MIMO PERFORMANCE OF LOW MUTUAL COUPLING ANTENNAS IN INDOOR AND HALLWAY ENVIRONMENTS. Yuchu He

Transcription

1 MIMO PERFORMANCE OF LOW MUTUAL COUPLING ANTENNAS IN INDOOR AND HALLWAY ENVIRONMENTS By Yuchu He i

2 Abstract MIMO Performance of Low Mutual Coupling Antennas in Indoor and Hallway Environments Yuchu He Master of Applied Science Graduate Department of Computer and Electrical Engineering University of Toronto 2013 In this thesis, the 2 2 MIMO performance of several low mutual coupling antennas has been investigated in indoor and hallway scenarios. Three compact antennas intended for mobile applications with low mutual coupling between the input ports are presented in this thesis. To gauge the performances of the three designed antennas, two reference antennas are also used. Channel capacity measurements were conducted in Bahen Center Antenna Lab room 8175 and the Bahen Center 8 th floor hallway by using the five antennas as receivers. The antenna spatial location, orientation, line-of-sight and non-line-of-sight situation and richness of multipath effect were considered in the measurements. By averaging the results, it is found that in an indoor environment, low mutual coupling antennas can outperform the reference high mutual coupling antennas especially in higher SNR scenarios. In the hallway environment, low mutual coupling antennas always outperform the reference high mutual coupling antennas due to pattern diversity. ii

3 Acknowledgements I would like to take this opportunity and thank the people who have made this thesis possible. First I would like to express my sincere gratitude to my supervisor Professor George V. Eleftheriades for his supervision, inspirations, and encouragements during my two years MASc study. His immense technical expertise and insightful ideas have been instrumental in my research. It is an honour to work under his supervision. I would like to express my gratitude to Professor Sean Hum for his generosity of using his antenna lab equipment which has been pivotal for this thesis work. His student Derek Zhou has been extremely helpful and patient in helping me setting up the measurements. I would also like to thank Professor Costas Sarris and Neeraj Sood for providing simulated channel capacity results and insights. I would like to thank my fellow graduate students for their support, knowledge and friendship during the two years of my graduate study. I m looking forward to work with them during my PhD study. Finally, I would like to express my truly gratitude to my parents for their unconditional support and encouragement. This thesis will not be possible without them. Financial support from the Natural Sciences and Engineering Research Council of Canada, and Research-in-Motion Inc. are gratefully acknowledged. iii

4 Contents Chapter 1 Introduction Emerging MIMO Application in Wireless Communications Motivation Thesis Goals Thesis Outline... 6 Chapter 2 MIMO Background Signal Propagation and Modeling Antenna Radiation Pattern and Efficiency Correlation Spatial correlation Envelope Correlation Environmental factors and full correlation Correlation Simulations iv

5 Chapter 3 MIMO Antenna Designs Introduction Low Efficiency Metamaterial Inspired Antenna (MIA) Array Improved High Efficiency Metamaterial Inspired Antenna Array PIFA-Slot Antenna λ Spaced Monopole Array λ Spaced Monopole Array Chapter 4 MIMO Capacity Measurements Indoor MIMO Experimental Setup Indoor MIMO Performance: Experimental Results MIMO performance result with absorbers in the room, no reflectors added MIMO performance result with reflectors added in the room Hallway MIMO Experimental Setup Hallway MIMO Experimental Results Summary Chapter 5 Conclusion and Future Work v

6 5.1 Conclusions Future work Appendix A MIMO Transmitting and Receiving Scheme Appendix B Capacity vs. SNR Curves for AUTs Bibliography vi

7 List of Acronyms AOA angles of arrival AOD angles of departure AUT antennas under test CPW co-planar waveguide LOS line-of-sight LTE Long-Term Evolution MIA metamaterial inspired antenna MIMO Multiple Input Multiple Output NLOS non-line-of-sight PDF probability density function PIFA planar inverted F antennas SISO Single-Input, Single-Output SNR signal-to-noise ratio XPD cross polarization ratio vii

8 List of Figures Figure 2.1 Signal propagation model for a SISO Figure 2.2 Phase difference between antenna #1 and antenna #2 for an incident plane wave arriving at an angle θ Figure 2.3 Spatial Correlation plotted as a function of antenna separation Δz for a 2D scenario Figure 2.4 Correlation under a nearly uniform angular power distribution Figure 2.5 Correlation under a realistic LOS angular power distribution Figure 2.6 Correlation under a highly directive angular power distribution Figure 2.7 Scattering model for a multipath MIMO simulation Figure 2.8 Scattered electric field by metallic spheres due to an incident plane wave Figure 2.9 Simulated channel capacity vs. transmitting SNR for closely-spaced dipoles and the metamaterial-inspired antenna Figure 2.10 Simulated channel capacity by using a ray tracer Figure 2.11 Simulated channel capacity by using a ray tracer viii

9 Figure 3.1 HFSS model and fabricated prototype of the low efficiency MIA array Figure 3.2 Simulated S-Parameter plot of the low efficiency MIA array Figure 3.3 Simulated gain patterns for the low efficiency MIA array in the XY, XZ and YZ planes Figure 3.4 HFSS model and fabricated prototype of the high efficiency MIA Array Figure 3.5 Simulated gain patterns for the high efficiency MIA array in the XY, XZ and YZ planes Figure 3.6 Simulated and measured S-parameters of the new MIA array Figure 3.7 Circuit configuration of a uniplanar two-branch directional coupler.. 50 Figure 3.8 Surface current distribution when different ports are excited Figure 3.9 S-Parameters of the original MIA array Figure 3.10 J vector on monopole patch when different ports are excited Figure 3.11 HFSS model and fabricated prototype of the PIFA-Slot antenna Figure 3.12 Simulated and measured S-parameter plot of the PIFA-Slot antenna Figure 3.13 Simulated and measured radiation patterns of PIFA-Slot antenna.. 58 Figure 3.14 Current distributions on the ground plane ix

10 Figure 3.15 Fabricated 0.1 λ spaced monopole antenna Figure 3.16 Simulated radiation pattern for the 0.1λ spaced monopole antenna. 61 Figure 3.17 Measured S-parameter plot for the 0.1λ spaced monopole array and the 0.5λ spaced monopole array Figure 3.18 Fabricated 0.5λ spaced monopole array Figure 3.19 Simulated radiation patterns for 0.5λ spaced monopole array Figure 4.1 Room layout for the MIMO measurements Figure 4.2 Measurement Setup, transmitting antenna locations, absorbers are placed at the back of the room Figure 4.3 Vertical measurement plane of the RX antenna, red dots represent the measurement positions Figure 4.4 Illustration of the three orientations used for the MIA arrays, monopole arrays and PIFA-Slot Antenna Figure 4.5 Rotation of the antenna under test Figure 4.6 Modified room environment with reflectors Figure 4.7 Average MIMO capacity for LOS1 scenario Figure 4.8 Average MIMO capacity for LOS2 scenario Figure 4.9 Average MIMO capacity for LOS3 scenario Figure 4.10 Average MIMO capacity for NLOS1 scenario x

11 Figure 4.11 Average MIMO capacity for NLOS2 scenario Figure 4.12 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with low transmitting SNR=10dB Figure 4.13 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with high transmitting SNR=30dB Figure 4.14 Channel Capacity with respect to high receiving SNR=30dB for all AUTs in different scenarios with absorbers in place Figure 4.15 Average MIMO capacity for LOS1 scenario Figure 4.16 Average MIMO capacity for LOS2 scenario Figure 4.17 Average MIMO capacity for LOS3 scenario Figure 4.18 Average MIMO capacity for NLOS1 scenario Figure 4.19 Average MIMO capacity for NLOS2 scenario Figure 4.20 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with high transmitting SNR=10dB Figure 4.21 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with high transmitting SNR=30dB Figure 4.22 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with high receiving SNR=30dB xi

12 Figure 4.23 MIMO measurement setup in a hallway, Bahen Centre 8 th floor, University of Toronto Figure 4.24 Transmitting and receiving antenna configurations Figure 4.25 Hallway experimental setup Figure 4.26 Capacity vs Measurement Plane at TX SNR=10dB for 5 AUTs Figure 4.27 Capacity vs Measurement Plane at TX SNR=30dB for 5 AUTs Figure 4.28 Capacity vs TX SNR=10dB for all AUTs with XY, XZ, YZ orientations Figure 4.29 Capacity vs Measurement Plane at RX SNR=30dB for 5 AUTs Figure A.1 MIMO implementation of dual transmitting antennas Figure B.1 Average MIMO capacity for the high efficiency MIA array, with absorbers Figure B.2 Average MIMO capacity for the low efficiency MIA array, with absorbers Figure B.3 Average MIMO capacity for the PIFA-Slot antenna, with absorbers Figure B.4 Average MIMO capacity for the 0.5λ spaced monopole array, with absorbers xii

13 Figure B.5 Average MIMO capacity for the 0.1λ spaced monopole array, with absorbers Figure B.6 Average MIMO capacity for the high efficiency MIA array, with reflectors Figure B.7 Average MIMO capacity for the low efficiency MIA array, with reflectors Figure B.8 Average MIMO capacity for the PIFA-slot antenna, with reflectors Figure B.9 Average MIMO capacity for the 0.5λ spaced monopole array, with reflectors Figure B.10 Average MIMO capacity for the 0.1λ spaced monopole array, with reflectors xiii

14 Chapter 1 Introduction 1.1 Emerging MIMO Application in Wireless Communications In wireless communications, multiple-input and multiple-output, or MIMO is a method that uses multiple antennas at both the transmitter and the receiver to improve communication performance. MIMO is an important part of modern wireless communication standards such as the IEEE n, WiMAX and the 4G LTE (Long-Term Evolution) systems. The concept of using multiple antennas in wireless communications dates back to the 1970s [1], but its first real application in wireless communication transceivers and the corresponding theoretical performance demonstration was published in 1996 by Greg Raleigh and Gerard J. Foschini [2]. Traditionally, two-way wireless systems, only 1

15 CHAPTER 1 INTRODUCTION communicate through a single antenna on each side. This is a single-input singleoutput system, or SISO system. Because of the unpredictable nature of the wireless channel between the two ends, the propagated signal may experience significant fading at the receiver and a severe drop in SNR (signal-to-noise ratio). A MIMO system attacks this problem by using multiple antennas at the transmitter and receiver. These multiple antennas can establish multiple communication links between the transmitter and receiver, so that even if one link is in deep fade, the others may have an acceptable SNR to maintain a critical level. Spatial multiplexing can be also employed in MIMO transmitting and receiving scheme. This is done by transmitting independent uncoded symbols over the different antennas as well as over the different symbol times. Spatial multiplexing provides additional degrees of freedom for communication such that information can be transmitted over quasi-independent channels. 1.2 Motivation With the rapid developments in wireless communications, personal handsets are now able to connect to the internet through 3G and emerging LTE 4G networks with ever increasing data rates to provide a better user experience. In terms of 2

16 CHAPTER 1 INTRODUCTION trends in fashion, handset manufactures are pushing for thinner and sleeker designs that place very tight space constraints on antennas. However, from the handset performance point of view, more antennas are needed for the coverage of different bands like 900MHz/1800MHz/1900MHz/2100MHz for GSM and 3G, 2.4GHz for Wi-Fi, and 780MHz for LTE 4G networks. With emerging MIMO technologies, even more antennas will be placed inside the handset to support increasing data communication rates. Most existing commercial approaches, e.g. cellular phones and pagers, utilize fixed microstrip antennas such as monopoles and PIFAs (planar inverted F antennas). However, due to the size of the handset, antennas have to be placed very close to each other, usually less than half wavelength. This close spacing between the antennas can lead to a high spatial correlation. High spatial correlation means that the communication channels of each receiving antenna are highly correlated. Therefore, if one channel goes into fade, the other channel may also fade. Close spacing can also lead to higher mutual coupling between the antennas which can also introduce higher correlation between the MIMO channels. Therefore, both spatial correlation and mutual coupling which can degrade the MIMO performance must be accounted for. As a result, a good antenna design that satisfies the space constraints and yet provides good MIMO performance has become the motivation of our study. 3

17 CHAPTER 1 INTRODUCTION However, the challenge in antenna design for mobile devices is that the response from the communication channel is a statistical process due to random scattering, yet the antenna characteristics are deterministic. Therefore, how do we design the antenna to cope with the random channel response? What antenna characteristics such as efficiency, mutual coupling and radiation patterns are the most important factors that affect MIMO performance? For example, there is no definite answer on how the mutual coupling, a key issue in MIMO, affects the MIMO capacity. Studies from [3], [4], [5] claim that low mutual coupling can improve MIMO capacity by providing better diversity gain and lower correlation. However, studies from [6] claim that high mutual coupling is beneficial due to an improved power collection capability of coupled antennas. Another study in [7] shows that when the antenna spacing is less than 0.4 λ, the coupled array performs better than the isolated antennas. Another study [8] claims that mutual coupling can have a positive impact or negative impact on performance depending on the propagation environment. A more thorough study in this topic can greatly contribute to the area of MIMO research. 4

18 CHAPTER 1 INTRODUCTION 1.3 Thesis Goals The general focus of this thesis is to design and demonstrate different antennas aiming at 2 2 MIMO applications and measure their MIMO performance by carrying out channel matrix measurements. The first objective of the thesis is to design different 2 2 MIMO antennas. The antennas should have low profile, compact size and could be integrated into contemporary mobile smartphones such as a Blackberry. This highlights a main goal of the thesis which is the evaluation of the possibility of low mutual coupling and correlation between closely spaced antennas when placed in the confinement of a modern smartphone. The second related objective of the thesis is to evaluate the MIMO performance of the designed antennas. This evaluation will be based on the measured channel matrix and computed channel capacity. Due to the scope of the thesis, the measurements will be performed in a typical indoor environment and a hallway environment. To make the measurement thorough, various factors are included such as different antenna orientations, angle of arrival of the incident signal at the receiver, line-of-sight vs. non-line-of-sight scenarios, and lastly, moderate multipath vs. rich multipath effects. By including various environmental factors and averaging the results, we can investigate how different antenna factors affect MIMO performances. 5

19 CHAPTER 1 INTRODUCTION 1.4 Thesis Outline This thesis is divided into different sections based on the nature of the work as follows. Chapter 2 reviews important concepts in MIMO communication such as channel matrix, antenna radiation pattern, efficiency and correlation. A major portion of the background will review the concept of correlation which is a key metric for evaluating the MIMO performance. The discussion of correlation is divided into spatial correlation which is related to antenna spacing and envelope correlation which is related to the antenna radiation patterns and mutual coupling between the ports. The spatial and envelope correlations are deterministic quantities and do not account for the environmental factors. Therefore, the full correlation accounts for environmental factors such as polarization and incident power distribution that will be discussed in detail. Some simulation results will also be presented to verify some of the concepts to help with understanding. Chapter 3 presents a set of antenna designs that are used for MIMO performance measurements at a design frequency of 2.28 GHz. There are 5 antennas considered in total. The first one is a MIA (metamaterial inspired antenna) array developed in [9] tuned to a design frequency with low radiation efficiency. The 6

20 CHAPTER 1 INTRODUCTION second antenna is a MIA array based on [9] with higher radiation efficiency. The third one is a PIFA (planar inverted F antenna) integrated with a slot antenna (PIFA-Slot). All these three antennas have low mutual coupling between their ports. The two MIA arrays and the PIFA-Slot antenna provide pattern diversity and polarization diversity. These three antennas will be compared to two reference antennas, namely the 0.1λ spaced and the 0.5λ spaced monopole arrays. The 0.1λ spaced monopole array is closely spaced with high mutual coupling to resemble the antennas in a handset. The 0.5λ spaced monopoles have low mutual coupling, low spatial correlation and high efficiency to represent an almost 'ideal' MIMO antenna. Chapter 4 discusses the MIMO performance measurements in detail. The measurements are performed in indoor and hallway environments. The five antennas discussed in Chapter 3 will be used as receiving antennas. By measuring the voltage at the antenna terminals, the channel matrix can be obtained and the channel capacity can be calculated from the channel matrix. The measurement includes various factors such as receiving antenna spatial location, elevation and orientation, transmitting antenna location, transmitting antenna line-of-sight or non-line-of-sight and richness of the multipath environment. The capacity results will be presented and discussed in detail. 7

21 CHAPTER 1 INTRODUCTION Finally, Chapter 5 summarizes the thesis with conclusions on all major findings and discusses possible improvements and further studies as future work. 8

22 Chapter 2 MIMO Background 2.1 Signal Propagation and Modeling In traditional wireless communications, the most direct and easy implementation is by using a single transmitter (TX) and a single receiver (RX) and this is called a SISO (Single-Input, Single-Output) system. Despite its simplicity, the performance of a SISO system can be severely undermined by the fading of the signal caused by destructive interference due to multipath propagation and Doppler shifts. The SISO signal propagation can be modeled as shown in Figure 2.1. The signal propagation from the transmitter to the receiver occurs over a series of multiple paths and is referred to as multi-path propagation, where each of the signal paths is a result of reflection, refraction or scattering of the original signal due to various objects in the environment. 9

23 CHAPTER 2 MIMO BACKGROUND Figure 2.1 Signal propagation model for a SISO system As a result of this so called multi-path propagation, if we transmit a sinusoidal signal then at the receiver we have a summation of different sinusoidal components scaled and delayed by amounts depending on the corresponding path distance and reflection coefficient for the particular path. The reflection coefficient and path distance determine the strength of the particular path denoted by α i, whereas the path distance determines the excess delay for the path denoted by τ i. These multi-path parameters may be fixed or time varying depending on whether or not there is motion of the transmitter and receiver with respect to the environment. For a very brief time window, the path parameters α i and τ i can be considered as constants, and then we can model the whole channel as a linear time-invariant 10

24 CHAPTER 2 MIMO BACKGROUND system by using the impulse response. The impulse response of the system as shown in Figure 2.1 can be modeled as: n h(t) = α i δ(t τ i ) i=1 (2.1) By applying Fourier Transform, we can obtain the channel response in the frequency domain for this SISO system. H(f) = h(t)e j2πft dt (2.2) n H(f) = α i e j2πfτ i i=1 (2.3) Since the SISO system is susceptible to multipath interference, to improve the reliability of the system, the core idea of a MIMO system is to utilize multiple antennas spaced far enough apart at the receiver, such that each receiving antenna receives a different copy of the signal that undergoes different processes of reflection or diffraction. Thus, when one of the RX antennas goes into fading, another RX antenna might not. The probability of both antennas going into a fade is reduced and the reliability of the communication link is increased. Aside from the increased reliability, signals from the RX antennas can be combined in such a way that the quality (bit-error rate or BER) or the data rate (bits/sec) of 11

25 CHAPTER 2 MIMO BACKGROUND the communication for each MIMO user will be improved. MIMO effectively takes advantage of random fading and multipath delay spread [2], [10], [11]. The ergodic (mean) capacity for a complex AWGN MIMO channel ignoring water-filling and TX power control can be expressed as in [2]: C = E H log 2 det I nr + P T σ T 2 n T HH (2.4) where I nr is the identity matrix, P T σ T 2 is the average SNR at each transmitting branch, n T is the number of transmitting antennas and H is the channel matrix. The H matrix in Eqn(2.4) is not normalized such that the path loss and energy dissipation in the receiving antenna are both included. The capacity can also be computed by using P R σ R 2, the average SNR at each receiving branch. The H matrix in this case should be normalized to the total received power at the receiver such that the path loss and antenna loss are neglected. C = E H log 2 det I nr + P R σ R 2 n T HH (2.5) In this thesis, the capacity is calculated by using the transmit diversity. In this case, the magnitude of the elements in the H matrix can be very small, so even 12

26 CHAPTER 2 MIMO BACKGROUND with a moderately high transmitting SNR levels, the identity matrix I nr cannot be ignored. The channel of a MIMO system can be described by a M N matrix where M is the number of receiving antennas, and N is the number of transmitting antennas. For example, a 2 2 MIMO system, the H matrix is of the form: H MIMO = h 11 h 21 h 12 h 22 (2.6) h ij is the power transfer coefficient from transmitter j to receiver i, which is usually a complex number. The element h ij not only depends on the multipath propagation of the environment or the channel response, but also on the antenna properties of the transmitter and receiver, specifically, the radiation pattern. Recall that in Section 2.1, the channel response is given in Eqn (2.3), if we assume both TX i and RX j have an isotropic radiation pattern, then we can obtain the channel matrix h ij (f) to this SISO system immediately from the channel response: h ij (f) H(f) = α i e j2πfτ i n i=1 (2.7) Otherwise, we would need to perform a dot product of the TX radiation pattern including the channel response with the RX radiation pattern as shown in Eqn (2.8). For simplicity, only one polarization is considered here. 13

27 CHAPTER 2 MIMO BACKGROUND n m h ij (f) f TXi (θ a, φ b )α(θ a, φ b )e j2πfτ(θ i,φ j ) f RXj (θ a, φ b ) a=1 b=1 (2.8) f TXi and f RXj are the complex radiation patterns of TX i and RX j respectively. Quantities θ a, φ b define the AOD (angles of departure) of the transmitted signal from the TX and θ a, φ b define the AOA (angles of arrival) of the incident signal at RX. We can think of the TX has a radiation pattern f TXi emitting incident rays in all directions. However, only a set of rays from the TX antenna can reach the RX antenna through the channel. These set of rays are defined by the angles (θ a, φ b ) with respect to the TX coordinate systems. As the rays travel through the channel, each ray is modified by the channel through an amplitude parameter α and a phase delay parameter τ. Finally, the rays arrive at RX from a set of specific angles described by (θ a, φ b ) with respect to the RX coordinate system. 2.2 Antenna Radiation Pattern and Efficiency It is important to define the radiation pattern and efficiency for antennas used in our MIMO simulation and experiment. The radiation pattern of a classical array antenna for line-of-sight systems is the product of two factors: the isolated element pattern (which is equal for identical elements at different locations) and the array factor. The isolated element pattern as defined in [12] is the radiation 14

28 CHAPTER 2 MIMO BACKGROUND field from one element of the array when all the other elements are removed. For example, in a dipole array, the isolated pattern is just the radiation pattern of a single dipole in free space. In theoretical work on MIMO systems, the elemental antennas are often treated as being isolated, but this is not a valid description for such systems. In addition, the array factor cannot be used for a MIMO antenna because each antenna element pattern can be different, thus the radiation patterns are different. A more appropriate description MIMO antenna radiation pattern is the embedded element pattern. This is the radiation pattern of a single excited element when all the other elements are present, but they are not excited and instead are terminated with loads representing the source impedance on their ports [13]. The excited element will induce radiating currents on the terminated coupled elements. Therefore, the embedded element pattern may be very different from the isolated element pattern due to the presence of the coupled elements. MIMO systems are made for use in multipath environments, and the excited or received voltage on each port is ideally independent of (uncorrelated with) the voltages on the others ports. Therefore, each port transmits (or receives) signals through their embedded element pattern. It is the embedded radiation patterns that are used in our correlation calculations. 15

29 CHAPTER 2 MIMO BACKGROUND Classical arrays for line-of-sight systems are characterised by a radiation efficiency that is not the same as the radiation efficiency of the embedded element. The radiation efficiency of the classical array gives the ratio between its realised gain and directivity, which relates to the radiation pattern of the whole array, not only an element as in the MIMO case. For the efficiency in MIMO, we define it as e = P rad P acc (2.9) P rad is the radiated power when one port is excited and the other ports are matched. P acc is the accepted power. For a two port antenna network with port 1 excited and port 2 terminated with a matched load, P acc is defined as in Eqn(2.10), P acc = a 2 (1 S 11 2 S 12 2 ) (2.10) where a is the complex voltage excitation at the port. Therefore, the radiation efficiency defined in Eqn(2.9) is essentially the measure of power dissipation from conductor or dielectric losses. Power coupled to the other port due to mutual coupling is not considered to be lost. Under certain circumstances, the coupled power may add constructively as mentioned in [6]. Radiation efficiency can be different depending on which port is excited. Both the radiation efficiency and 16

30 CHAPTER 2 MIMO BACKGROUND correlation are needed to predict diversity gain and maximum capacity theoretically. 2.3 Correlation For reliable communication, it is best for the channel response to be as different as possible between all the possible transmitter-receiver pairs. Therefore, if one receiver antenna goes into a fade, the probability of another receiver antenna going into a fade will be low. A key metric to evaluate such property is called correlation which can be divided into spatial correlation and antenna envelope correlation Spatial correlation In MIMO communications, the channels from a transmitter to the receivers could have similar characteristics and this will degrade the performance of the MIMO system. A useful metric that is widely used in wireless communication literature is called correlation distance and is a direct measure of the average spacing for uncorrelated channels. For example, a well-known result for the correlation distance in 2D can be calculated by the cross correlation R(Δz), where Δz is the spacing between the antennas. Assume a plane wave arriving at antenna #1 17

31 CHAPTER 2 MIMO BACKGROUND from the random direction angle θ, with the assumption that the source is very far away, and then this incident wave will arrive at antenna #2 with the same angle θ and amplitude as shown in Figure 2.2. If the phase of the signal arriving at antenna #1 is given by G 1 (t) = e j(w 0t+φ) (2.11) Then the signal at antenna #2 separated by distance Δz is given by: G 2 (t) = e j(w 0t+φ+k zsinθ) (2.12) If the incident plane wave can arrive at the antennas from any random angle, we can describe the angle of incidence as a probability function. In this case, the probability function is uniform since the angle of incidence is random with the probability for each angle of incidence being the same. The correlation of the two signals can be described by the cross correlation and it is a function of Δz. R( z) = E{G 1 (t)g 2 (t)} = E e jkδzsinθ = 1 2π 0 2π e j(w 0t+φ) e j(w 0t+φ+k zsinθ) dθ (2.13) = 1 2π 2π ej(k zsinθ) dθ 0 = 1 π π eixcosθ dθ 0 = J 0 (kδz) where J 0 (kδz) is the Bessel function of the first kind and zero order. 18

32 CHAPTER 2 MIMO BACKGROUND Figure 2.2 Phase difference between antenna #1 and antenna #2 for an incident plane wave arriving at an angle θ. The function J 0 is plotted vs. Δz as shown in Figure 2.3. The first zero of J 0 (kδz) occurs when Δz=0.43λ and this is the minimum distance to achieve zero correlation under a uniform scenario for 2D isotropic antennas. This minimum distance is defined as the correlation distance. For 3D isotropic antennas under a uniform scenario, the correlation is given by [14] R(Δz) = sin(kδz)/(kδz) (2.14) For zero correlation coefficient, the minimum antenna spacing Δz is 0.5λ. The limitation of the spatial correlation calculated above is that it implies that the incident power probability density distribution in the angular domain is assumed to be uniform, which is rarely the case in a real life scenario; the radiation 19

33 CHAPTER 2 MIMO BACKGROUND patterns are also assumed to be isotropic. Eqn (2.13) can be modified for correlation distance calculations for directional scenarios with arbitrary distributions of the incident signal power [14]. 2π R( z) = E{G 1 (t)g 2 (t)} = p θ (θ)g 1 (θ)g 2 (θ)dθ 0 (2.15) p θ (θ) is the angular power density, which can be omnidirectional or directional. G 1 (θ) and G 2 (θ) are the isolated radiation patterns of the antennas. If G 1 (θ) and G 2 (θ) are directional, then the correlation distance will increase. In the extreme case, if the transmitting and receiving antennas lie on a line-of-sight in free space, the angular power density is simply a delta function. Eqn (2.15) is then evaluated at a single angle θ and the function always has a magnitude one regardless of what the radiation patterns are. The correlation distance is not well defined in this case and the receiving antennas will always be fully correlated. 20

34 CHAPTER 2 MIMO BACKGROUND Figure 2.3 Spatial Correlation plotted as a function of antenna separation Δz for a 2D scenario. There are multiple zeros, but the first zero is at Δz=0.43 λ. This is defined as the correlation distance, the minimum distance to achieve zero spatial correlation Envelope Correlation The spatial correlation calculation, discussed in the previous section, only involves the antenna spacing and isolated radiation patterns. For some MIMO antennas, the antenna spacing cannot be well defined such as in [15], which uses different characteristic modes on a ground plane to radiate. A useful metric in this case is the envelope correlation calculated from the embedded radiation patterns. The envelope correlation can be calculated from the antenna far field embedded radiation patterns for a two-port antenna as shown below: 21

35 CHAPTER 2 MIMO BACKGROUND ρ e = 4π 0 4π E 1 (θ, φ) 2 0 [E 1 (θ, φ) E 2 (θ, φ)] dω dω 4π E 2 (θ, φ) 2 dω (2.16) 0 E 1 (θ, φ) is the far field radiation pattern of the antenna system when port #1 is excited and port #2 is matched. E 2 (θ, φ) is the far-field radiation pattern of the antenna system when port #2 is excited and port 1 is matched. Both E 1 (θ, φ) and E 2 (θ, φ) are embedded radiation patterns as mentioned in Section 2.2. The significance of zero or low envelope correlation is that the embedded radiation patterns are almost orthogonal and this is pattern diversity. This correlation is particularly useful to antenna designers since the envelope correlation can be directly related to the S-parameters [16]. ρ e = S 11 S 12 + S 21 S 22 2 (1 ( S S 21 2 ))(1 ( S S 12 2 )) (2.17) S ii is the reflection coefficient of antenna port i and S ij is the mutual coupling between antenna ports i and port j. Therefore, from the antenna design point of view, the envelope correlation can be reduced by reducing the magnitude of S ii or S ij. The diagonal element S ii is the reflection coefficient of that port and we would like to have a low value of S ii such that the power input to the ports is radiated instead of reflected. Maintaining both low reflection S ii and coupling S ij coefficients has become a guideline for our antenna design for MIMO applications. 22

36 CHAPTER 2 MIMO BACKGROUND By achieving low mutual coupling, we are essentially providing pattern diversity. Pattern diversity leads to diversity gain. It is important to review the concept or diversity and its relationship to receiving antenna pattern diversity. When the path is in a deep fade, any communication scheme will likely suffer from errors. A natural solution to improve the performance is to ensure that the information symbols pass through multiple signal paths, each of which fading independently. This will ensure that reliable communication is possible as long as one of the paths is strong. This technique is called diversity and it can dramatically improve the performance over fading channels. If there are multiple receiving antennas, they will provide diversity gain over a single receiving antenna if the channel response at each receiving antenna is sufficiently independent. If the channel response elements h ij are fully correlated across all receiving branches, then we only get a power gain but no diversity gain. Thus, when the receiving antennas have different radiation patterns, it is possible that each antenna experiences a different fading. The pattern diversity for a 2 port receiving antenna relates to the mutual coupling between the antenna ports. Low mutual coupling gives rise to more orthogonal patterns and thus lower correlation between the channel responses. High mutual coupling gives rise to high correlation. In high SNR scenarios, the 23

37 CHAPTER 2 MIMO BACKGROUND channel capacity depends on the condition number of the channel matrix. A wellconditioned matrix situation depends on maintaining the uncorrelated nature of the channel response elements h ij. Thus, low mutual coupling receiving antennas should provide a better conditioned channel matrix than high mutual coupling receiving antennas. In high SNR scenarios, low mutual coupling receiving antennas should provide better capacity results Environmental factors and full correlation The spatial correlation discussed in Section is mostly concerned with the antenna spacing factor. On the other hand, the envelope correlation discussed in Section only includes the antenna radiation pattern factor. Neither is a complete description of the physical correlation for antennas under the effect of realistic probabilistic environmental factors. The environment can change the polarization of the transmitted wave due to reflections, refractions or transmissions through different materials. These scattering or multipath effects can change the transmitted wave power profile or the angular power distribution as the wave incident on the receiving antenna. For example, the angular power density incident on the receiving antenna is more concentrated in a narrow angular region in rural areas compared to dense urban areas since urban areas result to more reflections, effectively creating a wider spread of the angular power 24

38 CHAPTER 2 MIMO BACKGROUND distribution. As a result, to account for the environmental factors, the full correlation should include spatial correlation, antenna envelope correlations and environmental effects. To account for the polarization effect, a time or space averaged linear polarization matrix for the channel can be defined which contains the angular correlations of the polarization components of the incident field. [14] Γ (θ 1, φ 1 ; θ 2, φ 2 ) = Γ θθ Γ θφ (2.18) Γ φθ Γ φφ Where the general element of the matrix is defined as, Γ θφ (θ 1, φ 1 ; θ 2, φ 2 ) = E θ (θ 1, φ 1, t) E φ (θ 2, φ 2, t) t (2.19) In this case, Γ θφ is time averaged. The quantities E θ (θ 1, φ 1, t) and E φ (θ 2, φ 2, t) are the θ and φ components of the incident field. If the polarization components of the incident wave are uncorrelated, then Γ θφ and Γ φθ are zero. Furthermore, the polarized distribution of the incident wave E θ (θ 1, φ 1, t) 2 and E φ (θ 1, φ 1, t) 2 can be written as P 1 p θ (θ, φ) and P 2 p φ (θ, φ), where P 1 is the total power in the θ polarization, and P 2 is the total power in the φ polarization. Both P 1 and P 2 are scalars. The quantities p θ (θ, φ) and p φ (θ, φ) are the PDFs (probability density functions) of the angular power per steradian in the θ and φ 25

39 CHAPTER 2 MIMO BACKGROUND polarizations, respectively. Normalizing the total power in both polarizations so that Tr Γ (N) = 1, the polarization matrix can be written as Γ (N) (θ 1, φ 1 ; θ 2, φ 2 ) = 1 δ(θ 1 θ 2 )δ(φ 1 φ 2 ) P (2.20) 1p θ (θ 1, φ 1 ) 0 P 1 +P 2 0 P 2 p φ (θ 2, φ 2 ) Finally, if p θ (θ 1, φ 1 ) = p φ (θ 2, φ 2 ) = S(θ, φ), then the polarization matrix can be written as, Γ (N) (θ 1, φ 1 ; θ 2, φ 2 ) = S(θ, φ) δ(θ 1 θ 2 )δ(φ 1 φ 2 ) XPD (2.21) where the cross polarization discrimination (XPD) of the incident wave from the environment is defined as XPD = Γ θθ = E θ(θ, φ, t) 2 Γ φφ E φ (θ, φ, t) 2 = P 1 (2.22) P 2 In this case, XPD is just a scalar. If p θ (θ 1, φ 1 ) p φ (θ 2, φ 2 ), then XPD will be a function of θ and φ. Aside from the polarization discrimination, the angular power distribution of the incident signal also depends on the environment. For example, in a line-of-sight free-space scenario, the angular distribution of the incident signal is ideally a delta function. In a dense downtown non-line-of-sight scenario, the distribution could be more uniform due to scattering. For line-of- 26

40 CHAPTER 2 MIMO BACKGROUND sight scenarios, a Gaussian function can be used to model the angular power distribution for a single polarization, P(θ, φ) exp (θ θ m) (φ φ m) 2 2, θ π 2σ θ 2σ φ 2, π 2, φ [ π, π ] (2.23) (θ m, φ m ) represents the nominal line-of-sight direction or at least the nominal center of a bundle of rays. For an indoor environment pertaining to our MIMO measurement, the angular power distribution of the vertically and horizontally polarized received signals is assumed to be distributed uniformly in azimuth and distributed as a Gaussian function in elevation which is consistent with the measured results reported in [17]. The distribution is then given by P θ (θ, φ) = A θ exp (θ θ v )2 2σ2, θ π, π (2.24) v 2 2 P φ (θ, φ) = A φ exp (θ θ h )2 2, θ π, π (2.25) 2σ h 2 2 where A θ and A φ are normalizing constants, θ v and θ h are the means and σ v and σ h are the standard deviations of the θ and φ polarized components. Therefore, the full correlation should include the following factors: polarization, antenna radiation patterns and incident signal angular power distribution. This full correlation expression is computed as the following 27

41 CHAPTER 2 MIMO BACKGROUND ρ e12 = H 12 H 1 H 2 (2.26) where H 12 = {XPD(θ, φ) P θ (θ, φ) E θ1 (θ, φ)e θ2 (θ, φ) + P φ (θ, φ)e φ1 (θ, φ)e φ2 (θ, φ)}e jβ z dθdφ (2.27) and H 1 = XPD(θ, φ) P θ (θ, φ)e θ1 (θ, φ)e θ1 (θ, φ) + P φ (θ, φ)e φ1 (θ, φ)e φ1 (θ, φ) (2.28) H 2 = XPD(θ, φ) P θ (θ, φ)e θ2 (θ, φ)e θ2 (θ, φ) + P φ (θ, φ)e φ2 (θ, φ)e φ2 (θ, φ) (2.29) Subscripts 1 and 2 denote the receiving antenna #1 and antenna #2. z is the spacing between the two antennas. β is the wave number. P θ and P φ are the angular power distributions, E θ and E φ are the embedded radiation patterns of the receiving antennas. Care should be taken when applying the full correlation since P θ and P φ are direction dependent respective to the antenna orientation. Therefore, it is necessary to match P θ and P φ to the coordinate system of the antenna. If we set P θ, P φ and XPD to unity, ρ e12 simply becomes the ordinary envelope correlation of the antenna radiation patterns as in Eqn(2.16). The importance of full correlation is that it is related to the correlation between the H matrix elements. Elements of the H matrix are complex values obtained by 28

42 CHAPTER 2 MIMO BACKGROUND performing correlation between voltages at the transmitter s ports and the receiver s ports. Voltages at the receiving antenna ports are a vector product between incident wave and the radiation patterns. As a result, the less the correlation computed by using Eqn(2.26), the less the correlation between the H matrix elements which is an indication of higher diversity gain. 2.4 Correlation Simulations For MIMO antennas in a handset, the spacing between the antennas is usually fairly close. Therefore, the spatial correlation calculated by Eqn (2.13) is usually high. However, if a special technique is used such as in [9] to reduce the mutual coupling or the envelope correlation, it is possible for the full correlation to be low depending on the environmental factors. It is interesting in this thesis to examine how closely-spaced MIMO antennas with low envelope correlation perform under different environmental factors, in other words, is it possible to have a low full correlation? For simplicity, we would like to investigate the effect of different angular power distributions on the full correlation described by Eqn (2.26)-(2.29). For example, a narrow spread of angular power distribution resembles more closely a line-of-sight rural 29

43 CHAPTER 2 MIMO BACKGROUND environment whereas a wide spread of angular power distribution resembles more closely a non-line-of-sight scenario urban environment. Simple simulations can be carried out to investigate the angular power distribution effect. The antenna presented in [9] is a 2 port metamaterial inspired antenna. The two ports are very closely spaced (λ/14) and yet exhibit a very low mutual coupling about -17.6dB. The HFSS model of the antenna is shown in Figure 2.7. The envelope correlation calculated by the S-parameters as in Eqn(2.16) is and the envelope correlation calculated by using the antenna radiation patterns as in Eqn(2.16) is , showing good agreement. For simplicity, XPD is set to one assuming there is equal power in both polarizations. P θ and P φ are assumed to be equal and can be modeled by a Gaussian function as in Eqn(2.23). However, if we apply Eqn(2.23) to a circle or a sphere, the range of the angles is bounded by θ [0, π], φ [0,2π] and the range of the Gaussian function is limited instead of going to infinity. Thus, when the spread of the distribution is large, Eqn(2.23) is clipped and is not an accurate representation of a Gaussian distribution anymore. Therefore, for simulation purposes, a spherical Gaussian distribution called the Von Mises-Fisher distribution is used as given below [18] 30

44 CHAPTER 2 MIMO BACKGROUND f 3 (x, μ, κ) = C 3 (κ) exp(κμ T x) C 3 (κ) = κ 4π sinh(κ) = κ 2π(e κ e κ ) (2.30) (2.31) where μ is the mean direction vector and κ controls the concentration which is analogous to the variance. The quantity x is the unit vector and C 3 is a normalization constant. Figure 2.4 to Figure 2.6 show the correlation value for k= of a nearly uniform angular power distribution to k=100 for a highly directive angular power distribution. The X, Y axes are the θ and ϕ angles representing different angles of arrival of the incident wave. The shape of the Von Mises-Fisher distribution itself is shown in the smaller graph on top of the correlation graph for better illustration. 31

45 CHAPTER 2 MIMO BACKGROUND Figure 2.4 Correlation is calculated by using Eqn(2.25), under a nearly uniform angular power distribution for the antennas in [9] with different angles of arrival. The smaller graph overlaid is a graphical representation of the angular power distribution (Von Mises-Fisher distribution). The magnitude of the Von Mises-Fisher distribution over all the theta and phi angles is relatively constant, so this is a nearly uniform distribution. 32

46 CHAPTER 2 MIMO BACKGROUND Figure 2.5 Correlation under a realistic LOS angular power distribution. The correlation value is dependent on the angle of arrival Figure 2.6 Correlation under a highly directive angular power distribution 33

47 CHAPTER 2 MIMO BACKGROUND From the correlation values plotted against different angular spreads, it becomes obvious that the correlation value is lowest on average in a more uniform angular spread. On the other hand, the correlation can be small in a highly directive scenario depending on the angle of arrival. However, the average correlation value in a highly directive scenario is much larger than the value in a more uniform scenario. Therefore, a low mutual coupling antenna system would benefit from a more uniform angular distribution from a correlation point of view. To investigate the MIMO channel capacity in a wide angular distribution for a realistic antenna, the low-mutual coupling metamaterial inspired antenna of [9] is used for a simple simulation that can be performed in the HFSS simulator by using the ring of scatterers model [19] to create a multi reflection effect as shown in Figure 2.7. The scatterers are modeled by small metallic spheres. Due to limited computing resources, the rings of scatterers are only placed in the XZ and YZ planes. Two plane-wave sources E 1 and E 2 are placed in the far field of the low mutual coupling antenna, half wavelength away from each other such that the angle of incidence at the receiver is slightly different. The plane wave will be scattered off the metallic spheres creating a multipath scenario. The scattering is shown in Figure 2.8. We can see that the electric field is fairly scattered, creating a fairly rich scattering environment. 34

48 CHAPTER 2 MIMO BACKGROUND Figure 2.7 Scattering model for a multipath MIMO simulation; the antenna shown is the low-mutual coupling metamaterial-inspired antenna of [9]. The spheres are made of PEC of size of 1cm to reflect the wave. The source is single polarized for simplicity, but from Figure 2.7, it is obvious that the incident wave becomes cross polarized after scattering. To investigate multipathing in the YZ plane, E 1 and E 2 are the two incident waves polarized in 35

49 CHAPTER 2 MIMO BACKGROUND the X direction (shown in black); by moving E 1 and E 2 around the X axis, we are essentially creating different angles of arrival at the receiver. To investigate multipathing in the XZ plane, E 1 and E 2 are polarized in the Y direction (shown in red) and they are moved around Y axis. The received port voltage on the coaxial cable can be extracted for each angle of arrival of the incident wave. By assuming a port voltage at the source and transmitting SNR, the channel capacity can be calculated by Eqn(2.4) for each angle of arrival and the result will be averaged over different angles of arrival. Figure 2.8 Scattered electric field by metallic spheres due to an incident plane wave. 36

50 CHAPTER 2 MIMO BACKGROUND A similar setup can be applied to a closely-spaced dipole array with high mutual coupling, such that the effect of mutual coupling on the MIMO capacity can be investigated. The simulated dipoles are spaced by λ/14 apart which is the same spacing as the metamaterial inspired antenna of [9] with a correlation value of compared to of the metamaterial one. The efficiencies of the dipole array are 100%. The efficiencies of the metamaterial inspired antenna array are 53% and 64%. The computed channel capacity is plotted against different transmitting SNRs for both antennas as shown in Figure 2.9. From the simulated channel capacity calculation, the metamaterial inspired antenna seems to perform better than the two closely-spaced dipoles with the same spacing as the metamaterial inspired antennas in a higher transmitting SNR scenario. It seems that by providing a low envelope correlation, the metamaterial inspired antenna provides better diversity gain than the dipole array. The ring of scatterers model is a fairly crude way to simulate a multipath environment. Despite its simplicity, the ring of scatterers method does provide some insight. 37

51 CHAPTER 2 MIMO BACKGROUND Figure 2.9 Simulated channel capacity vs. transmitting SNR for closely-spaced dipoles and the metamaterial-inspired antenna of [9], both antennas have a λ/13 spacing. The voltage at antenna ports can be extracted from the simulation with the assumption that the transmitter port is set to 1V. The ratio between each transmitter voltage and each receiver voltage is the H matrix element. By using Eqn (2.4), this capacity curve can be obtained. For a more accurate simulation, a ray tracer can be used. The ray tracing software can get the accurate incident wave distribution density due to the scattering environment. Upon obtaining the incident wave distribution, it can be dotted with the radiation pattern of the receiver to produce an effective voltage. The correlation can be computed through the voltages obtained. Figure 2.10 and Figure 2.11 present the ray tracing simulation result [20] of using the 38

52 CHAPTER 2 MIMO BACKGROUND metamaterial inspired antenna and dipole array with the same inter-element spacing as receiving antennas in a hallway line-of-sight setting. The hallway is modeled as simple rectangular corridor. The transmitters are isotropic antennas spaced at λ/14 and λ/2 respectively. The simulation result is averaged over spatial locations. Figure 2.10 Channel capacity calculated using the 2-element metamaterial inspired antenna array and a dipole array at the same spacing as receivers. i.i.d. MIMO channel and correlated MIMO channel are used as reference. The simulation is performed in a hallway scenario, the result is averaged over random spatial locations. The transmitters are 2 isotropic antennas with λ/14 spacing. The 2-element metamaterial inspired antenna array outperforms the dipole array at SNR=17dB. The dipole array has about the same performance of a correlated MIMO channel. 39

53 CHAPTER 2 MIMO BACKGROUND Figure 2.11 Channel capacity calculated using the 2-element metamaterial inspired antenna array and a dipole array at the same spacing as receivers. i.i.d. MIMO channel and correlated MIMO channel are used as reference. The transmitters are 2 isotropic antennas with λ/2 spacing. The 2-element metamaterial inspired antenna array outperforms the dipole array through all SNR. The capacity curve from the simple HFSS ring scatterers simulation shown in Figure 2.9 and the more accurate ray tracing simulation shown in Figure 2.10 share some interesting features. The dipole array outperforms the 2 element metamaterial inspired antenna array in the low SNR region. At a certain SNR threshold, the metamaterial array overtakes the dipole array. This shows that the in a low SNR region, the power collecting capability dominates the capacity performance. In the high SNR region, the pattern diversity becomes the dominating factor. The dipole array has better efficiency than the metamaterial 40

54 CHAPTER 2 MIMO BACKGROUND array, thus it can collect power better. However, the dipole array lacks pattern diversity due to high mutual coupling; thus, the low mutual coupling metamaterial array with good pattern diversity performs better when SNR is sufficiently high. 41

55 Chapter 3 MIMO Antenna Designs 3.1 Introduction To carry out the measurement campaign for a 2 2 MIMO system, 3 antennas are designed as receivers. From the practical point of view, the designed antennas are all very compact so they can be integrated into mobile devices. To investigate the role of low mutual coupling for closely spaced antennas in the MIMO performance, all the 3 antennas have low mutual coupling with some difference in radiation efficiencies and radiation patterns. For measurement purposes, all the antennas are designed at 2.28GHz. The first antenna is the metamaterial inspired antenna (MIA) array developed in [9] tuned to the design frequency of 2.28GHz. It has low efficiency and low mutual coupling between the two ports. The second antenna is an improved version of the original MIA array 42

56 CHAPTER 3 MIMO ANTENNA DESIGNS with low mutual coupling and higher radiation efficiency. The third antenna is a PIFA antenna integrated with a slot antenna with low mutual coupling and high radiation efficiency. The two MIA arrays and the PIFA-Slot antenna provide both pattern and polarization diversity. The three antennas will be compared to two reference antennas, a 0.1λ spaced monopole array and a 0.5λ spaced monopole array. In the 0.1λ spaced monopole array, the monopoles are closely spaced with high mutual coupling to resemble the antennas in a handset. The 0.5λ spaced monopoles have low mutual coupling, low spatial correlation and high efficiency to represent antennas in an ideal case. 3.2 Low Efficiency Metamaterial Inspired Antenna (MIA) Array The original MIA array has been proposed by Jiang Zhu et al. [9] with a design frequency at 2.5GHz. Since MIMO measurement are performed at 2.28GHz for minimum signal interference from the environment, the geometry of the original design is tuned through parametric study to make the MIA array resonate at 2.28GHz. The HFSS model and fabricated prototype are presented in Figure

57 CHAPTER 3 MIMO ANTENNA DESIGNS z 41.65mm 5.7mm 4mm 9.7mm 9.6mm 15mm 30mm y X Port 1 Port 2 Figure 3.1 HFSS model and fabricated prototype of the low efficiency MIA array The corresponding measured S-parameter plot is shown in Figure 3.2. At the resonant frequency, the measured S 11 is -10dB, S 22 is -14.5dB and S 12 is -15.5dB. The simulated efficiency is 77% when port 1 is excited and port 2 is matched. The simulated efficiency is 59% when port 2 is excited and port 1 is matched. The measured efficiencies are 69% and 64% respectively. The simulated radiation patterns are shown in Figure

58 CHAPTER 3 MIMO ANTENNA DESIGNS Figure 3.2 Simulated S-Parameter plot of the low efficiency MIA array 45

59 ANSOFT ANSOFT ANSOFT ANSOFT ANSOFT ANSOFT CHAPTER 3 MIMO ANTENNA DESIGNS Simulated Radiation Pattern, port 1 excited, port 2 matched XY Plane XZ Plane YZ Plane Curve Info db(gainphi) db(gaintheta) Curve Info db(gainphi) db(gaintheta) Curve Info db(gainphi) db(gaintheta) Simulated Radiation Pattern, port 2 excited, port 1 matched XY Plane Curve Info XZ Plane YZ Plane db(gainphi) db(gaintheta) Curve Info db(gainphi) db(gaintheta) Curve Info db(gainphi) db(gaintheta) Figure 3.3 Simulated gain patterns for the low efficiency MIA array in the XY, XZ and YZ planes. E ϕ patterns are represented by red curves. E θ patterns are represented by blue curves. 46

60 CHAPTER 3 MIMO ANTENNA DESIGNS 3.3 Improved High Efficiency Metamaterial Inspired Antenna Array The low efficiency MIA array has poor radiation efficiency which may undermine the MIMO capacity. The major cause of the poor efficiency was found out to be the lossy FR4 substrate. This motivated us to design an improved MIA array with better efficiency by using a low loss substrate. The new MIA array is designed on a low loss Rogers Duroid 3003 substrate. The geometry is tuned for impedance matching at 2.28GHz. Figure 3.4 shows the HFSS model and fabricated prototype. The simulated radiation pattern is shown in Figure 3.5. Z Y X Figure 3.4 HFSS model and fabricated prototype of the high efficiency MIA Array 47

61 ANSOFT ANSOFT ANSOFT ANSOFT ANSOFT ANSOFT CHAPTER 3 MIMO ANTENNA DESIGNS Simulated Radiation Pattern, port 1 excited, port 2 matched -30 XY Plane Curve Info db(gainphi) db(gaintheta) -30 XZ Plane Curve Info db(gainphi) db(gaintheta) -30 YZ Plane Curve Info db(gainphi) db(gaintheta) Simulated Radiation Pattern, port 2 excited, port 1 matched -30 XY Plane Curve Info db(gainphi) db(gaintheta) -30 XZ Plane Curve Info db(gainphi) db(gaintheta) -30 YZ Plane Curve Info db(gainphi) db(gaintheta) Figure 3.5 Simulated gain patterns for the high efficiency MIA array in the XY, XZ and YZ planes. E ϕ pattern are represented by red curves. E θ patterns are represented by blue curves. Figure 3.6 shows the corresponding simulated and measured S-parameters. The magnitude of the simulated S 11 and S 22 are -16dB and -34dB respectively. The measured S 11 and S 22 values are in good agreement with the simulation results. However, the resonant frequency of the measured S 11 an S 12 results are slightly higher due to fabrication errors. The width of the finger of the interdigital capacitor is slightly thinner. This leads to a smaller capacitance and causes an upshift in the resonant frequency. 48

62 CHAPTER 3 MIMO ANTENNA DESIGNS The measured and simulated S 12 are below -25dB. It is interesting to note that the high efficiency MIA array has improved mutual coupling compared to the low efficiency MIA array or the original MIA array designed by Jiang Zhu. The dip in the mutual coupling at the resonant frequency is not observed in those two MIA arrays. Figure 3.6 Simulated and measured S-parameters of the new MIA array The position of this dip in S 12 is found to be closely related to the ground plane length along the x-axis. Further investigation reveals that the ground plane structure essentially acts as a 4-port coupler. Excluding the two loaded monopole 49

63 CHAPTER 3 MIMO ANTENNA DESIGNS patches shown in Figure 3.4, the structure closely resembles the CPW (Co-Planar Waveguide) directional coupler proposed in [21] as shown in Figure 3.7. The 4 ports are at the two ends of the two slots. Figure 3.7 Circuit configuration of a uniplanar two-branch directional coupler When the signal is applied to port 1 in this uniplanar two-branch directional coupler, outputs appearing at ports 2 and 3 are equal in amplitude and differ in phase by 90 degrees. Port 4 represents the isolation port. By examining the current on the feedlines of the high efficiency MIA array as shown in Figure 3.8, we found that the asymmetric loading on the monopole patch causes odd mode current flow on the feedline and strongly excites the slot between its feedline and the ground plane. In addition, if we increase the L cpw in the uniplanar twobranch directional coupler to the length of the slot, the structure is the same as 50

64 CHAPTER 3 MIMO ANTENNA DESIGNS the ground plane structure in the high efficiency MIA array. The rectangular ground plane in the middle of the uniplanar two-branch directional coupler is connected to the ground plane that is on the top and bottom. This connection is accomplished by the SMA connector in the high efficiency MIA array. Figure 3.8 Surface current distribution when different ports are excited Furthermore, in order for this CPW coupler to work, the slot length should be λ/4. At 2.28GHz, the free space wavelength is 13.1cm. By including the relative 51

65 CHAPTER 3 MIMO ANTENNA DESIGNS permittivity of the substrate which is ε r =3, then λ/4 is found to be 1.9cm. This result is in very a good agreement with the slot length on the high efficiency MIA array which is 1.95cm. Therefore, the high efficiency MIA antenna array essentially has a coupler integrated with the antenna. The simulated current flow is shown in Figure By exciting port 1, current on the monopole patch 1 and patch 2 are almost in phase. By exciting port 2, the currents on the monopole patch 1 and patch 2 are almost 180 degrees out of phase. It is important to note that the impedance of the middle section of the 90-degree coupler is Z 0 / 2, while in the antenna ground structure, the feedline impedance is chosen to match to Z 0, consequently, the antenna ground structure is not a 90-degree coupler, in fact, it is somewhere between 90 degrees and 180 degrees. Therefore, we can treat port 1 as a sum port and port 2 as a difference port. Since port 2 excites the odd mode, we expect lower radiation efficiency, which is indeed the case. The simulated radiation efficiency is 84.3% and 79.6% for port 1 and port 2 respectively. The measured radiation efficiency is 85% and 82% respectively. As a result, the ground plane structure of the high efficiency MIA array acts as a directional coupler such that when antenna port 1 is the input port, antenna port 2 is the isolation port. This decoupling mechanism is not observed in the low efficiency MIA array and the Jiang Zhu s original design because the feedline length is

66 CHAPTER 3 MIMO ANTENNA DESIGNS cm which is shorter than λ/4. Since the ground structures of those two designs are similar to the high efficiency MIA array with a shorter feedline length, we expect the dip in mutual coupling to occur at a higher frequency. The S- parameter plot for Jiang Zhu s original MIA array is shown in Figure 3.9 where the dip is indeed observed at a higher frequency. Therefore, the original Jiang design has the same decoupling mechanism as the high efficiency MIA array, but the ground plane size isn t tuned properly for optimal results Original MIA array by Jiang Zhu Curve Info db(s(p1,p1)) db(s(p2,p1)) db(s(p2,p2)) ANSOFT S parameter [db] Freq [GHz] Figure 3.9 S-Parameters of the original MIA array designed by Jiang Zhu et al [9]. The dip of the mutual coupling is observed at a higher frequency due to the shorter feedline length compared to the high efficiency MIA array. The decoupling mechanism is essentially the same. 53

67 CHAPTER 3 MIMO ANTENNA DESIGNS Figure 3.10 J vector on monopole patch when different ports are excited 3.4 PIFA-Slot Antenna The motivation for designing a PIFA antenna integrated with a slot antenna is to achieve both high efficiency and low mutual coupling. Theoretically, a zero mutual coupling antenna can be designed if each antenna has a radiation pattern 54

68 CHAPTER 3 MIMO ANTENNA DESIGNS that represents a different spherical harmonic. Different orders of spherical harmonics are completely orthogonal. As a result, the antenna envelope correlation would become zero, thus, the mutual coupling between the antennas would become zero as well. However, exciting high order spherical harmonics is less efficient and sometimes they are hard to excite. For handset MIMO applications, maintaining a good efficiency is critical. Therefore, to maintain a good efficiency, it is desired to excite the lowest order spherical harmonics. In this case, the lowest order spherical harmonic which is easily achievable is a dipolar pattern. For a 2 2 MIMO antenna system, we can design the antenna to excite the dipolar pattern in different polarizations such that the antennas can achieve high radiation efficiency while maintaining low mutual coupling due to pattern orthogonality. The logical choice is to stack an electric dipole on top of a magnetic dipole. Orthogonal electric dipoles would be challenging to integrate since the form factor of smartphones is typically rectangular and not square. To achieve this in a compact planar fashion, a PIFA is used to resemble an electric dipole and a collinear slot on the ground plane is used to resemble a magnetic dipole. The design and fabricated prototype are shown in Figure Simulated and measured S-parameters are shown in Figure 3.12 and show good agreement. The simulated efficiency is 99% for the slot antenna and 98% for the PIFA 55

69 CHAPTER 3 MIMO ANTENNA DESIGNS antenna. The measured efficiency is 97% for the slot antenna and 93% for the PIFA antenna. The antenna system exhibits very low mutual coupling about -30 db at 2.28GHz. Figure 3.11 HFSS model and fabricated prototype of the PIFA-Slot antenna, tape is used to make sure there is no air gap between the stacked substrates of the fabricated prototype. 56

70 CHAPTER 3 MIMO ANTENNA DESIGNS Figure 3.12 Simulated and measured S-parameter plot of the PIFA-Slot antenna. Simulated and measured radiation patterns are in a good agreement as shown in Figure The slot antenna has dominant radiation in the E θ direction. The pattern is not exactly omnidirectional as in a theoretical magnetic dipole due to the finite ground plane size. The PIFA antenna has radiation in both the E θ and E Φ directions with the E Φ component having a slightly larger magnitude. The presence of E θ polarization comes from current on the ground plane flowing in the direction along the shorter edge. The E Φ component exhibits a typical pattern of a tilted beam rather than being omnidirectional due to the large 57

71 CHAPTER 3 MIMO ANTENNA DESIGNS ground plane length which is 0.8λ. Indeed, the PIFA antenna integrated with the slot antenna exhibits cross-polarization characteristics. Figure 3.13 Simulated and measured radiation patterns. The measured pattern has been provided by Research in Motion. The excited surface currents are plotted in Figure When the PIFA antenna is excited, the current flows along the longer edge of the ground plane. When the slot antenna is excited, the current flows along the short edge. The surface currents excited from each antenna are almost orthogonal. This orthogonality of the ground plane currents gives rise to orthogonality of the radiation patterns and leads to low mutual coupling. 58

72 CHAPTER 3 MIMO ANTENNA DESIGNS Figure 3.14 Current distributions on the ground plane when different antennas are excited. Orthogonality of the ground plane currents leads to low mutual coupling. 59

73 CHAPTER 3 MIMO ANTENNA DESIGNS λ Spaced Monopole Array Due to the tight space constraint in a mobile handset, antennas are often placed in the vicinity of each other. Small spacing often leads to high mutual coupling. To investigate the effects of high mutual coupling on MIMO capacity, a 0.1λ spaced monopole array is fabricated. The monopoles are made of thin copper wires soldered on to an SMA connectors. The ground plane is made of an aluminum plate with size of 19cm 19cm which is about 1.5λ 1.5λ at 2.28GHz. The monopoles are spaced 0.1λ away from each other. The fabricated prototype is shown in Figure The simulated radiation pattern is shown in Figure The simulated S 11 and S 22 are -9.2dB and S 12 is -5.3dB. The measured S 11 and S 22 are -9.5dB and S 12 is -6dB at the design frequency as shown in Figure The simulated radiation efficiencies are almost 100% for both ports. Due to the large size of the monopole array, it s not possible to measure the efficiency by the Wheeler cap method due to the metallic enclosure size constraint or the numerous cavity resonances occurring near the design frequency in a larger metallic enclosure. However, we can assume that the conductor loss is negligible, and then the maximum efficiency should be close to 100%. 60

74 CHAPTER 3 MIMO ANTENNA DESIGNS Figure 3.15 Fabricated 0.1 λ spaced monopole antenna Figure 3.16 Simulated radiation pattern for the 0.1λ spaced monopole antenna 61

75 CHAPTER 3 MIMO ANTENNA DESIGNS Figure 3.17 Measured S-parameter plot for the 0.1λ spaced monopole array and the 0.5λ spaced monopole array λ Spaced Monopole Array This monopole array consists of two monopoles that are spaced half wavelength away from each other. The ground plane is made of aluminum with size of 33cm 29cm which is about 2.5 λ 2.2 λ. Figure 3.18 is a photo of the fabricated antenna. The measured S-parameters of this monopole array are shown in Figure The simulated radiation patterns are shown in Figure At the design frequency, S 11 and S 22 are about -25dB with S 12 about -14dB. Due the large size 62

76 CHAPTER 3 MIMO ANTENNA DESIGNS of the antenna array, it is not possible to fit it into a Wheeler cap. The efficiency of this antenna is expected to be close to 100% due to low conductor loss. Both the 0.1λ spaced monopole array and the 0.5λ spaced monopole array have almost 100% efficiency, but the 0.5λ spaced monopole array leads to a more radiated power since when exciting port i, less power is coupled into the port j which flows back into the system. This monopole array is going to serve as an upper bound in our channel capacity measurements due to its superior performance. Figure 3.18 Fabricated 0.5λ spaced monopole array 63

77 CHAPTER 3 MIMO ANTENNA DESIGNS Figure 3.19 Simulated radiation patterns for 0.5λ spaced monopole array 64

78 Chapter 4 MIMO Capacity Measurements The MIMO capacity measurement campaign has been performed for an indoor and a hallway scenario. The five AUTs (antennas under test) presented in Chapter 3 have been used as receivers to investigate the impact on channel capacity due to various factors such as antenna orientation, mutual coupling, antenna efficiency and richness of multipath. Sections 4.1 and 4.2 present the experimental setup and the results for indoor measurements. Sections 4.3 and 4.4 present the experimental setup and the results for hallway measurements. 65

79 CHAPTER 4 MIMO CAPACITY MEASUREMENTS 4.1 Indoor MIMO Experimental Setup The MIMO measurement has been performed in the Antenna Lab of the Bahen Center (room BA8177) at the University of Toronto. The basic layout of the room is shown in Figure 4.1. The antenna under test is placed on an automatic positioner that can move the AUT to various positions on a vertical measurement plane. The positioner is situated in a smaller room inside BA8175. The dimensions of the larger room are about 13m 8m 3.3m, whereas the smaller room is about 5m 3.6 m 3.3m. There are some metallic cabinets in the room about the size of 1.8m 1m 0.4m and some other metallic objects to create a scattering environment. At the back of the smaller room, absorbers cover the entire wall. The measurement is undertaken by using the testbed developed in [22]. The testbed uses a monopole transmitter to send out a modulated signal. On the other hand, the AUTs presented in Chapter 3 are used as the receivers. The received voltage waveforms from the AUT are demodulated and captured on an oscilloscope. By computing a cross correlation between the sent waveform and the received waveform, the elements in the voltage transfer matrix (H matrix) can be obtained. By assuming a given SNR, the channel capacity can be computed by using Eqn (2.4). 66

80 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.1 Room layout for the MIMO measurements. Due to the limitation of the testbed, there is only one transmitting antenna. To perform a 2 2 MIMO measurement, we simply measure the channel response by placing the transmitter at position 1, then move the transmitter to another position 1 and measure the channel response again. Therefore, the channel capacity measured does not include any antenna envelope correlation between the transmitting antennas, only the spatial correlation is included. The spacing between positions 1 and 1 will be half wavelength to represent a half-wavelength spaced transmitting antenna system. The results measured from the two positions will be combined in post processing to a full 2 2 MIMO measurement. 67

81 CHAPTER 4 MIMO CAPACITY MEASUREMENTS To make a thorough investigation of MIMO performance, several factors are considered in the measurement: angle of arrival, orientation of the antenna, degree of multipath, angular power distribution, antenna efficiency and antenna mutual coupling. The angular power distribution can be controlled by placing the transmitting antenna in the LOS (line-of-sight) or NLOS (non-line-of-sight) situation with respect to the receiving antenna. In the LOS scenario, the angular power distribution is more concentrated compared to the NLOS scenario as shown in Figure 4.2. The angle of arrival can be controlled by the placement of the transmitting antenna at different positions in combination with different positions of the RX antennas. The transmitter antenna height at each location is maintained at 1.4m. The position of the RX antenna is controlled by an automatic positioner. The positioner moves the RX antenna at 5 different positions in the horizontal direction and 5 different positions in the vertical direction. Therefore, the RX antenna will be moved sequentially to 25 different positions in a square vertical plane as shown in Figure 4.3. The vertical plane size is 1.4m by 1.4m; therefore, the spacing between adjacent RX positions is 0.35m in both the horizontal and vertical directions. The center position has a height of 1.4m above the ground; therefore, the total height variation ranges from 0.7 m to 2.1m above the ground. The distance between the TX and RX antennas is about 68

82 CHAPTER 4 MIMO CAPACITY MEASUREMENTS 5m for all locations. As a result, the incident wave angle of arrival to the RX antenna has a variation of about 30 degrees in both the elevation and azimuthal planes in the line-of-sight situation. Figure 4.2 Measurement Setup, transmitting antenna locations, absorbers are placed at the back of the room. 69

83 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.3 Vertical measurement plane of the RX antenna, red dots represent the measurement positions. The orientations of the RX antennas are also considered in our MIMO measurement. There are a total of three orientations of the RX antennas. For example, for the MIA array, the substrate of the antenna can lie in the XY plane, the XZ plane or the YZ plane as shown in Figure 4.4. Care needs to be taken when manually changing the orientation of the receiving antenna. If the antenna is in a slightly different location compared to its original location after changing orientation, the channel response could be different due to a location offset. Therefore, the antenna should be rotated around its phase center to ensure good 70

84 CHAPTER 4 MIMO CAPACITY MEASUREMENTS accuracy. However, the phase center is unknown; as a result, the geometric center is used instead. To do this experimentally, the antenna geometric center is aligned with a corner of the mounting platform to aid the rotation as shown in Figure 4.5. For the entire five AUTs, their geometric centers are all aligned to this corner to ensure maximum measurement consistency. Figure 4.4 Illustration of the three orientations used for the MIA arrays, monopole arrays and PIFA-Slot Antenna. The coordinate system shown in this figure is consistent with the coordinate system of Figure 4.3. The TX antenna lies on the positive x-axis. 71

85 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.5 The Antenna under test is rotated about its geometrical center; the geometrical center is aligned to the corner of the mounting platform to ensure the rotation is as accurate as possible. The degree of the multipath effect can be controlled by adding or reducing reflections. Due to the absorbers in the original lab environment, the multipath effect is reduced. Therefore, we can add some aluminum foil to cover the absorbers and at various areas of the room to enhance the multipath as shown in Figure 4.6. All the aluminum foils were in the far field of the transmitter and 72

86 CHAPTER 4 MIMO CAPACITY MEASUREMENTS AUTs such that the aluminum foils do not distort the antenna radiation patterns significantly. As a result, the degree of multipath effect on the MIMO performance can be studied. Figure 4.6 Modified room environment with reflectors (aluminum foils); aluminum foils are used to cover the absorbers to create more reflections. 73

87 CHAPTER 4 MIMO CAPACITY MEASUREMENTS 4.2 Indoor MIMO Performance: Experimental Results The MIMO performance can be evaluated separately from the scenarios that have added absorbers or reflectors. The captured voltage waveform can be used to compute the channel matrix and the channel capacity as mentioned in Chapter 2.1 using Eqn(2.4). The capacity results are averaged over all the spatial locations and the three antenna orientations to evaluate the antenna performance under generic situations. The channel capacity is plotted against the transmitting SNR such that the loss due to the receiving antenna efficiency is included MIMO performance result with absorbers in the room, no reflectors added The computed mean capacity curves of all AUTs in each scenario are shown in Figure Figure The capacity curves of each individual AUT in all scenarios are shown in Figure B.1 - Figure B.5 in Appendix B. The experimentally captured H matrices used for computation are not normalized. Therefore, the capacity curves include losses from antenna efficiency and multipath effects. The line-of-sight (LOS) scenarios have a higher capacity 74

88 CHAPTER 4 MIMO CAPACITY MEASUREMENTS compared to the non-line-of-sight (NLOS) scenarios. This is an expected result in the NLOS scenarios, since a significant portion of power is either reflected away or absorbed by the absorbers. The result of lower incident power at the receiver leads to a lower channel capacity. Figure 4.7 Average MIMO capacity for LOS1 scenario. 75

89 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.8 Average MIMO capacity for LOS2 scenario. Figure 4.9 Average MIMO capacity for LOS3 scenario. 76

90 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.10 Average MIMO capacity for NLOS1 scenario. Figure 4.11 Average MIMO capacity for NLOS2 scenario. 77

91 CHAPTER 4 MIMO CAPACITY MEASUREMENTS To compare the performance of different antennas better, the capacity of each antenna at a certain transmitting SNR is plotted against different transmitting scenarios as shown in Figure 4.12 and Figure Figure 4.12 shows the case when the transmitting SNR is low, at 10dB. Figure 4.13 shows the case when the transmitting SNR is high, at 30dB. Figure 4.12 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with low transmitting SNR=10dB. 78

92 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.13 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with high transmitting SNR=30dB. Generally, the 0.5λ spaced monopole array has the best capacity performance. The PIFA-slot antenna has the second best performance; it outperforms the 0.5λ spaced monopole array in LOS2 scenario. The high efficiency MIA array outperforms the low efficiency MIA array in most scenarios due to the higher received power. The 0.1λ spaced monopole array has comparable performance to the low efficiency MIA array. Even though the 0.1λ spaced monopole array has better efficiency, it has a high correlation compared to the low efficiency MIA array. Hence in average, they balance out. It is interesting to note that at the LOS2 transmitting scenario with high TX SNR as shown in Figure 4.13, both monopole antennas have a significant drop in capacity compared to LOS1. The 79

93 CHAPTER 4 MIMO CAPACITY MEASUREMENTS high efficiency MIA array outperforms the 0.5λ spaced monopole array in LOS2 scenario. Even the low efficiency MIA array has a performance on par with the monopoles antenna arrays. The PIFA-Slot antenna has the best performance. A possible explanation is that in the LOS2 scenario, the environment creates more polarization diversity; therefore, the environment may have changed the XPD (cross polarization ratio) from the linearly polarized source. Utilizing their polarization diversity features, the PIFA-Slot antenna and MIA arrays could collect power in both polarizations, while the monopole antennas suffer due to their singly-polarized radiation pattern. By comparing Figure 4.12 and Figure 4.13, we can see that in LOS2 low SNR (SNR=10dB) scenarios, the 0.5λ spaced monopole array outperforms the high efficiency MIA array; however, in high SNR scenarios (SNR=30dB) the high efficiency MIA array was able to outperform the 0.5λ spaced monopole array. Furthermore, at low transmitting SNR, the 0.1λ spaced monopole array can sometimes outperform the MIA arrays, but at high transmitting SNR, the 0.1λ spaced monopole array has the worst performance due to its high correlation; in other words, it lacks diversity gain. This can be confirmed by plotting the capacity by using the normalized H matrix where the receiving SNR is used as shown in Figure The difference between the receiving SNR and the transmitting SNR is that the H matrix calculation in the 80

94 CHAPTER 4 MIMO CAPACITY MEASUREMENTS receiving SNR case is normalized; therefore, the received power is factored out and the capacity from the receiving SNR is a reflection of the diversity gain. The MIA arrays have better capacity than the 0.5λ spaced monopole array in LOS2 and LOS3 scenarios and better capacity than the 0.1λ spaced monopole array in all scenarios. This result is also observable in Figure 4.7- Figure The MIA arrays can overtake the 0.1λ spaced monopole array or the 0.5λ spaced monopole array at certain SNR threshold. Similar behavior is also observed in the simulated results shown in Figure 2.9 and Figure It seems that at low TX SNR, the received power or power gain plays the most important role; while at high TX SNR, the diversity gain starts to dominate. Consequently, this suggests that low mutual coupling can improve the MIMO performance at high SNR levels. From Figure 4.12 and Figure 4.13, we can see that the low efficiency MIA array slightly outperforms the high efficiency MIA array in NLOS2 situation which is an unexpected result. By examining Figure 4.14, the high efficiency MIA array actually has a better diversity than the low efficiency MIA array. Therefore, the cause of the discrepancy is possibly due to the difference in antenna radiation patterns that results to different received powers. 81

95 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.14 Channel Capacity with respect to high receiving SNR=30dB for all AUTs in different scenarios with absorbers in place. The H matrix is normalized MIMO performance result with reflectors added in the room Figure 4.15-Figure 4.19 show capacity curves of all AUTs in each scenario with a modified environment that has more reflections. The capacity curves of each individual AUT in all scenarios are shown in Figure B.6 - Figure B.10 in Appendix B. The PIFA-Slot antenna, the high and low efficiency MIA arrays show a slight increase in capacity compared to scenarios with no reflectors added. 82

96 CHAPTER 4 MIMO CAPACITY MEASUREMENTS The 0.1λ spaced monopole array and the 0.5λ spaced monopoles show much more increased capacity. Figure 4.15 Average MIMO capacity for LOS1 scenario. 83

97 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.16 Average MIMO capacity for LOS2 scenario. Figure 4.17 Average MIMO capacity for LOS3 scenario. 84

98 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.18 Average MIMO capacity for NLOS1 scenario. Figure 4.19 Average MIMO capacity for NLOS2 scenario. 85

99 CHAPTER 4 MIMO CAPACITY MEASUREMENTS The performance of each antenna is compared side by side in Figure 4.20 and Figure The transmitting SNR is fixed at 10dB and 30dB. It is surprising to see that the MIMO performance for the 0.1λ spaced monopole array has improved by a lot. The 0.1λ spaced monopole array outperforms the MIA arrays in all scenarios; it even outperforms the 0.5λ spaced monopole array in LOS1 scenarios. The big improvement in LOS1 could be a result of better power collection due to high mutual coupling as mentioned in [6]. However, if we carefully examine Figure 4.15, the capacity of the 0.5λ spaced monopole array will surpass the 0.1λ spaced monopole array at a higher SNR than 30dB. This indicates that the 0.5λ spaced monopole array still has better diversity gain. On average, the 0.5λ spaced monopoles just perform better. Figure 4.20 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with high transmitting SNR=10dB. 86

100 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.21 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with high transmitting SNR=30dB. It is hypothesized that the high capacity gain of the monopole arrays is a result of more collected power from the reflections. The transmitter in our experiment is a monopole with single polarization. The reflections from the added aluminum foils could also be in the same polarization as the transmitter. As a result, more power is in the polarization that is collinear with the transmitter polarization. This could be more favorable to the monopole arrays. This has been confirmed by visually inspecting the received voltage waveform from the 0.1λ spaced monopole array on the oscilloscope; there is a large gain of the voltage amplitude 87

101 CHAPTER 4 MIMO CAPACITY MEASUREMENTS especially when the receive monopoles lie in an orientation that is collinear with the transmitting monopole. It is possible to obtain a quantitative comparison of the averaged received power for each receiving antenna. The magnitudes of the elements in the H matrix are related to the received power at the antenna ports. The element h 11 is the channel response from TX1 to RX1 and the h 12 element is the channel response from TX2 to RX1. Both h 11 and h 12 are captured as voltage signals. Hence, we can assume that the total power received at RX1 is proportional to h h 12 2, where Z 0 is the antenna port impedance which is 50Ω. Z 0 The received power for each AUT is tabulated in Table 4-1. From the tabulated data, it is clear that the 0.1λ and 0.5λ monopole arrays receive much more power in the case when the reflectors are added. As a result, the added reflectors create a scenario that is more favorable to the monopole arrays with polarization that is collinear with the transmitter. The capacity vs. the receiving SNR is shown in Figure It is obvious that the 0.1λ spaced monopole array has the lowest capacity versus the receiving SNR in most cases. The 0.1λ spaced monopole array has high mutual coupling; therefore, it should have the lowest capacity and this is what we observe in Figure The 0.5λ spaced monopole array with low mutual coupling has comparable capacity as the other low mutual coupling antennas. 88

102 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Table 4-1 Average Power Received for 5 AUTs under Different Scenarios (Unit: mw) Comparison of received power under different scenarios High Efficiency MTM Array Low Efficiency MTM Array PIFA-Slot 0.1λ spaced monopole array 0.5λ spaced monopole array RX1 RX2 RX1 RX2 RX1 RX2 RX1 RX2 RX1 RX2 Scenarios with no reflectors added (reduced Multipath) Scenarios with reflectors added (enhanced Multipath) LOS1 LOS2 LOS3 NLOS1 NLOS2 LOS1 LOS2 LOS3 NLOS1 NLOS

103 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.22 Comparison of channel capacity for 5 AUTs under different transmitting scenarios, with high receiving SNR=30dB. Hence, from the above observation, it is evident that the high capacity gain for the 0.1λ spaced monopole array and the 0.5λ spaced monopole array comes from the metallic reflectors that have altered the power distribution in different polarizations, or the cross polarization discrimination (XPD, which is the power ratio between the θ and ϕ polarizations of the incident wave as given in eqn(2.18)). If power distribution is the same in both polarizations, then XPD is one; otherwise, XPD will diverge from one. Since the reflected waves are in the same polarization as the incident wave, consequently, there is more power concentrated in the polarization that is collinear with the transmitting monopole. 90

104 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Therefore, a linearly polarized monopole that is collinear to the transmitting monopole can collect power better compared to cross-polarized antennas such as the PIFA-Slot and MIA arrays. Even though the result is averaged over three antenna orientations, significantly improved results from one antenna orientation can still bring the average power received up. In conclusion, the monopole antennas have better performance in the environment with the added aluminum reflector foil due to a polarization advantage. Comparing the channel capacity in Figure 4.14 from Section and Figure 4.22 in this section, we can see that with the added reflectors, all the AUTs have better performances. Since the results in Figure 4.14 and Figure 4.22 are computed by using a normalized H matrix, the improved capacity is due to the better diversity gain rather than the received power gain. This is consistent with the discussion in Chapter 2 which shows that full correlation decreases with wider angular power distribution. Hence, in a rich scattering environment, MIMO performance indeed improves due to the reduced correlation. Furthermore, the results in this section show that the XPD from the incident wave plays an important role in the channel capacity. The MIA arrays and the PIFA-Slot antenna can perform better in an environment with polarization diversity. 91

105 CHAPTER 4 MIMO CAPACITY MEASUREMENTS 4.3 Hallway MIMO Experimental Setup The hallway MIMO measurement can be performed by using the same testbed introduced in the previous sections. The measurement setup is shown in Figure The hallway is located on the 8th floor of the Bahen Center at the University of Toronto. The hallway is 3.3 meters in height and 2.8 meters in width. The transmitter is the same as that mentioned in section 4.1, namely a single monopole antenna. The transmitter's location is fixed, situated right in the middle of the hallway, 1.4 meters above the ground. Same as for the indoor measurement, the single TX monopole position is displaced by half wavelength; the channel response is measured at each position and combined to create a 2 2 channel response. The AUTs are the 5 antennas introduced before. The AUTs will be measured in 4 vertical measurement planes, 9 positions in each plane. The transmitter is 8.5 meters to the first measurement plane, 9.6 meters to the second measurement plane, 12.7 meters to the third measurement plane and 14.5 meters to the fourth measurement plane. In the measurement plane, the lowest position is 91cm above ground, the middle position is 151cm above ground and the highest position is 184cm above the ground. The center positions are aligned to the vertical center line of the hallway. Both the left and right positions are 95 cm away from the center positions. 92

106 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.23 MIMO measurement setup in a hallway, Bahen Centre 8 th floor, University Figure 4.24 Transmitting and receiving antenna configurations. 93

107 CHAPTER 4 MIMO CAPACITY MEASUREMENTS The transmitting and receiving antennas are mounted on a tripod as shown in Figure Special care is taken when mounting the receiving antenna. Since the tripod is metallic, to ensure the tripod does not change the radiation pattern of the receiving antenna, a wooden block and a piece of foam are added on top of the tripod. The antenna is mounted on the foam. The wooden block and the foam add about 30cm of height such that the metallic part of the tripod is in the far field of the receiving antenna. Same as for the indoor measurement, three possible orientations of the receiving antenna are taken into account: The substrate of the metamaterial antennas and PIFA-slot antenna, and the ground plane of the monopole antennas can lie within the XY, YZ or XZ planes with a coordinate system that is the same as the coordinate system in Figure A top corner of the foam is used for alignment when changing orientation to ensure maximum consistency. The entire hallway environment is shown in Figure The lighting system on the top, the concrete columns, the metallic doors and the testbed systems and human body can all create scattering. The movement of human body can change the channel response; therefore, the measurement is performed at midnight when there is no one present in the hallway. Each spatial location measurement of the receiving antenna is done by manually moving the tripod or changing the height 94

108 CHAPTER 4 MIMO CAPACITY MEASUREMENTS of the tripod. To ensure good accuracy, masking tape is placed on the ground. By aligning the foot of the tripod to the tape, the error is controlled within 1cm. Figure 4.25 Hallway experimental setup 95

109 CHAPTER 4 MIMO CAPACITY MEASUREMENTS 4.4 Hallway MIMO Experimental Results All the antennas are compared with each other in different measurement planes. The results are shown in Figure 4.26 at a transmitting SNR=10dB and in Figure 4.27 at a transmitting SNR=30dB, averaged over 9 spatial locations and 3 antenna orientations. The antennas in measurement plane 1 have the best performance due to the least free-space loss. The PIFA-slot antenna has the best performance in all measurement planes whereas the 0.1λ spaced monopole array has the worst performance in all measurement planes. At a low SNR (TX SNR=10dB) scenario, the 0.5λ spaced monopole array has a slightly better performance than the high efficiency MIA array and the low efficiency MIA array. 96

110 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.26 Capacity vs Measurement Plane at TX SNR=10dB for 5 AUTs. Figure 4.27 Capacity vs Measurement Plane at TX SNR=30dB for 5 AUTs. At a high SNR (TX SNR=30dB) scenario, the high efficiency MIA array, the low efficiency MIA array and the 0.5λ spaced monopole array have comparable 97

111 CHAPTER 4 MIMO CAPACITY MEASUREMENTS performances. It is surprising to see that the monopole arrays are not performing as great as in the indoor environment. Carefully examining the voltage waveform captured on the oscilloscope shows that the hallway environment has significantly altered the polarization of the transmitted wave. Even though the transmitted wave has a single polarization in the z-direction, after all the scattering and reflection from the walls, the received wave has power in both the θ and φ polarizations. Especially at the spatial location that is near the wall, there is a significant amount of power in the cross polarization. This speculation is confirmed by plotting the capacities for all AUTs in XY, XZ and YZ orientations individually as shown in Figure XY orientation is the orientation for which the monopole arrays are collinear with the TX monopole and thus in the YZ and XZ orientations, the monopole arrays are not able to collect as much power as in XY orientation. As a result, unlike the MIA arrays and the PIFA-slot antenna that collect power in both polarizations, the 2 monopole arrays can only collect power in one polarization. Thus, the hallway channel favors a cross polarized antenna in this case. The average received power is tabulated in Table 4-2. The PIFA-Slot antenna has the highest received power whereas the 0.1λ spaced monopole array has the lowest average received power. 98

112 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.28 Capacity vs TX SNR=10dB for all AUTs with XY, XZ, YZ orientations. XY orientation is the orientation which monopole arrays are collinear with the TX monopole. By further examining the capacity plotted against the receiving SNR as shown in Figure 4.29, we can see that the difference between the 0.5λ spaced monopole antenna, the MIA arrays and the PIFA-slot antenna are not as great as in Figure 99

113 CHAPTER 4 MIMO CAPACITY MEASUREMENTS 4.26 and Figure All the low mutual coupling antennas have comparable capacities. The 0.1λ spaced monopole antenna has the worst performance which is expected due to its high mutual coupling. In this case, the major factor that impacts the performance of the monopole antennas is the loss of power due to polarization mismatch. It is also interesting to note that the low efficiency MIA array can slightly outperform the high efficiency MIA array in some cases. The possible cause is that the two MIA arrays have slightly different radiation patterns and the measurement carried out is spatially under-sampled. Compared to the indoor measurement which has 25 samples in the measurement plane, we only have 9 samples in each measurement plane. With increasing spatial samples, we should expect the high efficiency MIA array to outperform the low efficiency MIA array. 100

114 CHAPTER 4 MIMO CAPACITY MEASUREMENTS Figure 4.29 Capacity vs Measurement Plane at RX SNR=30dB for 5 AUTs. Table 4-2 Average Power Received for 5 AUTs in Different Measurement Planes (Unit: mw) Comparison of received power under different scenarios Measurement Plane1 Measurement Plane2 Measurement Plane3 Measurement Plane4 High Efficiency MTM Array Low Efficiency MTM Array PIFA-Slot 0.1λ spaced monopole array 0.5λ spaced monopole array RX1 RX2 RX1 RX2 RX1 RX2 RX1 RX2 RX1 RX