DESIGN AND ANALYSIS OF RECONFIGURABLE MIMO ANTENNAS

FOR NEXT GENERATION WIRELESS COMMUNICATION SYSTEMS

BY

JIE BANG YAN

DISSERTATION

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2011

Urbana, Illinois

Doctoral Committee:

Professor Jennifer T. Bernhard, Chair Professor Andreas C. Cangellaris Professor Steven J. Franke Professor José E. Schutt-Ainé

ABSTRACT

In the United States, the forthcoming Long Term Evolution (LTE) and cognitive radio (CR) systems are going to operate in the spectrum vacated with the digital television transition (LTE: 698 MHz – 806 MHz; CR: 512 MHz – 698 MHz “TV white space frequencies”). Both of the systems are going to include multiple-input multiple-output (MIMO) technology as a standard feature due to the exemplary performance of MIMO links in rich-scattering environments over the traditional single-input single-output (SISO) configuration. To achieve the capacity gain from MIMO, it is essential to keep the mutual coupling between the antenna elements low so multiple signals can be resolved effectively. Given the lower operating frequency of the new systems as compared to the WiFi and the existing cellular standards, the antennas in portable devices must be electrically small and are likely to be inefficient. It is also impractical to separate antennas to get low mutual coupling. As a result, the coverage of the systems would not only be limited, but the capacity of the systems would also suffer. A remedy to the problem is to push the cellular concept further down to the femtocell level. The femtocell base station can be considered as a small-sized, low-power access node serving customer premises such as home or office areas. As the operating bands of the new systems are adjacent to each other, it could be economical to build a single hybrid LTE/CR low-power access node that supports both systems. Therefore, there is a need for a new MIMO antenna solution that covers the LTE and CR bands. The design must also be compact and robust in the face of unknown packaging and deployment positions.

The first part of this dissertation describes the boundary perturbation method for inducing degenerated modes in dielectric resonator for MIMO operation. Based on the proposed method, a 700 MHz dual-mode MIMO dielectric resonator antenna for LTE femtocell base station is designed and tested. The maximum dimension of the proposed antenna is only 0.2λ0 while the worst case measured mutual coupling between the radiating ports is less than –30 dB. It is estimated that the proposed antenna is able to offer an average of 14% improvement of the channel capacity as compared to a pair of orthogonal dipole antennas. Furthermore, a frequency reconfigurable version of the proposed MIMO antenna for the hybrid LTE/CR low-power access node is described. Depending on the mobile user’s need and the propagation environment, the proposed antenna can have two modes of operation: MIMO mode for capacity enhancement and

ii frequency sweep mode for channel optimization. The proposed antenna can hence allow for a more flexible and efficient use of the radio spectrum. Finally, this work concludes with a comprehensive study of nonlinear effects in frequency reconfigurable MIMO antennas with integrated solid state switching and tuning devices. The effect of mutual coupling and device placement on the antenna nonlinearity as well as potential remedies for the undesirable nonlinear effects are discussed thoroughly.

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For my parents

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ACKNOWLEDGMENTS

I would like to express my sincere gratitude to my adviser, Professor Jennifer Bernhard, for offering me an opportunity to begin my Ph.D. study at the University of Illinois, and also her invaluable guidance, patience and encouragement throughout the process. I would like to extend my sincere thanks to my committee members, Professors Andreas Cangellaris (Prelim and Defense), Steven Franke (Prelim and Defense), Jianming Jin (Qual), Jonathan Makela (Qual), and José Schutt-Ainé (Qual, Prelim and Defense). I would also like to thank my fellow group members in the Electromagnetics Laboratory. Thank you all for your insightful suggestions about my research work. I must also thank my parents for their love and support. Finally, I would like to recognize the Motorola Center for Communications at Illinois and the Croucher Foundation for sponsoring this research.

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TABLE OF CONTENTS

LIST OF FIGURES ...... ix

CHAPTER 1: INTRODUCTION ...... 1 1.1. INTRODUCTION TO NEXT GENERATION WIRELESS SYSTEMS ...... 1 1.1.1. Long Term Evolution ...... 2 1.1.2. Cognitive Radio ...... 2 1.2. DISSERTATION RESEARCH ...... 3 1.2.1. Research Roadmap and Its Impact ...... 6 1.2.2. Impact of This Research ...... 8 1.2.3. Organization of This Dissertation ...... 8

CHAPTER 2: BACKGROUND ...... 10 2.1. GENERAL DESIGN REQUIREMENTS FOR MIMO ANTENNAS ...... 10 2.1.1. MIMO Capacity ...... 10 2.1.2. Effect of Mutual Coupling ...... 11 2.2. A SURVEY OF MIMO ANTENNA DESIGNS ...... 13 2.2.1. Physically Spaced MIMO Antennas ...... 14 2.2.2. MIMO Antennas with Decoupling Networks ...... 14 2.2.3. Orthogonally Polarized Antennas ...... 15 2.2.4. Reconfigurable MIMO Antennas ...... 15 2.3. CHAPTER SUMMARY ...... 16

CHAPTER 3: THEORY AND DESIGN OF AN LTE FEMTOCELL BASE STATION ANTENNA ...... 17 3.1. SELECTION OF A BASE ANTENNA DESIGN ...... 17 3.2. BASE ANTENNA CONFIGURATION ...... 18 3.3. DESIGN OF A MIMO DRA ...... 20 3.3.1. Boundary Perturbation Method...... 20 3.3.2. Boundary Perturbed MIMO DRA ...... 24 3.3.3. Boundary Approximation Method ...... 25 3.4. SIMULATION RESULTS ...... 26 3.4.1. Antenna Radiation Characteristics ...... 26

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3.4.2. MIMO Performance Evaluation ...... 28 3.5. MEASUREMENT RESULTS ...... 31 3.6. CHAPTER SUMMARY ...... 34

CHAPTER 4: IMPLEMENTATION OF FREQUENCY RECONFIGURATION ...... 35 4.1. FREQUENCY RECONFIGURATION VIA MATERIAL PERTURBATION ...... 35 4.1.1. Analysis with Eigenvalue Perturbation ...... 36 4.1.2. Example on Microstrip Patch Antenna ...... 37 4.1.3. Application to MIMO Dielectric Resonator Antenna ...... 39 4.2. FREQUENCY RECONFIGURATION VIA PARASITIC LOADING ...... 42 4.2.1. Antenna Configuration...... 42 4.2.2. Simulation Results ...... 45 4.2.3. Integration with DC Bias Networks and Active Components ...... 50 4.2.4. Measurement Results ...... 56 4.2.5. Application to a Hybrid LTE/CR Low-Power Access Node ...... 62 4.3. CHAPTER SUMMARY ...... 63

CHAPTER 5: NONLINEAR EFFECTS IN FREQUENCY RECONFIGURABLE MIMO ANTENNAS ..... 64 5.1. FREQUENCY SWITCHABLE DUAL-SLOT ANTENNA ...... 64 5.1.1. Antenna Geometry ...... 64 5.1.2. Equivalent Circuit Model ...... 67 5.2. TWO-TONE MEASUREMENT ...... 71 5.2.1. Measurement Setup ...... 71 5.2.2. Measurement Results ...... 73 5.2.3. Comparison with Circuit Simulation Results ...... 75 5.2.4. Results Interpretation ...... 76 5.3. EFFECT OF DC BIAS ...... 77 5.4. EFFECT OF ANTENNA MUTUAL COUPLING ...... 80 5.4.1. Orthogonal Dual-Slot Antenna ...... 80 5.4.2. Transmission Spectrum Measurement ...... 82 5.5. HARMONIC TRAP ...... 84 5.6. TWO-TONE MEASUREMENT WITH PROPOSED FREQUENCY AGILE MIMO DRA ...... 86 5.7. CHAPTER SUMMARY ...... 87

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CHAPTER 6: CONCLUSIONS AND FUTURE WORK ...... 89 6.1. CONCLUSIONS ...... 89 6.2. CONTRIBUTIONS ...... 90 6.3. FUTURE WORK ...... 90 6.3.1. Design of a Robust DC Bias Network ...... 90 6.3.2. Reduction of Active Device Redundancy in Reconfigurable Antennas ...... 95 6.3.3. Effect of Radiation Patterns on Harmonic and Intermodulation Products ...... 95 6.3.4. Switch Design for Reconfigurable Slots for High Power Applications ...... 95 6.3.5. Harmonic Trap Implemented Using Transmission Lines ...... 96

APPENDIX A: STUDY OF DTV SIGNAL COVERAGE IN RURAL AREAS ...... 97 A.1. STUDY OF DTV SIGNAL PROPAGATION AND ITS SIGNIFICANCE ...... 97 A.2. AN INTRODUCTION TO THE INDOOR RECEPTION PROBLEM ...... 97 A.3. ANALYTICAL DESCRIPTION OF AN INSULATED HOUSE ...... 98 A.4. RAY TRACING SIMULATION ...... 99 A.4.1. Simulation Scenarios ...... 99 A.4.2. Simulation Results ...... 101 A.5. PROPAGATION MODEL FOR INDOOR RECEPTION ...... 102 A.6. EFFECT OF ANTENNA DIRECTIVITY ...... 105 A.7. SUMMARY ...... 106

REFERENCES ...... 107

AUTHOR’S BIOGRAPHY ...... 117

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LIST OF FIGURES

Figure 1. Location of the LTE and CR systems in the electromagnetic spectrum...... 1 Figure 2. (a) A typical modern smartphone,1 (b) two PIFAs with operating frequency at 700 MHz, and (c) mutual coupling between two PIFAs as a function of antenna separation...... 5 Figure 3. Simulated capacities of a MIMO system with uncoupled and coupled antennas and their comparison to ideal capacities with the example channel matrix Hc shown...... 13 Figure 4. Perspective view of the split-cylindrical DRA...... 18 Figure 5. Theoretical magnetic field distributions for the (a) TE011+δ mode, and (b) HE11δ mode (unit in mm)...... 19 Figure 6. Simulated S-parameters of the unperturbed cylindrical DRA in HFSS...... 20 Figure 7. Boundary perturbation from the base of the split-cylindrical DRA (cross-sectional (yz-plane) view)...... 24 Figure 8. Plot of change of resonant frequency f0 against the perturbation parameter α...... 25 Figure 9. Elliptical approximation of the perturbed cylindrical boundary (cross-sectional (yz- plane) view)...... 26 Figure 10. Simulated S-parameters of the proposed MIMO DRA...... 27 Figure 11. Radiation patterns of (a) port 1 (HE mode) and (b) port 2 (TE mode)...... 28 Figure 12. The floor plan of the office environment that was used to estimate the MIMO channel capacity (notice that there is no line-of-sight (LOS) path between the transmitter and any of the receivers)...... 29 Figure 13. Estimated channel capacity of the proposed MIMO DRA...... 31 Figure 14. Measured S-parameters of the perturbed cylindrical DRA...... 32 Figure 15. Comparison between the measured and simulated S11 (HE) and S22 (TE) of the perturbed cylindrical DRA on a Smith chart ...... 32 Figure 16. Comparison of the simulated (with markers) and measured (without markers) radiation patterns of (a) port 1 (HE mode) and (b) port 2 (TE mode)...... 33 Figure 17. Sets of elements for material perturbation for maximum frequency agility: (a) TM10, (b) TM01, (c) TM11, and (d) TM20 (the green elements are the elements needed to be perturbed)...... 38 Figure 18. Simulated field distributions of the microstrip patch antenna: (a) TM10, (b) TM01, (c) TM11, and (d) TM20...... 38 Figure 19. Simulated electric field distribution inside the MIMO DRA...... 39 Figure 20. A MIMO DRA with material perturbation. The grey volumes indicate the portion of the dielectric cavity perturbed (a) Perturb. A and (b) Perturb. B...... 40 Figure 21. Simulated S11 (HE mode) and S21 of the MIMO DRA with Perturb. A...... 40 Figure 22. Simulated S22 (TE mode) of the MIMO DRA with Perturb. A...... 41 Figure 23. Simulated S11 (HE mode) of the MIMO DRA with Perturb. B...... 41 Figure 24. Simulated S22 (TE mode) and S21 of the MIMO DRA with Perturb. B...... 42 Figure 25. A MIMO DRA excited by two slots fed by coaxial cables...... 43 Figure 26. Simulated S-parameters of the MIMO DRA shown in Figure 25...... 44 Figure 27. Ground planes with parasitic slots: (a) Ground Plane A with a slot for HE mode excitation, (b) Ground Plane B with a slot for TE mode excitation ...... 44

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Figure 28. Simulated S11 (HE mode) of the MIMO DRA. The frequency agility is achieved by reconfiguring the parasitic slot on Ground Plane A...... 45 Figure 29. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA. The frequency agility is achieved by reconfiguring the parasitic slot on Ground Plane A...... 46 Figure 30. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA. The frequency agility is achieved by reconfiguring the parasitic slot on Ground Plane B...... 47 Figure 31. Simulated S11 (HE mode) of the MIMO DRA. The frequency agility is achieved by reconfiguring the parasitic slot on Ground Plane B...... 47 Figure 32. Simulated S-parameters of the frequency reconfigurable MIMO DRA...... 49 Figure 33. Simulated radiation patterns of the frequency reconfigurable MIMO DRA: (a) HE mode (port 1) and (b) TE mode (port 2)...... 50 Figure 34. A schematic showing the actual implementation of a DC bias network on Ground Plane A...... 51 Figure 35. An equivalent circuit model of the parasitic slot...... 51 Figure 36. A schematic showing the actual implementation of a DC bias network on Ground Plane B...... 52 Figure 37. An equivalent circuit model of the excitation slot...... 52 Figure 38. Simulated S11 (HE mode) of the MIMO DRA with bias networks...... 54 Figure 39. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA with bias networks...... 54 Figure 40. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA with bias networks...... 55 Figure 41. Simulated S11 (HE mode) of the MIMO DRA with bias networks...... 55 Figure 42. Fabricated prototype of the proposed frequency reconfigurable MIMO DRA: (a) Ground Plane A, (b) Ground Plane B, and (c) perspective view...... 56 Figure 43. Measured S11 (HE mode) of the fabricated antenna for HE mode reconfiguration. .... 58 Figure 44. Measured S22 (TE mode) and S21 (mutual coupling) of the fabricated antenna for HE mode reconfiguration...... 58 Figure 45. Measured S11 (HE mode) and S21 (mutual coupling) of the fabricated antenna for TE mode reconfiguration...... 59 Figure 46. Measured S22 (TE mode) of the fabricated antenna for TE mode reconfiguration. .... 59 Figure 47. Measured S-parameters of the fabricated antenna in frequency reconfigurable MIMO mode...... 62 Figure 48. Application of the proposed frequency reconfigurable MIMO DRA in a hybrid LTE/CR low-power compact base station: (a) frequency sweep mode and (b) MIMO mode. .... 63 Figure 49. A frequency switchable dual-slot antenna (λ0 is calculated at 800 MHz)...... 65 Figure 50. (a) Actual implementation of the PIN diode bias network, and (b) equivalent circuit model of the bias network...... 65 Figure 51. Simulated and measured S-parameters of the dual-slot antenna when both diodes are OFF...... 66 Figure 52. Simulated and measured S-parameters of the dual-slot antenna when both diodes are ON...... 66 Figure 53. Simulated and measured S-parameters of the dual-slot antenna when only one of the diodes is ON...... 67 Figure 54. Equivalent circuit model of the dual-slot antenna when both diodes are OFF...... 68 Figure 55. Equivalent circuit model of the dual-slot antenna when both diodes are ON...... 68

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Figure 56. Equivalent circuit model of the dual-slot antenna when only one of the diodes is ON...... 69 Figure 57. Comparison between the S-parameters obtained from the circuit simulation and the full-wave simulation when (a) both diodes are OFF, and (b) both diodes are ON...... 69 Figure 58. Normalized electric field distribution on the dual-slot antenna when (a) both diodes are OFF (840 MHz), (b) both diodes are ON (1100 MHz), (c) only D1 is ON (1100 MHz), and (d) only D1 is ON (840 MHz)...... 70 Figure 59. Experimental setup for measuring the transmission spectrum...... 72 Figure 60. Experimental setup for measuring the reception spectrum...... 72 Figure 61. Measured transmission spectrum of the frequency switchable dual-slot antenna...... 73 Figure 62. Measured reception spectrum taken at port 1 of the frequency switchable dual-slot antenna...... 74 Figure 63. Measured reception spectrum taken at port 2 of the frequency switchable dual-slot antenna...... 74 Figure 64. Comparison between the transmission spectra obtained from circuit model simulation and measurement...... 76 Figure 65. Measured S-parameters of the dual-slot antenna for 10 dBm of input power...... 77 Figure 66. Measured transmission spectrum for case (ii)...... 78 Figure 67. Measured transmission spectrum for case (iii)...... 79 Figure 68. Measured transmission spectrum for case (iv)...... 79 Figure 69. A frequency switchable orthogonal dual-slot antenna...... 80 Figure 70. Simulated and measured S-parameters of the orthogonal dual-slot antenna when both diodes are OFF...... 81 Figure 71. Simulated and measured S-parameters of the orthogonal dual-slot antenna when both diodes are ON...... 81 Figure 72. Simulated and measured S-parameters of the orthogonal dual-slot antenna when only D1 is ON...... 82 Figure 73. Measured transmission spectrum of the orthogonal dual-slot antenna when only D1 is ON and 0 V is applied to D2...... 83 Figure 74. Measured transmission spectrum of the orthogonal dual-slot antenna when only D1 is ON and D2 is reversed biased with 3 V...... 83 Figure 75. Harmonic traps placed next to the OFF diode for the suppression of 2f1...... 84 Figure 76. Measured transmission spectrum of the parallel dual-slot antenna when D1 is ON and D2 is OFF...... 85 Figure 77. Measured transmission spectrum of the parallel dual-slot antenna when D1 is ON and D2 is OFF...... 85 Figure 78. Measured transmission spectrum of the proposed frequency reconfigurable MIMO DRA...... 87 Figure 79. A schematic showing the modified DC bias network on Ground Plane A...... 91 Figure 80. An equivalent circuit model of the parasitic slot...... 91 Figure 81. A schematic showing the modified DC bias network on Ground Plane B...... 91 Figure 82. An equivalent circuit model of the excitation slot...... 92 Figure 83. Simulated S11 (HE mode) of the MIMO DRA with modified bias networks...... 93 Figure 84. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA with modified bias networks...... 93

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Figure 85. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA with modified bias networks...... 94 Figure 86. Simulated S11 (HE mode) of the MIMO DRA with modified bias networks...... 94 Figure 87. Single-pole PIN diode switch in shunt configuration...... 96 Figure 88. (a) Floor plan used in the simulations and (b) 3D view of the house...... 99 Figure 89. CDF plot of path loss within the house for NLOS case...... 102 Figure 90. CDF plot of path loss within the house for LOS case...... 102 Figure 91. Five randomly selected indoor propagation paths (dash lines) for each of the (a) LOS and (b) NLOS cases (the arrows indicate the direction of signal from the broadcasting station)...... 103 Figure 92. A ray diagram illustrating the negative dependence on log distance in the NLOS path loss equations...... 103 Figure 93. Path loss plot along the receiver routes in Figure 92. (Dotted lines: simulated path loss data; solid lines: trend line of the actual path loss data.) ...... 103 Figure 94. Path loss plots at 400 MHz: (a) NLOS, without insulation, (b) NLOS, with insulation, (c) LOS, without insulation, and (d) LOS, with insulation. (Dotted lines: simulated; solid lines: path loss models.)...... 104 Figure 95. CPF plot of path loss within the house for NLOS case (the use of directional antenna degrades indoor signal reception)...... 105 Figure 96. CDF plot of path loss within the house for LOS case (the use of directional antenna improves indoor signal reception)...... 105

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CHAPTER 1: INTRODUCTION

1.1. INTRODUCTION TO NEXT GENERATION WIRELESS SYSTEMS

Due to the use of advanced digital modulation schemes, compression techniques and error- correction codes in digital television (DTV) transmission, a portion of the radio spectrum in the ultra high frequency (UHF) band was vacated with the transition from analog television (ATV) broadcast [1]. In particular, full power TV stations are required to operate between 54 MHz and 698 MHz. The surplus spectrum which was used to carry Channels 52 – 69 (698 MHz – 806 MHz) was auctioned to a number of wireless service providers for the deployment of a new nationwide wireless broadband network based on Long Term Evolution (LTE) technology [2], [3]. This new wireless system is also regarded as the 4th Generation (4G) network. On the other hand, because of the higher spectral efficiency of the DTV link, there are unoccupied spectrum holes (also known as white space frequencies) within TV channels from 54 MHz to 698 MHz. According to the Federal Communications Commission (FCC) of the United States, cognitive radio (CR) enabled mobile devices are allowed to co-exist in the bands, provided that they do not interfere with the TV broadcast. Indeed, an organization called the Cognitive Networking Alliance (CogNea) has been formed to help drive the definition and adoption of industry-wide standards for low-power portable CR enabled devices to operate in the white space band ranging from 512 MHz to 698 MHz [4]. Figure 1 shows the location of both of the systems, LTE network and CR, in the electromagnetic spectrum.

30 MHz 300 MHz 3 GHz

VHF UHF SHF

TV Broadcast WLAN CR LTE GSM WiMAX (4G) (2G, 2.5G) WCDMA, HSDPA (3G, 3.5G)

Figure 1. Location of the LTE and CR systems in the electromagnetic spectrum. 1

1.1.1. Long Term Evolution

Long Term Evolution (LTE) is a next generation wireless system after Groupe Spécial Mobile (GSM) and High Speed Packet Access (HSPA), and is considered as a beyond-3G system. The most recent LTE standard under development is the Evolved Universal Terrestrial Radio Access (E-UTRA) LTE-Advanced Release 10 [5]. Currently, industry is focusing on the implementation of the LTE Release 8, which was frozen in December 2008. The LTE system is based on Orthogonal Frequency Division Multiplexing (OFDM) and supports scalable bandwidth from 1.4 MHz to 20 MHz. The cell size of the LTE system can vary from tens of meters in radius (femtocell) to a hundred kilometers (macrocell). The standard is expected to deliver a wireless data transfer rate of 300 Mb/s in the downstream and 75 Mb/s in the upstream. In order to achieve such a high mobile data rate, multiple-input multiple-output (MIMO) technology is employed in the system and up to 4 × 4 antenna configurations are supported [6]. To enhance global roaming capability, the LTE air interface can be adapted to all frequency bands used by International Mobile Telecommunications (IMT) systems. In the United States, the LTE system is going to operate at 698 MHz – 806 MHz, which belongs to a portion of the newly released spectrum resulting from DTV transition.

1.1.2. Cognitive Radio

Cognitive radio (CR) has been proposed for a more efficient utilization of the scarce radio spectrum [7]. It is estimated that the licensed spectrum remains idle or underutilized for an average of 90% of the time [8]. CR promises to take advantage of this and establish a communication link whenever spectrum holes (also known as white spaces) nearby are sensed. Indeed, the IEEE has given CR a formal definition [9]:

i. Radio in which communication systems are aware of their environment and internal state and can make decisions about their radio operating behavior based on that information and predefined objectives. The environmental information may or may not include location information related to communication systems.

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ii. Cognitive radio (as defined in i.) that utilizes Software Defined Radio, Adaptive Radio, and other technologies to automatically adjust its behavior or operations to achieve desired objectives.

One of the well-investigated CR standards is the IEEE 802.22 Wireless Regional Area Network (WRAN) [10]. The standard was designed to operate in the TV broadcast band and provide fixed wireless internet access to rural areas spanning up to 100 km in radius. The system, while providing broadband access, is not allowed to cause any harmful interference to incumbents such as TV broadcast and wireless microphones. This feature is enabled by spectrum sensing and geo- location that, whenever an incumbent transmission is detected or the device is in the proximity of an incumbent, the CR system would relocate the communication link. Since the system operates in TV broadcast spectrum, the bandwidth of an individual channel has to match that of a single TV channel, which is 6 MHz in the United States. The designated throughput of the standard is 1.5 Mb/s in the downstream and 384 kb/s in the upstream.

In addition to IEEE 802.22 WRAN, there are other emerging advanced CR standards, and the Cognitive Networking Alliance (CogNeA) [4] is one of those. The CogNeA network aims to provide wireless broadband access over TV white spaces for personal and mobile devices. Following FCC regulations, CogNeA will operate in Channels 21 – 51 (512 MHz – 698 MHz), except Channel 37 (608 MHz – 614 MHz), on a strict non-interference basis to existing incumbents. The channel bandwidth of the standard is 6 MHz for United States and the minimum proposed coverage is 30 m. Compared to IEEE 802.22, the CogNeA system not only can support portable devices, but it can also offer a much higher data rates (19.4 Mb/s – 30 Mb/s). Moreover, the standard supports multiple antennas for capacity improvement under multipath conditions.

1.2. DISSERTATION RESEARCH

Operating in the TV band offers advantages to the propagation of electromagnetic waves. Indeed, better coverage is the major driving force for operating at lower frequencies. For

3 example, as compared to Wireless Local Area Network (WLAN) which operates at 2.4 GHz, wireless systems that operate in the TV band could serve a much wider area (Appendix A provides an in-depth study of signal coverage in the TV band). This is because, according to the Friis free space equation [11], electromagnetic waves at lower frequencies propagate farther with less attenuation and penetrate/diffract around obstacles more easily. Hence, the new wireless systems, CR and LTE, are anticipated to offer much better coverage than any existing wireless service. In addition, lower operating frequencies generally require less effort in the design of active radio-frequency (RF) components, such as mixers, amplifiers, etc., because the parasitic effects are less significant.

Nevertheless, operating at lower frequencies may not be advantageous to the design of passive RF components, such as hybrids, phase shifters, filters and antennas. This is because the size of passive RF components scales up with increasing operating wavelength. Given the lower operating frequency of the LTE system, as compared to the WLAN and cellular standards, the antennas in handheld devices such as smartphones must be electrically small. This implies that mobile antennas are likely to be inefficient and the coverage of the system is therefore limited. This is especially true if MIMO operation is needed at both the mobile and base station since the actual radiated power would be further reduced due to the strong mutual coupling between closely packed mobile antennas. As an example, Figure 2 shows the simulated mutual coupling between two planar inverted F antennas (PIFAs) as a function of antenna separation. It can be seen that even for an antenna separation of a one-eighth-wavelength, the size of the antenna, including the ground plane, would be bigger than a modern smartphone. Notice that the mutual coupling could be minimized if the separation is about a quarter-wavelength. However, this is usually impractical to achieve in modern handsets.

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0.125λ0 short

feed

117.75 mm 142 mm

radiator

ground

63.5 mm 77.5 mm (a) (b)

0

-5

-10

-15

-20

Mutual Coupling (dB) MutualCoupling -25

-30 0 0.1 0.2 0.3 0.4 0.5 0.6 Antenna Separation (λ0) (c)

Figure 2. (a) A typical modern smartphone,1 (b) two PIFAs with operating frequency at 700 MHz, and (c) mutual coupling between two PIFAs as a function of antenna separation.

In view of this, the LTE architecture includes a femtocell solution, Home eNodeB (HeNB), for coverage extension and battery life improvement [12]. HeNB can be considered as a low-power access point serving customer premises such as home or office areas. To exploit the richness in multipath propagation in indoor scenarios, it is desired to employ MIMO antennas with a very low mutual coupling as the base station1antenna in a femtocell. One possible solution would be

1 Courtesy of Motorola, Inc. 5 the orthogonally polarized MIMO antennas proposed in [13]. However, the problem is that such antennas would be oversized when scaled to operate at 700 MHz. Hence, a new MIMO antenna solution for LTE femtocell base station is necessary.

Given the fact that the mobile CR band is from 512 MHz to 698 MHz and is adjacent to the LTE band, it could be economical to build a single low-power femtocell base station that supports both systems. To fulfill this purpose, an antenna that works from 512 MHz to 806 MHz is needed. If the center operating frequency of the antenna is at 700 MHz, then the antenna would need to have a bandwidth over 40%. Although wideband antennas, such as spiral antennas or log-periodic antennas, could be a solution, they are generally electrically large. Moreover, a low- power femtocell base station would not operate at all frequencies simultaneously. Therefore wideband antennas might not be the best option for modern compact low-power nodes. Frequency reconfigurable antennas (FRAs), on the other hand, might be a better choice [14]. As compared to wideband antennas, FRAs are usually more compact in size and have better impedance matching over the band of operation if properly designed. They may also eliminate the need for a band selection filter at the radio frequency (RF) front end, which can reduce system implementation cost.

1.2.1. Research Roadmap and Its Impact

The research encompasses the design and analysis of MIMO antennas for next generation wireless communication systems. Phase 1 of this research is to develop a base antenna design that supports solely the LTE system at 700 MHz. The design task is non-trivial because the size of the 700 MHz antenna should not be much greater than that of a typical wireless router and support for MIMO operation is required. To qualify as a good MIMO antenna design, the antenna should have low mutual coupling between the radiating ports so that the received multiple signals can be resolved. Specifically, the channel matrix of the link, in this case, is well- conditioned and can be decomposed into parallel sub-channels, and hence a degree of freedom gain can be achieved [15]. It is also important to maintain a good gain balance between the multiple ports so as to minimize the design effort of the automatic gain control unit at the RF

6 front end. Finally, the design must also be compact and robust in the face of unknown packaging environments.

Phase 2 of this project is to extend the functionality of the proposed antenna in Phase 1. The goal is to broaden the operating frequency range of the proposed antenna so that it can support both the LTE and the CR systems (from 512 MHz to 806 MHz). The approach is to add frequency reconfigurability to the antenna designed in Phase 1. Various methods for achieving frequency reconfiguration are investigated. The choice of using solid state switching and tuning elements is preferred because they are inexpensive and require a much lower control DC voltage than RF micro-electro-mechanical (MEM) devices. The primary design requirement is to maintain a low mutual coupling between the antenna ports over the band of reconfiguration. In addition, another desirable feature is that the operating frequency of the antenna ports can be individually tunable, so that the antenna ports can be individually allocated to support either the LTE system or the CR system, or both at the same time. Furthermore, a good frequency reconfigurable antenna should have a fairly constant radiation pattern over the band of interest. This allows the base station to be easily oriented to the optimal direction for the best coverage. In this research, a frequency reconfigurable MIMO antenna with the above stated features is demonstrated experimentally.

Finally, Phase 3 of this research concerns the study of nonlinear effects in frequency reconfigurable MIMO antennas. In Phase 2, the frequency agility of the proposed antenna is achieved with the integration of solid state switching and tuning devices. However, because of the nonlinear nature of the solid state devices, harmonic and intermodulation frequency products could be generated [16]. The goal is therefore to experimentally identify these intermodulation products in frequency reconfigurable MIMO antennas. Apart from this, circuit models based on the transmission line theory are developed to predict the levels of the intermodulation products generated. Finally, methods to suppress these intermodulation products are investigated.

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1.2.2. Impact of This Research

In the first part of this research, we develop a new design methodology for MIMO antennas with low mutual coupling. The design method is based on the analysis of modal field distributions within the antenna structure and is applicable to any antenna that is well modeled by the cavity model, such as dielectric resonator antennas and microstrip patch antennas. This offers a new design tool for antenna engineers and eliminates the need for trial-and-error in the design process. In addition to antenna designs, the proposed method provides a systematic way to design multimode dielectric resonators for multiband operation. As a demonstration, a MIMO antenna for the LTE femtocell base station is designed with the proposed method.

After that, based on the designed MIMO antenna, we introduce two different novel approaches to introduce frequency reconfigurability to the antenna. For the first time, we experimentally demonstrate a frequency reconfigurable MIMO antenna in which each radiating antenna port can be individually and electronically tuned. Leveraging the new antenna functionality, we envision extending further the capability of existing MIMO communication systems.

Finally, we try to answer the frequently raised concerns about the nonlinear effects in reconfigurable antennas in the context of MIMO systems. We experimentally study harmonic and intermodulation distortion in frequency reconfigurable MIMO antennas. Potential methods to suppress the undesirable nonlinear effects in frequency reconfigurable MIMO antennas are explored in this dissertation.

1.2.3. Organization of This Dissertation

The following chapter reviews of the general design requirements for MIMO antennas and the state-of-art in both fixed and frequency reconfigurable MIMO antenna designs. Original research work on the design and analysis of a MIMO antenna for application in the LTE system is presented in Chapter 3. Specifically, a design methodology based on the perturbation theory is introduced and performance evaluation of the proposed antenna is included. Chapter 4 focuses

8 on techniques for adding frequency reconfigurability into the MIMO antenna described in Chapter 3. The first modality investigated is based on material perturbation in the antenna structure. A complete mathematical analysis that gives the optimal location for placing the material perturbation for achieving maximum frequency agility is described. The second technique considered is to detune the operating frequency by parasitic loading of the antenna. A frequency reconfigurable MIMO antenna designed with the second method is experimentally demonstrated. After that, Chapter 5 presents a study of nonlinear effects in frequency reconfigurable MIMO antennas equipped with solid state devices. Finally, a conclusion and a discussion of future work are included in Chapter 6.

9

CHAPTER 2: BACKGROUND

2.1. GENERAL DESIGN REQUIREMENTS FOR MIMO ANTENNAS

The ultimate goal of a MIMO communication system is to achieve the maximum allowable channel capacity bounded by the laws of physics [17]. It is therefore important to understand how the mutual coupling between the antenna ports can affect the achievable capacity of the system. With that knowledge, the design requirements for MIMO antennas can easily be set. In the following sections, the fundamentals for calculating the capacity in a MIMO channel are first reviewed and the effect of mutual coupling on the channel capacity is then discussed.

2.1.1. MIMO Capacity

Consider a Nt × Nr MIMO channel with additive white Gaussian noise (AWGN), where Nt is the number of transmit antennas and Nr the number of receive antennas [15]. The channel is described by

y = Hx + n , (1)

where x and y are the transmitted and received signal vectors of length Nt and Nr, respectively, and n ~ Ɲ(0, N0 Ι ) is the white Gaussian noise vector where is a Nr × Nr identity matrix, Nr and H denotes the channel matrix with a dimension of Nt × Nr. The channel matrix H can be decomposed via singular value decomposition (SVD),

H = UΣV , (2) where U and V are unitary matrices and Σ is a diagonal matrix with diagonal elements

  ...   , where Nmin = min(Nt, Nr). If the transmitted signal vector x is pre-multiplied 12 Nmin

10 by V and the received signal vector y is multiplied by U* , the channel described by Equation (1) can be rewritten as

U**** y = U UΣV Vx + U n , (3) y Σxn, (4)

yxnii ii  , i = 1, 2, …, Nmin . (5)

The MIMO channel can thus be decomposed into parallel Gaussian channels. The total capacity is therefore the sum of the capacities of the parallel channels [17],

Nmin P 2 C  log 1 ii , (6) i1 N0

th where Pi is the power allocated to the i sub-channel. Here, each λi represents an eigenchannel. It should be noted that the above channel capacity can only be achieved when the matrix H has a full rank, i.e., all eigenmodes are non-zero. Moreover, the highest capacity is attained when all the λi are equal. Hence, the channel capacity can be measured by the condition number

(max(λi)/min(λi)) of the matrix H. Therefore, the channel matrix is well conditioned, and hence allows the maximum capacity, when the condition number is 1.

2.1.2. Effect of Mutual Coupling

To take mutual coupling into account, the channel matrix H can be broken into [18]

rt HSHS c , (7)

r t where Hc represents the physical propagation channel alone, and S and S are the response of the receive and transmit antenna arrays, respectively. For lossless antennas, and can be expressed in terms of the scattering parameters (S-parameters),

11

r r rr 1 S11 S 12 SS 131 N r Sr1 SS rr 21 222 Nr r rr S  SS1 , (8) 3133 S r (NNrr 1) Sr SSS rrr 1 Nr1 NN rr 2( NN rr 1) rN 

t t tt 1 S11 S 12 SS 131 N t St1 SS tt 21 222 Nt t tt and, S  SS1 , (9) 3133 S t (NNtt 1) St SSS ttt 1 Nt1 NN tt 2( NN tt 1)t N 

where Sii is the reflection coefficient at antenna port i, Sij is the coupling between antenna port i and port j, and the superscripts r and t denote the receive and transmit antenna, respectively. Hence, if the antenna ports are well matched and the mutual coupling is negligible, i.e.,

SSii ij 0 , then HHc  . In this case, the performance of the MIMO system would solely depend on the statistics of the physical channel. On the other hand, if mutual coupling is finite, i.e., Sii  0 and 10Sij , then the capacity of the system would depend on the aggregate response of the physical channel and the coupling between the antenna ports. As an example, the effect of mutual coupling on the achievable capacity of a fairly coupled 2 × 2 channel was simulated in MATLAB [19] and is shown in Figure 3. The reflection coefficients ( SS1122 ) and the mutual coupling ( SS2112 ) of the “uncoupled antennas” are −30 dB and −13.5 dB, respectively, and the “coupled antennas” are −10 dB and −3.6 dB, respectively. It can be seen that mutual coupling, in this case, degrades the achievable channel capacity of the system. More rigorous analyses that show the adverse effect of mutual coupling on MIMO capacity can be found in [20] – [23].

Therefore, in order to maximize the channel capacity of a system, the mutual coupling between the radiating ports in a MIMO antenna should be minimized. And this is the primary design requirement for MIMO antennas. 12

50

40

30

20 Capacity (b/s/Hz) Capacity 10

0 0 5 10 15 20 25 30 35 40 SNR (dB) Ideal SISO Ideal 2×2 Ideal 3×3 Uncoupled antennas Coupled antennas

Figure 3. Simulated capacities of a MIMO system with uncoupled and coupled antennas and their comparison to ideal capacities with the example channel matrix Hc shown.

2.2. A SURVEY OF MIMO ANTENNA DESIGNS

There has been a lot of published research on MIMO antenna design in recent years and it is impossible to list all of the existing designs in this dissertation. Nevertheless, noting that the primary objective in MIMO antenna design is to minimize the mutual coupling between the antenna ports, common MIMO antenna system designs generally fall into the following four categories:

i. Physically spaced MIMO antennas ii. MIMO antennas with decoupling networks iii. Orthogonally polarized antennas iv. Reconfigurable MIMO antennas

13

In the following sections, some of the existing designs from each category that are most relevant for the research here are selected and discussed.

2.2.1. Physically Spaced MIMO Antennas

Physically spaced MIMO antennas are similar to conventional antenna arrays, but the signal at each antenna element is processed independently and incoherently. They can be arrays of microstrip patch antennas, dipoles, or other types of antennas [24] – [28]. The mutual coupling between the antenna elements is a function of antenna separation. The design philosophy is to utilize the space available and maximize the antenna spacing. A general design rule of thumb is to keep at least a quarter-wavelength between the antenna elements. Because of this, the total size of the resulting array is usually large and this limits the use of physically spaced MIMO antennas in practical systems. For example, a 4 × 1 MIMO monopole array operating at 700 MHz would have dimensions of 321 mm × 107 mm. Such an array would not fit in modern portable devices (despite the fact that monopole is already considered as an electrically small antenna).

2.2.2. MIMO Antennas with Decoupling Networks

As mentioned in the above section, physically spaced MIMO antennas are generally too large to be integrated in practical MIMO systems. In order to reduce the size of the antenna, researchers have proposed to insert a decoupling network between the antenna elements. Electromagnetic band-gap (EBG) structures are one of the earlier methods used to reduce the mutual coupling between closely spaced antenna elements [29], [30]. However, due to the complicated design process and complex fabrication procedure, EBG structures are not commonly used. Later, Chiu et al. [31] and Alvey [32] separately developed modified ground plane structures for isolating cosite antennas. Since then, many researchers have reported work on the design of decoupling structures/networks for MIMO antennas, e.g., [33] – [35].

14

2.2.3. Orthogonally Polarized Antennas

There are three different types of orthogonally polarized MIMO antennas. The first type is orthogonally oriented linear-polarized antennas of the same kind. Examples of such include orthogonal dipoles and slots in [13], [13] and [36], and MIMO cubes with dipoles, slots and spiral microstrip antennas in [37] – [40]. Because the antenna elements are linearly polarized, by arranging them in an orthogonal fashion, very low mutual coupling can be achieved between the radiating elements. However, in some applications, orthogonally placed antennas would be too bulky to be integrated in a package. The second type of orthogonally polarized MIMO antennas consists of antenna elements with different polarizations. A combination of dipoles and loops is a good example of this kind of antenna [41]. Other examples include slot-PIFA [42] and slot-patch [43] pairs, etc. This kind of design enables much greater flexibility on antenna placement since the antenna elements are orthogonal by nature. Finally, the third type of orthogonally polarized MIMO antennas has only a single radiating structure but with multiple excitations/ports. Multimode spiral [44], MIMO dielectric resonator antenna (DRA) [45], [46], dual-fed microstrip patch antenna [47] and multimode ring antenna [48] are examples of this type. In these antenna designs, multiple ports excite orthogonal radiating modes on the antenna structure. The mutual coupling between the antenna ports is hence intrinsically low because of the orthogonality. It is obvious that these multimode antennas are the most compact form of MIMO antennas because there is only a single radiating structure and no decoupling networks are required.

2.2.4. Reconfigurable MIMO Antennas

The final category is reconfigurable MIMO antennas. A multifunctional reconfigurable MIMO antenna has first been suggested in [49]. The operating frequency and the polarization of the proposed antenna can be reconfigured electronically. Later, the research focus turned to pattern reconfigurable MIMO antennas [50] – [53]. These antennas have the capability of switching their radiation patterns at a fixed operating frequency while maintaining a low mutual coupling between the antenna ports. Another type of reconfigurable MIMO antenna that can be found in the literature is frequency switchable MIMO antennas [54], [55]. In this case, the design

15 objective is to keep a constant radiation pattern and low mutual coupling for all the configurations. Finally, a more general form of frequency reconfigurable MIMO antenna that has continuous frequency tuning capability is yet to be reported in the literature.

2.3. CHAPTER SUMMARY

In this chapter, the fundamentals of a MIMO communication system are described. The effect of antenna mutual coupling plays a significant role in the achievable capacity of the system. Under most practical scenarios, antenna mutual coupling degrades the channel capacity and reduces the total radiated power of the MIMO antenna. In addition, a survey of existing MIMO antenna design has been included in this chapter. We have seen that multimode antennas offer the most compact MIMO antenna solution. In terms of reconfigurable MIMO antennas, there are a considerable number of reported research works for pattern/polarization reconfigurable and frequency switchable MIMO antennas. MIMO antennas with continuously and electronically tunable operating frequency have not been reported in the literature.

16

CHAPTER 3: THEORY AND DESIGN OF AN LTE FEMTOCELL BASE STATION ANTENNA

Noting that the operating frequency of the LTE system is at 700 MHz, conventional MIMO antennas, such as physically spaced and orthogonally oriented MIMO antennas, would be too big to be packed into a volume of a typical wireless router. Nevertheless, in Chapter 2, we have seen that a multimode design could offer a compact MIMO antenna solution. In this chapter, we will focus on the design of a multimode antenna for an LTE small-sized low-power femtocell base station.

3.1. SELECTION OF A BASE ANTENNA DESIGN

Our antenna is based on the dielectric resonator antenna (DRA), which can be considered a lossy resonant cavity for which the major loss mechanism is radiation. Although the cost of DRAs may be high compared to traditional PIFAs or microstrip antennas, they have the advantages of relatively compact size, high radiation efficiency, and wide impedance bandwidth (~ 10% for dielectric constant εr ~ 10) [56]. Another important feature of DRAs is that the three-dimensional structure offers an additional degree of freedom in exciting various orthogonal resonant modes. Each mode, if properly excited, can be utilized to transmit and receive information independently. This makes DRA an ideal candidate for application in MIMO communication systems.

In terms of MIMO DRA, the concept was first described and demonstrated by Ishimiya et al. in

[45]. Ishimiya’s design is a cubic DRA (0.14λ0 × 0.14λ0 × 0.14λ0 with εr = 21) with three excitations. It was experimentally measured in a reverberation chamber that the cubic MIMO DRA has an average diversity gain of 9.6 dB across the ports. Moreover, in an actual IEEE 802.11n system throughput measurement, the system equipped with the cubic MIMO DRA can offer 36.9% and 3.9% improvement over a traditional 3 × 1 MIMO dipole array in line-of-sight (LOS) and non-line-of-sight (NLOS) scenarios, respectively.

17

Although Ishimiya’s design is able to increase the system performance over a traditional MIMO dipole array, no explicit design method was described in the paper. For the purpose of MIMO DRA designs in general, and an antenna design for a LTE femtocell base station in particular, we would like to introduce a systematic design methodology for MIMO DRAs.

3.2. BASE ANTENNA CONFIGURATION

In order to have a design with lower profile and greater flexibility as compared to Ishimiya’s, we consider a half-cylindrical DRA as shown in Figure 4. The dielectric has a dielectric constant εr of 18, a radius a of 44 mm and a length h of 80 mm. The dielectric block is bounded by two perpendicular ground planes so that its modal field distributions resemble those in a full- cylindrical block. The resonant frequency of the half-cylindrical dielectric block can thus be maintained while a lower profile can be achieved and the dielectric block can be excited more easily. The TE011+δ mode and the HE11δ mode can be excited simultaneously using appropriate excitation methods, such as probe feeds, aperture coupling or microstrip feeds. The value of the subscript δ ranges between zero and one, depending on the method of feeding [57]. Here, a 50 Ω microstrip-fed rectangular slot and a coaxial probe feed were chosen to excite the TE011+δ and

HE11δ modes, respectively (see Figure 4). FR-4 epoxy board (εr = 4.4) with thickness of 1.6 mm is used as the substrate of the microstrip line. The dimensions of the slot are 50 mm × 4 mm and the probe that excites the HE11δ mode has a length of 27 mm. The dimensions were tuned such that the two modes are impedance matched to 50 Ω.

z coaxial feed a

x y a a split-cylindrical DRA h

a ground plane a FR-4 substrate slot microstrip line

Figure 4. Perspective view of the split-cylindrical DRA. 18

Figure 5 shows the plots of the theoretical magnetic field distributions for the two modes inside the DRA computed using Wolfram Research Mathematica [58]. It can be seen that the TE011+δ mode behaves as a magnetic dipole on the x-axis while the HE11δ mode radiates as a short magnetic dipole oriented along the y-axis. The two modes are therefore orthogonal to each other and should exhibit low mutual coupling. The resonant frequencies of the TE011+δ mode and HE11δ mode can be derived from the separation equation and are found to be 653 MHz and 520 MHz, respectively,

 2 2 TE011 c  01     f r       , (10) 2  r  a   2h 

2  2 HE11 c 11  fr , (11) 2r ah2

where c is the speed of light in free space,  and  are the first zeros of the zero-order Bessel 01 11 function and the derivative of the first-order Bessel function, respectively. A full-wave simulation was performed using Ansoft HFSS [59] and the simulated S-parameters of the antenna are shown in Figure 6. The theoretically predicted and simulated operating frequencies of the modes agree very well with each other. It can also be seen that the coupling S21 between the two modes is very low as expected.

(a) (b)

Figure 5. Theoretical magnetic field distributions for the (a) TE011+δ mode, and (b) HE11δ mode (unit in mm). 19

0

-10

-20

-30

parameters parameters (dB)

- S -40

-50 500 550 600 650 700 Frequency (MHz)

SS11 (HE) S22 (TE) S21 (mutual coupling)

Figure 6. Simulated S-parameters of the unperturbed cylindrical DRA in HFSS.

3.3. DESIGN OF A MIMO DRA

From the previous section, it has been seen that the proposed dual-mode DRA has two distinct resonant frequencies. However, in order to work in a MIMO system, the two modes of the antenna should have the same resonant frequency and share a common impedance bandwidth. To accomplish this, we propose a mode degeneration method based on boundary perturbation.

3.3.1. Boundary Perturbation Method

For an arbitrarily shaped perfect electric conductor (PEC) cavity resonator, the change in resonant frequency due to a change of the cavity wall was derived using perturbation theory by Harrington in [60], and is given by

20

HE22 dv ff   00 0  v , (12) 22 f0 HE dv   00 V

where ε and μ are the permittivity and the permeability of the cavity respectively; ω and ω0 are the resonant frequencies of the perturbed and unperturbed cavity, respectively; Δv and V are the volume perturbed and the original volume of the cavity, respectively; and E0 and H0 are the original fields. Noting that the DRA is well modeled by a perfect magnetic conductor (PMC) cavity, Equation (12) must be re-derived for a PMC cavity before it can be applied to our proposed design.

Now, consider a PMC cavity and its perturbed counterpart. The fields inside the cavities must satisfy Maxwell’s equations,

EH00   j0  , (13a)  HE00  j0 EH   j and,  , (13b)  HE  j

where E0 and Η0 are the original fields in the unperturbed cavity, and E and H are the fields in the perturbed cavity. Following the same procedure in [60] and applying the vector identity,

ABBAAB      , (14) yields

*** HEEEHH 0 jj  0  0  0  , (15a)

*** HEHHEE0  jj  0  0  0  . (15b)

Adding these two equations and integrating over the volume of the perturbed cavity V gives

21

H E* H ** EEdv E  * jdv H  H     . (16)  0  00 0  0    VV

Applying the divergence theorem, the left-hand side (LHS) of Equation (16) then becomes

LHS H  E**  ndS  H  E  n dS  00    , (17) SS where S denotes the surface enclosing the perturbed volume and n is the unit normal vector of

** the surface . Since H E00  n  E  n  H and with the boundary condition nH0 on the perturbed PMC surface , LHS reduces to

H*  E ndS   0  . (18) S

* In addition, since nH0 0 on the unperturbed PMC surface S,

H*  E  ndS  0   0  , (19) S and noting that S  S   s (where s represents the perturbed surface), LHS becomes

HEn****dS HEn  dS HEn  dS HEn  dS  0  0  0   0  . (20) S S S s

Therefore, Equation (16) now can be written as

H***  E  ndS  j    E  E   H  H dv  0  0   0 0  . (21) sV

After re-arranging, Equation (21) becomes

22

jdS H*  E n   0   S . (22) 0 EEHH**   dv   00 V 

Now, for small perturbation, the perturbed fields E and H can be approximated by the original fields E0 and Η0 , yielding

jdS H*  E n   00 S 0 . (23) HE22 dv   00 V 

From the conservation of complex power and by neglecting any loss in the system, the numerator can be rewritten as

S** ndS  E  H  n dS   j  H22   E dv , (24)   00 0 0 0  S  Sv where S* is the complex conjugate of the Poynting vector. Finally, substituting Equation (24) into Equation (23), we get

H22 E dv    00 0  v , (25) 22 0 H E dv   00 V

which is identical to Equation (12). Hence, the change in resonant frequency due to the perturbation on the cavity can be estimated using the same equation regardless of the boundary material. A physical interpretation of Equation (12) or (25) is that the change in resonant frequency is proportional to the portion of electric and magnetic energies removed by the perturbation [60], i.e.,

23

cylindrical boundary of perturbation, α the DRA radius, a

ground plane

   W  W 0  m e , (26) 0 W

where We and Wm are time-averaged electric and magnetic energies originally contained in the volume perturbed (Δv) and W is the total energy stored in the original cavity.

3.3.2. Boundary Perturbed MIMO DRA

Now consider a boundary perturbation from the base of the half-cylindrical DRA as depicted in

Figure 7. The changes in resonant frequencies of the TE011+δ mode and HE11δ mode were computed using Equation (26) using Mathematica, and the results are given in Figure 8. It can be observed that as the electric boundary on the xy-plane is moved up, the resonant frequency of the

HE11δ mode increases more rapidly than that of the TE011+δ mode. Hence, at a certain perturbation value, the two resonant frequencies should overlap and thus fulfill the primary requirement for MIMO antenna designs. According to Equation (26), the difference in the rate of change of resonant frequency can be explained by the difference in the energy stored by the two modes in the perturbation volume Δv. To verify the boundary perturbation method, an HFSS simulation was carried out and the result is also shown in Figure 8. It can be seen that the result predicted by the boundary perturbation method starts to deviate from the result obtained from HFSS as the perturbation, α, increases. This is due to the approximation of the original fields by the perturbed fields in Equation (23). The difference between the original fields and the

cylindrical boundary perturbation, α of the DRA radius, a

ground plane Figure 7. Boundary perturbation from the base of the split-cylindrical DRA (cross-sectional (yz-plane) view).

24

50

40

30

(%)

o f

20

Change of Change 10

0 0 2 4 6 8 10 12 14 Perturbation, α (mm) TE (HFSS) TE (Perturb.) TE (Elliptical) HE (HFSS) HE (Perturb.) HE (Elliptical)

Figure 8. Plot of change of resonant frequency f0 against the perturbation parameter α.

perturbed fields would be intolerable when the perturbation is too large. Thus, this deviation at large perturbations is inherent from the perturbation analysis. Nonetheless, the boundary perturbation method gives a good initial guess on how much perturbation is required to make the two modes resonate at the same frequency. According to the HFSS simulation result, the two modes both resonate at 700 MHz when α is 13 mm.

Lastly, it shall be noted that in Equation (26), there is no specific constraint on the geometry of the cavity; hence, the proposed boundary perturbation method can be applied to DRAs of any other shapes with arbitrary perturbations. However, the difficulty associated with the analysis of other arbitrary structures would be the evaluation of the integrals in Equation (26).

3.3.3. Boundary Approximation Method

While the above described boundary perturbation method obtains the solution by approximating the fields, the boundary approximation method estimates the change in resonant frequency by 25

minor axis of perturbed cylindrical the ellipse boundary of the DRA elliptical boundary

ground plane Figure 9. Elliptical approximation of the perturbed cylindrical boundary (cross-sectional (yz-plane) view). approximating the structure of the resonator. As shown in Figure 9, a perturbed cylindrical boundary can be approximated by a half ellipse. The accuracy of this method depends on how well the perturbed circular arc is modeled by an elliptic arc. The resonant frequencies of various modes in an elliptical DRA can be found analytically by expanding the fields inside the cavity in Mathieu functions and applying the technique of separation of variables. A detailed analysis of an elliptical DRA can be found in [61]. The resonant frequencies of a set of half-elliptical DRAs with decreasing minor axes (with correspondence to the previously described set of perturbation values α) were computed, and the corresponding change in resonant frequency is plotted in Figure 8. The results obtained agree very well with those calculated by both the boundary perturbation method and full-wave simulations.

3.4. SIMULATION RESULTS

3.4.1. Antenna Radiation Characteristics

From Section 3.3.2, the TE011+δ mode and the HE11δ mode of the half-cylindrical DRA both resonate at 700 MHz when the perturbation, α, is 13 mm. After the perturbation, the dimensions of the antenna become 80 mm × 84 mm × 31 mm (208320 mm3). For a comparison, the dimensions of a 2 ×1 MIMO PIFA with half-wavelength antenna separation would be 107 mm × 214 mm × 10 mm (228980 mm3), given the same resonant frequency and similar bandwidths. Since coupling between antenna ports is another important parameter to characterize MIMO antennas, the proposed antenna structure is simulated in HFSS. The simulated S-parameters of

26

0

-10

-20

-30

parameters parameters (dB)

- S -40

-50 500 550 600 650 700 750 800 Frequency (MHz) SS 11 (HE,(HE, original)original) SS 11 (HE, (HE, perturbed) original)

SS 22 (TE,(TE, original)original) SS 22 (TE, (TE, perturbed) original)

SS 21 (mutual(mutual coupling,coupling, original)original) SS 21 (mutual (mutual coupling, coupling, perturbed) original)

Figure 10. Simulated S-parameters of the proposed MIMO DRA. the antenna are given in Figure 10. It can be observed that the mutual coupling between the two modes is insensitive to the perturbation and is less than –40 dB. This is significantly lower than the mutual coupling in conventional MIMO antennas that are based on dipole antennas, patch antennas or PIFAs [62] – [65]. The impedance bandwidths (defined as VSWR < 2:1) of the

TE011+δ mode and the HE11δ mode are 10 MHz and 35 MHz respectively. The TE011+δ mode has a relatively narrow bandwidth and limits the overall bandwidth of the antenna. Nevertheless, the bandwidth of the TE011+δ mode can be improved using well known bandwidth broadening techniques, such as inserting an air gap between the ground plane and the DRA [66] – [67], or adding a matching stub at the end of the microstrip line [68]. The simulated gains of the TE011+δ and HE11δ modes are 3.96 and 3.19 dBi, respectively. The simulated radiation patterns of the two modes are given in Figure 11. As seen in the figure, the radiation patterns of the two modes are orthogonal to each other. Because of the pattern orthogonality, the antenna is also able to exploit polarization diversity.

27

(a)

(b)

Figure 11. Radiation patterns of (a) port 1 (HE mode) and (b) port 2 (TE mode). (Solid line: Eθ; Dotted line: Eφ.)

3.4.2. MIMO Performance Evaluation

The channel capacity gain by using the proposed antenna was evaluated with the aid of Remcom Wireless Insite [69]. In the simulation setup, a single transmitter and 1000 identical receivers were placed in an office environment as shown in Figure 12. The office environment was constructed to resemble a rich scattering environment (i.e., the channel statistics are approximately Rayleigh distributed). In order to resemble a time-varying MIMO channel, the receivers were randomly spread across the designated area of the office such that 1000 non-line- of-sight (NLOS) communication links were established. In all the simulations, there were 80

28

receivers

transmitter

Figure 12. The floor plan of the office environment that was used to estimate the MIMO channel capacity (notice that there is no line-of-sight (LOS) path between the transmitter and any of the receivers).

physical propagation paths considered for each channel realization. The simulated complex radiation patterns (including both polarizations, Eθ and Eφ) of the proposed antennas were used at the transmitter and all the receivers. 1000 samples of the unnormalized channel matrix were then obtained from the simulation [70],

m m m h11 h12  H    , (27) hm hm  21 22 where there are m (= 1, 2, …, 1000) communication links, and H m is the unnormalized channel

th m th matrix of the m link. Here, huv represents the m sample of the complex channel gain between port u of the transmitter and port v of the receiver, where subscripts u = 1, 2 and v = 1, 2, with given by

29

km m m j m n huv   Pn e . (28) n1

Here k is the number of paths in the mth link, Pm is the received power contributed by the nth m n th m th th path in the m link, and  n is the phase of the n path in the m link. In this case, the number of paths km is limited to be 80, based on the fact that the propagation channel is sufficiently represented. From the simulated channel data, it is found that the coherence bandwidth of the wireless channel is much larger than the bandwidth of the proposed antenna. Hence, for equal power distributed among the transmit antennas, the flat-fading MIMO channel capacity of the mth link, Cm, can be calculated by [17]

   †  Cm  log det I  H m H m  2  Nr norm norm  , (29)   Nt 

where  is the mean signal-to-noise ratio (SNR) per receive branch; {·}† represents a complex

m th conjugate transpose; and Hnorm is the m normalized channel matrix [70],

m m H H norm  , (30) 2 H m F Nt Nr

2 where  denotes a Frobenius norm. The mean capacity and the maximum achievable capacity F obtained by using the proposed MIMO DRA are plotted in Figure 13. As a reference, Figure 13 also gives the theoretical channel capacities for single-input single-output (SISO), 2  2 and 3  3 channels with zero mean, unity variance, i.i.d. complex Gaussian distributed channel elements. The results indicate that the estimated mean channel capacity is 11.1 b/s/Hz at an SNR of 20 dB per receiver branch. The maximum achievable capacity is very close to the theoretical maximum 2  2 MIMO capacity of 13.4 b/s/Hz. The small discrepancy between the theoretical and simulated capacities may due to the non-perfect Raleigh scattering environment and the finite

30

50

40 )

30

20

10 Channel capacity (b/s/Hz capacity Channel

0 0 5 10 15 20 25 30 35 40 SNR (dB) Series1 Ideal 2×2 Ideal 3×3 Est. mean (DRA) Est. max. (DRA) Est. mean (dipole) Est. max. (dipole)

Figure 13. Estimated channel capacity of the proposed MIMO DRA.

mutual coupling between the modes. Furthermore, the achievable capacity of the MIMO DRA is also compared that would have been obtained using crossed half-wavelength dipoles, as shown in Figure 13. It can be seen that the mean capacity obtained with the MIMO DRA is 28% higher than that of crossed dipoles at an SNR of 20 dB. The maximum achievable capacities for both cases, however, are very close because of the finite mutual coupling.

3.5. MEASUREMENT RESULTS

The perturbed cylindrical DRA was built and tested in the Antenna Laboratory at University of

Illinois at Urbana-Champaign. The dielectric material (εr = 18 and loss tangent < 0.00015) was supplied by Countis Laboratories [71]. The dielectric block was bonded onto the ground plane with silver epoxy so as to prevent any air gaps between the dielectric and ground plane. This is important because the expected input impedance of DRAs with high permittivities could be

31

0

-10

-20

-30

parameters parameters (dB)

- S -40

-50 500 550 600 650 700 750 800 850 900 Frequency (MHz)

S11 (HE) S22 (TE) S21 (mutual coupling)

Figure 14. Measured S-parameters of the perturbed cylindrical DRA.

1.0

0.5

2.0 2.0

0.2

0 0.1 0.5 1.0 2.0 5.0

-0.2 TE (simulated)

HE (simulated)

-2.0 -2.0 TE (mesasured) -0.5 HE (measured)

-1.0

Figure 15. Comparison between the measured and simulated S11 (HE) and S22 (TE) of the perturbed cylindrical DRA on a Smith chart significantly altered even for air gaps of less than 0.05 mm [57]. Figure 14 shows the measured S-parameters of the perturbed cylindrical DRA and Figure 15 compares the measured and the simulated S11 and S22 on a Smith chart. The measurement results agree very well with the simulation. The coupling between the ports (S21) is less than –30 dB at the operating frequency.

32

(a)

(b)

Figure 16. Comparison of the simulated (with markers) and measured (without markers) radiation patterns of (a) port 1 (HE mode) and (b) port 2 (TE mode). (Solid line: Eθ; Dotted line: Eφ.)

The measured impedance bandwidths of the TE011+δ mode and the HE11δ mode are 13.5 MHz and 35 MHz respectively. The measured radiation patterns along the three principal cuts are given in Figure 16. The measured patterns agree reasonably well with the simulated ones and the complementary nature of the two orthogonal modes can be observed clearly.

33

3.6. CHAPTER SUMMARY

A two-port MIMO antenna based on a half-cylindrical DRA is described in this work. A mode degeneration method derived from perturbation theory is proposed to make the TE and HE modes of the half-cylindrical DRA resonate at the same frequency. The proposed method has been shown to agree with both full-wave simulations and the boundary (elliptical) approximation method, and can be applied to DRAs of any shape. Experimental measurements also confirm the design theory and the measured results with the fabricated MIMO DRA show a very good agreement with the simulated results. The proposed antenna is therefore potentially suitable as the femtocell base station antenna in the LTE bands 12 (698 MHz – 716 MHz, 728 – 746 MHz) and 17 (704 MHz – 716 MHz, 734 MHz – 746 MHz).

Finally, for the purpose of comparison, Ishimiya’s design would have dimensions of 92.9 mm × 92.9 mm × 92.9 mm (801765 mm3) if it was scaled to operate at 700 MHz. As a reference, our proposed design has dimensions of 80 mm × 84 mm × 31 mm (208320 mm3). Therefore, although our proposed antenna only has two ports, our design has a lower profile, a smaller ground plane and a much lower mutual coupling than the previously reported design.

34

CHAPTER 4: IMPLEMENTATION OF FREQUENCY RECONFIGURATION

To design an antenna for a hybrid LTE/CR low-power node, the approach is to investigate the feasiblility of adding frequency reconfigurability into the MIMO DRA previously described in Chapter 3. We will first introduce a frequency reconfiguration modality via material perturbation, from which we will develop a theoretical framework for achieving maximum frequency agility. After that, an alternative method based on parasitic loading for implementing frequency reconfiguration to the MIMO DRA will be described.

4.1. FREQUENCY RECONFIGURATION VIA MATERIAL PERTURBATION

The first step is to investigate how the resonance frequency of an antenna mode changes in response to a material perturbation inside an antenna. Consider an arbitrarily shaped antenna which can be modeled by a cavity (e.g., microstrip patch antenna, dielectric resonator antenna, etc.). The change of its resonance frequency due to a material perturbation inside the cavity V can be estimated using the perturbation technique given by Harrington [60],

E22   H dv ff   00 f 0   v , (31) 22 f0 E H dv   00 V where Δε and Δμ denote the amount of change in relative permittivity and permeability, respectively, in the perturbation volume v inside V. The above equation signifies that Δf would be maximized if the perturbation is placed at maximum electric field or magnetic field. Hence, this allows us to decide the location of material perturbation for maximum frequency agility.

35

4.1.1. Analysis with Eigenvalue Perturbation

If the locations of field maxima of an antenna are known, it would then be straightforward to apply Equation (31) to determine the optimal placement for the material perturbation. However in some cases, such information may not be known readily. Eigenvalue perturbation offers an alternative solution to the problem [72] – [73]. Again, consider an antenna which can be modeled by a cavity. The electric field inside the cavity should satisfy the Helmholtz vector equation, with boundary conditions nE0 on the electric walls and nE0 on the magnetic walls. By applying the Galerkin procedure in finite element analysis, one can convert the Helmholtz equation into a generalized eigenvalue problem [74],

2 [Att0 ]{eett } k z 0 B tt 0  { } , (32)

1 where BBBBB  (33)  tt0  tz 0 zz 0  zt 0  tt 0 

MM1 TT and [][]A Ake   d NNNN e    e 2 e e  e  (34a) tt0 tt 00 e e  t  t r     ee11r

MM1 T [][]B Bdee  e  NN (34b) tt00 tt e e     ee11r

MM 1 T [][]B BT  BN e  d N e   e  (34c) tz0 zt 0 tzt 0 e e     ee11r

MM1 TT []B Be   N e   N e  k2 e N e N e d  (34d) zz0 zz 0e e  t  t 0 r    ee11r

and et = kz0Et and ez = ‒jEz, where Et is the transverse component of the electric field and Ez the e e z-component; M is the number of elements;  r and r are the relative permittivity and th e e permeability of the e element, respectively; N and N are the basis functions for expanding Et and Ez respectively. With the given boundary conditions, Equation (32) can be solved for

36 eigenvalues k 2 and eigenvectors {e }. Now suppose a material perturbation is introduced to the z0 t antenna,

ee e pr +   for e r   e (35) r otherwise,

where is a subset of the elements ={1, 2, 3, …, M}. We expect the matrix [Att0] would vary e by a small amount as it has a dependence on εr (as seen in Equation (34a)), i.e., [Att] = [Att0] + [δAtt]. Therefore, it is expected that the corresponding eigenvalues would also be varied by a small amount, i.e.,

2 2 2 2 T kz k z00  k z  kA ztt eett    . (36)

Hence, a sensitivity analysis on k 2 with respect to the change in the entries of [A ] can be z tt0 performed to determine the optimal perturbation location for maximum frequency agility. Following the derivations in [72], one obtains

k 2 z ee(2 j ) , (37)  tt()()ij  i Att0( ij )

j where i and j are the indices of matrix [Att0]; i denotes the Kronecker delta. Thus, the precise location, or the set of elements , that needs to be perturbed for maximizing Δf can be determined easily using Equation (37).

4.1.2. Example on Microstrip Patch Antenna

As an example, a microstrip patch antenna, with dimensions 60 mm × 40 mm, built on a substrate with dielectric constant εr is considered. It is assumed that the height of a substrate is negligibly small as compared to the resonant wavelength. Using the cavity model, the resonant

37 frequency and the wavenumber for the first four TM modes were computed and are listed in Table 1. It can be seen that the results obtained from the MATLAB finite element method (FEM) cavity model match very well with that obtained from HFSS simulation. Next, we would like to put a material perturbation in the antenna so as to achieve frequency reconfigurability. Following the procedure described in the previous section, the optimal set of elements for material perturbation was found for the first four TM modes and is shown in Figure 17. In other words, the resonant frequency of the corresponding mode is the most sensitive to the perturbation in the colored elements given in Figure 17. For example, if one wanted to change the resonant frequency of the TM10 mode, then the most effective elements to be perturbed are the colored elements given in Figure 18(a). Moreover, it can be seen that the location of the colored elements coincides with the field extrema of the antenna (see Figure 18). Thus, the result from our analysis agrees with the prediction using Equation (31).

Table 1. Resonant frequency and wavenumber for the first four TM modes.

MATLAB FEM cavity model Ansoft HFSS Mode (m-1) (m-1) f0 (GHz) f0 (GHz) f0 (GHz) f0 (GHz) (ε = 1) (ε = 1) (ε = 5) (ε = 5) (ε = 1) (ε = 5) r r r r r r TM10 2.4989 -2303 1.1176 -547 2.4983 1.1173 TM01 3.7478 -5726 1.6761 -3970 3.7474 1.6759 TM11 4.5050 -8471 2.0212 -6714 4.5038 2.0142 TM20 4.9979 -10533 2.2351 -8777 4.9965 2.2345

(a) (b) (a) (b)

(c) (d) (c) (d) Figure 17. Sets of elements for material Figure 18. Simulated field distributions of the perturbation for maximum frequency agility: microstrip patch antenna: (a) TM10, (b) TM01, (a) TM10, (b) TM01, (c) TM11, and (d) TM20 (c) TM11, and (d) TM20. (the green elements are the elements needed to be perturbed). 38

4.1.3. Application to MIMO Dielectric Resonator Antenna

Now, we would like to apply the above analysis to the MIMO DRA described in Chapter 3. It is known that the electric field of the HE mode is the strongest near the feeding coaxial probe while that of the TE mode is the strongest around the feeding slot on the bottom ground plane (as seen in Figure 19). Hence, it follows that the perturbation should be placed at those field maxima and this is illustrated in Figure 20. The corresponding simulated S-parameters of the antenna for the two different perturbations are given in Figures 21 – 24. For Perturb. A, as εp increases, the operating frequency of the TE mode (S22) shifts downward from 700 MHz to 538 MHz, while that of the HE mode (S11) remains fairly constant (except when εp is lower than 18 which is the original relative permittivity of the DRA). A similar behavior can also be observed for Perturb.

B where only the operating frequency of the HE mode is sensitive to the changes in εp, sweeping from 800 to 665 MHz. It is also noticed that, for both perturbations, the mutual coupling (S21) between the modes is always kept below -40 dB. This indicates the modes are fairly decoupled and their operating frequencies can be adjusted individually. Hence, the antenna is tunable from 538 MHz to 800 MHz and operates in MIMO mode from 665 MHz to 700 MHz.

TE mode HE mode

Figure 19. Simulated electric field distribution inside the MIMO DRA. 39

(a) (b)

Figure 20. A MIMO DRA with material perturbation. The grey volumes indicate the portion of the dielectric cavity perturbed (a) Perturb. A and (b) Perturb. B.

0

-10

-20

-30 S11 S21

parameters (dB) parameters -40

- S

-50

-60 500 550 600 650 700 750 800 850 Frequency (MHz)

S11S11 ((εεpp=1) = 1) S11S11 ((εεpp=18) = 18) S11S11 ((εεpp=40) = 40) S11S11 (εp=60)p = 60)

S21S21 ((εεpp=1) = 1) S21S21 ((εεpp=18) = 18) S21S21 ((εεpp=40) = 40) S21S21 (εp=60)p = 60)

Figure 21. Simulated S11 (HE mode) and S21 of the MIMO DRA with Perturb. A.

40

0

-5

-10

-15

parameters (dB) parameters -20

- S Increasing εp -25

-30 500 550 600 650 700 750 800 850 Frequency (MHz)

S21S22 (εεpp=1) = 1) S21S22 (εpp=18) = 18) S21S22 (εεp=40)p = 40) S21S22 ((εεpp=60) = 60)

Figure 22. Simulated S (TE mode) of the MIMO DRA with Perturb. A. 22

0

-5

-10

-15

parameters (dB) parameters -20

- S

-25 Increasing εp

-30 500 550 600 650 700 750 800 850 Frequency (MHz)

SS2111 ( ε(pε p=1)= 1) S21S11 ((εεpp=18) = 18) S21S11 ( (εεpp=40) = 40) S21S11 ( (εεpp=60) = 60)

Figure 23. Simulated S11 (HE mode) of the MIMO DRA with Perturb. B.

41

0

-10

-20 S22

-30

parameters (dB) parameters -40 S21

- S

-50

-60 500 550 600 650 700 750 800 850 Frequency (MHz)

S11S11 (εpp=1) = 1) S11S11 (εpp=18) = 18) S11S11 ((εεp=40)p = 40) S11S11 ((εεpp=60) = 60)

S21S21 (εpp=1) = 1) S21S21 (εpp=18) = 18) S21S21 ((εεp=40)p = 40) S21S21 ((εεpp=60) = 60)

Figure 24. Simulated S22 (TE mode) and S21 of the MIMO DRA with Perturb. B.

4.2. FREQUENCY RECONFIGURATION VIA PARASITIC LOADING

In the previous section, material perturbation is studied as a means to add frequency agility to the MIMO DRA. Although the TE port is able to reconfigure from 538 MHz to 700 MHz and HE port from 665 MHz to 800 MHz, the overlapping tunable range for MIMO operation is only from 665 MHz to 700 MHz, which is fairly narrow. Moreover, it is practically difficult and cumbersome to vary the relative permittivity in a selected volume, although it has been experimentally demonstrated in [75] and [76]. A second modality for frequency reconfiguration is therefore presented in this section.

4.2.1. Antenna Configuration

It is known that the presence of a parasitic slot on the ground plane of a DRA can detune the resonant frequency of the antenna [77]. Both theoretical and measurement results in [77] show

42 that the amount of detune is directly related to the length of the parasitic slot. The next step is to investigate how parasitic slots can be incorporated into the MIMO DRA to provide frequency agility.

Consider the MIMO DRA shown in Figure 25. The dielectric block is the same as the one used in Chapter 3, but for simplicity, the two modes are now excited by two slots which are fed directly by coaxial probes. The coaxial feed of the slot for HE mode excitation is located at the center of the slot while that for the TE mode excitation is placed at 2.5 mm from the end of the slot. The corresponding simulated S-parameters of the antenna are given in Figure 26, which is almost the same as that shown in Figure 10, except for a slight frequency shift. Now, in order to enable frequency reconfigurability, the ground planes are modified to include parasitic slots as depicted in Figure 27. The parasitic slot on Ground Plane A has four switches (hard-wired for proof of concept) SWA1, SWA2, SWA3 and SWA4 (SW Set A), and a varactor CHE at the center of the slot. When SWA4 is OFF, the length of the parasitic slot can be varied electronically, depending of the states of SWA1, SWA2 and SWA3. On the other hand, when SWA4 is ON while all other switches in SW Set A are OFF, the parasitic slot is then loaded with the varactor CHE. For the excitation slot on Ground Plane B, two varactors (CTE1 and CTE2) can be switched to load the slot. Selection between the two loading slots can be made by controlling the switches SWB1 and

SWB2 (SW Set B).

z 52 mm Ground Plane A

y x 53 mm 2 mm coaxial feed (port 1, HE mode)

dielectric (εr = 18) Ground Plane B 4 mm coaxial feed (port 2, TE mode)

Figure 25. A MIMO DRA excited by two slots fed by coaxial cables.

43

0

-20

-40

parameters (dB) parameters -

S -60

-80 600 650 700 750 800 850 Frequency (MHz)

SS 11 (HE) S22 (TE) S21 (mutual coupling)

Figure 26. Simulated S-parameters of the MIMO DRA shown in Figure 25.

z y y dielectric boundary x excitation (TE) excitation (HE) 4 52

2 4 3 SWA4 SW 7 B2 66.5 CTE2 SWB1 2 CHE SW A3 4 2.5 SWA2 13 SWA1 ground plane 8 6 27.5 C TE1 4.5 13.5 55

(a) (b) Figure 27. Ground planes with parasitic slots: (a) Ground Plane A with a slot for HE mode excitation, (b) Ground Plane B with a slot for TE mode excitation (dimensions in mm).

44

4.2.2. Simulation Results

The performance of the MIMO DRA with the above described modified feeds was characterized using Ansoft HFSS. The first set of simulations was done to investigate the reconfigurability of the HE mode (port 1). During the simulations, SWB1 was kept OFF while SWB2 was switched ON and CTE1 was tuned to 11 pF. Figures 28 and 29 show the corresponding simulated S-parameters of the antenna. It can be seen that in Figure 27(a), SWA1, SWA2 and SWA3 are distributed along the parasitic slot. Different combinations of the switch states lead to six different slot lengths and therefore different operating frequencies. To achieve further frequency agility, varactor CHE can be connected to the parasitic slot by switching SWA4 ON. As the value of CHE decreases from 15 pF to 4 pF, the operating frequency of the HE mode can be continuously tuned from 701 MHz to 810 MHz. In summary, the operating range of the HE mode effectively covers from 630 MHz to 810 MHz. From Figure 29, it can also be seen that the operating frequency of the TE mode remains unchanged at 719 MHz during the reconfiguration, and the mutual coupling between the modes is also maintained under –17 dB. This implies that individual tuning of the HE mode is feasible without deteriorating the coupling.

0

-10

-20

-30 parameters (dB) parameters

- Continuously S tunable range -40

-50 600 650 700 750 800 850 Frequency (MHz)

S11S11 ((SWSW Set Set A A OFF) OFF) S11S11 ((SW_A1SWA1 ON ON)) S11S11 ((SW_A3SWA3 ON ON))

S11S11 ((SW_A1SWA1 & SW & SW_A3A3 ON) ON) S11S11 ((SW_A2SWA2 ON ON)) S11S11 ((SW_A2SWA2 & SW& SW_A3A3 ON) ON)

S11S11 ((C_HE1=4pF)CHE = 4 pF) S11S11 ((C_HE1=8pF)CHE = 8 pF) S11S11 ((C_HE1=15pF)CHE = 15 pF)

Figure 28. Simulated S11 (HE mode) of the MIMO DRA. The frequency agility is achieved by reconfiguring the parasitic slot on Ground Plane A.

45

0

-10

-20 S22

-30 S21

parameters (dB) parameters -40

- S

-50

-60 600 650 700 750 800 850 Frequency (MHz)

S22S22 (SW(SW Set AA OFF) OFF) SS2222 ( SW(SW_A1A1 ON) ON) S22S22 ((SW_A3SWA3 ON ON)) S22S22 (SW_A1(SWA1 & SW& SW_A3A3 ON) ON) SS2222 ( S(SW_A2WA2 ON) ON) S22S22 ((SW_A2SWA2 & SW & ASW_A33 ON) ON)

S22S22 (C_HE1=4pF)(CHE = 4 pF) SS2222 ( C(C_HE1=8pF)HE = 8 pF) S22S22 ((C_HE1=15pF)CHE = 15 pF)

S21S21 (SW(SW Set AA OFF) OFF) SS2121 ( SW(SW_A1A1 ON )ON) S21S21 ((SW_A3SWA3 ON ON)) S21S21 (SW_A1(SWA1 & SW& SW_A3A3 ON) ON) SS2121 ( S(SW_A2WA2 ON )ON) S21S21 ((SW_A2SWA2 & SW & ASW_A33 ON) ON)

S21S21 (C_HE1=4pF)(CHE = 4 pF) SS2121 ( C(C_HE1=8pF)HE = 8 pF) S21S21 ((C_HE1=15pF)CHE = 15 pF)

Figure 29. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA. The frequency agility is achieved by reconfiguring the parasitic slot on Ground Plane A.

The second set of simulations focused on the frequency agility of the TE mode (port 2). SW Set A was kept OFF throughout the simulations, except that SWA4 is switched ON and CHE was tuned to

15 pF. The simulated S-parameters of the antenna were shown in Figures 30 and 31. When SWB2 is switched ON while SWB1 is OFF, the excitation slot of the TE mode is loaded with CTE1. The operating frequency of the TE mode can be reconfigured from 650 MHz to 818 MHz as the value of CTE1 changes from 70 pF to 7 pF. When SWB1 is ON while SWB2 is OFF, the excitation slot of the TE mode is loaded with CTE2. The operating frequency of the TE mode can then be tuned continuously from 609 to 642 MHz, as the value of CTE2 changes from 9 pF to 4 pF. Hence the TE mode is able to cover from 609 MHz to 818 MHz. Similar to the first set of simulations, the HE mode is invariant at 718 MHz during the reconfiguration and the mutual coupling at the operating frequency can be kept below –20 dB, as seen in Figure 30. Again, this signifies the individual tunability of the TE mode.

46

0

-10 S

11

-20

-30

-40

parameters (dB) parameters

- S -50

-60 600 650 700 750 800 850 Frequency (MHz)

SS11 (CTE_1(CTE1 = 7= pF)x pF) SS 11 (CTE_1 (CTE1 = =9 xpF) pF) SS 11 (CTE_1 (CTE1 = =12 x pF)pF)

SS11 (CTE_1(CTE1 = 70= x pF) pF) SS 11 (CTE_1 (CTE2 = =4 xpF) pF) SS 11 (CTE_1 (CTE2 = =8 xpF) pF) SS11 (CTE_1(CTE2 = 9= pF)x pF) SS 21 (CTE_1 (CTE1 = =7 xpF) pF) SS 21 (CTE_1 (CTE1 = =9 xpF) pF)

SS21 (CTE_1(CTE1 = 12= x pF) pF) SS 21 (CTE_1 (CTE1 = =70 x pF)pF) SS 21 (CTE_1 (CTE2 = = 4 xpF) pF)

SS21 (CTE_1(CTE2 = 8= pF)x pF) SS 21 (CTE_1 (CTE2 = =9 xpF) pF)

Figure 30. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA. The frequency agility is achieved by reconfiguring the parasitic slot on Ground Plane B.

0

-10

-20

-30 parameters (dB) parameters - Continuously tunable range S -40

-50 600 650 700 750 800 850 Frequency (MHz)

SS 22 (C_TE1 (CTE1 = =7 9pF) pF) SS 22 (C_TE1 (CTE1 = =9 9pF) pF) SS 22 (C_TE1 (CTE1 = =12 9 pF)pF)

SS 22 (C_TE1 (CTE1 = =70 9 pF) SS 22 (C_TE1 (CTE2 = =4 9pF) pF) SS 22 (C_TE1 (CTE2 = =8 9pF) pF) SS 22 (C_TE1 (CTE2 = =9 9pF) pF)

Figure 31. Simulated S (HE mode) of the MIMO DRA. The frequency agility is 11 achieved by reconfiguring the parasitic slot on Ground Plane B.

47

From Figures 29 and 30, it can be seen the mutual coupling is relatively high when the tuning of the HE mode and TE mode is achieved by changing the length of the parasitic slot and the activation of the slot loading connected through SWB2, respectively. This is because the slot loadings are asymmetric about the x-axis and this disturbs the symmetry of the mode distributions.

Table 2 summarizes the controlling parameters for various antenna configurations. Frequency agile MIMO operation can be achieved from 630 MHz to 810 MHz (with a continuously tunable range from 701 MHz to 810 MHz, given the capacitance range specified in Table 2). The operating frequency of an individual mode can also be tuned separately. This is a new functionality for frequency reconfigurable MIMO antennas. Furthermore, it should be emphasized that the gain of the stationary mode (modes with invariant operating frequency during reconfiguration) is fairly steady. Therefore this allows a minimal gain calibration throughout the band of tuning, easing the burden on the gain control unit.

Table 2. A summary of the antenna parameters for various configuration settings.

SW Set A SW Set B CHE CTE1 CTE2 fHE fTE max(S21) GainHE GainTE

SWA1 SWA2 SWA3 SWA4 SWB1 SWB2 (pF) (pF) (pF) (MHz) (MHz) (dB) (dBi) (dBi) ON 11 630 719 −52.6 3.43 3.95

ON ON 11 644 719 −27.8 3.46 3.97

ON ON 11 659 721 −23.1 3.62 3.97

ON ON ON 11 670 719 −30.3 3.64 3.93

ON ON 11 680 719 −17.2 3.7 3.94

ON ON ON 11 696 719 −25.4 3.78 3.93

ON ON 15 11 717 719 −40.6 3.86 3.88

ON ON 8 11 739 719 −37.3 3.97 4.18

ON ON 4 11 784 719 −35.7 4.21 4.38

ON ON 15 7 718 818 −37.7 3.9 4.27

ON ON 15 9 718 755 −38.1 3.89 4.03

ON ON 15 12 718 708 −35.6 3.86 3.88

ON ON 15 70 718 650 −49 3.91 3.48

ON ON 15 4 717 642 −27.6 3.84 3.03

ON ON 15 8 717 622 −26 3.9 2.74

ON ON 15 9 717 609 −27.2 3.88 2.24

48

To demonstrate MIMO frequency reconfigurability, three different configurations of the antenna are considered (see Table 3). The corresponding simulated S-parameters of the antenna are given in Figure 32. It can be seen that both of the antenna ports are able to change the operating frequency while a low mutual coupling between the ports is maintained. The corresponding radiation patterns are given in Figure 33. It can be observed that the radiation patterns maintain orthogonality and do not change abruptly during reconfigurations (except that the cross polarization levels increase slightly as the operating frequency is decreased).

Table 3. Antenna configurations for demonstrating frequency reconfigurable MIMO functionality.

SW Set A SW Set B CHE CTE1 CTE2 Config. SWA1 SWA2 SWA3 SWA4 SWB1 SWB2 (pF) (pF) (pF) 1 ON 6.6

2 ON ON 15 11

3 ON ON 4 8

0

-10

Config. 1

-20 Config. 3 Config. 2

-30

parameters (dB) parameters

- S

-40

-50 600 650 700 750 800 850 Frequency (MHz)

S11S11 ((Config.Config. 11)) S22S22 ((Config.Config. 11)) S21S21 ((Config.Config. 11))

S11S11 ((Config.Config. 22)) S22S22 ((Config.Config. 22)) S21S21 ((Config.Config. 22))

S11S11 ((Config.Config. 33)) S22S22 ((Config.Config. 33)) S21S21 ((Config.Config. 33)) Figure 32. Simulated S-parameters of the frequency reconfigurable MIMO DRA. 49

(a)

(b) Figure 33. Simulated radiation patterns of the frequency reconfigurable MIMO DRA: (a) HE mode (port 1) and (b) TE mode (port 2). (Solid line: Eθ; Dotted line: Eφ; the color code can be referred to Figure 32.)

4.2.3. Integration with DC Bias Networks and Active Components

In the previous section, we have seen that parasitic slot loading provides a simple yet effective way to add frequency reconfiguration into the proposed MIMO DRA. The next step is to insert DC bias networks and active tuning/switching elements into the antenna structure. Figures 34 and 35 show the schematic of the actual implementation of a DC bias network on Ground Plane A and an equivalent circuit model of the parasitic slot. The bias network is designed with reference to [78]. In the design, a PIN diode was selected as the switching element because it is inexpensive and has a very low turn-on voltage. As seen in Figure 34, to accommodate the DC

50

dielectric boundary coaxial probe (HE)

RF choke DC block (inductor) (capacitor)

PIN diode varactor DC pad Figure 34. A schematic showing the actual implementation of a DC bias network on Ground Plane A.

Lc Lc Lc Lc VA1 VA2 VA4 VA3 C C Cb Cb Cb Cb Cb Cb b b

SWA4 SWA1 SW SWA2 Lc Lc A3 CHE

Cb Cb VHE Lc Figure 35. An equivalent circuit model of the parasitic slot.

bias network, the excitation of the HE mode has been changed back to a coaxial probe feed. In addition, Figures 36 and 37 respectively show the schematic of Ground Plane B with a DC bias network and an equivalent circuit model of the TE mode excitation slot. For both cases, the DC bias voltages (VA1, VA2, VA3, VA4, VB1, VB2, VHE, VTE1 and VTE2) are applied to the switches and varactors through RF choking inductors (Lc = 0.68 μH), and the DC bias lines are isolated from the ground plane by DC blocking capacitors (Cb = 51 pF). The corresponding impedances of the RF choke and DC block at 600 MHz are 2564 Ω and 5.2 Ω, respectively.

To investigate the effect of the bias networks on the antenna performance, the entire antenna structure with the DC bias networks was simulated in HFSS. As suggested in the component’s specifications, a resistive loss (Rloss = 0.5 Ω) was added in series to all lumped components in the bias networks in the simulation.

51

dielectric probe feed (TE) boundary

RF choke (inductor) PIN diode varactor DC block DC pad (capacitor)

varactor

Figure 36. A schematic showing the actual implementation of a DC bias network on Ground Plane B.

Lc VB2

Cb Cb

CTE2 SW B2 Cb Lc VB1 Cb Cb SWB1 Cb

Lc

VTE2

Cb L CTE1 c VTE1

Cb

Figure 37. An equivalent circuit model of the excitation slot. 52

Figures 38 and 39 show the simulated results for the HE mode reconfiguration. Throughout the simulations, SWB1 was turned ON while SWB2 was kept OFF, and CTE2 was biased to 5 pF. Although the setting is different from that described in Section 4.2.2, the operating frequency of the HE mode is able to reconfigure from 600 MHz to 680 MHz by manipulating the states of

SWA1, SWA2 and SWA3. By switching in CHE with SWA4 and varying the capacitance, the operating frequency can be continuously tuned from 680 MHz to 750 MHz. It can be further tuned to 800 MHz at the sacrifice of the impedance matching (VSWR ≈ 3:1). Hence the overall tuning range of the HE mode is from 600 MHz to 800 MHz. On the other hand, the simulated S-parameters for TE mode reconfiguration are given in Figures 40 and 41. In this case, only SWA4 was turned

ON in SW Set A and CHE was adjusted to 6 pF. As seen in Figure 41, the operating frequency of the TE mode can be tuned continuously from 600 MHz to 690 MHz through changing CTE2 from

10 pF to 3 pF, and from 690 MHz to 800 MHz with CTE1 changing from 15 pF to 7 pF. Hence, the frequency tuning range for both of the modes is roughly the same as previous despite the addition of DC bias networks. Here, the worst case mutual coupling between the modes is –13.4 dB, which is 3.6 dB higher than the original design value.

Finally, it should be pointed out that in the above simulations, the ground planes are built on single-sided Rogers RT/duroid 6010 substrates (εr = 10.2) with a thickness of 0.635 mm for the purpose of fabrication. Thus, the ground planes are not in direct contact with the dielectric block. In this case, the substrate not only acts as a uniform spacer between the dielectric block and the ground plane to eliminate air gap variability [79], but can also hold the lumped components across the slots. However, the drawback of such is the increased mismatch at the input ports for some configurations as observed from the simulation results.

53

0

-10

-20

parameters (dB) parameters - S -30

-40 550 600 650 700 750 800 850 Frequency (MHz)

S11S11 (SW(SW SetSet AA OFF) OFF) S11S11 ((SW_A1SWA1 ON ON)) S11S11 ( (SW_A3SWA3 ON ON))

S11S11 (SW_A1(SWA1 & SW& SW_A3A3 ON) ON) S11S11 ((SW_A2SWA2 ON ON)) S11S11 ( (SW_A2SWA2 & SW & A3SW_A3 ON) ON)

S11S11 (C_HE=3pF)(CHE = 3 pF) S11S11 ((C_HE=6pF)CHE = 6 pF) S11S11 ( (C_HE=15pF)CHE = 15 pF)

Figure 38. Simulated S11 (HE mode) of the MIMO DRA with bias networks.

0

-10 S22

S21

-20

parameters (dB) parameters - S -30

-40 550 600 650 700 750 800 850 Frequency (MHz)

S22S22 ((SWSW SetSet A A OFF) OFF) S22S22 ((SW_A1SWA1 ON )ON) S22S22 ((SW_A3SWA3 ON )ON) S22S22 ((SW_A1SWA1 & SW& SW_A3A3 ON) ON) S22S22 ((SW_A2SWA2 ON )ON) S22S22 ((SW_A2SWA2 & SW & ASW_A33 ON) ON) S22S22 ((C_HE=3pF)CHE = 3 pF) S22S22 ((C_HE=6pF)CHE = 6 pF) S22S22 ((C_HE=15pF)CHE = 15 pF)

S21S21 ((SWSW SetSet A A OFF) OFF) S21S21 ((SW_A1SWA1 ON ON)) S21S21 ((SW_A3SWA3 ON ON)) S21S21 ((SW_A1SWA1 & SW& SW_A3A3 ON) ON) S21S21 ((SW_A2SWA2 ON ON)) S21S21 ((SW_A2SWA2 & SW & ASW_A33 ON) ON) S21 (C_HE=3pF) S21 (C_HE=6pF) S21 (C_HE=15pF) S21 (CHE = 3 pF) S21 (CHE = 6 pF) S21 (CHE = 15 pF) Figure 39. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA with bias networks. 54

0

-10 S11

-20

parameters (dB) parameters - S -30

-40 550 600 650 700 750 800 850 Frequency (MHz)

S11S11 ((C_TE1=7pF)CTE1 = 7 pF) S11S11 ( (C_TE1=7pF)CTE1 = 10 pF) S11S11 (C_TE1=7pF)(CTE1 = 15 pF)

S11S11 ((C_TE1=7pF)CTE2 = 3 pF) S11S11 ( (C_TE1=7pF)CTE2 = 8 pF) S11S11 (C_TE1=7pF)(CTE2 = 10 pF)

S11S21 ((C_TE1=7pF)CTE1 = 7 pF) S11S21 ( (C_TE1=7pF)CTE1 = 10 pF) S11S21 (C_TE1=7pF)(CTE1 = 15 pF)

S11S21 ((C_TE1=7pF)CTE2 = 3 pF) S11S21 ( (C_TE1=7pF)CTE2 = 8 pF) S11S21 (C_TE1=7pF)(CTE2 = 10 pF)

Figure 40. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA with bias networks.

0

-10

-20

parameters (dB) parameters -

S -30

Tuning with CTE2 Tuning with CTE1

-40 550 600 650 700 750 800 850 Frequency (MHz)

S11S22 ((C_TE1=7pF)CTE1 = 7 pF) S11S22 (C_TE1=7pF)(CTE1 = 10 pF) S11S22 ((C_TE1=7pF)CTE1 = 15 pF)

S11S22 ((C_TE1=7pF)CTE2 = 3 pF) S11S22 (C_TE1=7pF)(CTE2 = 8 pF) S11S22 ((C_TE1=7pF)CTE2 = 10 pF)

Figure 41. Simulated S11 (HE mode) of the MIMO DRA with bias networks.

55

4.2.4. Measurement Results

The proposed frequency reconfigurable MIMO DRA was fabricated according to the design described in the previous section. Microsemi’s MPP4203 PIN diode [80] was used as the switches in SW Set A and SW Set B, and Infineon’s BB535 varactor (2 pF – 16 pF) [81] as CHE,

CTE1 and CTE2. The fabricated prototype is shown in Figure 42. The DC bias voltages are applied to the DC pads through semi-rigid coaxial cables.

(a) (b)

(c) Figure 42. Fabricated prototype of the proposed frequency reconfigurable MIMO DRA: (a) Ground Plane A, (b) Ground Plane B, and (c) perspective view.

56

HE mode reconfiguration was first tested and the measurement results are given in Figures 43 and 44. During the measurement, the operating frequency of the TE mode was fixed at 701 MHz by keeping SWB1 ON and setting VTE2 at 12 V (CTE2 ≈ 4.1 pF). It can be seen that the operating frequency of the HE mode increased incrementally from 615 MHz to 682 MHz as SWA1, SWA2 and SWA3 were set to the predefined states as depicted in Section 4.2.2. The return loss was maintained at around 10 dB despite the changes in switch state. After that, SWA1, SWA2 and SWA3 were turned OFF and SWA4 was switched ON such that the parasitic slot was loaded with CHE. As

VHE was increased from 0 V to 16 V, the operating frequency tuned from 674 MHz to 800 MHz.

The mutual coupling was the strongest (–11.8 dB) when VHE was set to 0 V. Nevertheless, the frequency response of the TE mode was barely affected. After the frequency agility of the HE mode was verified, TE mode reconfiguration was also tested and Figures 45 and 46 show the measured S-parameters. This time the operating frequency of the HE mode was set to be invariant at 700 MHz. This was achieved by only turning SWA4 ON in SW Set A and fixing VHE at

5.76 V (CHE ≈ 8.8 pF). Frequency tuning with CTE2 was first demonstrated. By switching SWB1

ON and SWB2 OFF, and varying VTE2 from 8.9 V to 13.9 V, the operating frequency of the TE mode was increased continuously from 628 MHz to 730 MHz. Next, the operating frequency was further tuned from 739 MHz to 836 MHz by setting SWB1 OFF and SWB2 ON, and ramping

VTE1 from 0 V to 13.8 V. The worst case mutual coupling observed was –14.4 dB when VTE2 was set to 13.9 V. Again, the frequency response of the HE mode was not altered during the reconfiguration of TE mode.

The overall tuning ranges for the HE and TE modes are therefore 615 MHz to 800 MHz and 628 MHz to 836 MHz, respectively. The maximum bias voltage required is 16 V. Table 4 provides a summary that compares the measured and the simulated results. The deviation in the operating frequency between the measured and simulated values for the HE mode is 2.6% and is 7.1% for the TE mode. In general, the measured results agreed very well with the simulated results shown in Figures 38 – 41, except that a few additional parasitic resonances were observed. These extra resonances are possibly due to the interaction between the other resonance modes of the antenna structure and the parasitics from the package of the lumped components and the solid state devices. These parasitic effects might be reduced if the lumped components are replaced by their transmission line equivalents, at the expense of increased antenna size.

57

0

-10

-20

parameters (dB) parameters - S -30

-40 550 600 650 700 750 800 850 Frequency (MHz)

S11S11 ((SWSW Set Set A A OFF) OFF) SS1111 ( S(SW_A1WA1 ON) ON) S11S11 (SW_A3(SWA3 ON ON))

S11S11 ((SW_A1SWA1 & SW & A3SW_A3 ON) ON) SS1111 ( S(SW_A2WA2 ON) ON) S11S11 (SW_A2(SWA2 & SW& SW_A3A3 ON) ON)

S11S11 ((C_HE=15pF)VHE = 16 V [3.3 pF]) SS1111 ( V(C_HE=6pF)HE = 9.1 V [5.7 pF]) S11S11 (C_HE=3pF)(VHE = 0 V)

Figure 43. Measured S11 (HE mode) of the fabricated antenna for HE mode reconfiguration.

0

S22

-10

-20

parameters (dB) parameters - S -30 S21

-40 550 600 650 700 750 800 850 Frequency (MHz)

S22S22 (SW(SW Set A OFF)OFF) S22S22 (SW_A1 (SWA1 ON ON)) S22S22 (SW_A3 (SWA3 ON ON)) S22S22 (SW_A1(SWA1 & &SW SW_A3A3 ON) ON) S22S22 (SW_A2 (SWA2 ON ON)) S22S22 (SW_A2 (SWA2 & & SW SW_A3A3 ON) ON) S22S22 (C_HE=3pF)(VHE = 16 V [3.3 pF]) S22S22 (C_HE=6pF) (VHE = 9.1 V [5.7 pF]) S22S22 (C_HE=15pF) (VHE = 0 V)

S21S21 (SW(SW Set A OFF)OFF) S21S21 (SW_A1 (SWA1 O NON)) S21S21 (SW_A3 (SWA3 O ON)N) S21S21 (SW_A1(SWA1 & &SW SW_A3A3 ON) ON) S21S21 (SW_A2 (SWA2 ON ON)) S21S21 (SW_A2 (SWA2 & & SW SW_A3A3 ON) ON) S21S (C_HE=3pF)(V = 16 V [3.3 pF]) S21 (C_HE=6pF) S21S (C_HE=15pF) (V = 0 V) 21 HE S21 (VHE = 9.1 V [5.7 pF]) 21 HE Figure 44. Measured S22 (TE mode) and S21 (mutual coupling) of the fabricated antenna for HE mode reconfiguration. 58

0

-10 S11

-20

parameters (dB) parameters - S -30

-40 550 600 650 700 750 800 850 Frequency (MHz)

S11S11 ( (C_TE1=7pF)VTE1 = 13.8 V [3.8 pF]) S11S11 ( V(C_TE1=7pF)TE1 = 8 V [6.7 pF]) S11S11 ((C_TE1=7pF)VTE1 = 0 V)

S11S11 ( (C_TE1=7pF)VTE2 = 13.9 V [3.7 pF]) S11S11 ( V(C_TE1=7pF)TE2 = 10.5 V [5 pF]) S11S11 ((C_TE1=7pF)VTE2 = 8.9 V [5.8 pF])

S11S21 ( (C_TE1=7pF)VTE1 = 13.8 V [3.8 pF]) S11S21 ( V(C_TE1=7pF)TE1 = 8 V [6.7 pF]) S11S21 ((C_TE1=7pF)VTE1 = 0 V)

S11S21 ( (C_TE1=7pF)VTE2 = 13.9 V [3.7 pF]) S11S21 ( V(C_TE1=7pF)TE2 = 10.5 V [5 pF]) S11S21 ((C_TE1=7pF)VTE2 = 8.9 V [5.8 pF])

Figure 45. Measured S11 (HE mode) and S21 (mutual coupling) of the fabricated antenna for TE mode reconfiguration.

0

-10

-20

parameters (dB) parameters - S -30

Tuning with CTE2 Tuning with CTE1

-40 550 600 650 700 750 800 850 Frequency (MHz)

S11S22 ( (C_TE1=7pF)VTE1 = 13.8 V [3.8 pF]) SS1122 ( V(C_TE1=7pF)TE1 = 8 V [6.7 pF]) SS1122 (V (C_TE1=7pF)TE1 = 0 V)

S11S22 ( (C_TE1=7pF)VTE2 = 13.9 V [3.7 pF]) SS1122 ( V(C_TE1=7pF)TE2 = 10.5 V [5 pF]) SS1122 (V (C_TE1=7pF)TE2 = 8.9 V [5.8 pF])

Figure 46. Measured S22 (TE mode) of the fabricated antenna for TE mode reconfiguration.

59

)

21

S

18 18

19.7 15.8 15.8 15.6 15.3 14.1 14.4 11.8 17.7 18.5 13.1 12.7 13.9

− −

(dB)

− − − − − − − − − − − − −

max(

TE

f

630 701 701 701 701 701 701 701 701 701 831 775 750 726 672

(MHz)

HE

f

694 621 630 643 645 648 673 693 721 797 702 702 700 696 695

(MHz)

) )

)

) ) ) ) ) )

2

TE

5

4.1 5.8 4.1 4.1 4.1 4.1 4.1 3.7

C (pF)

12 V 12 V 12 V 12 V 12 V 12 V

Measurement

8.9 V

( ( ( ( ( (

13.9 V 10.5 V

(

( (

)

) )

1

TE

3.8 6.7

8 V 0 V

~20

C (pF)

( (

13.8 V

(

) ) ) ) ) )

)

) )

HE

3.3 8.8 5.7 8.8 8.8 8.8 8.8 8.8

0 V 9 V

C

~20

(pF)

16 V

( (

5.8 V 5.8 V 5.8 V 5.8 V 5.8 V 5.8 V

(

( ( ( ( ( (

)

21

S

25.5 31.7 22.5 34.5 26.4 13.4 13.9 18.9 22.7 25.8 36.1 34.5 38.6 22.6 23.1

(dB)

− − − − − − − − − − − − − − −

max(

TE

f

598 675 675 675 675 675 675 675 675 675 801 736 700 688 637

(MHz)

HE

f

732 605 619 627 640 654 671 695 734 784 732 732 732 732 732

(MHz)

Simulation

2

TE

5 5 5 5 5 5 3 8

10

C (pF)

1

TE

7

10 15

C (pF)

HE

6 6 3 6 6 6 6 6

15

C

(pF)

2

B

ON ON ON

SW

1

A summary of the antenna parameters for various configuration settings. configuration for parameters the of various antenna summary A

B

.

SWSet B

ON ON ON ON ON ON ON ON ON ON ON ON

4

SW

4

A

ON ON ON ON ON ON ON ON ON

Table

SW

3

A

ON ON ON

SW

2

A

SW Set Set SW A

ON ON

SW

1

A

ON ON

SW

60

The radiation efficiency of the fabricated antenna with the third configuration from the bottom of Table 4 was measured with the Wheeler Cap method [82]. A rectangular metallic cavity, with dimensions 230 mm × 150 mm × 125mm, was used as the cap. The lowest-order mode of the cavity is therefore the TM110 mode and the corresponding resonant frequency is 1193.9 MHz. The measured radiation efficiency of port 1 (HE mode) at 732 MHz was 58.1%, and that of port 2 (TE mode) at 688 MHz was 47.1%. As a comparison, the corresponding simulated radiation efficiencies (without diode and varactor losses) were 73.4% and 76.8%, respectively.

Finally, the fabricated antenna was set to operate in MIMO mode at three difference frequencies (622 MHz, 700 MHz and 780 MHz) for the purpose of demonstration. The corresponding DC bias voltages are given in Table 5 and the measured S-parameters are given in Figure 47. The return losses for the TE mode in Config. 1 and the HE mode in Config. 3 were 7.3 dB and 7.8 dB, respectively. Again, this is due to the spacer inserted between the dielectric block and the ground plane as explained in Section 4.2.3. The return loss might be improved with a thinner substrate that allows a better coupling between the ground plane and the dielectric. Although it is not shown in the figure, the measured return loss for both modes was better than 10 dB from 650 MHz to 750 MHz. Parasitic resonances were also observed but were far away from the desired operating frequencies. The worst case mutual coupling between the modes was –14.4 dB for all three configurations shown. Indeed, the mutual coupling can be maintained under –15 dB during reconfiguration from 622 MHz to 800 MHz.

Table 5. Bias voltages for demonstrating frequency reconfigurable MIMO functionality.

VA1 VA2 VA3 VA4 VB1 VB2 VHE VTE1 VTE2 Config. (V) (V) (V) (V) (V) (V) (V) (V) (V) 1 0 0 0 0 1 0 0 0 8.6 2 0 0 0 1 1 0 6.24 0 12 3 0 0 0 1 0 1 14.4 8.9 0

61

0

-10

-20

parameters parameters (dB)

- S -30

-40 600 650 700 750 800 850 Frequency (MHz)

S11S11 (C_TE1=7pF)(Config. 1) S11S22 ((C_TE1=7pF)Config. 1) S11S21 ((C_TE1=7pF)Config. 1)

S11S11 (C_TE1=7pF)(Config. 2) S11S22 ((C_TE1=7pF)Config. 2) S11S21 ((C_TE1=7pF)Config. 2)

S11S11 (C_TE1=7pF)(Config. 3) S11S22 ((C_TE1=7pF)Config. 3) S11S21 ((C_TE1=7pF)Config. 3)

Figure 47. Measured S-parameters of the fabricated antenna in frequency reconfigurable MIMO mode.

4.2.5. Application to a Hybrid LTE/CR Low-Power Access Node

The proposed MIMO DRA described above is able to achieve frequency tuning from 615 MHz to 836 MHz (30.5% tuning ratio). The operating frequency of each antenna port can be individually tuned without affecting the frequency response of another port. This is mainly due to the orthogonal nature of the two modes. Hence, the proposed antenna design could be incorporated into a hybrid LTE/CR low-power base station that serves as a femtocell, as depicted in Figure 48. One of the antenna ports could be allocated to serve an LTE user at 700 MHz while the other port could sweep through the CR band and look for a potential user. If the system detects a vacant channel, a communication link could be set up and the femtocell base station could then simultaneously support both systems. On the other hand, if an LTE user requests a very high data rate, or whenever the propagation channel is favorable, the antenna could be reconfigured into a MIMO antenna. The capacity of the link could then be doubled. 62

LTE user

LTE user

CR user

(a) (b)

Figure 48. Application of the proposed frequency reconfigurable MIMO DRA in a hybrid LTE/CR low-power compact base station: (a) frequency sweep mode and (b) MIMO mode.

4.3. CHAPTER SUMMARY

This chapter investigates two different modalities for adding frequency agility into the MIMO DRA developed in Chapter 3. The first modality was achieved by introducing a material perturbation in the dielectric block. The strategy for placing the perturbation in an adequate location inside the dielectric cavity for maximum frequency agility has been outlined. After that, the addition of parasitic slot loading was studied as a second method to introduce frequency reconfiguration into the MIMO DRA. It has been experimentally shown that the proposed MIMO DRA is able to reconfigure from 615 MHz to 836 MHz, which covers more than half of the CR band. The major features of the proposed frequency reconfigurable MIMO DRA include the ability to allow individual tuning to the antenna ports and very small antenna performance variation across the band of reconfiguration.

63

CHAPTER 5: NONLINEAR EFFECTS IN FREQUENCY RECONFIGURABLE MIMO ANTENNAS

In Chapter 4, a frequency reconfigurable MIMO DRA designed for application in a hybrid LTE/CR low-power base station has been demonstrated experimentally. The frequency agility is achieved with the integrated PIN diodes and varactors in the antenna structure. However, PIN diodes and varactors are nonlinear devices; they generate harmonics which can mix with any signals circulating on the antenna structure and give rise to intermodulation products. If the signal levels presented to the antenna are high, these nonlinear products could create signal distortion that could degrade the system performance. Moreover, these spurious frequency components would interfere with and reduce the SNR of other nearby wireless channels. Therefore, this chapter provides an in-depth study of intermodulation distortion in frequency reconfigurable MIMO antennas.

5.1. FREQUENCY SWITCHABLE DUAL-SLOT ANTENNA

5.1.1. Antenna Geometry

For the purpose of the study of intermodulation effects in reconfigurable MIMO antennas, a frequency switchable dual-slot antenna was designed and the antenna geometry is given in Figure 49. The antenna has two resonant slots separated by approximately a quarter-wavelength and is built on a single-sided Rogers RT/duroid 5880 substrate (εr = 2.2) with a thickness of 1.575 mm. Each slot has a PIN diode attached near the end opposite to the excitation. The diode associated with port 1 is labeled as D1 while that with port 2 is named as D2. When the diode is OFF, the slot resonates at 800 MHz; on the other hand, the resonant frequency of the slot can be switched to 1050 MHz when the diode is ON.

The actual implementation of the PIN diode bias network and its equivalent circuit are given in Figure 50. The bias network was designed with reference to [16]. Microsemi’s MPP4203 PIN

64 diodes were used as the switches. The DC bias lines are isolated from the RF path with the use of semi-rigid coaxial cables, RF choking inductors (Lc = 182 nH) and DC blocking capacitors (Cb = 850 pF). The corresponding impedances of the RF choke and DC block at 800 MHz are 915 Ω and 0.23 Ω, respectively. Figures 51 – 53 show both the simulated and measured S-parameters of the antenna for different diode configurations. The mutual coupling between the slots is the strongest when both diodes are OFF (−6.4 dB). The worst case mutual coupling, however, is −18.3 dB when only one of the diodes is ON.

PIN diode port 1 (D1) 16 mm 41 mm

75 mm (0.2λ0) PIN diode port 2 (D2)

150 mm (0.4λ0)

Figure 49. A frequency switchable dual-slot antenna (λ0 is calculated at 800 MHz).

DC voltage thru a semi- rigid coaxial cable

PIN diode RF choke slot transmission line (inductor) toward feed toward short

Lc Cb VDC

PIN diode Slot DC ground Lc Cb DC block (capacitor) DC return

Figure 50. (a) Actual implementation of the PIN diode bias network, and (b) equivalent circuit model of the bias network.

65

0

-10

-20

parameters parameters (dB) -

S -30

-40 500 700 900 1100 1300 1500 Frequency (MHz)

S11S11 (measured) (measured) S21S21 (measured)(measured) SS2222 (measured) (measured) S11S11 ( (full-wave)full-wave) S21S21 ((full-wave)full-wave) SS2222 ( full(full-wave)-wave) S11S11 ( (circuitcircuit model model)) S21S21 ((circuitcircuit model)model) SS2222 ( circuit(circuit model model)) Figure 51. Simulated and measured S-parameters of the dual-slot antenna when both diodes are OFF.

0

-10

-20

parameters parameters (dB) -

S -30

-40 500 700 900 1100 1300 1500 Frequency (MHz)

SS1111 (measured) (measured) S21S21 (measured)(measured) S22S22 (measured)(measured) SS1111 ( full(full-wave)-wave) S21S21 ((full-wave)full-wave) S22S22 ((full-wave)full-wave) SSeries211 (circuit model) Series4S21 (circuit model) Series6S22 (circuit model) Figure 52. Simulated and measured S-parameters of the dual-slot antenna when both diodes are ON.

66

0

-10

-20

parameters parameters (dB) -

S -30

-40 500 700 900 1100 1300 1500 Frequency (MHz)

S11S11 (measured) (measured) SS2121 (measured) (measured) S22S22 (measured) (measured) Series7S11 (full-wave) SSeries921 (full-wave) Series11S22 (full-wave) Series2S11 (circuit model) SSeries421 (circuit model) Series6S22 (circuit model)

Figure 53. Simulated and measured S-parameters of the dual-slot antenna when only one of the diodes is ON.

5.1.2. Equivalent Circuit Model

In order to facilitate the prediction of intermodulation products, an equivalent circuit model of the dual-slot antenna is described in this section. The circuit model is based on the one proposed in [83] for a single slot antenna, where the slot is modeled as a lossless short-circuited transmission line with the radiation resistance located at the center of the line. Hence, an equivalent circuit model for the dual-slot antenna can be constructed by including the PIN diodes and adding a pair of mutual inductors in series to the radiation resistances for mutual coupling modeling. Figures 54 – 56 show the equivalent circuit models of the antenna for various diode configurations. When the diode is OFF, the radiation resistance (Rr1) is placed at the center of the entire slot. The mutual coupling between the slots is represented by the pair of coupled inductors

(Lm1), each attached in series to the radiation resistance. The mutual inductor is added in series to the radiation resistance because the magnitude of the mutual coupling is proportional to the current passing through the radiation resistance. On the other hand, the radiation resistance and the mutual inductor are moved toward the excitation of the slot when the diode is ON. This is

67 because the resonant length of the slot is shortened when the diode is switched ON. As the radiating structure is altered by the diode, the radiation resistance and the modeled mutual inductance are changed to Rr2 and Lm2 respectively. Finally, for the case when only one of the diodes is ON, the corresponding transmission line models also apply, but the values of the radiation resistance and the modeled mutual inductance are modified because the coupling between the slots is different.

l = 17 mm l = 82 mm l = 33 mm l = 47 mm 1 2 3 4 L c Cb Rr1 = 200 Ω VDC = 0 V port 1 DC D1 Lm1 = 115 nH ground Lc Cb

l1 = 17 mm l2 = 82 mm K1 = 1 l3 = 33 mm l4 = 47 mm

L c Cb VDC = 0 V Rr1 = 200 Ω port 2 DC D2 Lm1 = 115 nH ground L c Cb

Figure 54. Equivalent circuit model of the dual-slot antenna when both diodes are OFF.

l1 = 18 mm l2 = 55 mm l3 = 73 mm l4 = 45 mm

L c Cb VDC = 1 V Rr2 = 100 Ω port 1 DC D1 Lm2 = 30 nH ground K2 = 1 Lc Cb

l1 = 18 mm l2 = 55 mm l3 = 73 mm l4 = 45 mm L c Cb V = 1 V Rr2 = 100 Ω DC port 2 DC D2 Lm2 = 30 nH ground

Lc Cb

Figure 55. Equivalent circuit model of the dual-slot antenna when both diodes are ON.

68

l = 45 mm l1 = 18 mm l2 = 55 mm l3 = 73 mm 4 L c Cb VDC = 1 V Rr1 = 650 Ω port 1 DC D1 K = 0.5 Lm1 = 85 nH ground Lc Cb

l1 = 17 mm l2 = 82 mm l3 = 33 mm l4 = 47 mm

L c Cb Rr2 = 200 Ω VDC = 0 V port 2 D DC 2 Lm2 = 70 nH ground Lc Cb

Figure 56. Equivalent circuit model of the dual-slot antenna when only one of the diodes is ON.

The above circuits were simulated in the circuit simulator in Agilent ADS [84] and the simulated S-parameters are given in Figures 51 – 53. A standard nonlinear diode model in ADS was used in the simulation. The lengths of the transmission line sections and the values of the radiation resistances and mutual inductors were fine-tuned such that the simulated S-parameters are well matched with the measured results. Figure 57 also shows the comparison between the S- parameters obtained from the circuit simulation and the full-wave simulation in HFSS on a Smith chart.

1.0 1.0

0.5 0.5

2.0 2.0 2.0 2.0

0.2 0.2

0 0.1 0.5 1.0 2.0 5.0 0 0.1 0.5 1.0 2.0 5.0

-0.2 -0.2

Full-wave Full-wave

-2.0

-2.0 Circuit model -2.0 -2.0 Circuit model

-0.5 -0.5

-1.0 -1.0

(a) (b)

Figure 57. Comparison between the S-parameters obtained from the circuit simulation and the full-wave simulation when (a) both diodes are OFF, and (b) both diodes are ON. 69

Finally, it should be mentioned that the total lengths of the transmission line sections in the circuit model are greater than the length of the slot (150 mm) mentioned in Section 5.1.1. This is necessary if we want to match the circuit simulation results with the measured results. This is because the effect of a finite ground plane is not taken into consideration in the equivalent circuit model. The consequence for the finite ground plane is the increased field at the corners and along the edges (see Figure 58). This field acts as a reactive loading to the slot and hence reduces the electrical length of the slot. Therefore, the total lengths of the transmission line sections in the circuit model have to be increased to compensate for this finite ground plane effect.

(a) (b)

(c) (d) Figure 58. Normalized electric field distribution on the dual-slot antenna when (a) both

diodes are OFF (840 MHz), (b) both diodes are ON (1100 MHz), (c) only D1 is ON (1100 MHz), and (d) only D1 is ON (840 MHz).

70

5.2. TWO-TONE MEASUREMENT

5.2.1. Measurement Setup

Since the level of intermodulation products increases nonlinearly with the input excitation, the transmission and the reception scenarios are non-reciprocal. It is therefore necessary to measure both of the spectra, and Figures 59 and 60 show the corresponding experimental setups. For both cases, only D1 was turned ON such that port 1 was matched at 840 MHz and port 2 at 1100 MHz.

In the transmission spectrum measurement, the excitation frequencies for port 1 and port 2 were therefore 840 MHz (f1) and 1100 MHz (f2), respectively. The signals were fed to the antenna ports through a low pass filter and an isolator so as to eliminate the possibility of any harmonics or intermodulation products generated in the signal generators. The signal levels at the antenna ports were approximately 11 dBm after accounting for all losses in the cables and passive devices. The radiated fields were then detected with a standard horn antenna placed at R = 1 m away from the antenna-under-test (AUT) and the received signals were fed to a spectrum analyzer. The strongest signal power detected at the spectrum analyzer was about –15 dBm, which was insufficient to generate any detectable harmonics or intermodulation products in the spectrum analyzer. Moreover, it should be mentioned that the measurement was not in the far- field region. This is because we would like to detect spurious frequency components that might cause interference to other systems that reside in the vicinity as well as the far-field region of the AUT.

On the other hand, in the reception spectrum measurement, the positions of the horn antenna and AUT were exchanged. The horn antenna was excited with both signals from the output of a power combiner. The signals radiated by the horn antenna were then picked up by one of the ports of the AUT.

71

Agilent E8247C Mini-Circuits Fairview Microwave signal generator VLP-16 SFI1020 low pass filter isolator anechoic chamber

ETS-Lindgren 3106B D1 ON and D2 OFF horn antenna port 1 1100 MHz 18 dBm

~11 dBm AUT 840 MHz port 2 18 dBm

Agilent E4438C Mini-Circuits signal generator SLP-1000+ low pass filter Agilent E4440A

Fairview Microwave spectrum analyzer SFI8090 isolator Figure 59. Experimental setup for measuring the transmission spectrum.

Mini-Circuits Fairview Microwave Agilent E8247C VLP-16 SFI1020 signal generator low pass filter isolator

anechoic chamber 1100 MHz ETS-Lindgren 18 dBm 3106B horn antenna D1 ON and D2 OFF Mini-Circuits

ZFSC-2-2500 power combiner

840 MHz Signal taken at ~11 dBm AUT 18 dBm either port 1 or 2

Agilent E4438C Mini-Circuits signal generator SLP-1000+ low pass filter Agilent E4440A spectrum analyzer Fairview Microwave SFI8090 isolator Figure 60. Experimental setup for measuring the reception spectrum.

72

5.2.2. Measurement Results

The measured transmission spectrum is given in Figure 61. A number of intermodulation products and harmonics were observed in the measured spectrum. It is confirmed that the integrated PIN diode can generate harmonics and mix any frequency components presented to it, even when the input power is only 11 dBm. The strongest spurious frequency component was 2f1 and was 28 dB lower than the detected power level of f1. The measured power levels of the third- order intermodulation products, 2f1 – f2 and 2f2 – f1, were –55 dBm and –60 dBm, respectively. The corresponding input-intercepts are 30 dBm and 33 dBm, respectively. Figures 62 and 63 respectively show the measured reception spectra taken at port 1 and port 2. The measured spectrum taken at port 1 was clean and only two spurious frequency components were observed in the spectrum taken at port 2.

0

f1 f2 –16 dBm –14 dBm

-20

2f2 – f1 2f1 –60 dBm –44 dBm -40 3f1 – f2 –61 dBm 2f1 – f2 3f1 –55 dBm 4f1 – 2f2 f – f –57 dBm 1 2 2f + f –72 dBm –58 dBm 1 2 4f1 – f2 –61 dBm –74 dBm -60 2f2 2f2 – 2f1 –69 dBm 3f – 3f –82 dBm 2 1 ( –83 dBm

-80 Received signal strength (dBm) strength signalReceived -100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz)

Figure 61. Measured transmission spectrum of the frequency switchable dual-slot antenna.

73

0

f2 –21 dBm -20

f1 –40 dBm -40

-60

-80 Received signal strength (dBm) strength signalReceived -100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz)

Figure 62. Measured reception spectrum taken at port 1 of the frequency switchable dual-slot antenna.

0

f1 –21 dBm

-20 f2 –30 dBm

-40

-60 2f1 –71 dBm f1 + f2 –75 dBm

-80 Received signal strength (dBm) strength signalReceived -100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz)

Figure 63. Measured reception spectrum taken at port 2 of the frequency switchable dual-slot antenna.

74

5.2.3. Comparison with Circuit Simulation Results

To predict the transmission spectrum of the dual-slot antenna, the circuit model given in Figure 56 was imported to the harmonic balance simulator in ADS. The simulator was set to consider up to the fourth-order harmonic of the fundamental tone and up to sixth-order mixing. Two power spectra at the radiation resistances of the two slots were obtained from the harmonic balance analysis, and they were summed to give the “immediate” power radiated (PHB) by the dual-slot antenna as a whole. The final transmission spectrum PT, in dBm, was then obtained according to

PT = PHB + GH – L – LF , (38)

where GH is the “1 m gain” of the horn antenna given by the data sheet [85], L is the cable loss from the horn antenna to the spectrum analyzer, and LF is the free-space propagation loss. Here,

LF is approximated by the far-field propagation loss given by the Friis transmission equation [11],

4 Rf  . (39) LF  20log c

As the contribution from the near-field is not taken into account in the above equation, LF is over-estimated in this case. Nevertheless, Equation (39) incorporates the frequency dependent loss in the entire circuit model. Finally, the diode parameters were fine-tuned to give a transmission spectrum comparable to the measured spectrum. Table 6 shows the modified diode parameters and Figure 64 shows the corresponding simulated transmission spectrum. As seen in the figure, the results obtained from the circuit simulation agree reasonably well with the measurement results over a decade of frequency. The major spurious frequency component that the model failed to predict is 2f2 and that led to the error in estimating the power levels of those intermodulation products that contain 2f2 (such as, 4f1 – 2f2, 2f2 – f1, etc.). The overall accuracy of the circuit model might be further improved if the actual diode parameters were available and the near-field contribution was considered.

75

Table 6. Modified diode parameters in the circuit simulation.

Saturation Ambipolar I-region width current carrier lifetime (A) (m) (s)

1  1016 5  105 6  107

0

f2 f1 Circuit model

-20

2f2 – f1 -40 2f1 3f1 – f 2 3f1 2f1 – f2 f – f 1 2 2f + f 4f1 – f2 1 2 -60 2f2 – 2f1 2f2 4f1 – 2f2

3f1 – 2f2 3f2 – f1 3f2 – 3f1 -80 3f2 – 2f1

Received signal strength (dBm) strength signalReceived -100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz) Figure 64. Comparison between the transmission spectra obtained from circuit model simulation and measurement.

5.2.4. Results Interpretation

From the above measured spectra, it is seen that the intermodulation effect is much more significant when the AUT is placed at the transmitter. This is because the signal power presented to the antenna in the transmitting case is much higher than that in the receiving case. In the transmitting case, the relatively high levels of the intermodulation products are largely due to the strong harmonic frequency components 2f1 and 3f1.

Given the presence of the harmonic frequency components (2f1 and 3f1) in the transmission spectrum and the detection of two spurious frequency components in the reception spectrum taken at port 2, it is postulated that the “OFF” diode (D2) associated with port 2 is the source of

76

0

-10

-20

parameters parameters (dB)

- S -30

-40 500 700 900 1100 1300 1500 Frequency (MHz)

Series7S11 Series9S21 Series11S22 Figure 65. Measured S-parameters of the dual-slot antenna for 10 dBm of input power. S11 S21 S22

the intermodulation distortion. Therefore, in other words, D2 might not be properly turned OFF in the measurements, because a truly OFF diode should not contribute to the generation of any harmonic or intermodulation products. To understand this better, the S-parameters of the dual- slot antenna with both diodes OFF were measured again, but with the input signal power changed to 10 dBm (the original signal power was –17 dBm). The measured results are shown in Figure 65. As compared to the measured results given in Figure 51, the matching at both antenna ports was poorer when the input signal power was set to 10 dBm. This implied that the diodes were partially biased by the RF signal across them and therefore spurious frequency components were generated.

5.3. EFFECT OF DC BIAS

In the previous section, it was found that the “OFF” diode is susceptible to the biasing through the strong RF signal. In order to verify this, the transmission spectrum was measured again with

77 four different bias schemes for the OFF diode: (i) 0 V was applied to the OFF diode (original scheme). (ii) The voltage source was physically detached from the diode (the DC line was physically open). (iii) The diode was reverse biased. (iv) The RF choking inductance was increased to 5.6 H. The measured result for case (i) is already given in Figure 61 and those for the other cases are given in Figures 66 – 68. As a reference, the corresponding circuit simulation results are also included in the figures. It can be observed that almost all of the spurious frequency components disappeared in case (ii). In case (iii), it can be seen that reverse biasing the diode with 2 V reduced the level of the intermodulation products by a considerable amount. Further increasing the reverse bias voltage to 3 V eliminated most of the nonlinear by-products and the result is similar to that in case (ii). Finally, in case (iv), increasing the RF choking inductance from 182 nH to 5.6 H did not improve the situation at all. Hence, the results validated the hypothesis that the “OFF” diode was not properly turned OFF in the previous measurements. Therefore, a sufficient reverse bias voltage (3 V in this case) is necessary to ensure that the diode is turned OFF when the RF signal power exceeds a threshold.

0

Circuit model

-20

-40

-60

-80 Received signal strength (dBm) strength signalReceived -100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz) Figure 66. Measured transmission spectrum for case (ii).

78

0

Circuit model (D2 is reversed -20 biased with 3 V)

-40

-60

-80 Received signal strength (dBm) strength signal Received

-100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz)

d1D2 onis reversedd2 off (R.B.=2V) biased with 2 V d1D2 onis reversedd2 off (R.B.=3V) biased with 3 V Series3 Figure 67. Measured transmission spectrum for case (iii).

0

Circuit model -20

-40

-60

-80 Received signalstrength (dBm)

-100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz) Figure 68. Measured transmission spectrum for case (iv).

79

5.4. EFFECT OF ANTENNA MUTUAL COUPLING

It has been shown that the power level of the intermodulation products can be affected by the DC bias condition. In this section, we examine another important factor that might impact the level of intermodulation products: the mutual coupling between the antenna ports.

5.4.1. Orthogonal Dual-Slot Antenna

In order to investigate the effect of antenna mutual coupling on intermodulation distortion, an orthogonal dual-slot antenna was designed and fabricated. Figure 69 shows the geometry of the antenna. The substrate of the antenna is the same as that of the dual-slot antenna described previously. There are also two PIN diodes (D1 and D2) integrated to the resonant slots. Depending on the diode states, the operating frequency of the slots can be individually switched between 830 MHz (f1) and 1200 MHz (f2). Both the simulated and measured S-parameters of the antenna are shown in Figures 70 – 72. The measured mutual coupling between the slots is –33.8 dB at f1 when both diodes are OFF, and is –25 dB at f2 when both diodes are ON. When only D1 is switched ON, the maximum measured mutual coupling is –23.3 dB.

12.5 mm

port 2 PIN diode port 1 (D1) 27 mm 40 mm (0.11λ0) 150 mm

(0.41λ0) 170 mm (0.46λ0) PIN diode (D2)

40 mm

Figure 69. A frequency switchable orthogonal dual-slot antenna. 80

0

-10

-20

parameters parameters (dB) -

S -30

-40 500 700 900 1100 1300 1500 Frequency (MHz)

Series1S11 (measured) Series3S21 (measured) Series5S22 (measured) Series7S11 (full-wave) Series9S (full-wave) Series11S22 (full-wave) 21 Figure 70. Simulated and measured S-parameters of the orthogonal dual-slot antenna when both diodes are OFF.

0

-10

-20

parameters parameters (dB)

- S -30

-40 500 700 900 1100 1300 1500 Frequency (MHz)

Series1S11 (measured) Series3S21 (measured) SSeries522 (measured)

Series7S11 (full-wave) Series9S21 (full-wave) SSeries1122 (full-wave)

Figure 71. Simulated and measured S-parameters of the orthogonal dual-slot antenna when both diodes are ON. 81

0

-10

-20

parameters parameters (dB)

- S -30

-40 500 700 900 1100 1300 1500 Frequency (MHz)

SSeries111 (measured) Series3S21 (measured) Series5S22 (measured)

Series7S11 (full-wave) Series9S21 (full-wave) Series11S22 (full-wave)

Figure 72. Simulated and measured S-parameters of the orthogonal dual-slot antenna when only D1 is ON.

5.4.2. Transmission Spectrum Measurement

The transmission spectrum of the orthogonal dual-slot antenna was measured according to the procedure described in Section 5.2.1, except that the AUT was rotated by 45o. This is to balance the polarization mismatch between the two orthogonal slots, since the horn antenna is linearly polarized along one direction only. During the measurement, only D1 was turned ON such that port 1 was matched at 830 MHz and port 2 at 1200 MHz. Figures 73 and 74 respectively show the measured transmission spectrum when 0 V was applied to D2 and when D2 was reversed biased with 3 V. As seen from the results, 0 V is not enough to properly turn OFF D2 as harmonics of f1 were detected and their power levels were quite high. Specifically, the strength of 2f1 was 27 dB down from that of f1. This is comparable to the parallel dual-slot antenna for which the power of 2f1 was 28 dB lower than that of f1 (see Section 5.2.2). Nevertheless, the only intermodulation product observed was f1 + f2 and the other spurious frequency components were not detectable within the measurement noise floor. This is indeed due to the low mutual coupling

82 between the antenna ports. Because of the low mutual coupling, the signal from one port is not coupled to another port and thus is not mixed with the other signals.

0

f f 2 1 −17 dBm −19 dBm

-20

2f1 -40 −46 dBm

3f1 −60 dBm -60

f1 + f2 −82 dBm

-80 Received signal strength (dBm) strength signal Received

-100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz)

Figure 73. Measured transmission spectrum of the orthogonal dual-slot antenna when only D1 is ON and 0 V is applied to D2.

0

-20

-40

-60

-80 Received signal strength (dBm) strength signal Received

-100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz)

Figure 74. Measured transmission spectrum of the orthogonal dual-slot antenna when only D1 is ON and D2 is reversed biased with 3 V.

83

5.5. HARMONIC TRAP

As seen in Figure 61, the harmonic level (2f1) is 28 dB down from the power level of the fundamental and is the strongest among all of the spurious frequency components. Since the strengths of the intermodulation products containing 2f1 (such as 2f2 – 2f1, 2f1 – f2, 2f1 + f2) are directly related to the power level of 2f1, it might be useful to suppress a large portion of the intermodulation products by solely reducing the strength of 2f1. To accomplish this, a harmonic trap (HT) consisting of a parallel L-C network [86] is placed directly at the OFF diode, as depicted in Figure 75. The “OFF diode” here refers to the case that when 0 V is applied to turn

OFF the diode. The values of the inductor (Lt) and the capacitor (Ct) in the HT are chosen to be 8.2 nH and 1 pF, respectively, and that corresponds to a resonance at 1758 MHz. The resonant frequency of the HT does not exactly match with 2f1 (1680 MHz) due to the limitation imposed by the actual component values. Nevertheless, the HT offers an attenuation of 20 dB at 1680 MHz (89 dB at 1758 MHz) according to the simulation in ADS. Figures 76 and 77 show the measured transmission spectrum of the parallel dual-slot antenna with the HT placed at OFF diode only and at both diodes, respectively. For the case when the HT was placed at the OFF diode only, the power level of 2f1 was reduced by 9.1 dB and the intermodulation products were not suppressed at all. On the other hand, when the HT was placed at both diodes, the power level of 2f1 dropped by 21.8 dB while the intermodulation products were not drastically reduced.

toward feed slot transmission line toward short

Ct Lt

Lc Cb VDC = 0 V harmonic traps PIN diode DC ground Lc C b

Ct Lt

Figure 75. Harmonic traps placed next to the OFF diode for the suppression of 2f1.

84

0

-20

2f1

-40

-60

-80 Received signal strength (dBm) strength signalReceived

-100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz) d1Without on d2 offHT (short) d1With on d2HT off placed (HT at@ the D2) OFF diode only

Figure 76. Measured transmission spectrum of the parallel dual-slot antenna when D1 is ON and D2 is OFF.

0

-20

2f1 -40

-60

-80 Received signal strength (dBm) strength signalReceived

-100 300 600 900 1200 1500 1800 2100 2400 2700 3000 Frequency (MHz) d1Without on d2 offHT (short) d1With on d2HT off placed (HT at@ both D1 & diodes D2)

Figure 77. Measured transmission spectrum of the parallel dual-slot antenna when D1 is ON and D2 is OFF.

85

Indeed, the above results suggested not only that D2 (OFF diode) generates 2f1, but also that D1 contributes to the generation of harmonic. This agrees with the results shown in Figure 67 that a very low level of 2f1 was still detected even when D2 was reverse biased. Furthermore, the results implied that the rejection ratio of the designed HT is only around 10 dB at 2f1 and the HT is only effective in blocking 2f1 from the diode. The HT does not prevent the diode from mixing the signals together. Nevertheless, this demonstration shows that a spurious frequency component may be blocked at the antenna level by inserting HTs (that resonate at the frequency to be blocked) at the outputs of the PIN diode. This is provided that the HT does not affect the normal functionality of the diode switch. In other words, the HT cannot resonate near the operating frequency to be switched to; otherwise, the function of the diode switch would be voided.

5.6. TWO-TONE MEASUREMENT WITH PROPOSED FREQUENCY AGILE MIMO DRA

With the experimental setup described in Section 5.2, the transmission spectrum of the frequency reconfigurable MIMO DRA proposed in Chapter 4 was measured. The antenna was configured to the third last state listed in Table 4; i.e., port 1 (HE mode) of the antenna was tuned to 732 MHz and port 2 (TE mode) to 688 MHz. It should be noted that the two testing frequencies fell outside the manufacturer’s specified operating bands of the two isolators used. It was measured that the extra out-of-band isolator loss was –0.77 dB for port 1 and –3.48 dB for port 2. In addition to the isolator loss, polarization mismatch has to be taken into account since the MIMO DRA is orthogonally polarized while the horn antenna is vertically polarized. To reduce the difference in polarization mismatch between the two ports, the MIMO DRA was rotated by 210o on the xy-plane. The angle was selected based on the radiation patterns given in Figure 33. Figure 78 shows the measured transmission spectrum of the MIMO DRA. Although the “OFF” diodes were reverse biased with 3 V during the measurement, harmonics and the sum product of the testing frequencies were still observed. Nevertheless, their power levels were more than 30 dB down from the fundamental tones and no other intermodulation products were observed with the measurement noise floor. The proposed frequency reconfigurable MIMO DRA therefore has a fairly insignificant intermodulation and harmonic distortion. This is mainly due to the low mutual coupling between the radiating ports and the appropriate biasing condition to the PIN

86

0

f1 (TE) f2 (HE) -20

-40 f1 + f2

2f1 -60

2f2

-80 Received signal strength Received (dBm) signalstrength

-100 500 600 700 800 900 1000 1100 1200 1300 1400 1500 Frequency (MHz) Figure 78. Measured transmission spectrum of the proposed frequency reconfigurable MIMO DRA. diodes. Finally, the difference between the received power levels of the two testing tones was due to the difference in both the isolator loss and polarization mismatch of the two ports.

5.7. CHAPTER SUMMARY

This chapter investigated the intermodulation effect in frequency reconfigurable MIMO antennas with integrated PIN diodes. Intermodulation distortion is far more significant in the transmitting scenario than in the receiving case. This is because the transmitted power is usually higher than the received power by several orders of magnitude. It was also found that the bias condition for the OFF diode could drastically affect the level of harmonic and intermodulation products. Due to the high RF power, the OFF diode is partially biased by the RF signal and therefore a reverse bias voltage is necessary to properly turn OFF the diode. Otherwise, the “OFF” diode would generate harmonic frequency products and contribute to the mixing of signals. In terms of the mutual coupling between the antenna ports, our measurement results have shown that reduction of mutual coupling significantly reduces the level of intermodulation products, but not the level

87 of harmonic frequency products. Nonetheless, the harmonics can be filtered out easily at the system level. Finally, for antennas that have a high mutual coupling between the radiating ports, the harmonics and intermodulation products may be suppressed by inserting HTs at the output of the diodes.

88

CHAPTER 6: CONCLUSIONS AND FUTURE WORK

6.1. CONCLUSIONS

This work encompasses the design and analysis, implementation and experimental measurements of frequency reconfigurable MIMO antennas. The dissertation starts with the introduction of the boundary perturbation method as a means to efficiently design MIMO DRAs with inherently low mutual coupling. The method reduces the design effort of MIMO DRA of non-symmetric shapes in which more space-efficient antenna designs can be achieved. Using the proposed boundary perturbation method, a MIMO DRA for LTE femtocell base station was designed and fabricated. After that, two different modalities for implementing frequency reconfiguration into the designed MIMO DRA were investigated. The first method is based on material perturbation. It was found that an impractically wide range of dielectric constants is necessary to achieve a reasonable reconfiguration bandwidth. Nevertheless, a complete mathematical framework that finds the optimal location for placing the material perturbation for maximum frequency agility in general has been presented. The second modality for the implementation of frequency reconfiguration is through parasitic slot loading. It has been demonstrated experimentally that the proposed MIMO DRA with parasitic slot loading is able to achieve a frequency tuning ratio of greater than 30%. The major features of the proposed antenna include individual frequency tuning to each antenna port and small antenna performance variations across the band of reconfiguration. The proposed frequency reconfigurable MIMO DRA is potentially suitable for an application in a hybrid LTE/CR low power node. Finally, we studied in detail the intermodulation effect in frequency reconfigurable MIMO antennas. It was found that a proper DC bias condition is essential to reduce spurious frequency components under the high signal power scenario. It has also been shown that reduction of mutual coupling helps to suppress intermodulation products. Furthermore, the use of harmonic trap was studied for the reduction of the spurious frequency components in frequency reconfigurable MIMO antennas at the antenna level.

89

6.2. CONTRIBUTIONS

The major contribution of this dissertation research is the development of a systematic design flow for MIMO DRAs. The design methodology is also widely applicable to RF dielectric resonators. With the proposed design methodology, we designed a MIMO DRA for application in an LTE femtocell base station. We further extended the functionality of the antenna by introducing frequency reconfigurablity to the antenna by considering different modalities. The first one is based on material perturbation. We developed a complete mathematical analysis for determining the location of material perturbation for maximized frequency agility. This eliminates the need for trial-and-error in the design process. The second modality is based on the insertion of parasitic loading to the ground plane of the DRA. With the proposed design, we demonstrated experimentally a frequency reconfigurable MIMO DRA with individual tuning capability to each antenna port. Finally, we studied in detail the nonlinear effects in frequency reconfigurable MIMO antennas. It was found that harmonic and intermodulation distortion is not negligible in frequency reconfigurable MIMO antennas with integrated PIN diodes and is highly related to the excitation power in the antenna. We also identified ways to reduce harmonic and intermodulation products at the antenna level.

6.3. FUTURE WORK

6.3.1. Design of a Robust DC Bias Network

In the frequency reconfigurable MIMO DRA, the DC bias for the PIN diodes and varactors shares the same ground plane with the slots. To ensure better signal integrity, the DC ground may be isolated from the antenna ground plane by introducing an extra bias line as shown in Figures 79 – 82. This extra DC return line can also help prevent the leakage of any residual DC voltage to the rest of the antenna structure. Figures 83 – 86 show the simulated S-parameters of the frequency reconfigurable MIMO DRA with this modified bias network. It can be seen that modifying the bias network has very little impact on the overall tuning range of the antenna.

90

dielectric boundary coaxial probe (HE)

RF choke DC block (inductor) (capacitor)

PIN diode varactor DC pad Figure 79. A schematic showing the modified DC bias network on Ground Plane A.

Cb Lc L C Lc Cb Lc c Cb b VA4 VA1 VA2 VA3 Lc SW A4 SW SWA1 SWA2 A3 Cb Lc Cb Lc Cb Lc CHE Cb

C C b b VHE Lc Figure 80. An equivalent circuit model of the parasitic slot.

dielectric probe feed (TE) boundary

RF choke (inductor) PIN diode DC block (capacitor) DC pad

varactor

Figure 81. A schematic showing the modified DC bias network on Ground Plane B.

91

L c Lc VTE2 V B2 C Cb C b b

CTE2 SWB2 Cb Cb SWB1 VB1 Lc Cb C Cb b Lc Lc

Lc Cb Lc VTE1 Cb Cb CTE1

Figure 82. An equivalent circuit model of the excitation slot.

92

0

-10

-20

parameters (dB) parameters

- S -30

-40 600 650 700 750 800 850 900 Frequency (MHz) S11S11 ( (SWSW Set Set A A OFF) OFF) S11S11 ((SW_A1SWA1 ON ON)) S11S11 ((SW_A3SWA3 ON ON))

S11S11 ( (SW_A1SWA1 & SW & A3SW_A3 ON) ON) S11S11 ((SW_A2SWA2 ON ON)) S11S11 ((SW_A2SWA2 & SW & A3SW_A3 ON) ON)

S11S11 ( (C_HE=2pF)CHE = 3 pF) S11S11 ((C_HE=6pF)CHE = 6 pF) S11S11 ((C_HE=15pF)CHE = 15 pF)

Figure 83. Simulated S11 (HE mode) of the MIMO DRA with modified bias networks. 0

S22

-10

S21

-20

parameters (dB) parameters - S -30

-40 600 650 700 750 800 850 900 Frequency (MHz)

S22S22 ( (SWSW Set Set A A OFF) OFF) S22S22 ((SW_A1SWA1 ON ON)) S22S22 ((SW_A3SWA3 ON ON)) S22S22 ( (SW_A1SWA1 & SW & ASW_A33 ON) ON) S22S22 ((SW_A2SWA2 ON ON)) S22S22 ((SW_A2SWA2 & SW & ASW_A33 ON) ON) S22 (C_HE=2pF) S22 (C_HE=6pF) S22 (C_HE=15pF) S22 (CHE = 3 pF) S22 (CHE = 6 pF) S22 (CHE = 15 pF) S21 (SW Set A OFF) S21 (SW_A1 ON) S21 (SW_A3 ON) S21 (SW Set A OFF) S21 (SWA1 ON) S21 (SWA3 ON) S21 (SW_A1 & SW_A3 ON) S21 (SW_A2 ON) S21 (SW_A2 & SW_A3 ON) S21 (SWA1 & SWA3 ON) S21 (SWA2 ON) S21 (SWA2 & SWA3 ON) S21S ( (C_HE=2pF)C = 3 pF) S21 (C_HE=6pF) S21S ((C_HE=15pF)C = 15 pF) 21 HE S21 (CHE = 6 pF) 21 HE Figure 84. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA with modified bias networks. 93

0

S11

-20

-40

parameters (dB) parameters

- S -60

-80 600 650 700 750 800 850 900 Frequency (MHz)

S11S11 ( (C_TE1=7pF)CTE1 = 5.5 pF) S11S11 ((C_TE1=7pF)CTE1 = 7 pF) S11S11 ((C_TE1=7pF)CTE1 = 13 pF)

S11S11 ( (C_TE1=7pF)CTE2 = 3 pF) S11S11 ((C_TE1=7pF)CTE2 = 6 pF) S11S11 ((C_TE1=7pF)CTE2 = 8 pF)

S11S21 ( (C_TE1=7pF)CTE1 = 5.5 pF) S11S21 ((C_TE1=7pF)CTE1 = 7 pF) S11S21 ((C_TE1=7pF)CTE1 = 13 pF)

S11S21 ( (C_TE1=7pF)CTE2 = 3 pF) S11S21 ((C_TE1=7pF)CTE2 = 6 pF) S11S21 ((C_TE1=7pF)CTE2 = 8 pF)

Figure 85. Simulated S22 (TE mode) and S21 (mutual coupling) of the MIMO DRA with modified bias networks.

0

-10

-20

parameters (dB) parameters - S -30

Tuning with CTE2 Tuning with CTE1

-40 600 650 700 750 800 850 900 Frequency (MHz)

S11S22 ((C_TE1=7pF)CTE1 = 5.5 pF) S11S22 (C_TE1=7pF)(CTE1 = 7 pF) S11S22 ((C_TE1=7pF)CTE1 = 13 pF)

S11S22 ((C_TE1=7pF)CTE2 = 3 pF) S11S22 (C_TE1=7pF)(CTE2 = 6 pF) S11S22 ((C_TE1=7pF)CTE2 = 8 pF)

Figure 86. Simulated S11 (HE mode) of the MIMO DRA with modified bias networks.

94

6.3.2. Reduction of Active Device Redundancy in Reconfigurable Antennas

The frequency reconfigurable MIMO DRA presented in Chapter 4 is able to reconfigure from 615 MHz to 836 MHz and this corresponds to 30.5% frequency tuning ratio. In order to achieve the reconfiguration range and to enable individual frequency tuning to each port, six PIN diodes and three varactors were integrated into the antenna structure. This results in a relatively complicated DC bias network as seen in Section 4.2.3. Further inspection of the antenna structure reveals that three of the PIN diodes were used to achieve a small frequency reconfiguration for the HE mode. Hence, there is certainly room for improvement on the reconfigurable parasitic slot design for the HE mode reconfiguration. Indeed, a recent publication [87] suggests the use of graph models for reducing design redundancy in reconfigurable antennas. An interesting piece of future work is therefore to reduce the number of active elements required in the proposed frequency reconfigurable MIMO DRA. This would help reduce the design complexity and the implementation cost of the antenna.

6.3.3. Effect of Radiation Patterns on Harmonic and Intermodulation Products

In Chapter 5, the spectrum measurements were taken at a fixed antenna orientation. Since the radiation patterns of the designed signals (fundamental frequencies) are different from those of the harmonic and intermodulation frequencies, our measurements may not capture the worst case scenario. Therefore, the transmission spectrum of the antenna-under-test should be taken as a function of the antenna orientation for completeness. This is important if one would like to specify the worst case performance of a reconfigurable antenna during system design.

6.3.4. Switch Design for Reconfigurable Slots for High Power Applications

In Section 5.2.4, it is mentioned that the “OFF” diode in the dual-slot antenna is partially biased by the strong RF signal and that gives rise to the generation of harmonic and intermodulation products. This is inevitable because the diode is subjected to the RF current along the slot even

95 when it is in the “OFF” state. Indeed, such a situation might be avoided if other switch configurations are used (such as shunt configuration or even multiple-pole and/or multiple-throw configurations [88]). For example, the PIN diode can be isolated from the slot if it is used in a shunt configuration (as depicted in Figure 87). However, in this case, the RF current has to be drained to the ground and the ground is not physically defined in a slot. Therefore, further research efforts may be required to design a more robust switch for high power applications.

6.3.5. Harmonic Trap Implemented Using Transmission Lines

It is shown in Section 5.5 that the spurious frequency component generated by the PIN diode can be blocked by inserting HTs at the antenna level. In the proposed design, the HTs were implemented using lumped components. At high frequencies, the HTs may be realized using transmission lines. This can not only reduce the component count in the antenna, but also eliminate the need for considering the parasitic effects in the lumped components at high frequencies. Furthermore, the HTs may be co-designed with the antenna so that the total fabrication cost can be kept constant.

slot transmission line

towards feed towards short

Cb Lc PIN diode VDC

Cb

Figure 87. Single-pole PIN diode switch in shunt configuration.

96

APPENDIX A: STUDY OF DTV SIGNAL COVERAGE IN RURAL AREAS

A.1. STUDY OF DTV SIGNAL PROPAGATION AND ITS SIGNIFICANCE

This appendix provides a study of signal coverage at DTV broadcast frequencies. The study is relevant to the research project in that a CR system operates in any white spaces available within the DTV broadcast band. Therefore, it is important to provide an in-depth study of DTV signal propagation, and the output of the research would be beneficial to the implementation of a CR system (especially for the IEEE 802.22 system). The work here is focused on indoor DTV signal reception in a rural environment.

A.2. AN INTRODUCTION TO THE INDOOR RECEPTION PROBLEM

Indoor antennas are popular for DTV signal reception because they are easy to install and easily adjustable. However, as compared to traditional log-periodic antennas mounted on rooftops, indoor antennas generally have a much smaller aperture size. This implies that the indoor DTV antennas would have a lower gain and radiation efficiency [89]. Moreover, indoor antennas are more susceptible to complex indoor environments. For example, moving human bodies, reflective insulation or other metallic structures such as water pipes and windows could all affect indoor DTV signal reception. However, only a limited amount of research on these issues has been reported in the literature [90] – [93]. Eilers and Sgrignoli in [90] studied propagation of a DTV signal into a single-window house by modeling the window with a rectangular aperture antenna. The authors in [91] and [92] provided detailed measurement results for propagation of VHF/UHF signals into indoor sites. In addition, most of the existing outdoor-to-indoor propagation models are dedicated to cellular systems [94] – [97], and there is currently no explicit International Telecommunication Union (ITU) propagation model of indoor reception. In this appendix, we concentrate the study on the effect of reflective (or metallic) insulation on indoor DTV signal reception, based on a more realistic building model as compared to [90]. This

97 particular scenario is chosen since reflective insulation is commonly found in houses located in rural areas. The study is important to CR systems because they are targeted to deliver wireless broadband to rural areas at DTV frequencies.

A.3. ANALYTICAL DESCRIPTION OF AN INSULATED HOUSE

In the limiting situation, a well-insulated house can be modeled by a metallic cavity with random apertures, where the apertures represent windows and/or doorways of a house. Lossy dielectric objects can also be placed inside the cavity to account for the furniture and other interior structures of a house. With such an approximation, the average power density Sc inside an insulated house is given by [98]

 cQ S  t S , (40) c 2fV i

where Si is the incident power density at the perimeter of the house, ζt is the total transmission cross section of the apertures, Q and V are respectively the quality factor and the volume of the cavity, f is the frequency of the DTV signal and c is the speed of light in free space, and an isotropic receiving antenna is assumed. The total quality factor, Q, of the cavity can be decomposed into four components [98],

1 1 1 1 1     Q Q1 Q2 Q3 Q4

3V 2fV 4fV 2fV Q1  , Q2  , Q3  , Q4  , (41) 2r S c  a c  l c Ae

where, in this case, Q1, Q2, Q3, and Q4 represent wall losses, losses due to furniture and other interior structures in the house, power leaks through apertures, and power picked up by a receiving antenna, respectively. From the above expressions of quality factors, it can be seen that, as expected, the field strength inside an insulated house decreases as the broadcast

98 frequency increases. The aperture size, Ae, of the indoor receiving antenna also plays a role in the average power density because it determines the amount of signal that can be captured.

A.4. RAY TRACING SIMULATION

A.4.1. Simulation Scenarios

In order to validate the above analytical assumption and to better understand how reflective insulation can affect TV signal reception in a house located in a rural area, a ray-tracing simulation was performed using Remcom’s Wireless Insite [69]. A typical North American-style rural house model, having dimensions of 12.4 m  15.5 m, was first built in the simulation tool and is shown in Figure 88. The electrical properties of the construction materials used are listed in Table 7.

The reflective insulation is modeled by a thin sheet of perfect electric conductor (PEC). Noting that the thickness of the aluminum foil in household reflective insulation is approximately 76 μm [99] and the skin depth of aluminum at DTV broadcast frequencies only ranges from 3.2 μm to 11.5 μm, the PEC approximation of the insulation layer is justified. Each insulation unit has dimensions of 24 cm  300 cm and is spaced by a wooden frame of 6.4 cm width.

N

N

Interior wall Exterior wall

Window Door (a) (b) Figure 88. (a) Floor plan used in the simulations and (b) 3D view of the house.

99

Table 7. Electrical properties of the building materials.

Material Thickness εr σ Exterior wall i. Normal Brick 15 cm 4.44 0.001 Drywall 13 cm 2.8 0.001 ii. Insulated PEC 0.1 cm 1 ∞ Brick 15 cm 4.44 0.001 Interior wall Drywall 6 cm 2.8 0.001 Air 2 cm 1 0 Drywall 6 cm 2.8 0.001 Window Glass 0.3 cm 2.4 0 Floor i. Normal Wood 6 cm 5 0 ii. Insulated PEC 0.1 cm 1 ∞ Wood 6 cm 5 0 Ceiling i. Normal Wood 6 cm 5 0 ii. Insulated PEC 0.1 cm 1 ∞ Wood 6 cm 5 0 Roof Wood 6 cm 5 0

In the simulation setup, the DTV broadcasting station was placed 50 m away from the edge of the house and 20 m above the ground, such that the house was located in the far-field region. The distance between the broadcasting station and the house is relatively short because we are only interested in the propagation into the house. A set of uncoupled receivers was spread across the interior of the house uniformly on a 30 cm grid. An omnidirectional antenna and a linear dipole antenna with a length of 30 cm were used at the transmitter and receiver, respectively. All antennas are horizontally polarized. The length of the receiving dipole was chosen to be 30 cm such that its dimension is similar to common indoor DTV antennas. Three representative DTV broadcast frequencies, 70 MHz, 200 MHz and 600 MHz, were included in the simulation.

100

A.4.2. Simulation Results

Referring to Figure 88(a), the path loss within the house was computed under four different scenarios:

i. The transmitter is located at the north side of the house and the house has no insulation (NLOS case). ii. The transmitter is located at the north side of the house and the house is insulated (NLOS case). iii. The transmitter is located at the east side of the house and the house has no insulation (LOS case). iv. The transmitter is located at the east side of the house and the house is insulated (LOS case).

The simulated cumulative distribution function (CDF) plots of the path loss inside the house for NLOS and LOS situations are shown in Figures 89 and 90 respectively. From the results, it can be seen that the path loss increases with the broadcast frequency and this agrees with the measurement results given in [91]. For the NLOS situation, it can be observed that the CDF curve for the case with reflective insulation has a steeper slope than the case without reflective insulation. This implies that the reflective insulation can cause a large signal variation inside the house. In addition, over 50% of the receiving spots encounter an extra 10 dB of loss because of the presence of reflective insulation. At 600 MHz, the path loss could reach over 100 dB in some receiving spots. On the other hand, for the LOS situation, the path loss data for both of the cases have very similar distributions. This indicates that the effect of reflective insulation on indoor signal reception is insignificant under LOS situations. In fact, this coincides with the prediction described in [98] that when the loss inside a cavity is negligibly small and the cavity is randomly excited through apertures, the cavity should have zero shielding. In our case, the condition of random excitation is fulfilled for the LOS situation where a large number of transmission paths through windows exist.

101

Figure 89. CDF plot of path loss within the Figure 90. CDF plot of path loss within the house for NLOS case. house for LOS case.

A.5. PROPAGATION MODEL FOR INDOOR RECEPTION

Given the path loss data from the simulation, we derive a simple empirical model for indoor DTV reception. Five paths inside the house were randomly selected for various cases specified in Section A.4.2 (see Figure 91). Using the path loss data obtained at 70 MHz, 200 MHz and 600 MHz and applying a linear regression technique, the following path loss (PL) equations were obtained:

PLNLOS, no insulation = 44 + 0.043 f – 0.6 log(d) (42)

PLNLOS, with insulation = 50 + 0.041 f – 2.5 log(d) (43)

PLLOS, no insulation = 58 + 0.036 f + 3.5 log(d) (44)

PLLOS, with insulation = 54 + 0.044 f + 2.7 log(d) (45) where f is the DTV broadcast frequency in MHz and d is the path length within the house in meters (which is equal to the length of the dashed line in Figure 91). Similar to the path loss equation given in [96] and [97], the total path loss is divided into outdoor path loss, frequency- dependent loss and log-distance loss. The negative dependence of log-distance in Equations (44) and (45) can be explained in Figures 92 and 93. As the transmission through the exterior wall is relatively small, diffraction contributes most of the received power. Therefore, the farther behind

102 the wall the receiver is located, the higher the power received. Thus, in this case, the path loss curve has a negative slope (see Figure 93).

(a) (b)

Figure 91. Five randomly selected indoor propagation paths (dash lines) for each of the (a) LOS and (b) NLOS cases (the arrows indicate the direction of signal from the broadcasting station).

Strong diffraction path

Exterior wall Transmitting antenna Weak diffraction path Receiver routes Figure 92. A ray diagram illustrating the negative dependence on log distance in the NLOS path loss equations.

With insulation To test No insulation the vali dity

Figure 93. Path loss plot along the receiver routes in Figure 92. (Dotted lines: simulated path loss data; solid lines: trend line of the actual path loss data.) 103

To test the validity of the propagation models given in (42) – (45), they are applied to predict the trend of the path loss within the house at 400 MHz and the results are shown in Figure 94. As seen from the plots, the propagation models derived provide a good estimate of the average value of the path loss within the house. The following generalized empirical model for indoor DTV reception is proposed:

PL = PL0 + L(f) + β log(d) (46)

where PL0 represents the outdoor path loss, L(f) is the geometry- and frequency-dependent loss due to multipath scattering and penetration loss, and β is denoted as an insulation exponent. β can be a positive or negative number, depending on whether the channel is LOS or NLOS.

(a) (b)

(c) (d) Figure 94. Path loss plots at 400 MHz: (a) NLOS, without insulation, (b) NLOS, with insulation, (c) LOS, without insulation, and (d) LOS, with insulation. (Dotted lines: simulated; solid lines: path loss models.) 104

A.6. EFFECT OF ANTENNA DIRECTIVITY

Some companies selling passive, directional indoor DTV antennas claim an improved performance for signal reception. However, from [98], it is known that the average power density inside a cavity could be affected by the aperture size of a receiving antenna. Since the effective aperture of an antenna is related to its directivity, it is worthwhile to investigate whether the use of directional antennas can uniformly improve indoor DTV signal reception.

The same simulation setup described in Section A.4.1 was used except that the receiving dipole antenna (omnidirectional) is now replaced by a passive, directional antenna with an E-plane beamwidth of 75o and H-plane beamwidth of 120o. The path loss profile at 200 MHz within the house was then calculated. The resultant cumulative plots of the path loss data are given in Figures 95 and 96. It should be noted that the main beam of the receiving antenna is always directed to the window side (i.e., east side) of the house. From the results, it was found that the use of directional antenna does not necessarily improve indoor signal reception, but may significantly deteriorate signal reception under NLOS situations. In this case, an extra amplification of about 15 dB is required to compensate the degradation. Unless direct paths exist between the broadcasting station and the antenna, a passive, omnidirectional antenna may provide better indoor reception over a number of different stations.

Figure 95. CPF plot of path loss within the Figure 96. CDF plot of path loss within the

house for NLOS case (the use of directional house for LOS case (the use of directional

antenna degrades indoor signal reception). antenna improves indoor signal reception).

105

A.7. SUMMARY

In this work, ray-tracing simulations have been applied to study indoor DTV signal reception in detail. Simulation results show that both window location and the presence of conductor-backed insulation in a house could affect indoor DTV signal reception. Under the NLOS condition, the presence of reflective insulation could cause significant signal fluctuation within a house. However, the effect of reflective insulation is insignificant under the LOS condition. A simple empirical model has been suggested to predict the average signal level within a typical rural house. Furthermore, it was found that a passive, directional antenna does not necessarily improve indoor DTV signal reception.

106

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AUTHOR’S BIOGRAPHY

Jie Bang Yan received the B.Eng. degree (with first class honors) in electronic and communications engineering from the University of Hong Kong in 2006 and the M.Phil. degree in electronic and computer engineering from the Hong Kong University of Science and Technology in 2008. Yan is a Scholar with the Croucher Foundation. He was the recipient of the Best Paper Award at the 2007 IEEE (Hong Kong) Antenna and Propagation/Microwave Theory and Techniques Postgraduate Conference and the 2011 Raj Mittra Outstanding Research Award at Illinois. He also holds two U.S. patents and a U.S. pending patent related to novel antenna technologies. Following completion of his Ph.D., Yan will work at the University of Kansas as an assistant research professor in the Center for Remote Sensing of Ice Sheets.

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