specified signal-to-noise ratio. The simulation defines SNR as the
ratio of the root mean square power of the complete MTR signal (𝑚1(𝑡) + 𝑚2(𝑡)) to the root mean
square power of the noise. The simulation ensures that the multipaths arrive after the direct transmitter-
to-receiver path, but enables arbitrary timing of the multipaths beyond that constraint. The simulation
additionally emplaces no limitations on the multipath phases, which may be set arbitrarily by the user.
The simulation additionally mandates that the amplitudes of multipath components cannot exceed the
amplitude of the direct path at the receiver, but may be set arbitrary outside that restriction.
37
The received signal thus constitutes:
1. the amplitude-scaled original transmit signal,
2. amplitude- and phase-modulated copies of the transmit signal, and
3. additive white Gaussian noise.
The simulation performs MTR receiver processing of the received signal. The simulation does not
assume timing synchronization between the beaconing transmitters and the receivers, so the simulation
receiver performs data frame detection and alignment prior to decoding the time delays that correspond
to angle estimates. Following the exhaustion of transmit data frames, the simulation finally displays the
statistics associated with the receive processing. These measurements include the number of data
symbols the MTR receiver detected, the receiver angle estimate information computed following each
frame detection by the beaconing receiver, and a comparison of the system angle estimates to the ground
truth via numeric outputs, tabularized data and plots.
A. Analytic Results
The simulation generated a series of results plots that depict the angle estimation capacity of the
modified transmitted reference system. This performance comprises angle estimate as a function of
ground truth angle and estimate resolution. The simulation confirmed the theoretical predictions
regarding angle estimate resolution, including the critical role of the time scale parameter. The
simulation also verified that system angle estimation depends upon many parameters, including those
of the reference signal, 𝑏(𝑡). Additional simulations incorporated multipath propagation between the
transmitters and receiver. These simulations underscored the robustness of the MTR technique to
multipath, and clearly illustrated that the limit of multipath resilience depends upon the time scale
parameter.
The MATLAB® software accepts the user-specified parameters listed in Table 5-1. The simulation
additionally defines parameters abstracted from the user.
38
Table 5-1. Simulation parameters employed during MTR beaconing software simulations.
Simulation
Parameter
Parameter
Symbol
Value(s) during
Simulations
Parameter
Units
Data Symbol Length 𝑁 65536 samples
Time Scale 1, 2 𝑠1, 𝑠2 1.05, 1.01 –
Time Delay 1 𝜏1 2048 samples
Propagation Speed 𝑐 3e8, 343 meters per second
Carrier Frequency 𝐹𝐶 2.4e9, 915e6, 11.025e3 Hertz
Signal Bandwidth 𝐵 30e6, 26e6, 22.05e3 Hertz
Transmitter Baseline 𝐿 10, 50, 100, 1000 meters
Transmitter-to-Receiver Radius 𝑟 100 meters
Signal-to-Noise Ratio 𝑆𝑁𝑅 10 decibels
Ground Truth Angle(s) 𝜃 -30 to 30 in steps of 1 degrees
To confirm the theoretical hypotheses and quantify the impact of altering the parameters, the
MATLAB® software simulated the beaconing system using several parameter sets. Each figure that
follows lists the parameters unique to the accompanying results plot. Every simulation employed the
same parameters listed in Table 5-2, with additional parameters associated with the individual results
plots.
Table 5-2. Simulation parameters common to all MTR software simulations.
Simulation
Parameter
Parameter
Symbol
Value(s) during
Simulations
Parameter
Units
Data Symbol Length 𝑁 65536 samples
Time Scale 1, 2 𝑠1, 𝑠2 1.05, 1.01 –
Time Delay 1 𝜏1 2048 samples
Signal-to-Noise Ratio 𝑆𝑁𝑅 10 decibels
Ground Truth Angle(s) 𝜃 -30 to 30 in steps of 1 degrees
i. Radio Frequency Results
To fully characterize the applicability of the MTR technique to beaconing scenarios, the
simulations utilized variable propagation speeds, carrier frequencies, signal bandwidths and baselines.
The simulations employed parameter sets that represent common and pertinent signal configurations,
including signals in the industrial, scientific and medical (ISM) frequency bands made available by the
Federal Communications Commission (FCC) for unlicensed use, and acoustic frequencies that enable
operations using ubiquitous and inexpensive commercial off-the-shelf hardware.
39
Each of the first three simulations employs a signal carrier frequency and bandwidth consistent
with those used by 802.11 Wi-Fi systems operating in the 2.4-GHz ISM band. Each successive
simulation increased the transmitter aperture to achieve finer angular resolution.
Using this parameter set, the beaconing system attains acceptable angular resolution when the
transmitter aperture exceeds 50 meters. These simulations suggest that the MTR technique may provide
value for indoor beaconing systems that provide guidance in retail locations and public spaces. In indoor
environments, positioning information provided by satellite-based systems may be unattainable due to
excessive signal loss, and conventional positioning techniques suffer from excessive clutter associated
with multipath propagation. The modified transmitted reference technique may overcome the
constraints of multipath propagation in indoor environments to a sufficient extent as to allow reliable
beaconing.
Using a 10-meter transmitter aperture, the beaconing system cannot approximate the receiver
angle with any accuracy, and computes an angle of zero degrees regardless of the authentic receiver
position.
c =
3e8 m/s
FC =
2.412 GHz
B =
30 MHz
L =
10 m
Fig. 5-1. Simulation results for Wi-Fi parameterization and 10 m aperture.
40
Using the Wi-Fi parameterization, as transmitter aperture increases to 50 and 100 meters, the
beaconing system angular resolution improves, producing more accurate estimates and less error. At
the 100-meter aperture, the beaconing system achieves acceptable angle estimation performance, with
estimate errors less than five degrees. At a travel distance of 25 meters, typical for indoor environments,
an angle estimate error of less than five degrees translates to a positional ambiguity fewer than two
meters in radius. Using a transmitter separation of 100 meters and a Wi-Fi channel, the beaconing
system could guide shoppers to store sections or shelves, or direct museum patrons to exhibits.
c =
3e8 m/s
FC =
2.412
GHz
B =
30 MHz
L =
50 m
Fig. 5-2. Simulation results for Wi-Fi parameterization and 50 m aperture.
The “sawtooth” characteristic shown in Fig. 5-2 and replicated in subsequent figures results
from angle estimates shifting to adjacent bins. Assuming sufficient signal-to-noise ratio and transmitter
baseline, as the receiver angle increases, the beaconing system selects the angular bin that contains the
authentic transmitter-to-receiver angle (refer to the discussion associated with Fig. 4-5). This angle bin
has width and comprises a range of angles, leading to nonzero beaconing system error. As the authentic
angle increases within a beaconing system bin, the system initially overestimates the transmitter-to-
receiver angle by selecting the angle in the middle of the bin. The authentic angle then increases until
it matches the value at the center of the bin, producing zero estimate error. The authentic angle continues
41
to increase, while the estimate remains at the center of the bin. Therefore, the estimate underestimates
the angle, resulting in negative error. Finally, the authentic angle increases into the next estimate bin,
and the characteristic repeats, generating the sawtooth shape in estimate error.
c =
3e8 m/s
FC =
2.412
GHz
B =
30 MHz
L =
100 m
Fig. 5-3. Simulation results for Wi-Fi parameterization and 100 m aperture.
The software simulation then shifted the MTR beaconing system parameter set to explore the
FCC-unlicensed ISM frequency band centered at 915 MHz. The 915-MHz unlicensed band
encompasses 26 MHz of bandwidth, and while typical operations in this band feature narrowband
transmitters, FCC regulations permit utilization of the entire frequency range concurrently. The
following simulations employed all available spectrum at 915 MHz to maximize MTR angular
resolution. As this band provides similar bandwidth to that of the 2.4-GHz ISM spectrum, the beaconing
system performs roughly equivalently using each ISM band. Once again, the beaconing system yields
angle estimates with acceptable error (less than five degrees) using a transmitter baseline of 100 meters.
At this carrier frequency, the MTR beaconing system benefits from reduced interference, as fewer
unlicensed operators employ the 915-MHz band due to its relatively narrow spectral width.
Additionally, the beaconing system may attain longer functional distances due to more favorable
propagation characteristics.
42
c =
3e8 m/s
FC =
915
MHz
B =
26 MHz
L =
100 m
Fig. 5-4. Simulation results for 915 MHz ISM parameterization and 100 m aperture.
The modified transmitted reference technique may provide value at additional radio frequency
bands. For instance, MTR beaconing systems operating in the frequency spectrum likely to be used for
fifth-generation (5G) cellular communications gain access to signal bandwidths exceeding one
gigahertz, an increase of a factor of 30 or more relative to the 2.4-GHz ISM band. Signal processing
techniques that employ coherent processing across the entire frequency band must utilize complex and
processing-intensive schemes to mitigate the undesirable effects of multipath propagation.
Additionally, these coherent systems must cope with unequal impacts of interference across the band,
resulting in a frequency-variable signal-to-noise ratio.
In contrast, the modified transmitted reference technique requires no such equalization, and
copes with multipath propagation and frequency-selective distortion by combining multipaths into a
single time-frequency bin. The MTR beaconing system can leverage the inherent advantages of the
modified transmitted reference technique to employ the ultra-wideband 5G cellular channels without
requiring complex processing that, in addition to consuming considerable resources, begets
susceptibility to noise and interference. MTR beaconing systems can effectively use the increased
spectral width of the fifth-generation band to provide high-accuracy beaconing.
43
ii. Acoustic Results
The final MATLAB® simulations explored the use of acoustic frequencies for hardware
experiments. Because sound propagates much more slowly in air than does radio frequency energy
(approximately one-million times more slowly), the beaconing system can use greatly reduced signal
bandwidth and transmitter aperture to achieve the same angular resolution produced by RF beaconing
systems. The gains of using sound rather than RF are not without costs: by operating at audio
wavelengths and with narrower transmitter baseline, the beaconing system reduces its functional range
in both distance and angle (limited field of view). Despite these challenges, the acoustic test bed results
in a validation of the MTR technical approach and provides confidence in its extension to radio
frequencies. Fig. 5-5 illustrates acoustic beaconing performance using a 10-meter aperture, while Fig.
5-6 depicts beaconing performance using a 5-meter baseline.
In environments with high SNR and strong coherence and phasing between transmitters,
beaconing systems can achieve finer angular resolution than that generated by the simulated system.
By interpolating between time delay bins, beaconing systems may derive information beyond that
provided at the system bandwidth. Using this and other techniques, such as long integration periods,
beaconing systems may perform more accurately, and also may enhance accuracy by using higher
carrier frequencies. However, systems employing such techniques require precise phase coherence
between transmitters, as mismatches greatly inhibit interpolation capability and provide inaccurate and
false results. Such systems can only operate in environments with high SNRs, as interpolation and
integration techniques fail otherwise. Inexpensive beaconing systems may perform optimally using
acoustic frequencies as opposed to radio frequency signaling. Acoustic beaconing systems benefit from
relaxed timing requirements due to the slower propagation speed of sound in air.
Fig. 5-5 illustrates the benefits of acoustic frequencies: using only a 10-meter transmitter
separation and an inexpensive commercial sound card for MTR signal processing, the acoustic
beaconing system achieves angle estimate accuracy equivalent to that of the ISM-band system.
44
This audio beaconing system induces unique challenges not experienced by the RF systems
with respect to practical implementation. The acoustic system broadcasts at audible frequencies, facing
considerable ambient interference and irritating those near the system. Additionally, the acoustic
beaconing system has limited reach due to its narrow baseline and the relatively significant attenuation
of sound in air. The acoustic beaconing system may overcome these issues to an extent by shifting its
carrier frequency to ultrasonic. At ultrasonic frequencies, the beaconing system limits its potentially
aggravating effects, and gains access to additional bandwidth. However, using ultrasound, the MTR
beaconing system must use specialized transmitter and receiver hardware, and compensate for the
variability of the communications channel over the frequency band. Despite the challenges imposed
by acoustic operation, the audio MTR beaconing system performs capably while employing
comparatively short transmitter baselines.
c =
343 m/s
FC =
11.025
kHz
B =
22.05
kHz
L =
10 m
Fig. 5-5. Simulation results for acoustic parameterization and 10 m aperture.
Fig. 5-6 shows that an audio modified transmitted reference beaconing system using a 5-meter
transmitter baseline delivers accurate angle estimates within the -30 degree to 30 degree field of view.
While this beaconing system may have a limited field of view, it produces accurate angular estimates
within the narrow range.
45
c =
343 m/s
FC =
11.025
kHz
B =
22.05
kHz
L =
5 m
Fig. 5-6. Simulation results for acoustic parameterization and 5 m aperture.
iii. Incorporation of Analytic Multipath Propagation
Another set of simulations studied the impact of multipath propagation on the performance of the
modified transmitted reference system. The simulation first proceeded without multipaths, employing
only the direct transmitter-to-receiver path. The simulation thus created a performance baseline, shown
in Fig. 5-7. Using the 5-meter aperture, the simulation generated a beaconing result with minimal error
across a wide array of receiver angles.
The simulation then added multipath propagation components, scaled in amplitude relative to
the direct path. The simulation applied five multipaths to the direct path, each with a linear amplitude
scale factor between zero and one. First, the simulation configured all multipaths to arrive within
𝑁(𝑠2 − 1) samples of the direct path. Using the modified transmitted reference technique, such
multipath components contribute energy to the same time-frequency bin of the receiver correlation
result. As such, multipaths arriving with 𝑁(𝑠2 − 1) samples contribute useful energy to the received
signal, and enhance, rather than degrade, beaconing performance. Due to the resolution limits of the
beaconing system as parameterized in the simulation, the five-multipath beaconing performance
matches the baseline result, as depicted in Fig. 5-8.
46
c =
343 m/s
FC =
11.025
kHz
B =
22.05
kHz
L =
5 m
Fig. 5-7. Simulation results for acoustic parameterization and 5 m aperture (direct path only).
c =
343 m/s
FC =
11.025
kHz
B =
22.05
kHz
L =
5 m
Fig. 5-8. Simulation results for acoustic parameterization and 5 m aperture (close multipaths).
The simulation then applied five multipaths in addition to the direct path as before, but spaced
the multipaths to arrive at time lags beyond 𝑁(𝑠2 − 1) samples. Multipaths arriving beyond this lag
contribute energy to time-frequency bins other than the bin for the authentic receiver angle. As shown
in Fig. 5-9, multipaths arriving outside the maximum time lag have the potential to generate angle
47
estimate errors and/or missed detections. In the figure, gaps in the blue and black lines denote missed
detects, as the beaconing system could not achieve timing synchronization and provide an angle
estimate during this interval. The system failed to achieve timing synchronization when a multipath
caused an errant peak in the receiver correlation surface, overwhelming the transmitter-encoded peak
by producing significant energy at an incorrect time-frequency bin.
Clearly, the MTR beaconing system achieved data frame synchronization more frequently at
angles greater than zero than at angles below zero. This result arises due to the windowed processing
architecture of the beaconing receiver. For the analytic multipath simulation, the receiver captured more
signal energy in its processing window – and therefore achieved a higher SNR – at receiver angles
greater than zero, enabling an improved data frame synchronization rate.
c =
343 m/s
FC =
11.025
kHz
B =
22.05
kHz
L =
5 m
Fig. 5-9. Simulation results for acoustic parameterization and 5 m aperture (spread multipaths).
The modified transmitted reference analytic simulations verified the theoretical predictions
regarding the performance of the MTR beaconing system. The simulations additionally confirmed that
the technique adds value in beaconing applications by resisting multipath-induced performance
degradation. The simulations finally illustrated that, while the MTR technique performs reliably in
certain environments, severe communication channels worsen beaconing performance.
48
B. Incorporation of Experimental Data
To bridge the aforementioned software simulations and forthcoming experimental results, a set of
simulations included authentic communication channel data. These simulations utilized underwater
acoustic data obtained from the World Ocean Simulation System (WOSS) database [18]. The WOSS
data was extracted from the Atlantic Ocean, west of the Florida coast near Fort Lauderdale, at
coordinates North latitude 26.0667°, West longitude 79.8072°. The acoustic WOSS data were
processed using the BELLHOP acoustic ray tracing software, which generated the channel impulse
response from the information extracted from the WOSS database [19]. The BELLHOP software
produced an impulse response containing multipath components, as depicted in Fig. 5-10.
Fig. 5-10. Acoustic data channel impulse response.
For improved authenticity, the simulations incorporating the WOSS data employed a unique
impulse response for each transmitter-to-receiver channel. The simulations replaced the analytic free-
space path loss channels used in previous simulations with those selected from the acoustic database.
The simulations convolved the transmitted signal with the WOSS impulse response to generate the
received waveform. The simulations added a random instantiation of additive white Gaussian noise to
49
each component of the WOSS channel-effected signal, then performed the MTR beaconing system
processing on the resultant waveform.
While the communications channel remained fixed during the simulations, the modified
transmitted reference beaconing parameterization shifted to yield varying results. As discussed in
Chapter 4, the MTR settings, particularly the time scale, determine multipath integration and thus
performance in an environment that supports considerable reverberation. Table 5-3 presents the MTR
settings for the first simulation using the WOSS data.
Table 5-3. Simulation parameters employed during WOSS software simulation #1.
Simulation
Parameter
Parameter
Symbol
Value(s) during
Simulations
Parameter
Units
Data Symbol Length 𝑁 65536 samples
Time Scale 1, 2 𝑠1, 𝑠2 1.05, 1.01 –
Time Delay 1 𝜏1 4096 samples
Propagation Speed 𝑐 343 meters per second
Carrier Frequency 𝐹𝐶 11.025e3 Hertz
Signal Bandwidth 𝐵 22.05e3 Hertz
Transmitter Baseline 𝐿 50 meters
Signal-to-Noise Ratio 𝑆𝑁𝑅 10 decibels
Ground Truth Angle(s) 𝜃 -30 to 30 in steps of 1 degrees
Using the parameterization in Table 5-3, the MTR beaconing system integrates multipath
arrivals within 1
𝐵|𝑠−1|=
1
44.1𝑒3∗|1.05−1|= 454 microseconds of one another into a single time-frequency
bin. As shown in Fig. 5-10, multipaths arrive as long as 100 milliseconds apart, indicating that the
WOSS simulation #1 MTR parameterization did not fully integrate the received energy into a single
time-frequency bin. After receiving a signal comprising both the direct path and multipath energy, the
MTR beaconing system generated the desired correlation peaks, as well as unwanted peaks resulting
from the arrival of multipaths.
Fig. 5-11 presents the MTR correlation surface obtained by processing the MTR signal
following convolution with the WOSS channel impulse response. The correlation surface features three
significant peaks. The leftmost peak with the smallest time delay derives from the direct path, and this
50
peak arises at the transmitter-encoded time delay. The other two prominent peaks arise from a multipath
of the transmitted signal following a unique propagation path. The transmitter-encoded time delay
remains amongst the peaks, but the other peaks generate erroneous results if selected. Additionally, the
multipath-induced peaks may yield a false negative due to their cluttering of the MTR correlation
surface.
Fig. 5-11. MTR correlation surface following signal interaction with WOSS channel.
Fig. 5-12 depicts the angle estimates provided by the MTR simulation #1 system in the WOSS
and AWGN channel. The MTR system frequently estimated the correct receiver angle, but sporadically
selected the wrong correlation peak as the peak resulting from the receiver. In these instances, the MTR
system provided an incorrect receiver position, and the estimate error increased dramatically. The
beaconing system overestimated receiver angle on each of the 16 erroneous hypotheses of 61 total,
indicating that all multipath arrivals that generated angle estimate errors arrived after the direct (desired)
path from the receiver to the MTR receivers.
51
Fig. 5-12. Simulation results using WOSS environment data with coarse MTR time scales.
Although each of the erroneous results appears to generate the same angle estimate, the
incorrect estimates in fact track the authentic angle and vary from one another. Each incorrect estimate
results from the MTR receiver selecting the center of the three prominent correlation peaks in Fig. 5-11
as opposed to the correct, leftmost peak. This erroneous peak results from the first significant multipath
to arrive at the MTR beaconing receiver following the arrival of the desired direct-propagation signal.
As such, all erroneous estimates exceed the authentic receiver angle (the chosen peak produces a higher
time delay value and thus, a greater angle). Additionally, the incorrect angle estimates all result from
the same difference in time delay between the authentic receiver angle and the erroneous selection.
However, the delay-to-angle mapping constitutes a nonlinear transformation. Consequently, the
inaccurate measurements, deriving from time delays in the 8000- to 9000-sample range, generate a
much flatter slope (change in estimated angle vs. change in ground truth angle) than that produced by
the accurate estimates, which result from delays in the 3000-sample range.
52
A second MTR simulation using the WOSS channel data incorporated the same parameters as
those listed in Table 5-3, but altered the MTR time scale setting in an effort to integrate more multipath
energy into each time-frequency correlation bin. This simulation defined a beaconing system using time
scales of 1.001 and 1.005, allowing the system to integrate multipaths arriving within 1
𝐵|𝑠−1|=
1
44.1𝑒3∗|1.005−1|= 4.54 milliseconds of one another into a single bin. Due to the extreme nature of the
underwater acoustic channel, with multipath arrivals separated by hundreds of milliseconds, the MTR
system could not fully integrate all multipath arrivals despite the finer time scales. Nonetheless, as
illustrated in Fig. 5-13, the beaconing system utilizing finer time scales (those closer to unity) provided
a higher percentage of accurate estimates, with fewer erroneous results. Using finer scales, the MTR
beaconing system provided only ten erroneous estimates, a 37.5 percent reduction in error relative to
the performance of the beaconing system using coarser time scales.
Fig. 5-13. Simulation results using WOSS environment data with fine MTR time scales.
53
The simulation of the modified transmitted reference beaconing system using the WOSS acoustic
data permitted the analysis of system performance in an authentic environment. Concurrently, the
WOSS-data simulations reduced the complexity of the investigation relative to hardware
demonstrations by fixing aspects of the study, such as the precise nature of the channel impulse
response, that naturally vary across individual hardware tests. These simulations confirmed that the
MTR time scale enables flexible performance characteristics, allowing a system to integrate a tunable
amount of multipath energy. Using a parameterization appropriate for the environment in which it
operates, a modified transmitted reference beaconing system achieves robust performance despite
adverse channel effects.
The MATLAB® software simulations of the modified transmitted reference beaconing system
enabled the detailed investigation of the technique without requiring expensive investments in hardware
and embedded algorithm development. The simulations further permitted the study of the modified
transmitted reference technique using a variety of beaconing system configurations. The software
modeling also supported the repeated and repeatable deployment of the beaconing system in
unfavorable communications channels without the need to physically locate and analyze such
environments.
The simulations replicated theoretical expectations for beaconing system angle estimate
accuracy at acoustic and radio frequencies. The software trials confirmed the utility of the MTR
technique in adverse communications channels, particularly those encumbered by significant multipath
energy. As a specific example, the simulations investigated the performance of the MTR beaconing
system in an authentic underwater acoustic environment, exercising the algorithm in a manner that
hardware experiments could not. While the MTR algorithm enables significant resilience, the
simulations identified the performance limits of, and compromises required by, MTR operation in
challenging channels. The software investigations collected and examined data that supported the
theoretical development, and informed and improved the MTR hardware experiments.
54
6. MTR BEACONING EXPERIMENTATION
To confirm the practical utility of the modified transmitted reference technique for beaconing,
an experimental hardware-in-the-loop testbed was created. The hardware testbed operates at acoustic
frequencies to enable complete beaconing system functionality using inexpensive and
flexible/reconfigurable commercial hardware. Testbed replication of theoretical and simulation results
at acoustic frequencies supports extrapolation of simulation outcomes at radio frequencies to RF
hardware performance. Stated succinctly, if hardware performance matches simulation results and
theoretical expectations at acoustic frequencies, the same trend can be assumed to hold at RF.
The MTR acoustic hardware testbed comprises several components, all controlled by a
MATLAB® software processing script housed on a computer. The MATLAB® script directs the
hardware peripherals, and performs the MTR signal processing technique at the transmitter and
receiver. The script commands the sound card within the computer to dictate both transmitter and
receiver audio signal flow. The script additionally controls two UE MEGABOM speakers, which serve
as the spatially separated signal sources. The processing code interfaces to a Zoom H5 audio recorder,
which serves as the remote receiver (aboard the receiver) for the hardware testbed. Fig. 6-1 depicts a
block diagram of the hardware testbed.
The MTR MATLAB® processing script controls acoustic hardware tests by conducting a series
of coordinated commands. The processing script first generates the transmit signal samples using user-
defined parameters. The script then transmits the samples from the speakers by way of the computer
sound card. Concurrently, the script receives audio data samples recorded by the Zoom H5 via the Line
Out port on the device. As the received samples stream to the processing script, the code performs
modified transmitted reference signal processing to detect receiver presence and decode receiver angle
relative to the transmitter baseline. The processing script finally generates and displays results both in
real-time (raw angle measurements displayed to the screen) and for post-analysis (angle vs. time data).
55
Fig. 6-1. Modified transmitted reference acoustic hardware testbed.
The MTR hardware testbed permits user definition of signal processing parameters. Table 6-1
lists the parameters employed during hardware trials. The data symbol length and bandwidth parameters
in Table 6-1 define an update rate of approximately 4.10 seconds, while the total trial duration permits
computation of 30 receiver angle estimates per trial. The hardware testbed utilized a zero-mean white
Gaussian reference signal with a flat spectral envelope from 500 Hz to 3500 Hz.
Table 6-1. MTR hardware testbed trial parameters.
Simulation
Parameter
Parameter
Symbol
Value(s) during
Hardware Trials
Parameter
Units
Data Symbol Length 𝑁 32768 samples
Time Scale 1, 2 𝑠1, 𝑠2 1.05, 1.01 −
Time Delay 1 𝜏1 750 samples
Propagation Speed 𝑐 343 meters per second
Carrier Frequency 𝐹𝐶 4 kilohertz
Signal Bandwidth 𝐵 8 kilohertz
Trial Duration 𝑇 122.9 seconds
56
The MTR hardware testbed instantiates an MTR receiver that performs all functions required
to synchronize to the MTR data symbols and decode data following successful timing synchronization.
The receiver processes 75 percent-overlapped 𝑁-sample blocks of data, searching for a peak in the
MTR correlation surface at time scale 𝑠1. The receiver searches for a correlation peak that exceeds a
pre-determined threshold in only the subset of correlation lags that should contain the synchronization
peak. When the receiver detects a threshold-exceeding correlation peak, it performs timing
synchronization to align with the 𝑁-sample data symbol. The receiver shifts the data buffer forward or
backward by the number of samples required to align the buffer with the start of the 𝑁-sample data
symbol. The receiver adjusts the buffer by 𝛥𝑇 samples, where 𝛥𝑇 is defined by:
∆𝑇 =𝜏𝑑 − 𝜏1
|𝑠1 − 1| samples =
𝜏𝑑 − 𝜏1
𝐵|𝑠1 − 1| seconds (21)
MTR systems that employ coarser time scales (farther from unity) achieve more precise timing
synchronization, but integrate less multipath energy and are more susceptible to performance
degradation in reverberant communications channels. MTR system parameterization must balance
these simultaneous and opposing constraints
Following timing synchronization, the receiver decodes the time delay that defines the time
difference of arrival between the two MTR transmitters. The receiver performs correlation processing
on the 𝑁-sample symbol at time scale 𝑠2, and decodes the maximum correlation peak at that scale. The
𝑠2 correlation peak comprises the encoded time delay 𝜏1, and the time delay, 𝜏𝑠𝑝𝑎𝑡𝑖𝑎𝑙, induced by the
difference in propagation path length between the transmitter 1-to-receiver path and the transmitter 2-
to-receiver path. Because the receiver knows the transmitter-encoded 𝜏1, it can compute the 𝜏𝑠𝑝𝑎𝑡𝑖𝑎𝑙
delay following correlation processing and peak selection.
The receiver finally maps the 𝜏𝑠𝑝𝑎𝑡𝑖𝑎𝑙 delay to a time difference of arrival between the
transmitter paths via the procedure illustrated in Fig. 4-3. Using the approximations noted in Fig. 4-1,
the hardware MTR receiver computes the receiver angle for all detections.
57
To exercise the MTR hardware system, a series of experiments placed the Zoom H5 “receiver”
at various known angles relative to the transmitters and recorded the angle estimates. The experiments
separated the transmitters by approximately two meters (𝐿 = 2 m) and placed the receiver at a radius of
roughly 10 meters from the transmitter baseline. The experiments comprised transmission of 30 MTR
beaconing data symbols for each of 11 receiver angles. During the experiment, the ambient environment
supported signal-to-noise ratio of approximately 10 dB, with significant variation due to fluctuations in
local noise sources. Table 6-2 summarizes the results of the experiments.
Table 6-2. MTR audio hardware experiment results summary.
Authentic
Receiver Angle
(degrees)
Number of
Data Symbols
Transmitted
Number of Data
Symbols
Detected
Receiver Angle
Estimate Mean
(degrees)
Receiver Angle
Estimate Error
(percent)
-50 30 29 -37.66 24.68
-40 30 30 -32.75 18.13
-30 30 26 -26.25 12.51
-20 30 28 -18.93 5.34
-10 30 28 -9.73 2.68
0 30 30 0.00 0.00
10 30 22 9.73 2.68
20 30 25 18.93 5.34
30 30 23 26.25 12.51
40 30 30 32.75 18.13
50 30 28 37.66 24.68
TOTAL 330 299 – 11.79
Table 6-2 indicates that the audio MTR beaconing system achieved a probability of detection
of 90.6 percent, successfully identifying 299 of the 330 transmitted data symbols. The MTR beaconing
system endured dynamic noise from the ambient environment during the experiment, particularly
during collection at angles 10, 20 and 30 degrees. As reflected in Table 6-2, the system detected a
smaller percentage of the transmitted symbols at these angles, likely due to the increased interference
level.
Fig. 6-2 depicts graphically the angle estimates performed by the acoustic hardware MTR
receiver for the 11 test angles. The figure contains 11 lines, each of which signifies an authentic receiver
angle using the simplified geometric assumptions. The figure also overlays the beaconing system
58
estimates as markers. Fig. 6-2 illustrates a tight grouping of angle estimates per authentic angle, with
minimal variation and considerable overlap. The figure additionally demonstrates the accuracy of the
MTR system at angles close to zero. However, as the authentic angle increases relative to zero degrees,
the MTR system provides less accurate estimates. The MTR beaconing system assumes the simplified
geometry described in Fig. 4-1, but this geometry is not satisfied by the audio hardware testbed
configuration. As such, the MTR beaconing system estimates the receiver angle with increasing error
as a function of increasing authentic receiver angle.
Fig. 6-2. MTR audio hardware experiment results graphic vs simplified geometry model.
Due to the physical constraints of the modified transmitted reference acoustic hardware testbed,
the hardware cannot assess MTR beaconing performance across a broad range of angles. The hardware
testbed also does not support fine angular resolution due to baseline constraints, limiting the number of
test angles. To overcome these concerns, the audio testbed altered its configuration following the
aforementioned wireless experiments to support wired testing. Fig. 6-3 illustrates a pictorial block
diagram of the wired configuration: the “spatially separated” sources combine into the line in path of
the Zoom H5, which loops the audio data back to the computer for MATLAB® analysis. This
configuration maintains the MTR receiver processing, but alters the transmitter paradigm by manually
59
introducing the TDOA via time delay of the transmitter 2 waveform relative to the transmitter 1 signal.
Following synthesis of the composite signal (𝑚1(𝑡) and 𝑚2(𝑡)) but prior to broadcasting, the
transmitter shifts each 𝑚2(𝑡) data symbol by a time delay equivalent to the TDOA associated with the
desired transmitter-to-receiver angle. The computer sound card transmitter then emits 𝑚1(𝑡) on the left
audio channel, and the time-shifted 𝑚2(𝑡) on the right audio channel. The Zoom H5 receiver collects
these signals following their combination by an audio hardware adapter.
Fig. 6-3. Alternate MTR audio hardware testbed configuration.
Using the acoustic hardware testbed in wired mode, experiments sought to analyze the accuracy
and precision of the MTR beaconing technique across an array of receiver angles. During these
experiments, the transmitter synthesized the time-offset MTR data symbols to simulate receiver angles
from −70 degrees to 70 degrees. The wired experiment transmitter broadcast data symbols with TDOA
values starting at the −70-degree TDOA and incrementing by the finest resolution – one sample – on
each successive data symbol. The MTR receiver processor decoded the time delay and computed the
receiver angle estimate. Fig. 6-4 plots the MTR estimates as a function of the authentic angle encoded
by the transmitter. The figure depicts that, as expected with a wired configuration, the acoustic hardware
MTR receiver estimates the receiver angle with high accuracy. Fig. 6-5 plots the MTR estimated errors
as a function of the authentic angle encoded by the transmitter. The MTR receiver performs best at
small receiver angles, and performance degrades, albeit only slightly, as angle increases.
60
Fig. 6-4. MTR audio hardware angle estimation vs. authentic angle.
Fig. 6-5. MTR audio hardware angle estimation error vs. authentic angle.
61
As shown in Fig. 6-4 and Fig. 6-5, the MTR beaconing system achieved perfect receiver angle
estimates from approximately −23 degrees to 33 degrees. At angles outside this range, the beaconing
system suffered minimal error, with a maximum estimate offset of 1.05 degrees at approximately −24
degrees. On each side of the errorless estimate range, the beaconing system provided suboptimal
receiver bearings due to missed data symbols, which misalign the estimate with the authentic receiver
angle. The beaconing system may also have generated inferior performance due to the resolution of the
system at angles divergent from zero degrees. Despite nonzero error, the MTR beaconing system
estimated receiver angles with considerable accuracy during wired experiments, confirming the robust
performance delivered by the system during wireless tests.
The wired experiments also provided an opportunity to extend the MTR transmitter baseline
beyond physically realizable lengths to study the impact of increased baseline on hardware beaconing
system implementations. During these investigations, the MTR hardware receiver employed a
transmitter baseline of 200 meters for computations, with all remaining settings retained from previous
hardware experiments. Fig. 6-6 and Fig. 6-7 present the results of tests with the lengthened baseline.
Aligning with theoretical predictions and simulation results, the hardware system used the increased
baseline to enhance receiver angle estimation accuracy, albeit over a narrower range of angles.
Fig. 6-6 plots the MTR receiver angle estimates using the 200-meter baseline as a function of
the authentic bearings, while Fig. 6-7 displays the estimate error. The figures illustrate that the hardware
beaconing system achieved a high degree of estimate accuracy from −35 degrees to 55 degrees. Outside
of this window, the beaconing system failed to determine the receiver bearing, but nonetheless returned
an estimate value. The beaconing system properly synchronized to the 𝑚1(𝑡) signal, and thus advanced
into the angle estimation state. When selecting the correlation lag, 𝜏2, that defines the time difference
of arrival, the beaconing system could not detect the proper peak. The excess time delay, 𝜏𝑠𝑝𝑎𝑡𝑖𝑎𝑙,
induced by the considerable path length difference, exceeded the beaconing system correlation lag
space for the system parameterization used in the experiment. As such, the system failed to search the
62
lag space containing the 𝜏2 lag, and selected a random delay rather than the authentic lag, resulting in
erroneous estimates.
To overcome the field of view constraints encountered during the wide-baseline hardware
experiments, a modified transmitted reference beaconing system can increase its symbol duration. This
allows a greater range of valid time delays and thus, a larger span of time differences of arrival.
Beaconing systems that employ longer data symbol durations additionally benefit from enhanced
signal-to-noise ratio resulting from the integration of an increased number of data symbols. Beaconing
systems additionally enhance frequency resolution by integrating for longer durations. Conversely,
MTR beaconing systems reduce angle estimate update rate with increasing symbol duration, trading
robustness for speed. The modified transmitted reference architecture, particularly the time scale
parameter, also influences the compromise between beaconing system performance attributes.
Fig. 6-6. Wide-baseline MTR audio hardware angle estimation error vs. authentic angle.
63
Fig. 6-7. Wide-baseline MTR audio hardware angle estimation error vs. authentic angle.
The modified transmitted reference hardware experiments substantiated the results derived in
theoretical analyses and simulations. Using both wireless and cabled configurations, the hardware tests
analyzed a practical implementation of the MTR technique. The experiment results aligned with those
produced by software trials, and also revealed robustness to the realities of hardware systems.
Inexpensive sound cards feature inconsistent sample rates, and speakers and microphones deliver
directionality that may contribute to suboptimal performance. Despite the inherent challenges of the
hardware, and the significant potential for multipath propagation within the environment in which the
hardware operated, the MTR beaconing system consistently delivered accurate angle estimates. The
experimentation supported only limited beaconing system transmitter baselines, reducing the field of
view of the beaconing system. Nonetheless, wired hardware configurations relieved aperture limitations
and supported broadening the field of view. In these experiments, the modified transmitted reference
beaconing system generated angle estimates with minimal error across a broad range.
64
7. CONCLUSION
The modified transmitted reference signal processing technique described in this thesis
possesses many unique characteristics that enable its robust functionality in challenging
communications channels. The MTR technique broadcasts two copies of the same signal, the reference
signal and the modulated offset copy. The MTR algorithm modulates the offset copy relative to the
reference signal via time scale and time delay. Because the MTR transmitter sends two very similar
signals, the receiver employs a simple correlation-based process to reliably extract the encoded data,
typically without complex equalization required by traditional signal processing algorithms.
Additionally, the MTR technique allows the utilization of arbitrary waveforms to convey information.
Conventional embedded reference schemes use only time delay modulation, making them susceptible
to ambiguities from multipath propagation, as multipaths may appear indistinguishable from the
transmitted reference offset copy. The MTR technique mitigates multipath-induced performance
degradations by leveraging its time scale processing dimension to combine multipath energy arriving
over a time interval. When parameterized properly, the modified transmitted reference algorithm
performs virtually identically in channels with many multipaths as in benign environments.
Modified transmitted reference signaling has utility in a number of applications, including
communications, sensing and navigation. In this thesis, the MTR technique is used in beaconing for
radionavigation and acoustic direction finding. Using multiple spatially-separated signal sources and
sensors, a modified transmitted reference beaconing system determines the position of receivers by
measuring time difference of arrival between the receiver and the dispersed receivers. The MTR
beaconing system broadcasts a reference waveform that enables the dispersed sensors to synchronize
in time. The beaconing system also transmits a spatially-segmented signal, which the modified
transmitted reference beaconing receiver utilizes to compute the time difference of arrival. Employing
the known system geometry, the beaconing system converts the time difference information into a
receiver position.
65
In this thesis, the modified transmitted reference beaconing system was analyzed via theoretical
formulation, software simulation and hardware-in-the-loop experimentation. The MTR technique
employs time scale to achieve resilience against multipath propagation, and alteration of the scale
setting enables adjustable performance relative to multipath as well as resolution in time and angle.
Additionally, MTR systems modulate other parameters, such as signal duration and bandwidth, to
modify frequency resolution and other pertinent performance parameters.
Modified transmitted reference simulations reinforced the conclusions of the theoretical
analysis, and explored the impact of adverse communications channels on MTR system performance.
The simulations demonstrated the consequence of the transmitter baseline on angle estimate accuracy,
and found the minimum baseline required to achieve acceptable estimate accuracy across a 60-degree
field of view for a typical MTR reference signal. The simulations incorporated free-space path loss and
multipath propagation effects to impair MTR beaconing performance. The simulations concluded that
the MTR technique enables reliable beaconing in adverse channels, but cannot overcome arbitrarily
severe environments. The simulation finally exercised the beaconing system against environmental data
collected in the field, and illustrated the impact of altering the MTR parameterization.
A series of hardware-in-the-loop experiments confirmed the practical utility of the modified
transmitted reference technique in beaconing. The experimental beaconing system employed
commercial hardware and operated at acoustic frequencies, permitting the use of comparatively short
transmitter baselines while maintaining angle estimate performance. In an indoor environment with
reverberation (acoustic multipath), the MTR hardware beaconing system accurately estimated receiver
angles over a 50-degree field of view.
Through theoretical, simulation and experimental investigation, this thesis evaluated the
modified transmitted reference technique and its applicability for beaconing. The MTR technique
enables reliable beaconing in adverse channels, and may be valuable for indoor navigation when
satellite-based services are unavailable, radionavigation, radar and sonar.
66
MATLAB® SOURCE CODE
Modified Transmitted Reference Simulation with User Parameterization
function MTR_Simulation
%% PARAMETER DEFINITION
% MTR Parameters N = 65536; S = [1.001, 1.005]; T = [4096, 4096]; A = [0.5, 0.5]; Tmin = 200; Tmax = 10000; peakThreshold = 0.6;
% Physical Parameters c = 343; % m/s Fc = 22050; % Hz Fs = 44100; % Hz txSeparation = 5; % meters SNR = 10; % dB
% Simulation Parameters %numSymbols = 1; use_WOSS = 1; targetAngles = -30:1:30;
%% TRANSMITTER AND RECEIVER SCENE INSTANTIATION
receiverYvals = 100 * tand(targetAngles); receiverPositions = [100 * ones(1, length(targetAngles));
receiverYvals];
distFromReference = sqrt(receiverPositions(1, :).^2 +
(receiverPositions(2, :) - round(txSeparation/2)).^2); distFromOffset = sqrt(receiverPositions(1, :).^2 +
(receiverPositions(2, :) + round(txSeparation/2)).^2);
receiverAngleGroundTruth = atand(receiverPositions(2, :) ./
receiverPositions(1, :));
numSymbols = size(receiverPositions, 2);
%% TRANSMIT SIGNAL SYNTHESIS
x = randn(1, N * numSymbols) + 1i * randn(1, N * numSymbols);
[y1,y2] = MTR_Transmitter(x,x,N,T,S,A);
referenceTransmit = x + y1; offsetTransmit = y2;
67
%% COMMUNICATIONS CHANNEL SIMULATION
if ( use_WOSS == 1 )
ir1 = load('bellhopcase1ImpResp.mat'); ir1 = ir1.impRespShort;
ir2 = load('bellhopcase2ImpResp.mat'); ir2 = ir2.impRespShort;
for currSymbol = 0:(numSymbols-1)
referenceTransmit(currSymbol*N+(1:N)) = filter(ir1, 1,
referenceTransmit(currSymbol*N+(1:N))); offsetTransmit(currSymbol*N+(1:N)) = filter(ir2, 1,
offsetTransmit(currSymbol*N+(1:N)));
end
attenuationReference = ones(1, numSymbols); attenuationOffset = ones(1, numSymbols);
else
referenceTransmit = MultipathGenerator(referenceTransmit, 5,
round(N * abs(min(S)-1))); offsetTransmit = MultipathGenerator(offsetTransmit, 5,
round(N * abs(min(S)-1)));
attenuationReference = FSPL(Fc, distFromReference); attenuationOffset = FSPL(Fc, distFromOffset);
end
distDeltas = distFromReference - distFromOffset; % meters timeDeltas = distDeltas / c; % seconds timeDeltas = round(timeDeltas * Fs); % samples
%% MTR RECEIVER SIMULATION
angleEstimates = zeros(1, numSymbols);
for currSymbol = 0:(numSymbols-1)
if ( timeDeltas(currSymbol+1) < 0 ) rxSignal = [attenuationReference(currSymbol+1) *
referenceTransmit(currSymbol*N +(1:N)), zeros(1, N/2 +
abs(timeDeltas(currSymbol+1)))]; rxSignal = rxSignal + [zeros(1,
abs(timeDeltas(currSymbol+1))), attenuationOffset(currSymbol+1) *
offsetTransmit(currSymbol*N +(1:N)), zeros(1, N/2)]; else
68
rxSignal = [attenuationOffset(currSymbol+1) *
offsetTransmit(currSymbol*N +(1:N)), zeros(1, N/2 +
abs(timeDeltas(currSymbol+1)))]; rxSignal = rxSignal + [zeros(1,
abs(timeDeltas(currSymbol+1))), attenuationReference(currSymbol+1) *
referenceTransmit(currSymbol*N +(1:N)), zeros(1, N/2)]; end
noiseSignal = randn(size(rxSignal)); noiseSignal = noiseSignal * 10^(-SNR / 10) * rms(rxSignal(1:(end-
N/2))) / rms(noiseSignal); noiseSignal = noiseSignal - mean(noiseSignal);
rxSignal = rxSignal + noiseSignal;
try angleEstimates(currSymbol+1) =
MTR_Receiver(rxSignal.',c,Fs,N,T,Tmin,Tmax,S,peakThreshold,txSeparation); catch angleEstimates(currSymbol+1) = NaN; end
end
%% DISPLAY RESULTS
%disp(angleEstimates);
figure(136); subplot(211); plot(receiverAngleGroundTruth, angleEstimates, 'b-', 'LineWidth', 2); grid on; set(gca, 'FontSize', 16); xlabel('Ground Truth Angle (degrees)', 'FontSize', 17, 'FontWeight',
'bold'); ylabel('Estimated Angle (degrees)', 'FontSize', 17, 'FontWeight',
'bold');
subplot(212); plot(receiverAngleGroundTruth, angleEstimates -
receiverAngleGroundTruth, 'k', 'LineWidth', 2); grid on; set(gca, 'FontSize', 16); xlabel('Ground Truth Angle (degrees)', 'FontSize', 17, 'FontWeight',
'bold'); ylabel('Estimate Error (degrees)', 'FontSize', 17, 'FontWeight',
'bold');
69
Modified Transmitted Reference Hardware Control Function
function MTR_Acoustic_Hardware_RealTime
%% PARAMETER DEFINITION
% MTR Parameters N = 32768; S = [1.01, 1.05]; T = [4096, 4096]; A = [ 1, 1]; Tmin = 200; Tmax = 10000; peakThreshold = 0.3;
% Physical Parameters c = 343; % m/s %Fc = 22050; % Hz Fs = 8000; % Hz txSeparation = 1.33; % meters
% Test parameters testDuration = 120; % seconds
% Real-time audio interface parameters ai = analoginput('winsound', 0); addchannel(ai, 1); ai.SampleRate = Fs; ai.SamplesPerTrigger = N; ai.TriggerRepeat = inf;
ao = analogoutput('winsound', 0); addchannel(ao, 1); ao.SampleRate = Fs;
[b, a] = butter(5, [500, 3500] / (Fs / 2));
%% TRANSMIT SIGNAL SYNTHESIS
x1 = randn(1, N); x1 = filter(b, a, x1); x1 = x1 - mean(x1);
x2 = randn(1, N); x2 = filter(b, a, x2); x2 = x2 - mean(x2);
[y1,y2] = MTR_Transmitter(x1,x2,N,T,S,A);
referenceTransmit = x1 + x2 + y1; offsetTransmit = y2;
% Equate the transmit power on each channel referenceTransmit = referenceTransmit / rms(referenceTransmit); offsetTransmit = offsetTransmit / rms(offsetTransmit);
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txSymbols = [repmat(referenceTransmit.', 25, 1),
repmat(offsetTransmit.', 25, 1)];
ao = analogoutput('winsound', 0); addchannel(ao, [1, 2]); ao.SampleRate = Fs; putdata(ao, txSymbols);
%% HARDWARE RECEIVER IMPLEMENTATION
start(ai); start(ao);
angleEstimates =
MTR_Receiver_RealTime(ai,ao,testDuration,txSymbols,c,Fs,N,T,Tmin,Tmax,S,p
eakThreshold,txSeparation,b,a);
figure; plot(angleEstimates, '-o');
stop(ai); stop(ao); delete(ai); delete(ao);
end
Generation of Multipaths of an Input Signal
function [sigMP] = MultipathGenerator(sigIn, numMP, maxMPlag)
sigMP = [sigIn, zeros(size(sigIn))];
MPlags = randi([1, maxMPlag], 1, numMP) +6000;
for currLag = 1:length(MPlags)
currMP = [zeros(1, MPlags(currLag)), rand(1) *
sigIn(1:min(length(sigIn), 2*length(sigIn)-MPlags(currLag))), zeros(1,
2*length(sigIn)-MPlags(currLag)-min(length(sigIn), 2*length(sigIn)-
MPlags(currLag)))];
sigMP = sigMP + currMP;
end
end
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