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);

70

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

71

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