Study of Performance of Reference MIMO Antenna Configurations using Experimental Propagation Data

Transcription

1 HELSINKI UNIVERSITY OF TECHNOLOGY Faculty of Electronics, Communications and Automation UNIVERSITAT POLITÈCNICA DE CATALUNYA Escola Tècnica Superior d Enginyeria en Telecomunicació Mònica Salicrú Cortés Study of Performance of Reference MIMO Antenna Configurations using Experimental Propagation Data Master Thesis report, Supervisor: Prof. Pertti Vainikainen Espoo, June 6, 29

2 Abstract Helsinki University of Technology Universitat Politècnica de Catalunya Abstract of the Master s Thesis Author: Mònica Salicrú Cortés Name of the Thesis: Study of Performance of Reference MIMO Antenna Configurations using Experimental Propagation Data Date: June 6, 29 Number of pages: 86 Department: Professorship: Supervisor: Department of Electrical and Communications Engineering S-26 Radio Engineering Prof. Pertti Vainikainen During the last years, the performance of Multiple Input Multiple Output (MIMO) systems has been well established from the theoretical point of view. By introducing a set of multiple antennas in both ends of the link, MIMO systems provide an improvement of channel capacity of wireless systems without increasing the transmission bandwidth. This thesis studies how close to the theoretical optimal performance of MIMO systems one can get with antenna structures when used in realistic propagation environments. In order to do that, Measurement Based Antenna Test Bed (MEBAT), a tool developed by TKK/SMARAD is used. The studied antenna configurations are combinations of reference ideal dipoles. In the first part of the work, a theoretical development of MIMO systems and a definition of the magnitudes used for the study are presented. In the second part of the work, MEBAT and its operating principle are introduced. Next, the considered reference antennas and scenarios for the study of performance are also presented. In the last part of the work the results of the performance study are evaluated and analyzed. As a conclusion, it is possible to point that although MIMO systems provide an improvement of channel capacity, the values achieved in real conditions are not as optimistic as the theoretical ones. Keywords: Multiple Input Multiple Output, MIMO, Mutual Information, Eigenvalue Dispersion, Radiowave Propagation, Radio Channel Measurement.

3 Preface This Master s thesis was carried out in Helsinki University of Technology as a result of cooperation with the Universitat Politècnica de Catalunya. First, I would like to thank Professor Pertti Vainikanen, the supervisor of this thesis, for giving me the opportunity to work in this project. Veli-Matti Kolmonen and Dr. Katsuyuki Haneda deserve special thanks for answering my questions and giving me useful and helpful advice. I want to give particular thanks to William Martin for his exceptional scientific writing support. To Jaime Arroyo, thank you for being the best officemate and for helping me during this stay in Finland. I would also sincerely like to express my gratitude to Josep Pegueroles for his support and encouragement during the whole course of my studies. I owe special thanks to my friends for their patience and for being there during the toughest moments of my life. To my family, especially to my parents, I warmly want to give thanks for their love, patience, constant encouragement and endless support. I really appreciate all the help they have given to me. And to the most special person in my life, Dani, thank you for your love and support. My dearest thanks belong to the person who I want to dedicate this thesis, my grandfather. You ll always be in my heart. Espoo, June 6, 29 Mònica Salicrú Cortés 2

4 Contents Abstract... Preface... 2 Contents... 3 List of Acronyms Introduction Principle of operation of MIMO Systems MIMO System model Channel matrix decomposition Capacity in MIMO systems Transferred Signal Power in MIMO systems Spatial Multiplexing Efficiency in MIMO systems Definition of the study of performance Measurement Based Antenna Test Bed (MEBAT) Description of reference MIMO antenna structures description Considered scenario for the study of performance Evaluation of MEBAT results Description of the selected routes Presentation of the results Analysis of the results Conclusions and future work References Appendix I Quantile q=.5 for the Mutual Information, Transfer Signal Power, Spatial Multiplexing Efficiency and Eigenvalue Distribution Appendix II Graphic representation of the results

5 List of Acronyms AoA AoD AWGN CSC ECE MEBAT MEG MELG MI MIMO PPS SAGE SISO SMARAD SME SNR SVD TKK TSP WLAN Angle Of Arrival Angle Of Departure Antenna Under Test Additive White Gaussian Noise Computer Science Electrical and Communications Engineering Measurement Based Antenna Test Bed Mean Effective Gain Mean Effective Link Gain Mutual Information Multiple Input Multiple Output Pulse Per Second Space-Alternating Generalized Expectation-Maximization Single Input Single Output Centre of Excellence in Smart Radios and Wireless Research Spatial Multiplexing Efficiency Signal to Noise Ratio Singular Value Decomposition Helsinki University of Technology Transferred Signal Power Wireless Local Area Network 4

6 CHAPTER I: Introduction Chapter Introduction Due to the necessity of both obtaining higher data rates in wireless communications and extending the network capacity in order to accommodate increasing traffic and a growing number of users, Multiple Input Multiple Output (MIMO), a new useful technology, has been developed []. Multiple antennas are utilized at both ends of the link in order to enhance the transmission performance without extra frequency and power resources. During the last decade, E. Telatar, F. Foschini and M. J. Gans have verified the potential of MIMO systems. The main advantage of these systems is that they provide the opportunity to form parallel orthogonal transmission channels, especially in environments with rich scattering. MIMO systems have been proposed and used for various applications, for example, wireless local area network (WLAN) applications or for ad-hoc type solutions with mobile stations at both ends of the link [2] [3] [4]. For all these scenarios, MIMO antenna prototypes need to be tested to estimate their effect on the communication system performance [5]. 5

7 CHAPTER I: Introduction This thesis is to studies how close to the theoretical optimal performance the MIMO systems are with the reference antenna structures used in realistic propagation environments. Reference antenna structures refer to ideal reference antennas, in this work, theoretical dipoles placed in different positions depending on the configuration used. In order to do that, Measurement Based Antenna Test Bed (MEBAT), a tool developed by TKK/SMARAD will be used. MEBAT makes possible simulating the performance of certain antennas under test in different environments with propagation channel data previously measured by TKK researchers. More precisely, MEBAT combines the radiation patterns of the antennas that one wants to test with real measurement data. The thesis is divided into five chapters. Chapter 2 expounds the theoretical development of MIMO systems as well as presents the figures of merit that will be used for the study. Chapter 3 presents MEBAT and its operating principle. In this chapter, the considered reference MIMO antennas configurations and the considered scenarios for the study of performance are also presented. In Chapter 4, the results of the study are presented and analyzed. Conclusions of the work are presented and future lines of investigation are drawn in Chapter 5. 6

8 CHAPTER 2: Principle of operation of MIMO Systems Chapter 2 Principle of operation of MIMO Systems 2.. MIMO System model The main characteristic of MIMO (Multiple Input Multiple Output) systems is the use of multiple antennas at both ends of the link to improve the communication performance. If we define N as the number of transmit antennas and M as the number of receive antennas the system can be described as in Figure Input DEMUX 3 3 MUX Output N M Transmitter X Radio Channel Y Receiver Figure 2.: MIMO system with N transmit antennas and M receive antennas When one frame of L modulated and coded symbols is transmitted from the n= N transmitter antennas, the received signal at the m= M receiver antennas is expressed by 7

9 CHAPTER 2: Principle of operation of MIMO Systems (2.) where is the channel response for the the s-th symbol taking into account the MxN channels defined by the n-th transmitter antenna and the m-th receiver antenna. is Additive White Gaussian Noise (AWGN) with zero-mean and variance at the s- th symbol on the m-th received antenna [6]. We denote the transmitted signal vector by, the received signal vector by and the additive white Gaussian noise by. The notation denotes the transpose operation. The channel matrix is defined as: (2.2) If we consider the transmission of one symbol we can simplify the expressions above by ignoring the sub index s: (2.3) On their way from the transmitter to the receiver, the transmitted waves suffer changes due to the phenomena which characterize the wireless channel [7]. The most important ones are listed below: The effects of both transmit and receive antennas radiation patterns. Reflection occurs when the signal encounters obstacles similar to smooth surfaces of walls or hills. Transmission occurs when the signal is absorbed by walls, doors and by the atmosphere. Scattering occurs when the signal hits small objects as leaves and branches of the trees or rough surfaces such as buildings. 8

10 CHAPTER 2: Principle of operation of MIMO Systems Diffraction happens when the signal is addressed at the edge of an impenetrable body, such as building rooftops and hilltops. In order to facilitate the comprehension of these phenomena, Figure 2.2 is presented below: Reflection Transmission Scattering Diffraction Figure 2.2 Wireless channel phenomena On the other hand, it is usual to divide the factors that affect the received signal on a wireless medium in three categories: Path loss (or path attenuation) is the reduction in field strength when the electromagnetic wave propagates though space. Generally, the path loss is expressed in dbs. It is typically modeled as where is the so called path loss exponent, which is determined by the environment. is the path loss at the reference distance depending on the environment. The free space path loss at is defined by Path loss is represented in Figure

11 CHAPTER 2: Principle of operation of MIMO Systems -5 Path Loss (-db) Distance between transmitter and receiver (m) Figure 2.2: Path Loss Shadowing (or slow fading) is caused by large obstructions such as a hills or buildings that obscure the main signal path between the transmitter and the receiver. In practice, buildings, trees, or other obstacles along a path at a given distance will be different for every path, causing variations with respect to the nominal value given by the path loss models. Figure 2.4 shows how shadowing performs. 2 5 Shadowing (db) Distance between transmitter and receiver (m) Figure 2.3: Shadowing Fast fading (or multipath fading) results from the interference between multiple waves reaching the receiver from the transmitter. Fast fading is very rapid and it is shown in Figure 2.4. Multipath refers to the many different paths that the signal can take between the receiver and the transmitter due to reflection, scattering and diffraction

12 CHAPTER 2: Principle of operation of MIMO Systems Fast Fading (db) Distance between transmitter and receiver (m) Figure 2.4: Fast Fading 2.2. Channel matrix decomposition The ideal MIMO radio channel models assume a Rayleigh fading environment, which has enough separation between the transmit and the receive antennas to assume that the fades for each transmitting-receiving antenna pair are independent. According to [8], entries of the ideal form are independent and identically distributed complex Gaussian variables with independent real and imaginary parts. Nevertheless, we assume that the realization of is known to the receiver and the distribution of is known at the transmitter [9]. Then, any can be characterized applying the singular value decomposition (SVD) as (2.4) where and are complex unitary matrices with sizes MxM and NxN respectively. The notation denotes the complex conjugate transpose operation and is an MxN non-negative and diagonal matrix. Actually, the diagonal elements of are the non-negative square roots of the eigenvalues of. The columns of are the eigenvectors of and the columns of are the eigenvectors of. Now, it is possible to rewrite Equation (2.3) as (2.5)

13 CHAPTER 2: Principle of operation of MIMO Systems Defining, and we can express the transmission Equation (2.5) into (2.6) Note that has the same distribution as. Let be the maximum rank of the channel matrix. The system consists of useful independent channels called eigenmodes, each one amplified by the corresponding eigenvalue and corrupted by the complex Gaussian noise []. Figure 2.5 shows the symbol transmission scheme for an M=N=2 MIMO system according to Equation (2.6). n= m= n=2 m=2 Figure 2.5: Parallel eigenmode transmission for a 2x2 system 2.3. Capacity in MIMO systems Considering the system described in Figure 2.6, the mutual information for the MIMO system is defined in [] by (2.7) 2

14 CHAPTER 2: Principle of operation of MIMO Systems The notation denotes the probability density function. It is assumed that the transmitted signal follows Gaussian distribution and the noise follows Gaussian distribution. N X H Y Figure 2.6: MIMO transmission system Considering this context,, and the joint X,Y probability density functions are described respectively as where and denote the vectors of the mean values of and and, and the covariance matrices. According to Equation (2.3), and where 3

15 CHAPTER 2: Principle of operation of MIMO Systems where denotes the covariance. Then, the mutual information can be expressed as (2.8) Considering the following property for mean quadratic forms [2], where and are the mean vector and the covariance matrix of the random vector A, respectively. is a constant matrix and denotes the matrix trace. The mutual information described in Equation (2.8) can be written as (2.9) since and 4

16 CHAPTER 2: Principle of operation of MIMO Systems Then, after some algebra described in [2], the instantaneous mutual information can be expressed as (2.) Since the reflections, transmissions, refractions, diffractions, among other things, provide a random component to the channel conditions, the mutual information behaves as a random variable which characterizes the various temporal samples, for the temporal instant. For this reason, at the sample level, it is usual to represent the cumulative distribution function and to determine the quantiles being to characterize moments of the mutual information distribution mean and standard deviation. It is interesting to have a reference when one wants to compare channel responses obtained from different antennas. That distinction can be achieved based on an isotropic reference antenna at the receiver with the same configuration as the antenna system that one wants to study. This isotropic reference antenna receives all signals with unitary gain and is independent of the polarization [3]. That is why from this point we will consider. To unify notation with further equations, the antennas under study will be called antennas under test (). As it is presented at [4] and [5], the normalized channel used in this work is defined as (2.) 5

17 CHAPTER 2: Principle of operation of MIMO Systems where (2.2) is the measured channel matrix for reference antennas isotropic antennas at the receiver at the instant, the number of channel samples over a sliding window and denotes the Frobenius norm. is the measured channel matrix for antennas at the instant. The calculation of the sliding mean over the reference channel matrix reveals the effect of slow fading due to obstacles in the propagation route. With infinite code length and fast fading channel conditions the Shannon capacity is given by of the noise, so. The noise covariance matrix is defined as the mean power. In this work, it will be assumed that the transmitted power is equally distributed to the transmitter antennas (uniform power allocation). In this case, the transmitted signal covariance is defined as. Therefore, it is possible to define the capacity of a MIMO system as (2.3) being the Signal to Noise Ratio defined by (2.4) and (2.5) 6

18 CHAPTER 2: Principle of operation of MIMO Systems To achieve the maximum robustness in the estimation of the capacity, in this work, the estimation of the Shannon capacity will be done based on the median, the quantile. To find the maximum capacity that a MIMO system can achieve it is necessary to find For this purpose, we must return to Equation (2.). Using the determinant identity, it is possible to express the mutual information as follows (2.6) Using Equation (2.4) and the product property for Hermitian matrices, it is possible to express. The matrix D is the diagonal matrix that contains the eigenvalues of. Applying the following change of variable it is posible to rewrite Equation (2.6) as (2.7) According to [9], using again the determinant identity, Equation (2.7) can be expressed as Then, defining, (2.8) For any non-negative matrix A,. Applying this property to (2.9) (2.9) (2.2) The equality is achived when is a diagonal matrix. The coefficients of the diagonal of represent the transmitted power assigned to each i th channel 7

19 CHAPTER 2: Principle of operation of MIMO Systems Hence, (2.2) Then, inserting this in Equation(2.2) the maximum mutual information can be expressed by (2.22) and the maximum capacity by (2.23) If the channel is only known at the receiver, the power is shared through the channels uniformally (uniform power allocation). As it is mentioned before, in this case, the transmitted signal covariance is defined as and the maximum capacity as follows (2.24) It is possible to increase the capacity in a MIMO system if the channel is known also at the transmitter. Under this condition, it is possible to assign to each channel the power that maximizes the capacity. This method to allocate the power through the channels is called water-filling [5]. This solution suggests to fill up to a common level defined as (2.25) that makes Equation (2.2) true. Then, the transmitted power allocated to each channel is 8

20 CHAPTER 2: Principle of operation of MIMO Systems (2.26) and the maximum capacity (2.27) In general, for some channels the product is close to zero. The contribution of those channels is almost insignificant in Equation (2.27). For this reason, when the water-filling method is used, the power is only distributed with the channels that contribute to increase the capacity. The maximum capacity of a MIMO system is achieved when is full rank and all the eigenvalues have the same value [6]. The closest value to this maximum capacity can be obtained by considering an independent and identically distributed channel with certain set of eigenvalues Transferred Signal Power in MIMO systems In a Single Input Single Output (SISO) system, the mean power level using certain antenna under test and, later on, a reference antenna isotropic antenna at the receiver in this work in a wireless communication scenario can be obtained by averaging the signal levels received while each antenna moves along the same route [7]. Then, the Mean Effective Gain (MEG) of the antenna under test related to the reference antenna can be obtained by comparing the mean power level of the antenna under test with that of the reference antenna. MEG contains the mutual effect between the antenna power gain pattern and the propagation characteristics along the route, and varies depending on the measuring route [8]. To generalize MEG to MIMO systems, something known as the Mean Effective Link Gain (MELG) is defined. MELG, is the sample mean power of an antenna system under test divided by a sample mean power of a reference antenna system [9]. 9

21 CHAPTER 2: Principle of operation of MIMO Systems (2.29) It is defined that the number of reference isotropic antennas is the same as the number of the antennas under test in the system. refers to the number of measured samples of the channel. Multiplying and dividing Equation (2.29) for and and afterwards regrouping the terms, the MELG can be expressed as follows where and can be considered as SNR fading and the instantaneous Transferred Signal Power (TSP) defined by (2.3) Empirical distribution of TSP,, takes into account the radiation properties of the antennas as well as their orientations and locations. Besides, variations of describe the fluctuation of the TSP refered to the channel and antenna properties. Generally, all non-idealities like dielectric, metallic and matching losses as well as mutual coupling are included in these definitions [5]. To achieve the maximum robustness in the estimation of the real TSP, in this work, the estimation of the power will be done based on the median, the quantile. 2

22 CHAPTER 2: Principle of operation of MIMO Systems 2.5. Spatial Multiplexing Efficiency in MIMO systems According to [2], when the SNR is high and, it is possible to approximate Equation (2.3) as (2.3) After applying the previously mentioned property, considering the geometric mean arithmetic mean and the and performing some algebra it is possible to write where. It has also been assumed that. Separating terms as a product of three elements is it possible to express Then, where refers to the supreme capacity defined when all the eigenvalues of the channel matrix are equal. is the effect of channel fading on the mutual 2

23 CHAPTER 2: Principle of operation of MIMO Systems information. Defining the eigenvalue dispersion ratio,, the Spatial Multiplexing Efficiency (SME) is determined by (2.32) is used to study the multipath richness of the channel, that is, the ability of different MIMO antenna systems to utilize spatial multiplexing to increase the link capacity. Being, the maximum value is achieved if and only all the eigenvalues have the same value. That occurs when there are independent parallel channels with equal gain. has always negative values and can be interpreted as a loss on the capacity of the system due to the eigenvalue dispersion from the capacity. This loss is lower in rich than in poor scattering environments. To achieve the maximum robustness in the estimation of the Spatial Multiplexing Efficiency, in this work, the estimation of the will be done based on the median, the quantile. 22

24 CHAPTER 3: Definition of the study of performance Chapter 3 Definition of the study of performance 3.. Measurement Based Antenna Test Bed (MEBAT) Measurement Based Antenna Test Bed (MEBAT) is a tool developed by TKK/SMARAD. MEBAT makes possible simulating the performance of different multi-antenna structures under test in different propagation environments previously measured by TKK. More precisely, MEBAT combines the radiation patterns of the antennas under test with the estimated channel parameters from the measurements to provide the MIMO channel matrices. The key to obtain that result is to consider the plane-wave assumption. That means that the antennas produce a field that is approximately a plane wave in the far field region. The implications for MIMO systems are described below with the help of Figure 3.. Blue and yellow bidirectional arrows represent the channel between the pair, where is the receiver antenna and is the transmitter antenna. Unidirectional arrows inside the blue and yellow arrows represent the multipaths associated to each channel. 23

25 CHAPTER 3: Definition of the study of performance For a concrete channel sample, there are always the same number of multipaths (N) for each pair. Each multipath is determined by an angle of arrival (AoAn) and an angle of departure (AoDn). AoAn and AoDn are the same for each pair. For the n th multipath, the received signal is the contribution of the four components which correspond to the contributions for each pair of polarizations VH, HV, VV, HH. V represents vertical or -polarized and H horizontal or -polarized. θ - polarized φ - polarized a a a a θ - polarized φ - polarized AoD AoD N AoA AoA N Figure 3.: Plane wave assumption in a 2x2 MIMO system The measured channel contains information of the radiation patterns resulting of both transmitter and receiver antennas used for the measurement and information of the channel itself. A block representation is shown in Figure

26 CHAPTER 3: Definition of the study of performance N M Radiation patterns of the transmitter antennas used for the measurement Parameters of Measured Propagation Paths Radiation patterns of the receiver antennas used for the measurement Measured Channel Figure 3.2: SAGE algorithm performance The goal is to separate the antenna radiation patterns from the information of the channel (parameters of measured propagation paths). Those parameters include the number of multipaths (N) of the channel and both signal angles of arrival (AoA) and departure (AoD) for each multipath and the complex signal amplitudes for different signal polarizations. To obtain the measured propagation path parameters the measured channel has been estimated with the Space-Alternating Generalized Expectation-Maximization (SAGE) algorithm [2] at both ends of the link. Now, since the parameters of measured propagation paths and the radiation patterns resulting from both transmitter and receiver antennas used for the measurement are not longer dependent, is it is possible to combine those parameters of measured propagation paths with any antenna system under test that one wants to test. That is the fundamental idea behind MEBAT. Figure 3.3 shows a representation of MEBAT s principle of operation. 25

27 CHAPTER 3: Definition of the study of performance Transmitter Radiation patterns Parameters of Measured Propagation Paths MEBAT Channel Response Reveiver Radiation patterns Figure 3.3: MEBAT operating principle The narrow band case is considered in this study. The coefficients of a Channel narrowband response obtained from one particular measured sample, are calculated by (3.) where represents the number of multipaths of the i th channel sample and and the angles of departure and arrival of the signal for the n th path, respectively. Radiation patterns for transmitter and receiver antennas are represented by and, respectively, being the polarization of the radiation. The complex signal amplitudes for different signal polarizations are defined in being the combination of polarizations for the transmitter-receiver pair Description of reference MIMO antenna structures description The configurations selected for the antenna systems under test performance study are shown from Figure 3.4 to Figure 3.6. The antennas used at the receiver for Configurations,2,5,6 and 7 are electrical dipoles. At Configurations 3 and 4 are 26

28 CHAPTER 3: Definition of the study of performance magnetic dipoles and; at Configurations 8 and 9, electrical dipoles of quarter and /8 wave length respectively. For the transmitter the chosen antennas are vertically or horizontally polarized patches (at the figure, arrows represent the polarization). Conf Receiver Transmitter z 2 z 3 y 3 2 y x λ/2 λ/2 Half wave length electric dipoles (x, y and z oriented) Vertically polarized patches 2 z 2 z 3 y 3 2 y x λ/2 λ/2 Half wave length electric dipoles (x, y and z oriented) Horizontally polarized patches 3 z 2 z 3 y 3 2 y x λ/2 λ/2 Half wave length magnetic dipoles (x, y and z oriented) Vertically polarized patches 4 z z y y x λ/2 λ/2 Half wave length magnetic dipoles (x, y and z oriented) Horizontally polarized patches Figure 3.4: 3x3 MIMO configurations 27

29 CHAPTER 3: Definition of the study of performance Conf Receiver Transmitter 5 λ/2 z λ/2 z 5 λ/2 4 y y 2 λ/2 λ/2 x Half wave length electric dipoles (x and y oriented) Horizontally polarized patches 6 λ/2 5 λ/2 3 z 6 3 z 2 4 y y λ/2 λ/2 2 x Half wave length electric dipoles (x and z oriented) Figure 3.5: 6x6 MIMO configurations Vertically and horizontally polarized patches The θ- and φ- polarized far field components at a radial distance R from the field source [7] [22] are described as (3.2) 28

30 CHAPTER 3: Definition of the study of performance Conf Receiver Transmitter 7 z z λ/ y y λ/2 λ/2 x Half wave length electric dipoles (x, y and z oriented) 8 z Vertically and horizontally polarized patches z λ/ y y λ/2 λ/2 x /4 length electric dipoles (x, y and z oriented) 9 z Vertically and horizontally polarized patches z λ/ y y λ/2 λ/2 x /8 length electric dipoles (x, y and z oriented) Figure 3.6: 2x2 MIMO configurations Vertically and horizontally polarized patches 29

31 CHAPTER 3: Definition of the study of performance where is the free space intrinsic impedance, the wave number and, and the components of the radiation vector (3.3) (3.4) The electric currents for and polarizations are represented by, and.the coordinates identify the position of the source in terms of wave length and is the volume where the current sources are placed. Considering the finite and cylindrical antenna model [9], the current distribution for the and oriented electric dipoles (used at the receiver in Configurations, 2, 5-9) are (3.5) where, and are the amplitudes of the excitation currents and the length of the dipole. It is important to note that those currents have their central feed point at, and respectively. Combining first Equation (3.5) with Equations (3.3) - (3.4) and then, applying the result to Equation (3.2) the θ- and φ- polarized far field components for an oriented dipole placed in are stated by 3

32 CHAPTER 3: Definition of the study of performance The same magnitudes but for a oriented electric dipole can be written as and for a z oriented electric dipole At the receiver in Configurations 3 and 4, the magnetic dipole is used instead of the electrical. The field expressions for the x oriented magnetic dipole are 3

33 CHAPTER 3: Definition of the study of performance For the y oriented magnetic dipole and for the z oriented magnetic dipole The selected antennas used at the transmitter are patches with 86 degrees of beamwidth, vertically and horizontally polarized (depending on the Configuration). The field expressions for the vertically polarized patch are assumed to be and for the horizontally polarized patch 32

34 CHAPTER 3: Definition of the study of performance The maximum directivity is determined by [23] where is the maximum value for the radiated power density defined by The notation denotes the cross product and the real part. and fields represent root mean square (RMS) values. A factor should be added for peak values. The total radiated power can be obtained as the integral of the radiated power density through a spherical surface which contains the antenna Then, the maximum directivities for the antennas used in the above mentioned reference configurations are summarized in Table 3. Table 3.: Under Test Antenna directivities Antenna Directivity Half wave length electric/magnetic dipole.64 Quarter wave length electric dipole.53 /8 wave length electric dipole.5 Vertically/Horizontally polarized patch 6.4 The radiation pattern is defined by Figure 3.7 shows the 3-D radiation pattern for the patch antenna with 86 degree beamwidth. Note that the maximum value that it achieves is. 33

35 CHAPTER 3: Definition of the study of performance Figure 3.7: Patch antenna radiation pattern Figure 3.8: x and y oriented dipole radiation pattern Figure 3.9: z oriented dipole radiation pattern 34

36 CHAPTER 3: Definition of the study of performance Figure 3.8 pictures the 3-D radiation pattern representation for an and oriented dipole with half wave length. Note that the maximum value that it achieves is. Figure 3.9 shows the 3-D radiation pattern representation for a oriented dipole with half wave length. Note that the maximum value that it achieves is. The reference antennas used for all the configurations are isotropic antennas placed at the same place as the antennas under test at the receiver and the same patch antennas as for the studied configurations at the transmitter Considered scenario for the study of performance The scenarios that will be considered in this work are placed in the TKK campus area, more precisely at the Electrical and Communications Engineering Department (ECE) and Computer Science Department (CSC) buildings. Maps with measured routes at the mentioned buildings are presented in Figure 3. and Figure m BS Figure 3.: Electrical and Communications Engineering Department 35

37 CHAPTER 3: Definition of the study of performance BS 5 m Figure 3.: Computer Science Department The coordinate system used for the measurements can be found in [24]. The measurements have been carried out on the st of April, 24 at the ECE Department and on the 27 th of May, 24 at the CSC Department. Some of the measurement parameters are shown in Table 3.2. Table 3.2: Measurement parameters st of April 24 Measurements 27 th of May 24 Measurements Carrier frequency 5.3 GHz 5.3 GHz TX power 37 dbm 37 dbm RX elements 6 dual polarized (32 feeds) 6 dual polarized (32 feeds) RX antenna array semispherical semispherical RX height.6 m (from the ground).6 m (from the floor) TX elements 6 dual polarized (32 feeds) 6 dual polarized (32 feeds) TX antenna array 4x4 URA, 45 grades slanted Semispherical TX height 7 m (from the ground).7 m (from the floor) Both URA and Semispherical antennas used for the measurements are shown in Figure

38 CHAPTER 3: Definition of the study of performance Figure 3.2: Semispherical and URA antennas Each element of the TX and RX antenna array is a patch antenna. The specifications of the patch antenna used are presented in Table 3.3. Table 3.3: Array element parameters Frequency range GHz Gain 7 db Return Loss db Isolation (d=λ/2) 5 db Polarization discrimination 8 db Diameter 3 mm All the details of the measurement system can be found in [25] [26]. Nevertheless, it is important to mention that in both measurement campaigns, at the receiver antenna array, the first feed was replaced with a discone antenna. For the st of April 24 measurements, at the transmitter array, the second feed was terminated and was used as a marker channel. For the 27 th of May 24 measurements, at the receiver array, the second feed was terminated and at the transmitter, the second but last feed was terminated and was used as a marker channel. The last one was connected to a horn antenna. The measurement system used was the TKK sounder [27] [28]. The TKK sounder uses a Pseudo Noise (PN) code as a transmission signal. The code has 255 chips and the chip rate at the transmitter is 6 MHz, that means, a generation of a transmission 37

39 CHAPTER 3: Definition of the study of performance code every 4.25µs. At the receiver, the sample rate is 2MHz. The sampling unit consists of two computers with their own sampling boards. The sounder uses I-Q sampling. For that reason, one computer samples the I-channel and the other the Q- channel. During one channel snapshot, the measurement system captures N transmitter channels. For every transmitter channel, M receiver channels are measured. Furthermore, for every receiver channel K transmission codes are measured. Receiver and transmitter switching are controlled using a Pulse Per Second (PPS) and a trigger signal. The trigger signal is synchronized to the PPS signal and determines the beginning and the end of a channel snapshot. This synchronization is shown in Figure Measurement Measurement Measurement Measurement N M K Tpps /fs Lc- Lc... /fchip Figure 3.3: Sounder Syncronization In this work, two environment types will be considered: the indoor/outdoor and the indoor/indoor environments. The first one is represented by routes, 2 and 3 since the transmitter was located on the roof (outdoors) and the receiver was moved indoors. The second one is represented by routes 4 and 5 as the transmitter was placed indoors and the receiver was moved indoors. 38

40 CHAPTER 4: Evaluation of MEBAT results Chapter 4 Evaluation of MEBAT results 4.. Description of the selected routes As mentioned before, in this work, indoor/outdoor and the indoor/indoor environments will be considered. A description of the used routes in this work introduced in Chapter 2 is presented below: Route : At the beginning of the route, the receiver was placed in the furthest corner from the coffee room door. Next, the receiver was moved out of the coffee room, through the main corridor. The end point of the route was the door to enter to the other lab corridor. During the whole route the transmitter was placed in the same position. Route 2: At the beginning of the route, the receiver was placed at the main corridor. Next, the receiver was moved along the corridor until the front of the electronics laboratory. During the whole route the transmitter was placed in the same position. 39

41 CHAPTER 4: Evaluation of MEBAT results Route 3: At the beginning of the route, the receiver was placed at the end point of the Route. The receiver was moved along the corridor and then, it was directed inside the laboratory room. During the whole route the transmitter was placed in the same position. Route 4: At the beginning of the route, the receiver was placed in the middle of the corridor. Then, it was moved along the corridor until the end. During the whole route the transmitter was placed in the same position. Route 5: At the beginning of the route, the receiver was placed in the middle of the corridor. Then, it was moved along the corridor until the end. During the whole route the transmitter was placed in the same position. The used measurement system has provided about four samples per wavelength in Routes -5. Table 4. shows the amount of snapshots used for each route. Table 4.: Number of snapshots for each route Route Snapshots Presentation of the results The parameters of interest that are evaluated in this work are the Mutual Information, the Transferred Signal Power and the Spatial Multiplexing Efficiency presented earlier in Chapter 2. In order to compare the mutual information of the system to the mutual information that would be obtained with an independent and identically distributed channel matrix, an channel matrix has been computationally created. The has been normalized and used for the calculation. 4

42 CHAPTER 4: Evaluation of MEBAT results The SNR used for this study is db. Regarding Transferred Signal Power, three magnitudes will be presented in this work:, and which represent the Transferred Signal Power for the system, for the reference system and for a system with an independent and identically distributed channel matrix. The Spatial Multiplexing Efficiency will be only calculated with the eigenvalues of the matrix,. Also, the distribution of the eigenvalues will be presented for the 3x3, 6x6 and 2x2 systems defined in the Configurations -9 in Chapter 2. Table 4.2 shows the antenna configurations that have been tested for the selected routes. Table 4.2: Tested configurations for the selected routes Route Configurations Graphics with all the distributions obtained in this simulation study can be found in the Appendix II. Nevertheless, as it was pointed in Chapter 2 in order to achieve the 4

43 [bits/s/hz] CHAPTER 4: Evaluation of MEBAT results maximum robustness in the estimation of Mutual Information, Transferred Signal Power and Spatial Multiplexing Efficiency, in this work, the estimation will be done based on the median, the quantile. All the median values can be found in the Appendix I Analysis of the results The goal of this section is to present and analyze the quantile of the Mutual Information, the Transferred Signal Power and the Spatial Multiplexing Efficiency for all the Configurations tested for each route. Moreover, in this work, the receiver antennas have been rotated computationally in 6 degree steps in the azimuth plane. The results for Route are presented in Figures As expected, the mutual information is higher when increasing the number of antennas at the transmitter and the receiver. However, as shown in Table 4.3 when additional antennas in the system are used, the ratio is between the real and the theoretical achievable mutual information is greater MI MI iid Figure 4.: Medians of the Mutual Information for Route 42

44 [bits/s/hz] [db] CHAPTER 4: Evaluation of MEBAT results Table 4.3: Ratio MI iid/mi for Route Ratio (MI iid/mi ) Configuration.82 Configuration 2.77 Configuration 3.76 Configuration 4.85 Configuration Configuration 6 2. Configuration 7 3. Configuration 8 3. Configuration ,5 - -,5-2 -2,5-3 -3,5 TSP TSP REF TSP iid Figure 4.2: Medians of the Transferred Signal Power for Route SME Figure 4.3: Medians of the Spatial Multiplexing Efficiency for Route 43

45 [db] CHAPTER 4: Evaluation of MEBAT results The maximum capacity would be achieved when the channel matrix is full rank and all the eigenvalues have the same value. As it can be seen in Figure 4.4 although the number of elements of the system increases between Configurations -4, 5-6 and 7-9, the rank of the channel matrix does not. For this reason, the distance between the eigenvalues increases and with that, the Spatial Multiplexing Efficiency presented in Figure 4.3 takes very low values especially for Configurations 7-9. As the Spatial Multiplexing Efficiency is a loss in the capacity as it was explained in Chapter 2, the mutual information has low values. The reason why the rank of the channel matrix does not increase when using more antennas in the system is because the environment does not support the system st Eigenvalue 2nd Eigenvalue 3rd Eigenvalue 4th Eigenvalue 5th Eigenvalue 6th Eigenvalue 7th Eigenvalue 8th Eigenvalue 9th Eigenvalue th Eigenvalue st Eigenvalue 2nd Eigenvalue Figure 4.4: Medians of the eigenvalues for Route 44

46 CHAPTER 4: Evaluation of MEBAT results As expected, the median of the received power is lowest for the s,. It is important to notice that there is no relevant difference between Configurations 7-9. That is because the difference in the lengths of the dipoles of the MIMO Cube does not make any substantial change in the radiation pattern of the structure. Comparing the 3x3 systems in Route, the maximum mutual information is achieved by Configuration 3 (4.68 bits/s/hz), the maximum transferred signal power by Configuration 4 (-2.75 db) and the minimum spatial multiplexing efficiency by Configuration 3 (-.87 bits/s/hz). However, the difference between these systems is not significant. Comparing 6x6 systems in Route, the maximum mutual information is achieved by Configuration 6 (8.9 bits/s/hz), the maximum transferred signal power by Configuration 5 (-.78 db) and the minimum spatial multiplexing efficiency by Configuration 6 ( bits/s/hz). Configuration 6 performs considerably better for this route. As said before, there is almost no difference between Configurations 7-9. The mutual information is around.8 bits/s/hz, the maximum transferred signal power around -2.6dB and the minimum spatial multiplexing efficiency around -26 bits/s/hz. The results for Route 2 are presented in Figures The tendencies of the results are the same as in Route but the absolute values are a slightly lower. As it is interesting to see the rank of the channel matrices, the median of the eigenvalues is also presented for Route 2, in Figure

47 [db] [bits/s/hz] CHAPTER 4: Evaluation of MEBAT results MI MI iid Figure 4.5: Medians of the Mutual Information for Route 2 Table 4.4 shows the ratio is between the real and the theoretical achievable mutual information for Route 2. Table 4.4: Ratio MI iid/mi for Route 2 Ratio (MI iid/mi ) Configuration 2.5 Configuration 2.9 Configuration 3 2. Configuration 4.94 Configuration Configuration ,5 - -,5-2 -2,5-3 -3,5-4 -4,5 TSP TSP REF TSP iid 46

48 [bits/s/hz] CHAPTER 4: Evaluation of MEBAT results Figure 4.6: Medians for the Transferred Signal Power for Route SME Figure 4.7: Medians of the Spatial Multiplexing Efficiency for Route 2 Comparing the 3x3 systems in Route 2, the maximum mutual information is achieved by Configuration 2 (4.29 bits/s/hz), the maximum transferred signal power by Configuration 4 (-2.97 db) and the minimum spatial multiplexing efficiency by Configuration 3 (-2. bits/s/hz). However, the difference between these systems is not significant. Comparing the 6x6 systems in Route 2, the maximum mutual information is achieved by Configuration 6 (8.5 bits/s/hz), the maximum transferred signal power by Configuration 5 (-.67 db) and the minimum spatial multiplexing efficiency by Configuration 6 ( bits/s/hz). This last value is significantly higher than for Configuration 5. That is because, as Figure 4.8 shows, the rank of the channel matrix for Configuration 5 is lower than for Configuration 6. Configuration 6 performs considerably better for this route. 47

49 [bits/s/hz] [db] CHAPTER 4: Evaluation of MEBAT results st Eigenvalue 3rd Eigenvalue 5th Eigenvalue 2nd Eigenvalue 4th Eigenvalue 6th Eigenvalue Figure 4.8: Medians of the eigenvalues for Route 2 The results for Route 3 are presented in Figures The tendencies of the results are the same as in Route and Route 2 but the absolute values are slightly lower than for those. As it is interesting to see the rank of the channel matrices, the median of the eigenvalues is also presented for Route 3, in Figure 4.2. The main observation in that figure is the difference in the rank of the channel matrix for Configurations 5 and 6. In Configuration 5 almost all the eigenvalues are practically zero MI MI iid Figure 4.9: Medians of the Mutual Information for Route 3 48

50 [bits/s/hz] [db] CHAPTER 4: Evaluation of MEBAT results Table 4.5 shows the ratio is between the real and the theoretical achievable mutual information for Route 3. Table 4.5: Ratio MI iid/mi for Route 3 Ratio (MI iid/mi ) Configuration 2.6 Configuration 2.92 Configuration Configuration 4.98 Configuration Configuration ,5 - -,5-2 -2,5-3 -3,5-4 -4,5 TSP TSP REF TSP iid Figure 4.: Medians of the Transferred Signal Power for Route SME Figure 4.: Medians of the Spatial Multiplexing Efficiency for Route 3 49

51 [db] CHAPTER 4: Evaluation of MEBAT results st Eigenvalue 2nd Eigenvalue 3rd Eigenvalue 4th Eigenvalue 5th Eigenvalue 6th Eigenvalue Figure 4.2: Medians of the eigenvalues for Route 3 Comparing the 3x3 systems in Route 3, the maximum mutual information is achieved by Configuration 2 (4.27 bits/s/hz), the maximum transferred signal power by Configuration 4 (-3.4 db) and the minimum spatial multiplexing efficiency by Configuration 2 (-2.25 bits/s/hz). However, the difference between these systems is not significant. Comparing the 6x6 systems in Route 3, the maximum mutual information is achieved by Configuration 6 (7.57 bits/s/hz), the maximum transferred signal power by Configuration 5 (-2.8 db) and the minimum spatial multiplexing efficiency by Configuration 6 (-56.6 bits/s/hz). Configuration 6 performs considerably better for this route. The results for Route 4 are presented in Figures The tendencies of the results are the same as in Route -Route 3 but the absolute values are higher for those. The median of the eigenvalues are also presented for Route 4, in Figure

52 [db] [bits/s/hz] CHAPTER 4: Evaluation of MEBAT results MI MI iid Figure 4.3: Medians of the Mutual Information for Route 4 Table 4.6 shows the ratio is between the real and the theoretical achievable mutual information for Route 4. Table 4.6: Ratio MI iid/mi for Route 4 Ratio (MI iid/mi ) Configuration.87 Configuration 2.6 Configuration 3.67 Configuration 4.75 Configuration Configuration 6.6 -,5 - -,5-2 -2,5-3 -3,5-4 TSP TSP REF TSP iid Figure 4.4: Medians of the Transferred Signal Power for Route 4 5

53 [db] [bits/s/hz] CHAPTER 4: Evaluation of MEBAT results SME Figure 4.5: Medians of the Spatial Multiplexing Efficiency for Route st Eigenvalue 3rd Eigenvalue 5th Eigenvalue 2nd Eigenvalue 4th Eigenvalue 6th Eigenvalue Figure 4.6: Medians of the eigenvalues for Route 4 Comparing the 3x3 systems in Route 4, the maximum mutual information is achieved by Configuration 2 (5.4 bits/s/hz), the maximum transferred signal power by Configuration 4 (-2.92 db) and the minimum spatial multiplexing efficiency by Configuration 2 (-7.35 bits/s/hz). However, there is not much difference between these systems. 52

54 [bits/s/hz] CHAPTER 4: Evaluation of MEBAT results Comparing the 6x6 systems in Route 4, the maximum mutual information is achieved by Configuration 6 (.4 bits/s/hz), the maximum transferred signal power by Configuration 5 (-.5 db) and the minimum spatial multiplexing efficiency by Configuration 6 (-7.87 bits/s/hz). Configuration 6 performs considerably better for this route. The results for Route 5 are presented in Figures The tendencies of the results are the same as in Route -Route 4 but the absolute values are higher than Route -Route 3 and lower than Route 4. The median of the eigenvalues are also presented for Route 5, in Figure MI MI iid Figure 4.7: Medians for the Mutual Information for Route 5 Table 4.7 shows the ratio is between the real and the theoretical achievable mutual information for Route 5. 53