INVESTIGATIONS OF RETRODIRECTIVE

ARRAY TRANSPONDERS

by

Rachana M. Shah

A thesis submitted to the Graduate Faculty ofNorth Carolina State University

in partial fulfillment of therequirements for the Degree of

Master of Science

Electrical Engineering

Raleigh

November 2002

APPROVED BY:

Chair of Advisory Committee

ABSTRACT

RACHANA M SHAH. Investigations of Retrodirective Array Transponders. (Underthe direction of Dr. Michael Steer.)

Retrodirective arrays, when illuminated by an interrogator signal, transmit a sig-

nal back towards the interrogator in the same direction as the incoming signal, without

any prior knowledge of the source direction. With a retrodirective array the system

efficiently transmits a signal without any digital signal processing. The added feature

of being frequency autonomous allows it to transmit back at the same frequency as

the incoming signal, without knowing the exact source frequency as well. The system

is modelled using a system simulator from Elanix, SystemView Simulink. The system

shows good retrodirectivity at various frequencies.

ii

Dedication

This thesis is dedicated to my parents Mahesh Shah and Hemlata Shah who have

raised me with a freedom of choice and have given me boundless opportunities. I

also dedicate this thesis to my beloved brothers Aalok and Bhavin, whose words of

encouragement will always be cherished by me.

iii

BIOGRAPHY

Rachana M. Shah was born on 3rd April, 1980 in Ahmedabad, India. She received a

degree in Electronics Engineering in May 2001 from the Dwarkadas J. Sanghvi College

of Engineering, Mumbai, India. She was admitted to the Master’s program at North

Carolina State University in the Fall of 2001. Her interests are in the fields of RF

and Analog circuit design.

iv

ACKNOWLEDGEMENTS

I would like to express my gratitude to my advisor Dr. Michael Steer for his support

and guidance during my graduate studies, research work and thesis preparation. It

was a privilege to be a part of his MARRS research group. Thank you very much.

I would also like to express my sincere appreciation to Dr. Griff Bilbro, and Dr.

Gianluca Lazzi for serving on my M.S. committee and suggestions. I would like to

thank my good friends, Harshit, Priti, Karthik, Sonali, Vikas, Jayanthi who have

been helpful to me.

Most of all, I would like to thank my Mother and Father, who have always stood

by me and made it possible for me to pursue graduate studies. My brother Aalok,

has also been a constant source of motivation.

Finally, I would like to thank Aditya for all his support and encouragement.

v

Contents

List of Figures vii

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Organization Of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Original Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Literature Review 42.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Phased Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Working . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.2 Drawbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Phase Conjugation Arrays . . . . . . . . . . . . . . . . . . . . . . . . 72.3.1 Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.2 Drawbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Self Phased Antenna Array . . . . . . . . . . . . . . . . . . . . . . . 132.4.1 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.2 A novel Phase Conjugator Concept . . . . . . . . . . . . . . . 15

3 System Modeling 173.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Retrodirective Array transponder . . . . . . . . . . . . . . . . . . . . 18

3.2.1 Base Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.2 Antenna Array . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.3 Demodulation and Phase Detection of RF carrier . . . . . . . 213.2.4 Phase Conjugation . . . . . . . . . . . . . . . . . . . . . . . . 223.2.5 Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4 Results 264.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.2 Results for a Single Antenna Element . . . . . . . . . . . . . . . . . . 26

vi

4.3 An Array of Phase Conjugating Elements . . . . . . . . . . . . . . . . 284.3.1 In a Line of Sight (LOS) environment . . . . . . . . . . . . . . 284.3.2 In a Multipath Environment . . . . . . . . . . . . . . . . . . . 30

5 Conclusions and Future Research 365.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Bibliography 38

vii

List of Figures

2.1 Linear Phased Array. . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Signals received across the array. . . . . . . . . . . . . . . . . . . . . 62.3 Phase-conjugation property: retro-directivity. . . . . . . . . . . . . . 82.4 Recording on the holographic plate of the interference fringes between

the monochromatic wavefield and a reference plane wave. . . . . . . . 102.5 The illumination of the transparency by the complex conjugate of the

plane reference wave leads to the generation of the complex conjugateof the incident wave. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.6 Principle of PCM. An incident wave is reflected and phase conjugated. 122.7 The effect of PCM on phase velocity discontinuities. . . . . . . . . . . 132.8 Generation of phase conjugate waves at each antenna element. . . . . 142.9 Schematic of a phase conjugating element. . . . . . . . . . . . . . . . 152.10 Signals in the frequency domain. . . . . . . . . . . . . . . . . . . . . . 16

3.1 A Retrodirective Array Transponder in a Multipath environment. . . 183.2 System model of a Base Station. . . . . . . . . . . . . . . . . . . . . . 193.3 Line of Sight environment. . . . . . . . . . . . . . . . . . . . . . . . . 203.4 Multi-Path environment. . . . . . . . . . . . . . . . . . . . . . . . . . 213.5 Block diagram of the Costas Loop. . . . . . . . . . . . . . . . . . . . 223.6 System Model for Demodulation using a Costas Loop. . . . . . . . . . 233.7 System Model for phase conjugation. . . . . . . . . . . . . . . . . . . 24

4.1 System Model for a single antenna element. . . . . . . . . . . . . . . 274.2 Result for a signal arriving with a phase of 0 degree. . . . . . . . . . . 284.3 Result for a signal arriving with a phase of 90 degree. . . . . . . . . . 294.4 Power Spectrum of the output signal. . . . . . . . . . . . . . . . . . . 304.5 Block diagram: An array of phase conjugating elements and a single

LO generator circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.6 Polar plot of linear array of 4 antenna elements. The phase differ-

ence between each element d is λ/2. The phase difference between theelements δ is 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

viii

4.7 Polar plot of linear array of 4 antenna elements. The distance betweeneach element d is λ/4. The phase difference between the elements δ is90. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.8 Separated Multipath signals. . . . . . . . . . . . . . . . . . . . . . . . 334.9 System Model for an array of antenna elements. . . . . . . . . . . . . 344.10 Outputs for multipath signals arriving at 5, 90 and 0 degree. . . . . . 35

1

Chapter 1

Introduction

1.1 Background

Forthcoming mobile communication systems are expected to provide a wide variety

of services, from high-quality voice to high-definition videos, through high data rate

wireless channels anywhere in the world. Due to the rise in demand of high quality

multimedia mobile communication, there has been an increase in high bit rate mobile

communication systems research. This high data rate requires broad frequency bands.

Using higher frequency bands such as microwave, Ka-band, and millimeter-wave,

sufficient broadband can be achieved.

In a high bit rate microwave mobile communication system, the following problems

may arise.

• Inter-symbol interference

The multipath nature of the mobile propagation environment results in the

time dispersion of the channel response. This causes the inter-symbol inter-

ference(ISI) when the bit length is comparable to or smaller than the delay

spread.

• Signal to noise ratio

The required Eb/N0, for obtaining the same bit error rate(BER), is independent

of the transmission bit rate. The transmission power must be proportional to

2

the bit rate to realize the same Nb, since N0 is the receiver RF front end noise.

• Propagation Loss

Propagation loss is mainly introduced due to free space attenuation. In addition

to this, shadowing loss which occurs due to the buildings and the trees increase

the propagation loss. As a result multipath effects have to be taken into account.

The last two problems are related to the signal characteristics in the space domain,

and these can be solved by using an adaptive array antenna or a diversity combiner.

Diversity techniques are used at the base station to overcome multipath fading. The

researches on these temporal and spatial adaptive signal processing algorithms have

been studied for long years [1].

1.2 Motivation

The detrimental effect of multipath fading on data integrity and signal-to-noise ratio

is one of the driving factors in smart antenna research [2]. Smart antennas, using

digital algorithms have the capability of determining the direction of the desired

signal. After applying spatial correlation functions, smart antennas are able to modify

the amplitude and/or time delay of the received signals in such a way that there is an

improvement in the reception of the desired signal. Likewise, the transmitters adjust

beam directions to strengthen the link gain between the transmitter and the receiver.

Smart antennas require lot of digital signal processing.

On the other hand a time division duplex (TDD) retrodirective array has shown

much promise in enabling high efficiency, low cost wireless sensor systems using a

microwave frequency band [3]. The retrodirective array is able to radiate a signal in

response to an interrogator signal in a direction same as the incoming signal direction,

without any prior knowledge of the arrival direction. In addition to this, it can

transmit at a frequency the same as that of the incoming signal without knowing the

source frequency. The retrodirective array requires less digital signal processing. This

is a main advantage over smart antennas. The array is modelled using the system

simulator SystemView.

3

1.3 Organization Of Thesis

Chapter 2 is a review of the issues in Phased Arrays and Phase Conjugating arrays.

In Chapter 3, a system model of the retrodirective array transponder is discussed.

Chapters 4 and 5 discuss the results, conclusions and future work.

1.4 Original Contributions

A prototype 4-element retrodirective antenna array was built in University of Cali-

fornia, Los Angeles [3]. It relies on the principles of phase conjugating mixers. The

antenna array was built on RT/Duroid 25 mil εr = 10.2. The quasi-Yagi antenna

was used, whose radiation pattern is quite broad. Also, it has low adjacent-element

mutual coupling. The array spacing was chosen to be half-wavelength at 5.2 Ghz.

Retrodirectivity was measured by transmitting a single tone interrogation signal

at a fixed position and measuring the radiated response of the retrodirective array.

The observation was that the array is able to track the position of the interrogator

well. The system architecture returns a signal at exactly the same frequency of the

interrogator signal. Thus frequency autonomous was achieved. By modulating the

array response with a 25 Khz sinusoidal signal, the receiver can distinguish between

the return signal and the interrogator signal. Thus, the functionality of the array as

a information transponder is demonstrated.

4

Chapter 2

Literature Review

2.1 Introduction

In recent years, many RF/Microwave systems have been designed that are imple-

mented using the directed beam forming capability. These systems are used for

various military and civilian communication applications. These systems are located

on wireless platforms such as land vehicles, aircraft and space vehicles. In addition

to this the environment in which these platforms are being operated in is congested.

Therefore it is necessary to use technologies such as multiple frequencies, code division

multiple access, or directed RF transmission in order to obtain signal isolation.

2.2 Phased Arrays

For many years, there has been an interest in dynamically constructing desired wave-

fronts of electromagnetic waves. A significant amount of theoretical and experimental

work has been developed on this subject. The development of such techniques in the

microwave and millimeter-wave regime has concentrated on phased array antennas.

Phased arrays are a type of smart or adaptive antenna that modifies its receive or

transmit characteristics in order to enhance the antenna’s performance. Smart an-

tennas are important for reducing the deleterious effects of intentional jamming of

signals, unintentional co-channel interference, and multipath.

5

Phase Shifters

Elements

d

Scan

Figure 2.1: Linear Phased Array.

2.2.1 Working

In radio systems, directed RF transmission or beam steering may be accomplished

by switching antenna elements or by changing the relative phases of the RF signals

driving the elements. In the phased array system only the phase of the current is

controlled. The amplitude taper is unchanged as the beam is steered through the

array. A one-dimensional phased receiving array is shown in Figure 2.1.

A linear array of n-elements are spaced d wavelength apart. Each element drives

a phase shifter. The outputs of these phase shifters are summed to form the input to

the receiver. The plane wave arriving at angle θ0 from the array normal travels an

increasing incremental distance d sin θ0 to each successive element. The phase shift

across the array due to the planar wave is

ψn = knd sin θ0 (2.1)

where

x = nd defines the element locations

k = 2π/λ defines the wave number.

The function of the bank of phase shifters is to compensate for this linear phase

progression across the array. There is a need to co-phase all incoming received signals

6

n 1

nj1

n

exp

Figure 2.2: Signals received across the array.

arriving from the direction θ0. The following equation is used to co-phase the incoming

signals.

φn = −knd sin θ0 (2.2)

The phase sifters and the summer constitute the beamformer. The phase shifters

constitute the beam steerer which is used to co-phase all the signals received across

the array. Figure 2.2 shows the received signals prior to their passage through the

phase shifters. The same principle holds for the two-dimensional array.

2.2.2 Drawbacks

Although the principle of beamforming becomes simple, using phased arrays, many

problems arise when they are used. Unlike the continuous aperture, at each N inde-

pendent element locations, radiation field needs to be separated and phase controlled.

A minimum of N separate antenna elements is needed. Each element requires a phase

shifter, and these elements need to be connected to a RF summer or an equivalent

interconnecting network.

In general, the large amounts of hardware associated with a large array provides

strong motivation for low-cost, efficient array modules. It also provides motivation for

7

novel and efficient system design that places minimum requirements upon the array

modules. An example is the use of quantized phase shifters and the use of only three

or four bits to specify a phase shift. Special techniques such as adding a random

phase shift to each quantized phase shifter have been devised to minimize the effects

of course quantization.

Another technique exists to calculate the narrow beam tracking, essentially devel-

oped in 1955 called the phase conjugation method, which is described in detail in the

next section.

2.3 Phase Conjugation Arrays

The phase conjugation arrays can be thought of as automatically configured phased-

array systems, which on illumination by an incoming signal, is capable of directing

their outgoing signals back to the illuminating sources. In other words, a phase

conjugation array time reverses the incident signal and precisely returns it to the

original source location. This phenomenon occurs independent of the complexity of

the medium. The time reversal procedure can be accomplished by the implementation

of a retransmission procedure. The medium fluctuations is embedded in the received

signal so that if retransmission can occur on a time scale, less than the dominant fluc-

tuations, the medium variability will be eliminated since one propagates and undoes

the variability. This procedure greatly avoids the digital circuit speed ‘bottle-neck’

related to conventional smart antenna systems.

2.3.1 Idea

Phase conjugation, in general, utilizes the nonlinear susceptibility of a medium to

reverse the phase factor of an incoming wave [4]. A phase conjugate wave propagates

backward. It has the same wavefronts as those of the incoming wave, as shown in

Figure 2.3.

This unique property of phase conjugating waves has found many applications

including automatic pointing and tracking, phase aberration correction, and phase

8

Phase

Conjugate

Figure 2.3: Phase-conjugation property: retro-directivity.

conjugate resonators. To further illustrate the phase conjugating properties consider

an EM wave propagating along the positive z -direction. Its electric field can be

written as

E = A(r)ei[ωt−kz−φ(r)] (2.3)

where

ω = angular frequency

k = wave number of the EM wave.

The amplitude A and the phase φ are real functions of position r. Normally, A is a

slow-varying function of z compared with ei[ωt−kz−φ(r)], therefore the wave propagation

can be understood in terms of the motion of wavefronts, which are three-dimensional

surfaces defined by

kz + φ(r) = constant (2.4)

The phase conjugate wave of Equation (2.3) is defined as

EC = A(r)ei[ωt+kz+φ(r)] (2.5)

Comparing Equations (2.3) and (2.5), it is shown that the two waves have the same

wavefronts at any point in space, but they travel in opposite directions. Also notice

that the conjugate wave can be obtained by a time reversal t → −t transformation

or by taking the complex conjugate only of the spatial part of the electric field.

9

Consider a plane wave propagating through a distorting medium. Due to the non-

uniform distribution of refractive index n(r), the incident wavefronts are no longer

planar after passing through the distorting medium. Equations (2.3) and (2.5) have

shown that the conjugate wave has the same wavefronts as those of the incident

wave through both space and the distorting medium. Consequently the distortion

is automatically removed [5]. Another important feature of phase conjugation is

that there is a need to generate only the conjugate field EC on one plane, this field

propagate backward and remain the phase-conjugate field of E everywhere [5].

This enabled us the possibility of accomplishing microwave and millimeter- wave

phase conjugation using electronic-mixing phased-array system.

2.3.2 Drawbacks

Most of the phase conjugation development has been concentrated in the optical and

acoustic regime. Efforts to extend this technique to microwave and millimeter-wave

frequencies have encountered severe difficulties due to small non-linearity of natural

materials and the low-power density sources at these frequencies. The time reversal

principle is an extension of optical phase-conjugated mirror. If P (r, ω) is the temporal

Fourier transform of p(r, t), then the temporal Fourier transform of p(r,−t) is P ∗(r, ω).

Therefore, time reversal of pulsed signals is equivalent to the phase conjugation of

monochromatic waves. However, this equivalence is only valid fundamentally, there

are some fundamental differences between these two techniques [4].

Nonlinearity

An optical Phase Conjugated Mirror (PCM ) requires non-linear effects to measure

and to conjugate the phase information of a monochromatic field, since the time

response of optical detectors are very long compared to the period of optical waves.

The optical phase conjugation can be understood as a real time holographic method.

The basic principle of holography consists in the superposition of the incident

wavefield with a reference wave, and in the measurement of the resulting interference

fringes on the holographic plate. The interference of the two waves transforms the

10

Film

Figure 2.4: Recording on the holographic plate of the interference fringes betweenthe monochromatic wavefield and a reference plane wave.

phase information of the incident wave, that is necessary but not otherwise available.

This is a non-linear process.

After the development of the holographic plate, a photographic transparency is

obtained with the information of the incident wave and its complex conjugate. An

approximate illumination of this photographic transparency leads to the generation

of the complex conjugate of the incident wave. This technique involves two reference

waves, one during the recording step and a second one during the reading step.

Figures 2.4 and 2.5 explain the principle of phase-conjugated holography.

In case of PCM, the holographic plate is replaced by a non-linear photorefractive

medium that spatially changes its photorefractive index in reaction to the interference

of the incident wave with one of the reference waves. The refractive index changes are

due to electrooptic effects. Interference between the incident beam and the reference

beam results in phase volume gratings in the photorefractive media. The second

reference wave is then diffracted by this resulting grating , thus generating the complex

conjugate of the incident wave. This type of wave mixing is called four wave-mixing.

In the time reversal technique, wave mixing is not required and non-linear effects

are not necessary. They are replaced by the use of linear reversible transducers linked

11

Transparency

Figure 2.5: The illumination of the transparency by the complex conjugate of theplane reference wave leads to the generation of the complex conjugate of the incidentwave.

to a read-write memory. All these steps are linear.

Continuous Regime

In optics, once the photorefractive medium has modified its photorefractive index, a

continuous state is reached. That means that the concept of time disappears from the

process. All the continuous monochromatic waves generated in the aberrating media

and in the photorefractive medium will interfere. This requires laser coherence length

to be much longer than dimensions of the circuit. Due to causality requirements,

there is a transient period during which the different waves cannot interfere. In the

time-reversal experiments, the ultrasonics signals are brief and all the processes occur

in the transient regime

In the continuous regime, the interference between the incident wave and the any

subsequent multiply reflected waves between the PCM and the aberrator play a very

particular role. It can be shown that the resulting interference between all these

waves allows the exact compensation of the distortion due to the aberrating medium.

A PCM works in a continuous mode and phase conjugates an incident wave, for

example, a plane wave of amplitude A propagating in medium 1 of sound velocity c1.

12

P.C. M

Figure 2.6: Principle of PCM. An incident wave is reflected and phase conjugated.

Refer to Figures 2.6 and 2.7.

Consider the effect of inserting a new medium 2 as shown in Figure 2.7, of velocity

c2 between the source of the incident wave and the PCM. An initial reflected wave of

amplitude T results. The transmitted wave T is then phase conjugated by the PCM.

This phase conjugated wave is reflected and transmitted through the interface 2 to

1. A new reflected wave comes back to the PCM with new incidence and is phase

conjugated. the process itself repeats periodically. The observation here, is that the

set of waves, generated in medium 1 from all the phase conjugated waves, produces

a resulting plane wave of amplitude A in the reverse direction of the incident wave

and complete destructive interference in the direction of the initial reflected wave.

Increasing the nonlinear susceptibility by many orders of magnitude can be one

possible solution for the above mentioned efficiency problem. Artificial Kerr media

were found to be have much larger non-linearity than that of natural materials. Using

shaped micro-particle suspensions and microelectromechanical system (MEMS) struc-

tures, volume grating formation for microwave phase conjugation has been demon-

strated with DFWM (four wave-mixing) techniques. Although these artificial Kerr

media have demonstrated χ(3) as high as 10−4cm.s2/g, they have number of intrinsic

problems. Thus, these techniques are not suitable for practical systems and applica-

tions.

13

P.C. M

Figure 2.7: The effect of PCM on phase velocity discontinuities.

2.4 Self Phased Antenna Array

One possible approach to the difficulty encountered in Section 2.3.2, using tradi-

tional DFWM techniques is to do electronic-mixing. Instead of third order non-linear

dipoles, electronic mixing makes use of second order three-wave mixing to provide a

high artificial non-linearity for generating phase-conjugate waves.

Microwave circuits consisting of antennas and mixers, replace the roles of the non-

linear dipoles of a medium. The basic idea behind this approach is to ‘sample’ the

incident wave at different positions of the wavefront using antenna elements. After

sampling, each antenna element generates a phase conjugate current using microwave

mixers. The currents will then excite a phase conjugate field at each sampling point.

The combined field at all antenna elements is the phase-conjugated beam of the

incident beam. This approach of sample-then-mix was first proposed in the 1960′s,

but due to the lack of modern semiconductor and photonic technologies, researchers

did not have practical ways to realize this concept [6], [7].

2.4.1 Approach

The self phased array idea is based on the arrangement shown in Figure 2.8. The

antenna array receives an unmodulated electromagnetic wave. Each antenna element

14

Ln

returnref

out in

Reference Plane

Figure 2.8: Generation of phase conjugate waves at each antenna element.

has its own set of mixers and filters to provide the necessary phase conjugation. The

unmodulated signal travels a certain distance Ln from a reference plane to an antenna

element. Suppose the wavelength of the signal is λ. The phase at the reference plane

φRef is zero. The round trip phase or the return phase is

φReturn = 2(2πLn/λ) + φn (2.6)

To obtain constructive interference at the reference plane, the round trip phase or

the return phase at the reference plane due to each antenna element should be zero.

From Equation (2.6) we get

φoutput = −φinput = −2πLn/λ (2.7)

Thus, we see from Equation (2.7) that to achieve constructive interference at

the reference plane, we need to produce a phase conjugate wave at the output of the

antenna element. That is phase conjugation of RF signal is necessary at each antenna

element for the signal to go back at the source. As long as the phase conjugation is

done to within the same additive constant in phase, retrodirectivity is achieved.

15

Antenna

90 degree at RF frequency

180 degree at LO frequecny

Mixer

Mixer

LO SignalIF Signal

RF Signal

Figure 2.9: Schematic of a phase conjugating element.

2.4.2 A novel Phase Conjugator Concept

For active retrodirective applications, a novel phase conjugator was presented in [8].

This concept makes use of electronic mixing of the signals, to produce the required

phase conjugated signal. The mixing is done using heterodyne techniques. The

schematic is shown in Figure 2.9.

There are two ports in the circuit. One is for the LO signal, while the other port

is the combined RF/IF port. The LO signal is applied in phase to the two channels.

The channels are identical except for the 900 phase delay line for the RF signal. This

approach provides good isolation at the RF/IF port, which is due to the cancellation

of the RF signal.

To achieve phase conjugation, the LO signal is twice the frequency of the incoming

RF signal. The LO from the two channels experiences a 1800 delay combined at the

RF/IF port, giving good LO isolation. This architecture allows an extremely compact

design. The signal when fed to an antenna is transmitted with the same polarization

as that of an incoming signal.

Using normalized values of the LO and RF signal we get

vIF(t) = vRF(t)vLO(t) = cos(ωt + φ) cos(2ωt) (2.8)

This is the expanded as the sum and difference in phase.

vRF,out(t) = vIF(t) ∝ [cos(3ωt + φ) + cos(ωt− φ)] (2.9)

16

RFin LO = 2RFin

0 frequency

RF out

Figure 2.10: Signals in the frequency domain.

The output of the mixer is then bandlimited to get the desired phase conjugated

signal.

vIF(t)BPF−→ cos(ωt− φ) (2.10)

From Figure 2.10 and Equation (2.10), we can see that the IF signal consists of

the negative phase of the RF signal, thus achieving phase conjugation.

17

Chapter 3

System Modeling

3.1 Introduction

A transponder is a repeater which receives, amplifies, downconverts and retransmits

a signal. A retrodirective array transponder is capable of retransmitting a signal

towards the source in the same direction in which it receives. This is accomplished

without the use of phase shifters or digital signal processing. It makes use of phase

conjugation which was explained in detail in Section 2.4.2. The added feature of the

system is that it is frequency autonomous, i.e it retransmits the signal with a frequency

same as the incoming frequency. The response of the retrodirective transponder to a

multipath environment is examined.

An end-to-end retrodirective array transponder was implemented in the simula-

tion environment, SystemView with specifications from real world RF components.

This system simulator allows one to observe what unpredicted effects that the actual

circuits working in concert may have and how it may affect the overall system design.

It also enables the designer in examining various tradeoffs by varying the parameters

of each model. For example, trade off of linearity and gain, or of linearity and drive

level required for reduced spurious output. The multipath environment is simulated

in Matlab, and then incorporated within SystemView.

18

MultipathEnvironment

MultipathEnvironment

Antenna ElementReceiver

Interrogator

Antenna Array Demodulation, Carrier Recovery At Each

Antenna Array

Transmitter

at each elementof RF phase

Detection

Modulation

Phase

Conjugation

SignalInterro

gation

Figure 3.1: A Retrodirective Array Transponder in a Multipath environment.

3.2 Retrodirective Array transponder

A block diagram of the retrodirective array transponder in a multipath environment

is shown in Figure 3.1. The system can be divided into

1. Base Station

2. Reception of the signal

• Antenna Array

• Demodulation at each antenna element

• Detection of RF phase at each antenna element

3. Phase Conjugation of the signals

4. Base Band Modulation

5. Transmission

19

Figure 3.2: System model of a Base Station.

3.2.1 Base Station

The base station, or the interrogator sends a one tone interrogation signal towards

the target. The retrodirective array transponders have a lot of applications that

are military based. The interrogation signal can be some kind of query towards the

intended target.

System Model Implementation

The base station implementation in SystemView is shown in Figure 3.2. A binary

phase shift keying (BPSK) modulated signal is generated by multiplying a sinusoidal

wave by a pseudo-random sequence. The parameters of the PN sequence source is

set to two levels. This generates a signal which has a one fixed phase when the data

is at one level and when the data is at the other level, the phase is different by 180

degree.

3.2.2 Antenna Array

The directivity of an antenna is increased by forming an assembly of radiating ele-

ments in an electrical and geometrical configuration. The total field of an array is

20

d

0

AntennaElements

Figure 3.3: Line of Sight environment.

determined by the vector addition of the fields radiated by each individual element.

Consider a linear antenna array of n elements which are identical. Figure 3.3

shows a line of sight environment, where all signals arrive with the same direction

of arrival (DOA). Let d be the distance between two antenna elements. Assuming

that the signal rays are coming from the same direction at the antenna elements,

i.e., direction of arrival is φ0. To determine the antenna radiation pattern of a linear

array of 4 antenna elements can be found out as in [9].

E = 1 + ejψ + e2jψ + e3jψ (3.1)

where ψ in Equation 3.1 is the total phase difference between the elements.

ψ =2πd

λcos φ0 + δ (3.2)

where

δ =phase difference of the signals arriving at the elements

φ0 = Direction of arrival of the signal.

In a multipath environment, due to reflections, a signal may arrive at an an-

tenna element from one or more directions. The signals may add constructively or

21

1DOA

1DOA

1DOA

2

2

2

Elements

d

Antenna

Figure 3.4: Multi-Path environment.

destructively. Figure 3.4 shows a signal arriving with different DOA’s. The phase

information of a signal is given by ψ which is calculated using Equation (3.2).

The signal transmitted by the base station may or may not suffer multipath fading.

In the case of Line-of-Sight transmission, the signal arrives with the same DOA at the

antenna elements. In a multipath environment, the phase information conveys the

signal’s direction of arrival. The signals in a multipath environment are generated in

Matlab. This data from Matlab is imported in the simulator. The response of the

retrodirective array to this environment is then observed.

3.2.3 Demodulation and Phase Detection of RF carrier

The receiver demodulates the received BPSK signal to recover the RF carrier. A

Costas Loop [10] or a Phase Locked Loop (PLL), can be used to recover the carrier.

This carrier is then used to synchronously demodulate the received signal. From

theory, synchronous demodulation of BPSK data gives the best BER performance.

Figure 3.5 shows a breakdown of the loop where the input is a simple sine wave.

This design employs an NCO (numerically controlled oscillator) that the designer sets

to generate a nominal frequency close to the range of the incoming frequency. The

system mixes (multiplies) the incoming waveform independently with a cosine and

22

LPF

LPF

NCOError Signal

−sin

cos

Signal

Difference Signal

Difference Signal

Figure 3.5: Block diagram of the Costas Loop.

sine wave it gets from the NCO. The system essentially performs a down-conversion.

The difference term signal makes it through each low pass filters (LPF). The goal

over time is to reduce the error term to zero with feedback.

System Model Implementation

A third-order Costas loop, which is used to coherently demodulate PSK signals is

available as a token in the simulator, SystemView. The input to this token is the

BPSK signal. The outputs of this token are the demodulated inphase I(t) and

quadrature Q(t) signals. Also it gives the VCO cosine and the sine waves at its

output. Figure 3.6 shows the demodulation of a BPSK signal using Costas Loop.

3.2.4 Phase Conjugation

The RF signal recovered by the demodulator is used to generate the LO signal required

by the phase conjugating mixers. To achieve the required phase conjugation the LO

signal should be twice the frequency as the RF signal. The required LO frequency is

achieved as follows.

sin(2θ) = 2 cos θ sin θ (3.3)

Thus a LO signal, twice the RF signal can be achieved, if the received RF signal is

multiplied by its delayed version. The LO signal is applied 180 degree out of phase

23

Figure 3.6: System Model for Demodulation using a Costas Loop.

to the mixer inputs.

The LO signal and the RF signals are then fed to a passive mixer. Using normal-

ized values of the LO and RF signal,

vIF(t) = vRF(t)vLO(t) = cos(ωt + φ) cos(2ωt) (3.4)

This is the expanded as the sum and difference in phase, at the output of the mixers.

vRF,out(t) = vIF(t) ∝ [cos(3ωt + φ) + cos(ωt− φ)] (3.5)

The output of the mixer is then bandlimited to get the desired phase conjugated

signal.

vIF(t)BPF−→ cos(ωt− φ) (3.6)

We can see that the IF signal consists of the negative phase of the RF signal, thus

achieving phase conjugation. Also, the frequency of the IF signal is same as the RF

signal, thus achieving frequency autonomous.

24

Figure 3.7: System Model for phase conjugation.

System Model Implementation

Figure 3.7 is a model of a phase conjugating element implemented in SystemView.

The passive mixer token models the classic diode-ring double-balanced mixer. This

mixer is designed to allow the user to directly enter catalog type parameter data.

Because of non-linearity, not only does the desired signal appear at the output, but

an array of harmonic products as well. This model allows the exact specification of

the third harmonic product, which is the dominant spur plus the 2-tone Input IP3.

The model produces all odd harmonics of the LO signal and all harmonics to the 5th

order of the RF signal [11]. The Filter token used here is a 4th order butterworth low

pass filter.

25

3.2.5 Transmission

In cases when the interrogator sends an unmodulated RF carrier or an extremely slow

varying modulated waveform, the incoming RF signal and the outgoing IF signal have

the same frequency. In order to allow base station to recognize between the array

response and the interrogator signal, the outgoing signal is modulated by a sinusoidal

waveform. The signal is then transmitted. The conjugation of the signal’s phase

allows it to be travel towards the source in the same direction in which it receives.

26

Chapter 4

Results

4.1 Introduction

The earlier chapters described the approach towards an system model environment

for design of retrodirective array transponders. In this chapter various results are

presented. The achievement is that the same results are obtained with the current

design environment compared to previous results in [3].

4.2 Results for a Single Antenna Element

Consider the system model in Figure 4.1. The system is composed of three main

subsystems.

1. Transmitter

2. RF carrier recovery and phase detection

3. Phase conjugation

A sinusoidal RF signal of frequency 5 GHz, is transmitted using BPSK modulation.

At the receiver the demodulator, a Costas loop recovers the carrier frequency and

phase. The RF carrier is then used to generate the LO signal. The RF and the LO

27

Figure 4.1: System Model for a single antenna element.

signals are then fed to a passive mixer. The parameters of the LO mixer are set in

accordance with the results obtained in [3].

LO Power = 3 dBm (4.1)

In P1 = −3 dBm (4.2)

In IP3 = 7 dBm (4.3)

Conversion Loss = 0 (4.4)

RF isolation = 20 dBc (4.5)

LO isolation = 20 dBc (4.6)

The LO signal is applied 180 degree out of phase to the passive mixers, in accor-

dance with the phase conjugator described in Section 2.4.2. Increasing the conversion

loss attenuates the output return signal.

28

SystemView

0

0

250.e-12

250.e-12

500.e-12

500.e-12

750.e-12

750.e-12

1.e-9

1.e-9

1

500.e-3

0

-500.e-3

-1

Am

plit

ude

Time in Seconds

Overlay Sink 2, Sink 18

Figure 4.2: Result for a signal arriving with a phase of 0 degree.

The filter at the output of the mixer is a 4th order butterworth low pass filter.

The lower cut-off frequency is set to 5 GHz. It allows the difference frequency to pass

while rejecting the sum frequency.

The response of the retrodirective system for an incoming signal with phase 0 and

90 degree is show in Figures 4.2 and 4.3. The phase conjugated output for a 0 degree

phase is an inphase signal. And for a 90 degree signal, it is out of phase. The power

spectrum of the output signal is shown in Figure 4.4.

4.3 An Array of Phase Conjugating Elements

4.3.1 In a Line of Sight (LOS) environment

In Section 4.2, a single element is modelled. Now, we consider an linear array of 4

elements. At each element the signal arrives in the same direction as was shown in

Figure 3.3.

Consider the block diagram shown in Figure 4.5. The figure is an array of phase

conjugating elements and a LO generator circuit. Associated with each incoming sig-

29

SystemView

0

0

250.e-12

250.e-12

500.e-12

500.e-12

750.e-12

750.e-12

1.e-9

1.e-9

1

500.e-3

0

-500.e-3

-1

Am

plit

ude

Time in Seconds

Overlay Sink 37, Sink 48

Figure 4.3: Result for a signal arriving with a phase of 90 degree.

nal to the antenna element, is a phase conjugating mixer. In this particular system,

a single LO generator circuit drives all the phase conjugating mixers in the transpon-

der. In other words, a LO signal is generated using RF power of one incoming signal.

This LO signal is then used to feed the other phase conjugating mixers.

The array shows good retrodirectivity at various frequencies.

Antenna Radiation Pattern

To observe the radiation pattern for the antenna array, a matlab program is run. The

polar plots for different phase and distance between antenna elements is plotted.

Figure 4.6 is a plot for an array spaced by λ/2. The phase difference between antenna

elements is 0. Thus, field is maximum in the direction normal to the array. An array

of this type is more commonly called as “broadside” array.

Figure 4.7 is a plot for an array spaced by λ/4. The direction of arrival is 90. Thus,

field is maximum in the direction of the array. An array of this type is known as

“end-fire” array.

30

SystemView

-40e+9

-40e+9

-20e+9

-20e+9

0

0

20e+9

20e+9

40e+9

40e+9

60e+9

60e+9

80e+9

80e+9

100e+9

100e+9

120e+9

120e+9

0

-20

-40

-60

-80

dB

mIn

50

oh

ms

Frequency Hz)in Hz (dF = 38.15e+6

Figure 4.4: Power Spectrum of the output signal.

Thus depending on the antenna array spacing and the direction of arrival, a

retrodirective array transmits in a corresponding direction.

4.3.2 In a Multipath Environment

Figure 3.4 shows an array receiving signals from line of sight. Also it receives signals

suffering from multipath. Thus signals arrive with different direction of arrivals.

For the kind of multipath environment described above, the antenna array sees

either a constructive interference or a destructive interference of the incoming signals.

Thus the retrodirective array sees a resultant signal. It transmits a signal in a direction

specified by the resultant signal.

Consider a situation in Figure 4.8. Here the multipath signals are separated before

feeding a retrodirective array. In other words a digital signal processor is required at

the front end which is able to capture each multipath signal. There is an ongoing

research on this topic. Spatial-temporal diversity and MIMO techniques are employed

to receive each multipath signal separately and determine its response.

31

Recovery

Carrier Coupler

Branch Line

Recovery

Carrier Coupler

Branch Line

Carrier

RecoveryX2

Recovery

Carrier

90 deg RF

0 deg RF

LO

LO

CouplerBranch Line

modulated by a RF signal

Base Band Signal

180 deg LO

Multipath Channel

Amp AmpFrequencyMultiplier

Phase Conjugated output

Figure 4.5: Block diagram: An array of phase conjugating elements and a single LOgenerator circuit.

A matlab code is written which generates sinusoidal waves with different direction

of arrivals. The phase information of each individual sinusoidal wave contains the

direction information.

E = A sin ωt + ψ (4.7)

where

ψ = d cos φ + δ (4.8)

In the above equations,

A = amplitude of the incoming wave

d = antenna spacing in radians

φ = direction of arrival

δ = phase difference between the incoming signals.

The matlab outputs are exported to the retrodirective array, in SystemView. The

response of the retrodirective array to these outputs are observed. Figure 4.9 shows a

32

1

2

3

4

30

210

60

240

90

270

120

300

150

330

180 0

Figure 4.6: Polar plot of linear array of 4 antenna elements. The phase differencebetween each element d is λ/2. The phase difference between the elements δ is 0.

system model of a linear array of 4 elements. The system shows 4 metasystems. Each

metasystem is a phase conjugating element, a block in itself. Also, each is fed with

a sinusoidal wave exported from matlab. The LO generator circuit feeds the phase

conjugating elements.

The retrodirective array shows good retrodirective properties, for different direc-

tion of arrivals. In other words, each multipath signal is phase conjugated and thus

sent back on the same direction in which it came from.

The response of the system to the multipath signals is shown in Figure 4.10.

33

1

2

3

4

30

210

60

240

90

270

120

300

150

330

180 0

Figure 4.7: Polar plot of linear array of 4 antenna elements. The distance betweeneach element d is λ/4. The phase difference between the elements δ is 90.

1DOA

2DOA

3DOA

Elements

d

Antenna

Figure 4.8: Separated Multipath signals.

34

Figure 4.9: System Model for an array of antenna elements.

35

5.3in

SystemView

0

0

1.e-3

1.e-3

2.e-3

2.e-3

3.e-3

3.e-3

4.e-3

4.e-3

1

0

-1

Am

plit

ude

Time in Seconds

Overlay Sink 2, Sink 18

0

0

1.e-3

1.e-3

2.e-3

2.e-3

3.e-3

3.e-3

4.e-3

4.e-3

800.e-3

400.e-3

0

-400.e-3

-800.e-3

Am

plit

ude

Time in Seconds

Overlay Sink 21, Sink 34

0

0

1.e-3

1.e-3

2.e-3

2.e-3

3.e-3

3.e-3

4.e-3

4.e-3

1

0

-1

Am

plit

ude

Time in Seconds

Overlay Sink 51, Sink 62

Figure 4.10: Outputs for multipath signals arriving at 5, 90 and 0 degree.

36

Chapter 5

Conclusions and Future Research

5.1 Conclusions

Investigations of retrodirective array transponders is aimed at in this work. An fre-

quency autonomous retrodirective array transponder is modelled in Simulink Sys-

temView, which is a system simulator. The transponder’s primary property of retrodi-

rectivity is checked for various frequencies. Validation has been done by correlating

data from previous results [3].

The simulation of the RF system took parameters from real world components.

For example, RF-LO isolation, IIP3, LO power in a passive mixer. Thus the non-

linear effects of RF circuits were also considered. The parameters were set based on

experiments conducted before [3].

The array transponder generates a phase conjugated signal which has the same

frequency as the incoming RF signal. This enables the transponder to transmit back

a signal in a direction same as the incoming signal’s direction. This greatly improves

the directivity, as energy is concentrated in one direction.

A multipath environment is simulated using Matlab. The signals from this multi-

path environment are exported to the system simulator. The multipath environment

is simulated in two ways.

In the first method, resultant phase and strength of the signals suffering from

multipath is considered. This is due to the fact that the signals arriving at the

37

transponder suffer constructive or destructive interference. The system then transmits

a signal in the direction of the incoming resultant signal, and not on each multipath

direction.

In the second method, each multipath signal is considered separately. Then, each

signal is fed to a phase conjugating element. The retrodirective array transponder

transmits a signal from each conjugating element on its corresponding multipath

direction. A digital signal processor is required at the front end to separate out the

multipath signals and feed it to a phase conjugator. This is a research topic in itself,

where spatial–temporal diversity is used.

Thus the system build here, transmits a signal in the direction in which it came,

given that it receives individual signals and not the resultant waves.

5.2 Future Research

In the present work, the system is simulated for a single user. Next we may try for

multi-user schemes. Combined with our current considerations, future directions for

this work could be:

1. Integrate the current system for multi-user detection and estimation

2. In multipath environment, signals arrive from different directions. In order for

the system to retransmit a signal back on each multipath direction, a signal pro-

cessor is needed at the front end, which will separate out each multipath signal.

Then the retrodirective array can use the phase and frequency information of

each multipath signal and transmit back on the individual paths.

An integration of the signal processor and the transponder is later required.

3. Channel Coding schemes can be inserted.

4. MIMO (multiple input multiple output) techniques can be used.

38

Bibliography

[1] S. Haykinh, Adaptive Filter Theory, 3rd edition, Prentice Hall, 1996.

[2] W.L.Stutzman, J.H. Reed, C.B. Dietrich, B.K. Kim, D.G. Sweeney,“Recent

Results from Smart Antenna Experiments – Base Station and Handheld Ter-

minals,”2000 IEEE Radio and Wireless Conference, pp. 139–142.

[3] Kevin M. K. H. leong, Ryan Y. Miyamoto, Seong-Sik Jeon, Yuanxun Wang,

Tatsuo Itoh, “A Frequency Autonomous Retrodirective Array Transponder,”

Microwave Symposium Digest, 2002 IEEE MTT-S Int. Microwave Symposium,

2002, pp. 1349–1352 Vol. 2.

[4] Mathais Fink, “Time Reversal of Ultrasonic Fields -Part I: Basic Principles,”

Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on Vol.

39 Iss. 5 , Sept. 1992, pp. 555–566

[5] B. Ya. Zel’dovich, N. F. Pilepetsky, V. V. Shkunov, “Principles of Phase Con-

jugation,” Berlin, Germany: Springer-Verlag, 1985.

[6] E. L. Gruenberg, H. P. Raabe, C. T. Tsitsera, “Self-directional microwave

communication system,” IBM J. Res. Develop., Vol. 18, no. 2, pp. 149–163,

1974.

[7] C. C. Cutler, R. Kompfner, and L. C. Tillotson, “A self-steering array re-

peater,”Bell Syst. Tech. J., Vol.42, pp. 2013–2032, 1963.

[8] R. Y. Miyamato, Y. Qian and T. Itoh, “A Novel Phase Conjugator for Active

39

Retrodirective Array Applications,” Antennas and Propagation Society, 1999.

IEEE Int. Symp.,1999 , Vol. 3.

[9] John D. Kraus, Antennas, Mcgraw-Hill Publications, 1950.

[10] Costas, J. P., “Synchronous communications,” proceedings of the IRE, Vol. 47,

pp. 2058–2068, 1959.

[11] SystemView User Guide.

[12] Constantine Balanis, Antenna Theory, Analysis And Design, Wiley Publica-

tions, 2001.

[13] Herbert Taub, Donald Schilling, Principles Of Communication Systems,

Mcgraw-Hill Publications, 1971.

[14] John G. Proakis Digital Communication, Mcgraw-Hill Publications, 2001.

[15] Bernard D. Steinberg, Principles Of Aperture Array Design, A Wiley In-

terSceince Publication, 1976.

[16] Peyton Z. Peebles, Radar Principles, A Wiley InterSceince Publication, 1998.

[17] Merrill Skolnik, Radar Handbook, Mcgraw-Hill Publications, 1990.

[18] S.L. Karode, V. Fusco, “Self-tracking duplex communication link using planar

Retrodirective antennas,” IEEE Trans. Antennas and Propagation, Jun 1999,

pp. 993–1000.

[19] L. D. DiDomenico , V. Fusco, “Digital communications using self-phased ar-

rays,”IEEE MTT-S Intl. Microwave Symposium Digest, pp. 1705–1708, Jun

2000.

[20] Y. Chang, H. R. Fetterman, I. newberg, and S. K. Panaretos, “Microwave

phase conjugation using antenna arrays,” IEEE Trans. Microwave Theory and

Techniques, Nov. 1998, pp. 1910–1919.

40

[21] C.W.Pobanz, T. Itoh, “A conformal Retrodirective array for radar applications

using a heterodyne phased scattering element,” IEEE MTT-S Intl. Microwave

Symposium Digest, pp. 905–908, Jun 1995.

[22] R. Y. Miyamato, Y. Qian and T. Itoh, “Active retrodirective array for re-

mote tagging and wireless sensor applications,” IEEE MTT-S Intl. Microwave

Symposium Digest, pp. 1431–1434, Jun 2000.

[23] Kevin M. K. H. leong, Ryan Y. Miyamoto, Seong-Sik Jeon, Yuanxun Wang,

Tatsuo Itoh, “An Adaptive Multi-Functional Array for Wireless Sensor Sys-

tems”, Microwave Symposium Digest, 2002 IEEE MTT-S International, 2002

pp. 1369–1372, vol.2.

[24] Seong-Sik Jeon, Yuanxun Wang, Tatsuo Itoh,“A Balanced Adaptive Beam-

forming System for Broadband Wireless Communications,” Microwave Sym-

posium Digest, 2002 IEEE MTT-S International, 2002, pp. 1357–1360, vol.2.

[25] B. Y. Toh, V.F. Fusco, “Self Steering Arrays for Mobile Communications,”

High Frequency Postgraduate Student Colloquium, 1999, pp. 99–104

[26] A. Yariv, P. Yeh,“Optical Waves in Crystals,” New York: Wiley 1984.