Direction-of-Arrival estimation of RF signals based on virtual circular arrays Lanseloet Erbuer

Promotor: prof. dr. ir. Hendrik Rogier Begeleiders: ing. Patrick Van Torre, ir. Pieterjan Demarcke Masterproef ingediend tot het behalen van de academische graad van Master in de ingenieurswetenschappen: elektrotechniek Vakgroep Informatietechnologie Voorzitter: prof. dr. ir. DaniÂ¨ el De Zutter Faculteit Ingenieurswetenschappen en Architectuur Academiejaar 2010-2011

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The author gives the permission to use this thesis for consultation and to copy parts of it for personal use. Every other use is subject to the copyright laws, more specifically the source must be extensively specified when using from this thesis. Ghent, August 2008 The Author

Lanseloet Erbuer

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Acknowledgments Thank you Ghislaine Duerinckx and John Erbuer for raising me and giving me the freedom to follow my own path. Thank you ing. Patrick Van Torre for assisting me throughout the year with this thesis, for showing the necessary patience towards me and for providing me with numerous helpful tips. Thank you Prof. dr. ir. Hendrik Rogier for providing me with the subject of my thesis and the all-important guidance. Thank you Moenen and Merlijn Erbuer for forgiving me my India catastrophe. I am terribly sorry. Thank you Joylene Dumarey for all the incredible fun we have together. I love you.

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Direction-of-Arrival estimation of RF signals based on virtual circular arrays by Lanseloet ERBUER Scriptie ingediend tot het behalen van de academische graad van Master in de Ingenieurswetenschappen: Elektrotechniek Academiejaar 2010-2011

Promotor: Prof. dr. ir. H. Rogier Begeleiders: ing. P. Van Torre, ir. P. Demarcke Faculteit Ingenieurswetenschappen en Architectuur Universiteit Gent Vakgroep Informatietechnologie Voorzitter: Prof. dr. ir. D. De Zutter

Abstract Wireless communication services have known an explosive growth in the last decade. As the group of wireless users unceasingly expands and with the recent shift in emphasis from voice towards multimedia applications, research towards Smart Antennas emerged to cope with the necessary increase in channel throughput. Smart antennas allow Spatial-Division Multiple Access, which spatially separates signals based on their position, using Directionof-Arrival finding algorithms. In this work, using virtual circular arrays, we build and test a number of well known DoA estimation algorithms, such as Bartlett, Capon, MUSIC, RootMUSIC and ESPRIT. We compare their performance through simulations and subject the best performing DoA estimation algorithm to the challenge of estimating the location of multiple transmitters in an outdoor environment, subject to fading, multipath propagation and thermal noise.

Keywords Direction-of-Arrival (DoA) Estimation, Bartlett, Capon, MUSIC, Root-MUSIC, ESPRIT, Virtual Uniform Circular Array (UCA), Smart Antennas, Model Order Estimation.

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Direction-of-arrival estimation of RF signals based on virtual circular arrays Lanseloet Erbuer Supervisor(s): ing. Patrick Van Torre, prof. dr. ir. Hendrik Rogier Abstract – Wireless communication services have known an explosive growth in the last decade. To enable the necessary increase in channel throughput, research towards smart antennas (SAs) emerged. Using direction- of-arrival (DoA) finding algorithms, SAs allow to spatially separate signals based on their position. In this work, using virtual circular arrays, we examine a number of well known DoA estimation algorithms, namely Bartlett, Capon, MUSIC, and ESPRIT. We compare their performance through simulations and subject the best performing algorithm to the challenge of estimating the location of multiple receivers in a realistic outdoor environment, subject to fading and multipath propagation. Keywords – Direction-of-Arrival Estimation, MUSIC, Virtual Uniform Circular Array

I. Introduction Today, mobile communication technology is omnipresent. Limited available bandwith and a growing number of mobile subscribers, introduces major challenges. Over the years, FDMA, TDMA and CDMA were the perfect answer to the high demands. As the group of wireless users unceasingly expands, research towards smart antennas (SAs) emerged, to attain improvements in the system capacity. SAs allow the application of Space-Division Multiple Access, which spatially separates signals – i.e. based on their location. To determine the positions of the users, Direction-of-Arrival (DoA) finding algorithms are used. The aim of this work is to examine a number of well known DoA estimation algorithms that use virtual circular arrays as array configuration. We subject the best performing DoA finding algorithm to the challenge of estimating both azimuth and elevation angle of multiple transmitters in a realistic outdoor environment.

II. Implementation A. DoA finding Algorithms We can subdivide the DoA estimation methods into spectral-based and model-based DoA methods. Spectral-based DoA estimation tech-

niques [1] will estimate the mean power P in function of the look angle Φ. By determining the local maxima in the power spectrum P (Φ), we find the DoA estimates. A problem with these techniques is that they are not always sufficiently accurate, as their resolution depends on the search step. Model-based DoA estimation [1] computes the DoAs directly and is thus search-free. Drawbacks of this procedure are added complexity and a higher computational load.

Figure 1: Mean estimation error vs. SNR.

We compare the mean estimation error of Bartlett, Capon, MUSIC (spectral-based) and UCA-ESPRIT (model-based) for varying SNR. Result are shown in Figure 1. For relatively high SNR, MUSIC and UCA-ESPRIT are preferred. ESPRIT is not considered further due to practical implications of the measurement setup that limit its efficacy. We thus concentrate on the use of MUSIC.

v B. Measurement Setup The main interest of this work lies in DoA estimation using virtual uniform circular arrays [2]. These, compared to linear arrays, offer the important advantages that they are able to scan (1) the full azimuthal range and (2) a (restricted) elevation range. Disadvantage is that circular arrays have a higher side lobe level than that of linear arrays. Figure 3: MUSIC spectrum with LoS.

B. Results Next we conduct the experiment as depicted in Figure 2. The results, after applying spatial smoothing (SS) and a Chebyshev window, are shown in Figure 4.

Figure 2: Test environment.

In our experiment (see Figure 2), after extensive testing of the algorithms, we estimate the DoAs of two transmitters, present in an alley and in absence of a line-of-sight (LoS) between them and the receiver. We add complexity to the situation by placing a car in the alley, which generates a lot of extra reflections.

III. Results A. Validation First we validate our algorithms by introducing a LoS between transmitters and receiver, in the alley shown in Figure 2. The car is not yet in place. The resulting MUSIC power spectrum is shown in Figure 3. The crosses denote the real DoAs, the peaks in the contour plot the estimations. We obtain this result by multiplying the spectra from two separate measurements, where we first horizontally and then vertically align the UCA. This removes the ambiguities from the estimation. The mean estimation errors are 3.3◦ and 8.2◦ for azimuth and elevation angle resp.

Figure 4: MUSIC spectrum non LoS.

We only measured with a horizontally placed UCA, this causes elevation ambiguity. We see that MUSIC looses a big part of its resolution, mainly caused by SS and the Chebyshev window. In the spectrum, we clearly see (1) the sources – the signal diffracts around the corner – and (2) the car who reflects the signals. Further works should concentrate on ESPRIT, which provides both higher accuracy and resolution compared to spectral-based methods.

References [1] Z. Chen, G. Gokeda, and Y. Yu. Introduction to Direction-of-Arrival Estimation Artech House Publishers, 2010. [2] H. Rogier. Antennas and Propagation University of Ghent, 2008.

Contents 1 Introduction 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Structure of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Methods of Direction-of-Arrival Estimation 2.1 The Direction-of-Arrival Estimation Problem 2.2 Data Model . . . . . . . . . . . . . . . . . . 2.3 Spectral-Based DoA Estimation Techniques 2.3.1 Bartlett . . . . . . . . . . . . . . . . 2.3.2 Capon . . . . . . . . . . . . . . . . . 2.3.3 Subspace Methods . . . . . . . . . . 2.3.4 Spectral-MUSIC . . . . . . . . . . . 2.3.5 Resolution Threshold . . . . . . . . . 2.4 Model-Based DoA Estimation Techniques . 2.4.1 Root-MUSIC . . . . . . . . . . . . . 2.4.2 ESPRIT . . . . . . . . . . . . . . . . 2.5 Preprocessing . . . . . . . . . . . . . . . . . 2.5.1 Estimation of Number of Sources . . 2.5.2 Decorrelating Coherent Signals . . . 2.6 Matlab Simulations . . . . . . . . . . . . . . 3 Measurement Setup 3.1 Introduction . . . . . . . . . . . 3.2 Measuring Equipment . . . . . 3.2.1 Circular Antenna Arrays 3.2.2 Virtual Arrays . . . . . . 3.2.3 Anechoic Chamber . . . 3.2.4 Signalion . . . . . . . . . 3.3 Anechoic Chamber Experiment

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Chapter 1 Introduction 1.1

Motivation

In the last decade, wireless communication services have known an explosive growth. According to the International Telecommunication Union (ITU)(1), in the past five years the number of mobile cellular subscriptions worldwide doubled, from 2.2 billion in 2005 to a tremendous 5.3 billion in 2010. 90 percent of the world population now has access to mobile networks. There is a constant demand for cheaper and more efficient portable devices. To sustain this enormous expansion of the mobile telecommunication market, the modern mobile technology has to evolve in like manner.

Figure 1.1: Number of the mobile cellular subscriptions from 2005 to 2010, according to the ITU (1)

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Chapter 1. Introduction

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The ever increasing number of mobile subscribers and limited available bandwidth, introduces major challenges for the wireless technology, especially in densely populated areas. Mobile communication techniques have to improve the capacity of the network and reduce co-channel interference. Over the years, a number of technologies have emerged that, very effectively, deal with these high demands. Channel access methods such as Frequency Division Multiple Access (FDMA), Time Division Multiple Access (TDMA) and Code Division Multiple Access (CDMA) allow different data streams to be transmitted in parallel over the same communication channel by dividing frequency bands and time slots and allocating different code schemes respectively. They efficaciously increase the channel throughput and avoid interference between the users. As the number of wireless users unceasingly expands and with the recent shift in emphasis from voice to multimedia applications, research towards smart antennas (SAs) emerged to attain an even higher system capacity. Smart antennas exist out of multiple antennas collaborating, forming an antenna array. The use of SAs allows the application of Space-Division Multiple Access (SDMA). SDMA spatially separates signals, i.e. based on their location and independent from their carrier frequency, time slot or assigned code. To determine the positions of the users, Directionof-Arrival (DoA) finding algorithms are used. This thesis concentrates on these DoA estimation algorithms.

1.2

Objective

The aim of this work is to build and test a number of well known DoA estimation algorithms that use virtual circular arrays as antenna array configuration. Comparing their performance through simulations, we ultimately make a choice and subject the best performing DoA estimation algorithm to the challenge of estimating the location â€“ both in azimuth and elevation angle â€“ of multiple transmitters in an outdoor environment, subject to fading, multipath propagation and thermal noise and in absence of a direct communication link between transmitter and receiver.

1.3

Structure of this Thesis

This thesis discusses all the necessary steps to be able to properly estimate DoAs of RF signals using virtual circular arrays. The structure is as follows. Chapter 2 is a literature review of a few available and well-known DoA estimation

Chapter 1. Introduction

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algorithms. We begin discussing the DoA estimation problem and the difficulties that arise with it. Then we explain the data model that we will be using throughout this thesis. In a next step the different DoA estimation algorithms are reviewed. We split the methods up in two seperate parts; spectral and model-based DoA estimation techniques. In the first part, we explain the operation of Bartlett, Capon and Spectral MUSIC. We end the section with a comparison of the resolution threshold of the different algorithms. The second part discusses Root-MUSIC and ESPRIT, and the necessary procedures to extend these methods to circular arrays. Finally we discuss some preprocessing steps, which allow estimating the number of sources and handling of coherent signals. At the end of the chapter, using computer generated simulations, we test the algorithms we have built to verify their behavior. Having finished the design of the DoA estimation algorithms, we subject them to a series of tests in Chapter 3. We gradually increase the complexity of situations in which the methods have to estimate the DoAs correctly. The first section discusses the measuring equipment that we use and explains our choice for a virtual circular array. Next we review the measurement setup for the most elementary tests; one and two-dimensional DoA estimation of RF signals, transmitted by non-coherent sources inside the anechoic chamber. In a next phase, we subject the DoA estimation algorithms to a series of outdoor tests and again discuss the measurement setups designed for these experiments. We distinguish two main situations for the outdoor experiments. The first is a setup in which there exists a direct communication link between transmitter and receiver. In the subsequent experiment there is no direct communication link. The final test simulates a real life situation. Finally, we discuss the obtained results in Chapter 4. Our main focus lies on spectral-based methods. We suggest a solution to remove the ambiguity in twodimensional spectral-based DoA estimation and explain our technique to keep the execution time of the algorithms as low as possible.

Chapter 2 Methods of Direction-of-Arrival Estimation 2.1

The Direction-of-Arrival Estimation Problem

Consider multiple signals si (i = 1, . . . , L) impinging on a receiver from different directionof-arrivals (DoAs). We assume that these signals are plane waves arriving from a directionof-arrival ÎŚi .

Figure 2.1: The Direction-of-Arrival Estimation Problem

The impinging signals can be either reflections â€“ delayed copies from the same signal â€“ or signals arriving from different transmitters. When the receiver is able to properly es4

Chapter 2. Methods of Direction-of-Arrival Estimation

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timate the DoAs of the received signals using a smart antenna system, it can direct its antenna beam in these angles. It thus improves considerably the efficiency of the reception. There are several problems the receiver has to deal with, while estimating the anglesof-arrival. Firstly the communication channel is introducing noise. Secondly the waves arriving from different angles-of-arrival can have unequal amplitudes, which sometimes makes it difficult to distinguish between an actual and an interfering signal. Another difficulty is reflection, which causes signals to be highly correlated and – if not properly treated – causes the DoA estimation algorithms to produce misleading results. An additional complication is that the receiver is unaware of the number of signals that are impinging. Finally the receiver has to cope with it’s own imperfections, e.g. mutual coupling, sensor position errors or platform effects.

2.2

Data Model

We consider an M -element uniform array on which signals s1 (t), s2 (t), . . ., sL (t) are incident from L different DoAs (Φ1 , Φ2 , . . . , ΦL ). We write for the received signal – the array data – X(Φ, t) ∈ CMx1 x1 (Φ, t) x2 (Φ, t) = A(Φ)S(t) + N (t) (2.1) X(Φ, t) = .. . xM (Φ, t) where A ∈ CMxL is the array response matrix, S(t) ∈ CLx1 the matrix containing the impinging signals and N ∈ CMx1 is the noise matrix. Under the assumption that the incident signals and the noise are uncorrelated the signal correlation matrix can be represented as RX = A(Φ)RS AH (Φ) + σ 2 IM

(2.2)

where RS is the signal correlation matrix, σ 2 the noise power at each array element and IM a M xM identity matrix. To estimate RX we compute ˆ X = 1 XM X H R M T

(2.3)

Chapter 2. Methods of Direction-of-Arrival Estimation

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where T denotes the number of samples. 2.2.0.5

Array Response

Consider the case of a M -element uniform linear array on which a plane wave sl impinges from a direction-of-arrival Φl . Under far field assumptions, we write for the time delay τm between a reference element – element 1 in Figure 2.2 – and the m-th element in the array τm = (m − 1)

dx cos(Φl ) c

(2.4)

Figure 2.2: Plane wave sl impinging from direction-of-arrival Φl on a M -element ULA

where c is the speed of light and dx the inter-element distance. Now we can write the antenna array response A(Φ) to the impinging plane wave sl as h i A(Φ) = a1 (Φ1 ) a2 (Φ2 ) . . . aL (ΦL ) h iT al (Φl ) = al 1 ejkdx cos(Φl ) ej2kdx cos(Φl ) . . . ej(M −1)kdx cos(Φl )

(2.5) (2.6)

where al (Φl ) is the response of the l-th antenna element and k is the wavenumber of the plane wave. We can now expand this to a uniform planar array (UPA), see figure 2.3. If the reference element of the antenna array coincides with the origin of the coordinate system we

Chapter 2. Methods of Direction-of-Arrival Estimation

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can write for the response of the (m1 xm2 )-th antenna element of an M1 xM2 -element UPA al (φl , θl ) = al ej(m1 −1)kdx cos(φl )cos(θl )+j(m2 −1)kdy sin(φl )cos(θl )

(2.7)

where φ and θ correspond to the azimuthal and the elevation angle respectively.

Figure 2.3: Plane wave sl impinging from direction-of-arrival (φl , θl ) on a M1 xM2 -element UPA

Starting from equation 2.7 we can easily find the expression for the response of the m-th antenna element of a M element uniform circular array (UCA) and thus al (φl , θl ) = al ejkrcos(θl )cos(φl −2π(m−1)/M )

(2.8)

Figure 2.4: Plane wave sl impinging from direction-of-arrival (φl , θl ) on a M -element UCA

Chapter 2. Methods of Direction-of-Arrival Estimation 2.2.0.6

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Noise

We write for the noise matrix h iT N = n0,1 , n0,2 , . . . , n0,N We assume the noise components to be Additive White Gaussian Noise (AWGN). This models the background noise of the communication channel.

2.3

Spectral-Based DoA Estimation Techniques

We can subdivide the direction-of-arrival estimation methods into two main groups. We distinguish between spectral-based and model-based DoA estimators. Spectral-based DoA estimation techniques (2) will estimate the mean power P in function of the look angle Φ. It then estimates the DoAs by determining the local maxima in the power spectrum P (Φ). We discuss several spectral-based DoA estimation methods, starting with the Bartlett procedure. The Capon DoA estimator is also presented. Finally we introduce MUSIC. Model-based DoA estimators don’t calculate the DoAs through the measured power spectrum, but instead they compute the angles of arrival directly. More about this in section 2.4.

Figure 2.5: Spectral-Based DoA Estimation

2.3.1

Bartlett

The Bartlett DoA estimator (2), (3), (4) – also known as the conventional beamformer – is the best known and oldest example of the DoA estimation techniques. The Bartlett estimator steers the antenna array in a certain direction Φ by adjusting the individual phases of the antenna elements of the antenna array, so that they interfere

Chapter 2. Methods of Direction-of-Arrival Estimation

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constructively in the desired direction Φ. For each Φ he then measures the mean power P . Doing this, the estimator is able to measure the mean power P in relation to the scan angle Φ, P (Φ). Bartlett then only needs to determine the peaks in the power spectrum P (Φ) to estimate the DoAs. We can express the Bartlett estimation technique by following formula

PB (Φ) = A(Φ)H RX A(Φ)

(2.9)

where A(Φ) is the antenna array response, Rx is the signal correlation matrix and H is an operator denoting the hermitian transpose. Bartlett suffers from poor resolution, which can only be increased by increasing the number of antenna array elements which is a fairly expensive technique and thus undesired for. Also, Bartlett faces spectral leakage problems. If an antenna array is steered in a direction Φ, the array not only measures the mean power P from signals arriving from that direction Φ, but it also measures the power of signals arriving from directions other than Φ – albeit with a strong attenuation. This effect, which is undesired for, can be prevented by making use of special weighing techniques, such as Dolph-Chebyshev or Taylor weighing of the antenna elements. This however decreases the resolution of the Bartlett estimator. An important advantage that the Bartlett DoA estimation method has over other DoA estimation techniques, is that it’s resolution is independent from the signal-to-noise-ratio in the communication channel.

2.3.2

Capon

A second spectral-based DoA estimation technique is Capon (5), (4), (2) – also known as the Minimum Variance Distortion-less Response (MVDR). Capon estimates the mean power P of a signal arriving from a point source in a certain look-angle Φ, while supposing that all other point sources in all other look-angles are sources of interference and thus need to be suppressed. The Capon DoA estimation expression is given by PC (Φ) =

1 A(Φ)H Rx−1 A(Φ)

(2.10)

again, A(Φ) is the antenna array response, Rx is the signal correlation matrix and H denotes the hermitian transpose.

Chapter 2. Methods of Direction-of-Arrival Estimation

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For high SNR, Capon will prove to deliver better results than Bartlett. It has higher resolution and the extra computation time is kept at a minimum, with only one inversion in addition needed.

2.3.3

Subspace Methods

Subspace methods, or eigenstructure methods (2), (6), exploit the properties of the array correlation matrix, Rx , namely that The group of eigenvectors E associated with the array correlation matrix Rx can be subdivided into two subgroups, the signal and the noise eigenvectors, which span the signal subspace ES and the noise subspace EN respectively H Rx = ES ΛS ESH + EN ΛN EN

where Λ are the eigenvalues associated to the eigenvectors E. The steering vectors A(Φ) corresponding to the directions Φ of the impinging signals are orthogonal to the noise subspace. As the signal subspace is orthogonal to the noise subspace as well, these steering vectors are a part of the signal subspace. A(Φ) ⊥ EN ES ⊥ EN

where Φ is a source of direction thus A(Φ) ∈ EN

If E contains K eigenvectors ~ek which are arranged in decreasing size ~e1 > ~e2 > . . . > ~eK and if we know that the number of DoAs is L, then the (K − L) smallest eigenvectors form the noise subspace and the L largest eigenvectors form the signal subspace. We write

h iT ES = ~e1 ~e2 . . . ~eL h iT EN = ~eL+1 ~eL+2 . . . ~eK In practice, subspace methods will search for directions Φ such that the steering vectors a(Φ) are orthogonal to the noise subspace EN . In other words, we search DoAs that make the product |A(Φ)H EN |2 zero.

Chapter 2. Methods of Direction-of-Arrival Estimation

2.3.4

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Spectral-MUSIC

Spectral-MUltiple SIgnal Classification (which will be referred to as MUSIC further in this thesis) (4), (5) is a widely used and well known DoA estimation technique. It overcomes the fundamental limitations of methods such as the Bartlett or Capon estimator. MUSIC is a high resolution technique and it is subspace based. MUSIC first divides the eigenspace E in it’s signal and noise subspaces ES and EN , see section 2.3.3. It then calculates the MUSIC pseudo spectrum PM (Φ) PM (Φ) =

1 H A(Φ)H EN EN A(Φ)

(2.11)

If Φ is the direction of a arrival of an impinging signal, the steering vector A(Φ) will be contained in the signal subspace ES . Thus the denominator will become zero, which causes a peak in the MUSIC spectrum. This in turn leads to the estimate of the DoA of the impinging signal by applying a search algorithm to the obtained spectrum. MUSIC shows some important disadvantages as well. As discussed in section 2.3.3, MUSIC needs to be able to separate the signal from the noise subspace. This is only possible if the array correlation matrix Rx is of full rank. Thus, if the impinging signals are correlated, MUSIC will show misleading results. This issue can be resolved by making use of the Spatial Smoothing technique, see further. Another problem that arises is that MUSIC needs to know the number of impinging signals, L. If not, MUSIC will be unable to divide the eigenspace E in its two subspaces ES and EN , see section 2.3.3.

Chapter 2. Methods of Direction-of-Arrival Estimation

2.3.5

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Resolution Threshold

We compare the theoretic resolution thresholds ∆ for Bartlett, Capon and MUSIC. We consider uncorrelated sources and a ULA with half-wavelength inter-element spacing. We determine these using (4) Bartlett : Capon : MUSIC :

∆B =

2π M

1 1 4 ∆C = 8.71 M 5ξ s ( ) 2880(M − 2) T M 2 ∆2M ∆M = ∆M : 1+ 1+ =ξ T M 4 ∆4M 60(M − 1)

(2.12) (2.13) (2.14)

where ξ denotes the SNR and T the number of samples taken. The resolution thresholds for Bartlett, Capon and MUSIC are shown in Figures 2.6, 2.7 and 2.8 for a varying number of array elements, varying SNR and a varying number of samples respectively. In Figure 2.6 we vary the number of array elements from 4 to 16 elements, when holding the SNR at 15dB and the number of samples at 100. It is clear that increasing the number of array elements decreases the resolution threshold. The decrease in resolution threshold becomes less significant for a large number of array elements, especially in the case of MUSIC. Bartlett performs the worst, followed by Capon and MUSIC. The differences in resolution thresholds between Bartlett, Capon and MUSIC become smaller for a large number of array elements.

Chapter 2. Methods of Direction-of-Arrival Estimation

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Figure 2.6: Comparison of the resolution threshold of three spectral-based DoA estimation techniques, Bartlett (blue), Capon (black) and MUSIC (red), for a varying number of array elements. We assume uncorrelated sources and a ULA with half-wavelength inter-element spacing. Example for SNR = 15 dB and number of samples = 100.

In Figure 2.7 we vary the SNR from 0 to 25 dB, when holding the number of array elements at 8 and the number of samples at 100. We see that the resolution threshold of Bartlett is not influenced by the SNR, a result that was already clear from Equation 2.12. This √ is not the case for Capon, as the threshold is inversely proportional to 4 ξ, see Equation 2.13. MUSIC threshold is more complex, and dependent from both SNR and the number of samples, as from the number of array elements. In this example, MUSIC’s threshold is not influenced by the varying SNR.

Chapter 2. Methods of Direction-of-Arrival Estimation

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Figure 2.7: Comparison of the resolution threshold of three spectral-based DoA estimation techniques, Bartlett (blue), Capon (black) and MUSIC (red), for varying signalto-noise-ratio. We assume uncorrelated sources and a ULA with half-wavelength inter-element spacing. Example for number of array elements = 8 and number of samples = 100.

In Figure 2.8 we vary the number of samples from 10 to 120, when holding the number of array elements at 8 and the SNR at 15dB. From Equations 2.12 and 2.13 it was already clear that Bartlett and Caponâ€™s resolutions are not influenced by the number of samples taken. We see that MUSICâ€™s threshold is greatly influenced by the number of samples taken. For a larger number of samples, MUSIC shows better results. A minimum of 100 samples seems necessary.

Chapter 2. Methods of Direction-of-Arrival Estimation

15

Figure 2.8: Comparison of the resolution threshold of three spectral-based DoA estimation techniques, Bartlett (blue), Capon (black) and MUSIC (red), for a varying number of samples taken. We assume uncorrelated sources and a ULA with half-wavelength inter-element spacing. Example for SNR = 15dB and number of array elements = 8.

Chapter 2. Methods of Direction-of-Arrival Estimation

2.4

16

Model-Based DoA Estimation Techniques

A problem with spectral-based DoA estimation techniques is that they are not always sufficiently accurate. MUSIC, despite being the best available spectral-based DoA estimation method, highly depends on the search step that is used in the algorithm. An alternative to spectral-based DoA estimation is model-based DoA estimation (4). Here, instead of calculating the power spectrum first and determining the peaks after, we compute the DoAs directly. Thus model-based DoA estimation is search-free. Drawbacks of this procedure are added complexity and a higher computational load. In this section we present two techniques, Root-MUSIC and ESPRIT.

2.4.1

Root-MUSIC

Root-MUSIC (6), (4) can only be used when the array configuration is linear and uniform. Recall the MUSIC spectrum PM (Φ) =

1 A(Φ)H E

H N EN A(Φ)

where, in the case of a M -element ULA with inter-element spacing d, the elements of the array steering vector are given by al (Φl ) = ejmkdcos(Φl )

with m = 0, 1, 2, . . . , M − 1

with Φ a DoA and L the total number of DoAs. We now replace the elements of the steering vector by the complex parameter z ∈ C. We then write the MUSIC spectrum in function of this new parameter z H PRM (z) = aT (z −1 )EN EN a(z)

(2.15)

solving the polynomial in Equation 2.15 we find 2(m − 1) roots. Of these 2(m − 1) roots we pick the L roots that lie the closest to the unit circle. Solving zl = ejkdcos(Φl ) for Φl we can determine the DoA estimates.

Chapter 2. Methods of Direction-of-Arrival Estimation 2.4.1.1

17

UCA Root-MUSIC

For using Root-MUSIC (7) in conjunction with UCA’s, we make use of the Phase Mode Excitation (PME) Theory (8), (9). The PME theory permits us to transform the steering vectors of a UCA into the steering vectors of a ULA. This procedure is referred to as Beamspace Transformation and it allows us to apply techniques, which were specially designed for ULA configurations, to UCA configurations. Examples are Root-MUSIC, Spatial Smoothing (see Section 2.5.2) and ESPRIT (see Section 2.4.2). UCA’s have the important advantage over ULA’s that they are able to scan the full azimuthal and elevation range, whereas ULA’s can only look in a conical area (10). Let us recall the expression for the UCA steering vector, denoted by A(Φ) h iT A(Φ) = ejkrcos(Φ) ejkrcos(Φ−2π/M ) . . . ejkrcos(Φ−2π(M −1)/M ) where r is the radius of the UCA, Φ the DoA and M the number of array elements. Note that the UCA steering vector A(Φ) has no Vandermonde structure, unlike the ULA steering vector (see Equations 2.5, 2.6). Techniques designed for linear arrays, such as Root-MUSIC, make special use of this Vandermonde structure. We apply the Beamspace Transformation to A(Φ) to obtain this structure. Consider Wm , the weight vector that excites the UCA with phase mode m ∈ [−M, +M ] Wm =

iT 1 h −j2πn/M −j2πn(M −1)/M 1 e ... e N

By multiplying W with the UCA steering vector we obtain V (Φ) which has the Vandermonde structure and to which we can apply Root-MUSIC. W H A(Φ) = V (Φ)

(2.16)

We then replace ejΦ by the complex parameter z ∈ C. Inserting Equation 2.16 into the expression for the covariance matrix (see Equation 2.2) and after eigendecomposition, we obtain H (W H W )−1/2 W H RX W (W H W )−1/2 = ES ΛESH + EN ΛEN after which we find the UCA Root-MUSIC polynomial H PU CA,RM = V T (z −1 )(W H W )−1/2 EN EN (W H W )−1/2 V (z)

(2.17)

Chapter 2. Methods of Direction-of-Arrival Estimation

18

and we solve z = ejΦ for the L roots inside and closest to the unit circle.

2.4.2

ESPRIT

Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) (11), (10) is another model-based DoA estimation technique. ESPRIT is only applicable to ULA configurations that exist out of pairwise identical but shifted array elements. It exploits the rotational invariance between the signal subspaces of two equal but physically displaced arrays to estimate the DoA of signals impinging on the arrays. ESPRIT can be summarized in three steps: 1. Signal subspace Estimation 2. Solving of the Invariance Equation 3. DoA Estimation Consider a M -element ULA which we subdivide into two identical, (not necessarily) overlapping subarrays with MS elements. Recall the expression for the array steering vector of an M-element ULA with inter-element spacing d h

jkdcos(Φ)

A(Φ) = 1 e

e

j2kdcos(Φ)

j(M −1)kdcos(Φ)

... e

iT

we can now subdivide the ULA into two identical but physically displaced subarrays by selecting the proper elements from A(Φ). For this purpose we use two selection matrices J ∈ RMS xM . In the case of maximum overlap (MS = M − 1) between the two subarrays we find for the selection matrices h i J1 = IMS 0MS x1 ,

h i J2 = 0MS x1 IMS

We then express the rotational invariance between the two subarrays as J1 A(Φ)Ψ = J2 A(Φ)

Chapter 2. Methods of Direction-of-Arrival Estimation

19

Figure 2.9: Dividing of ULA into two subarrays with maximum overlap

where

ejkdcos(Φ1 ) 0 ... jkdcos(Φ ) 2 0 e ... Ψ= . . .. .. .. . 0

0

0 0 .. .

. . . ejkdcos(ΦL )

If ES denotes the signal subspace of the array data X and if the number of samples taken N 1 we can write J1 ES Ω ≈ J2 ES with Ω ≈ KΨK −1 (2.18) with K a non-singular l x l matrix. We then solve the equation in 2.18 using a least-squares (LS), total least-squares (TLS) or structured least-squares (SLS) method. This gives us Ω. After an eigendecomposition of Ω we find estimates of the phase factors ejkdcos(Φ) . From this we can easily determine the estimates of the DoAs via λ Φi = asin − vi with vi = arg(ejkdcos(Φi ) ) 2πd

2.4.2.1

UCA-ESPRIT

To apply ESPRIT on circular arrays instead of linear arrays, we need an additional step in the algorithm, where we transform the array data X to beamspace, see section 2.4.1.1. A summarize of the algorithm is then 1. Transformation to Beamspace 2. Signal subspace Estimation 3. Solving of the Invariance Equation 4. DoA Estimation

Chapter 2. Methods of Direction-of-Arrival Estimation

2.5 2.5.1

20

Preprocessing Estimation of Number of Sources

To properly estimate the DoA of an impinging signal, the subspace-based DoA estimation methods have to be able to separate the eigenspace into a noise space and an signal space. To do this, it is imperative that they know the correct number of DoAs. If a wrong number of sources is assumed, they will fail in estimating the correct DoA. Thus methods that properly estimate the number of sources are of great importance. We call these methods Model Order Estimators (12). Model order estimators can also help increase the resolution of the DoA Estimation method, if e.g. the model order estimation says there are four DoA but MUSIC can only detect three, we can assume that there is another DoA in one of the three DoA detected by MUSIC. We use three methods to estimate the number of DoA, the Akaike Information Criterion (AIC), the Minimum Description Length (MDL) and the Efficient Detection Criterion (EDC). These methods estimate the number of sources based on the eigenvalues of the covariance matrix of the received signal. They do this by determining how many of the smallest eigenvalues of the covariance matrix are equal. The AIC method is given by " ˆ = −2M log AIC(L)

QN

λi

PN

λi

ˆ i=L+1

1 ˆ N −L

ˆ i=L+1

# ˆ ˆ N −Lˆ + 2L(2N − L)

ˆ = 0, . . . , N − 1 for L the MDL method by " ˆ = −M log M DL(L)

QN

ˆ i=L+1

1 ˆ N −L

ˆ = 0, . . . , N − 1 for L

PN

λi

ˆ i=L+1

#

1ˆ ˆ N −Lˆ + 2 L(2N − L) log(M ) λ i

Chapter 2. Methods of Direction-of-Arrival Estimation

21

and the EDC method by " ˆ = −M log EDC(L)

QN

λi

PN

λi

ˆ i=L+1

1 ˆ N −L

ˆ i=L+1

#

ˆ ˆ 1 N −Lˆ + L(2N − L) 2 log(M )

ˆ = 0, . . . , N − 1 for L ˆ that For both AIC, MDL as EDC, we determine the number of sources as the argument L minimizes its function. ˆ M DL = min M DL(L) ˆ , L ˆ L

ˆ AIC = min AIC(L) ˆ , L ˆ L

ˆ EDC = min EDC(L) ˆ L ˆ L

We simulate these functions Figure 2.10 for varying signal-to-noise-ratio, using Matlab. We use 28 samples of pseudorandom code, a UCA with radius = wavelength of the signal and 3 DoA. We plot the estimation error made by AKIC, MDL and EDC versus the SNR. From Figure 2.10 It is clear that AKIC outperforms both MDL and EDC. EDC shows the worst results. In Figure 2.11 we repeat our simulations, but this time for varying number of samples and a SNR of 20dB. We see that all three estimators make large estimation errors when the number of samples is below 102 . Both MDL, AKIC as EDC converge to the correct number of estimators when the number of samples is chosen high enough.

Chapter 2. Methods of Direction-of-Arrival Estimation

22

Figure 2.10: Estimation of the number of sources, for varying SNR. We set out the estimation error versus the SNR. Clearly AKIC performs better than the EDC or MDL estimator.

Figure 2.11: Estimation of the number of sources, for varying number of samples. We set out the estimation error versus the number of samples.

Chapter 2. Methods of Direction-of-Arrival Estimation

2.5.2

23

Decorrelating Coherent Signals

Spatial smoothing (5) is a technique used when we have to estimate DoA in an environment where multiple copyâ€™s of the same signal arrive at the receiver. Since the subspace-based DoA estimation methods rely on the fact that the correlation matrix has to be of full rank, they will not be able to properly estimate the DoA when there is a strong multipath effect, i.e. the signals are highly correlated. To reduce this effect, we apply spatial smoothing to the received data before applying the DoA estimators. Spatial smoothing also causes a decrease in resolution, as the number of effective array elements decreases. Consider a M -element ULA. To apply spatial smoothing, we subdivide the ULA in P subarrays each containing Msub = N âˆ’ P + 1 elements. If we apply forward smoothing, the first subarray contains antenna elements 1, 2, . . . , Msub , the second subarray contains antenna elements 2, 3, . . . , Msub + 1 etc. This concept is shown in Figure 2.12

Figure 2.12: Forward and Backward smoothing applied to a ULA.

After we have divided the ULA into P subarrays, we calculate the P corresponding correlation matrices Rp . We then determine the new spatially smoothed correlation matrix by averaging over these P correlation matrices P 1 X Rp Rss = P p=1

Chapter 2. Methods of Direction-of-Arrival Estimation

24

Backward smoothing has a similar outcome. The procedure is obvious. We can increase the effective array size by combining forward and backward smoothing, i.e. averaging in both forward and backward directions. More about this in (5). We illustrate the spatial smoothing effect in Figure 2.13. Using Matlab, we simulate a 22-element ULA receiving four highly correlated signals from four different DoA. We use 28 samples of pseudorandom code with a SNR of 10dB. We divide the ULA in 10 sub arrays, with each 13 elements. MUSIC is applied to estimate the DoA. It is clear from Figure 2.13 that MUSIC with spatial smoothing provides far better results than without. Spatial smoothing removes the spectral leakage and provides better resolution.

Figure 2.13: Example of the spatial smoothing effect, if applied to MUSIC. Four highly correlated signals arrive from four different DoA on a ULA. Both the MUSIC spectrum with and without spatial smoothing are shown.

Chapter 2. Methods of Direction-of-Arrival Estimation

25

We repeat the previous experiment, but this time for varying SNR. We can easily see from Figure 2.14 that, for subspaced-based DoA estimation techniques, spatial smoothing is desirable when trying to estimate DoA in a multipath environment.

Figure 2.14: MUSIC with and without spatial smoothing.

2.5.2.1

UCA Spatial Smoothing

When the receiving array is circular instead of linear, we need to transform the received data before we can apply spatial smoothing since it was specially designed for ULA configurations. We do this by applying the beamspace transformation to the array data, see section 2.4.1.1.

Chapter 2. Methods of Direction-of-Arrival Estimation

2.6

26

Matlab Simulations

In this section, before starting the measurements, we validate the different DoA estimation algorithms we have built. We compare between Bartlett, Capon, MUSIC and ESPRIT, and see if the results meet the expectations. All the following results are obtained via simulations through Matlab. We simulate array data of a 19-element UCA with a radius of one wavelength. Four non-coherent sources, located at four different positions, transmit 29 samples of pseudorandom code at a carrier frequency of 2.45GHz. All the results are averaged over 50 realizations. Figure 2.15 shows the mean estimation error for Bartlett, Capon, MUSIC and ESPRIT at a SNR of 13dB. We see that Bartlett performs the worst and that ESPRIT is the most reliable DoA estimation method. Capon shows an acceptable mean error of approximately one degree. MUSIC and ESPRIT both show very good performance results, as their mean estimation error is smaller than one degree. We conclude that these results are fully in line with expectations.

Figure 2.15: Comparison of the mean estimation error. From left to right: Bartlett, Capon, MUSIC and ESPRIT.

Chapter 2. Methods of Direction-of-Arrival Estimation

27

Figure 2.16 displays the execution times for Bartlett, Capon, MUSIC and ESPRIT. Bartlett, Capon and MUSIC all require approximately the same computation time. ESPRIT requires more than two times the execution time of the spectral-based DoA estimation methods. This is because of (1) the higher complexity of the ESPRIT algorithm compared to the spectral-based methods, and (2) the fact that ESPRIT averages its estimations over 200 realizations. Looking at the spectral-based methods from left to right, we also see a slight increase in execution time. This also due to the added complexity.

Figure 2.16: Comparison of the execution time. From left to right: Bartlett, Capon, MUSIC and ESPRIT.

Finally we compare the mean estimation error for Bartlett, Capon, MUSIC and ESPRIT, for varying SNR. The result is shown in Figure 2.17. Bartlett shows a nearly constant error. ESPRIT clearly shows the best result. For SNR greater than 3 dB, MUSIC proves to be a good choice. Capon displays poor results, as the mean estimation error only drops below 5 degrees beyond 13dB. Conclusion For low SNR, Bartlett is a good choice since its error is approximately equal or lower than those of high resolution DoA estimation methods such as MUSIC or ESPRIT. For relatively high SNR, MUSIC and ESPRIT are preferred â€“ MUSIC is preferred over ESPRIT as it shows approximately the same results but outputs them faster.

Chapter 2. Methods of Direction-of-Arrival Estimation

28

Figure 2.17: Mean estimation error versus SNR for Bartlett, Capon, MUSIC and ESPRIT.

Chapter 3 Measurement Setup 3.1

Introduction

In this chapter we discuss the different measurement setups used in this thesis. We start with the most simple measurement possible. In the anechoic chamber we try to estimate the azimuthal angle-of-arrival of a single impinging signal. Gradually we increase the number of DoA. When we are successfully able to estimate the azimuthal DoA of four non-coherent sources, we extend the experiment to a two-dimensional estimation of the DoA, i.e. both azimuthal and elevation angles of the DoA are estimated. Again we increase the number of DoA, until we are able to discriminate between four non-coherent signals impinging on the receiver from four different DoA. In the next step we conduct an outdoor experiment. We start out with the simple case of a 2-D estimation of two DoA, with a direct communication link between transmitter and receiver. We then increase complexity by removing the line-of-sight between transmitter and receiver. In a final test, we place a car in the direct vicinity of the transmitter and receiver, creating additional reflections. The main interest of this thesis lies in DoA estimation using uniform circular arrays. All the experiments in this thesis are thus conducted using circular arrays as receivers. Mutual coupling was left out of consideration in the experiments, i.e. we used virtual circular arrays in every measurement setup. The different DoA estimation methods include Bartlett, Capon, MUSIC, root-MUSIC and ESPRIT. Spatial smoothing and Model Order Estimation were applied where necessary. 29

Chapter 3. Measurement Setup

3.2

Measuring Equipment

3.2.1

Circular Antenna Arrays

30

This thesis concentrates on the DoA estimation of signals, using circular antenna arrays. Circular antenna arrays (13) offer three important advantages over linear antenna arrays, 1. they are able to scan the full azimuthal regio, i.e. from 0◦ to 360◦ 2. they are capable of scanning both in elevation (restricted range: [−60◦ , +60◦ ]) and in azimuthal angle (range: [0◦ , 360◦ ]) 3. their beampattern does not change when shifted over an angle φ This in great contrast to the characteristics of linear arrays. The latter are only capable of scanning a restricted azimuthal region, smaller than 180◦ , and their beampattern does change when shifted over an angle φ. Also, circular array configurations are smaller in size in regard to linear arrays. Even though circular arrays have to cope with a side lobe level higher than that of linear arrays of the same size (13), these properties clearly demonstrate the benefits offered by circular arrays in DoA estimating.

3.2.2

Virtual Arrays

Through our experiments in this thesis we use virtual instead of real circular arrays. By doing this, we create an ideal situation for our measurements, eliminating unwanted array effects such as mutual coupling. In a real life situation, the DoA estimation methods should be able to deal with these effects. Virtual arrays are created by measuring with one antenna element only and by moving this element into space. E.g. we can describe a virtual circular array of 90 elements by letting one element describe a circle in the horizontal plane and conduct a measurement with this antenna element every time that it is moved 4◦ away from its last position. Using virtual arrays, it is important that the communication channel is invariant during the time of the measurement, i.e. when the antenna element is moved from its first to its last position. If this condition is met, a virtual array can also be a good choice for a real life situation.

Chapter 3. Measurement Setup 3.2.2.1

31

Mutual Coupling

In a real antenna array, all the antenna elements are coupled to each other (13). This means that in an M -element array, the m-th element is not only driven by its source but also by the M −1 radiating fields from the remaining elements. These fields induce currents in the m-th antenna element which alter its radiation pattern. Another effect that plays an important role, is that the antenna elements are located in each others near-field. Thus, if an element of the array is radiating, the other elements can act as an antenna for this element even if they are open-circuited. In our data model (see Section 2.2) we assumed the array elements to be ideal and uninfluenced by other array sensors. If however the inter-element distance is sufficiently small, the mutual coupling effect comes into play and makes it impossible for the DoA estimation algorithms to correctly estimate the DoA. Different solutions to the mutual coupling problem are proposed in (14), (15) and (16). A lot of research these days is done to address the mutual coupling effect, since it is more prominent with the ever smaller hardware.

Figure 3.1: The mutual coupling effect illustrated for a circular array. Left the stand-alone radiation pattern of an array element, right the active element pattern of that same array element.

If we want to include the mutual coupling effect, then we have to rewrite our data model (2.2). For a M -element array, we multiply each signal xm with a factor gm (Φl ). This factor gm (Φl ) contains the real amplitude and phase characteristic of the m-th antenna element in the direction-of-arrival Φl . xm = gm (Φl )am (Φl )s + nm,0 where am is the array response of the m-th element, s is the source signal and nm,0 is the

Chapter 3. Measurement Setup

32

noise component. We determine the factor gm (Φl ) by terminating all elements with a 50Ω impedance and exciting the m-th antenna element with a 1V voltage. The measured radiation pattern, referred to as the active element pattern, defines gm (Φ). The active element pattern for a UCA with a radius of 1/2 wavelength is illustrated in Figure 3.1, using simulations executed in 4NEC2 (17). Using 4NEC2 to compute gm (Φ), we simulate DoA estimation with the mutual coupling effect in place. We use a 16-element UCA, with radius 1/2 wavelength and one source located at azimuth angle φ = 50◦ . The result of this simulation can be seen in Figure 3.2. The blue sharp peak is the MUSIC power spectrum when no mutual coupling effect is present. The red curve denotes the MUSIC spectrum with the mutual coupling effect taken into account. It is clear that MUSIC is no longer able to estimate the angle-of-arrival of the source correctly, when the inter-element distance of the array becomes too small. Not only there’s a significant drop in resolution and the occurrence of large sidelobes, but MUSIC also produces an estimation error of approximately 100◦ . It is therefore important that in real systems, the mutual coupling effect is addressed.

Figure 3.2: DoA Estimation with mutual coupling. Simulation done with 4NEC2.

Chapter 3. Measurement Setup

3.2.3

33

Anechoic Chamber

The anechoic chamber (18), (19) we used during our experiments is on the inside fully covered with radar absorbing material (RAM), where the outside is completely made out of metal. These features provide the anechoic chamber with two important characteristics, namely that it 1. prevents unwanted reflections on the walls, effectively creating a free space measurement environment 2. shields the experiments from external influences such as wifi or cellphone communication so that the background noise is negligibly small The RAM exist out of polymeric foam, impregnated with carbon fibers and shaped in pyramids. These pyramid shapes eliminate front face reflection on the walls. The structure of the anechoic chamber is shown in Figure 3.3. On the left we have a transmitting antenna, which can be rotated to change its polarization. The right side contains the device-under-test (DUT), mounted on a flexible arm which can both rotate in the horizontal and in the vertical plane.

Figure 3.3: Structure of the Anechoic Chamber. On the left we have the transmitting antenna (Tx ), on the right the receiving antenna (Rx )

.

For all our measurements and processing, we assume the XY plane to be the horizontal plane, with the X-axis pointing towards the transmitting antenna. The azimuthal angle φ is the angle pointing from the X to the Y -axis and the elevation angle θ is the angle pointing from the X to the Z axis. Thus φ ∈ [0◦ , 360◦ ] and θ ∈ [−90◦ , 90◦ ] to describe the three-dimensional space.

Chapter 3. Measurement Setup

34

Figure 3.4: Coordinate system used throughout this thesis.

.

3.2.4

Signalion

The signalion hardware is used for both signal generation and signal analysis. In a first step, we use Matlab to generate signal frames. The signalion transmitter then periodically emits the frames until the transmission is stopped in Matlab. A signal frame exist out of three parts 1. The trigger signal: triggers the receiver and is followed by a block of zeros to avoid interference from the trigger signal to the data signal 2. The pilot signal: allows for an accurate estimate of the channel state information (CSI) which is then used for demodulation 3. The data signal: contains the transmitted data symbols modulated in QPSK An example of a signal frame is depicted in Figure 3.5, the three different parts are clearly visible. For all our measurements, we used 2000 samples for the trigger signal (1000 ones, 1000 zeros), 3000 samples for the pilot signal en 3960 samples (396 symbols at 10 samples/symbol) for the data signal. We transmit at a sample rate of 10 Ms/s, a carrier wave frequency of 2.45GHz and power of 0 dBm and 10 dBm for indoor and outdoor experiments respectively.

Chapter 3. Measurement Setup

35

Figure 3.5: An example of a received signal frame, when two sources are present.

3.3

Anechoic Chamber Experiment

In our first set of experiments, we estimate the angle-of-arrivals of non-coherent signals arriving from different sources. All the measurements take place in the anechoic chamber (see section 3.3), thus we can assume that there are no reflected signals arriving at the receiver. Since we know the angle-of-arrivals beforehand, we can easily verify if the DoA estimation algorithms are functioning properly and determine their estimation error. The end objective of this section is to be able to discriminate, in the anechoic chamber, both in azimuth and elevation and to do so when three different sources are present. We start with 1-D DoA estimation, i.e. we only discriminate in azimuth angle. A schematic representation of the measurement setup is depicted in Figure 3.6. The upper part represents the anechoic room, the lower part the test chamber. The anechoic chamber contains four transmitting antennas (a horn antenna and three monopoles) and a receiver (a circular array of M elements). Notice that the X-axis is pointing towards the horn antenna and that the Z-axis is pointing to the ceiling of the room. The test chamber contains the remaining test equipment, the Signalion receiver and transmitter, a splitter, two attenuators and two 50â„Ś terminators. The three monopoles are directly connected to the Signalion transmitter. A fourth output of the Signalion transmitter is connected, through a splitter, to the horn antenna. Another cable connects the Signalion transmitter directly to the Signalion receiver through the same splitter, providing a reference signal for the receiver. This reference signal is needed since we are working with a virtual array, i.e. each array

Chapter 3. Measurement Setup

36

element samples at a random time. The reference signal is therefore essential to restore the time-information of the signal. Without the reference signal, the phase of the array data would not be correct. The splitter attenuates the signal with 12dB. Note that we add an extra attenuator of 10dB in between the horn antenna and the Signalion transmitter. This is to weaken the horn antenna its signal so that emits at the same power as the three monopoles. In the direct link from the Signalion transmitter to the Signalion receiver we add an attenuator of 20dB, so that we donâ€™t overdrive the receiver.

Figure 3.6: Schematic representation of the measurement setup for experiments in the anechoic chamber.

Since we use a virtual circular array, we do not have to take possible phase differences in

Chapter 3. Measurement Setup

37

cables or equipment into account, for every array element uses the exact same equipment when measuring. In the case of a real array, phase differences in cables or other instruments are important and have to be dealt with before measuring. The virtual circular array is depicted in Figure 3.8. A monopole is mounted on an arm, which is then rotated in the XY plane, describing a circle. We use a monopole instead of a dipole as array element, simply because the latter shows a slightly less good radiation pattern. The normalized radiation patterns for both a dipole and a monopole are depicted in Figure 3.7. In both patterns we can clearly see the connectors of the antennas at 180◦ , where the dipole shows two nulls and the monopole only one. Also, the monopole shows higher average amplitude compared to the dipole. For these reasons, we choose to work with the monopole as array element. Note that these are not generalizations in any way, only a comparison of the instruments available, to see which one suits us the best.

Figure 3.7: Radiation patterns in the XY -plane of a monopole (left) and a dipole (right).

For a M -element array, we sample at azimuth angles αm , where αm = m

2π M

with m = 0, 1, 2, . . . (M − 1)

For this thesis we choose the number of array elements M = 90, with the radius of the circular array varying between 0.14 and 0.20m – depending on the experiment. In a series of first tests we chose the number of array elements M = 36 and the radius of the array 0.7m. This produced terribly wrong results, since the inter-element distance was too large to allow proper sampling according to the Nyquist theorem. Another important problem that occured with these settings was that, because of the large dimension of the

Chapter 3. Measurement Setup

38

array, the receiving antenna was not anymore in the far-field region of the transmitting antennas. Indeed, for the receiving array to be in the far field of the transmitting array, the condition 3.1 has to be met. 2 2Dmax (3.1) λ where Dmax stands for the largest dimension of the receiving antenna, λ for the wavelength and dmin for the minimum distance needed between transmitter and receiver. Equation 3.1 follows from the simple statement that the spherical wave, incident on the receiver, can only deviate a small fraction of a wavelength from a plane wave (20). With a UCA radius of 0.7m and a wavelength of 0.1224m, dmin has to be larger than 32m. This was not the case, which caused the DoA estimation algorithms to fail. The explanation is obvious. The algorithms compare phase information of the signals on the different antenna array elements under the assumption that the impinging waves are plane. If the transmitter is not inside the receiver’s far-field, spherical waves arrive at the receiver and the algorithms will fail as the assumption of plane waves does not longer hold.

dmin >

Figure 3.8: Virtual circular array, made from a monopole mounted on an arm, which is then rotated in the horizontal plane.

The four different sources are transmitting four non-coherent signals and there are no reflections present. Thus we can assume the correlation matrix of the received signal X to be of full rank, i.e. in this first stage we do not have to apply spatial smoothing as a preprocessing step for the array data. Also, since we know the number of sources beforehand, a model order estimator is not necessary either.

Chapter 3. Measurement Setup

39

The results of these measurements can be found in Chapter 4. 3.3.0.1

1-D DoA Estimation

We position four transmitters in the anechoic chamber. The coordinates of the transmitters are shown in Table 3.1. Thorn Tmonopole,1 Tmonopole,2 Tmonopole,3

Azimuth [◦ ] 0 -50.7 45.2 25.3

Elevation [◦ ] 0 0 0 0

Table 3.1: The azimuthal and elevation coordinates of the transmitters in the anechoic chamber, for a 1-D DoA estimation experiment.

3.3.0.2

2-D DoA Estimation

We position three transmitters in the anechoic chamber, of which only one lies in the horizontal plane. The coordinates of the transmitters are shown in Table 3.2.

Thorn Tmonopole,1 Tmonopole,2

Azimuth [◦ ] 0 -57 60

Elevation [◦ ] 0 59 -48

Table 3.2: The azimuthal and elevation coordinates of the transmitters in the anechoic chamber, for a 2-D DoA estimation experiment.

Chapter 3. Measurement Setup

3.4

40

Outdoor Experiment

After validating our DoA estimation algorithms in the anechoic chamber, we subject them to an outdoor test. We maintain the measurement setup as described in Section 3.3, only now we change the test environment from the anechoic chamber to a lane located outside the university building, surrounded by high walls. The lane in which we conduct our experiments is depicted in Figure 3.9. The effect of this change in environment is clear. Since the walls and other objects can reflect the transmitted signals, we now have to assume a multipath environment. In order to cope with this, we need additional preprocessing steps, namely spatial smoothing and model order estimation. In this section, we handle three different cases. At first, we try to estimate DoA when there is a line-of-sight (LoS) between the receiver and the transmitter. Then, we try to determine the angles-of-arrival when there is no line-of-sight (non LoS) between the transmitter and the receiver. In a last case, we conduct an experiment without direct path from the transmitter to the receiver and with extra reflections present.

Figure 3.9: The test environment: a lane located outside the university building, surrounded by high walls.

The results of these tests can be found in Chapter 4.

3.4.1

Direct Communication Link

In this experiment, we place one and two transmitters in direct sight of the receiver. High walls surround the lane in which we conduct our measurement, providing a multipath environment. In this first stage, we know the exact positions of the sources, seen from the receiversâ€™ viewpoint. The aim of this experiment is to validate our estimation algorithms

Chapter 3. Measurement Setup

41

in an outdoor environment, before we use them in a real life situation where there is no direct communication link and many reflections are present. We take the midpoint of the circular array as origin of the coordinate system. The X-axis is parallel with the direction of the street and pointing towards the transmitter on the other end of the street, and the Z-axis is pointing upwards. Both transmitters and receiver are depicted in Figure 3.10. The two images left show the transmitters, which are monopoles. One is mounted on a cart standing on the upwards sloping street, the other one is placed high up on the right wall. Both transmitters are thus located outside the horizontal plane, their positions are shown in Table 3.3.

Tcart Twall

Azimuth [â—Ś ] 2 -47

Elevation [â—Ś ] 6 22

Table 3.3: The azimuthal and elevation coordinates of the transmitters in the lane.

The right image in Figure 3.10 shows a virtual circular array serving as receiver. A monopole is mounted on a arm and then rotated in the horizontal plane. The radius of the circle described by the monopole is 0.181m. The array is built up by 90 array elements.

Figure 3.10: Direct communication link between transmitter and receiver. The two pictures left show the transmitters, the picture right the receiver.

Chapter 3. Measurement Setup

3.4.2

42

No Direct Communication Link

In this test we handle the problem of transmitter and receiver trying to communicate without a line-of-sight in between. The overview of the setup is depicted in Figure 3.9. Left around the corner, we placed the receiver. Right, at the other side of the corner, we put two transmitters. The objective is to estimate the angles-of-arrival of the impinging signals and reflections and to cope with the additional losses introduced by the non LoS. The situation seen from the transmitter and the receiver are shown in Figure 3.11.

Figure 3.11: No direct communication link between transmitter and receiver. The picture left shows the transmitters, the picture right the receiver.

3.4.3

No Direct Communication Link and Increased number of Reflections

In a final experiment, we again try to estimate the main DoA when two transmitters are present in the alley, without a direct communication link between them and the receiver. We add extra complexity to the situation by placing a car in the alley. This generates a lot of reflections and should be visible in the results of the DoA estimation. An overview of the situation is given in Figure 3.12.

Chapter 3. Measurement Setup

43

Figure 3.12: The test environment for the final experiment: a lane located outside the university building, surrounded by high walls and with a car placed nearby transmitter and receiver generating extra reflections.

Chapter 4 Results and Interpretation 4.1 4.1.1

Anechoic Chamber Virtual UCA with 90 elements

We estimate the DoAs of the impinging signals of the sources present in the anechoic chamber. We use a virtual UCA with 90 elements and a radius varying between 0.14 and 0.20m. In the first part we discuss the results of the one-dimensional DoA estimation with four sources present. Then we take a closer look at the outcome of a two-dimensional DoA estimation this time with three sources fixed in the anechoic chamber. 4.1.1.1

One-dimensional DoA Estimation

Four sources are emitting, at azimuth angles h

−50.7◦ 0◦ 45.2◦ 25.3◦

i

Using the rotor and a laser to determine the real DoAs, we are able to guarantee the accuracy of the real DoAs to the first decimal. The radius of the virtual UCA is 0.154m. Spectral-Based DoA Estimation In figure 4.1 the power spectra of both MUSIC and Capon are shown. Using MUSIC and Capon we scan the horizontal plane in search of the sources. We choose the scanning step for both algorithms to be 0.1◦ . The real DoAs are shown as dash-dotted vertical black lines in the graph. The solid red curve and the dashed blue curve represent the MUSIC and Capon spectrum respectively. The estimates of the DoAs are visible as peaks in the power spectra. These peaks are

44

Chapter 4. Results and Interpretation

45

determined by a search algorithm and shown in Table 4.1, together with their estimation error in degrees. To not overcomplicate things, the Bartlett spectrum was left out of consideration in this study. In this situation it does not contribute to better results, as we are not dealing with very low SNR (see Section 2.3.5).

Figure 4.1: One-dimensional Spectral-Based DoA Estimation of four non-coherent sources. We apply MUSIC and Capon

The methods applied in this test provide satisfactory results. Since we know the exact DoA, we easily verify the MUSIC and Capon estimates. Capon shows both the largest maximum estimation error, 2.4◦ , and the largest mean estimation error, 1.75◦ . As expected, MUSIC clearly performs the best, as it shows the smallest estimation error, 0.1◦ , together with a mean estimation error smaller than 1◦ , namely 0.9◦ . In the graph showing the power spectra, we also note that the MUSIC spectrum renders the most accurate es-

Chapter 4. Results and Interpretation

46

timates. Exactly four distinctive peaks can be distinguished in the MUSIC spectrum and the sidelobes measure only approximate 10% of the amplitude (in dB) of the peaks. The Capon spectrum shows peaks that are more broad than those of the MUSIC spectrum. This decreases resolution. Also, relatively high sidelobes (50 and 35 % of the amplitude of the peaks) occur which can be wrongly taken for real DoA by the search algorithm in case that the number of DoA is not known. Real [◦ ] DoA1 DoA2 DoA3 DoA4

-50.7 0 25.3 45.2

Estimation [◦ ] Capon MUSIC -51.8 -51.9 -1.2 -1.8 23 24 47.6 45.3 Mean Error [◦ ]

Estimation error[◦ ] Capon MUSIC 1.1 1.2 1.2 1.8 2.3 0.5 2.4 0.1 1.75 0.9

Table 4.1: One-dimensional Spectral-Based DoA Estimation of four non-coherent sources. We apply MUSIC and Capon. Both DoA estimations and estimation errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values.

Model-Order Based DoA Estimation Figure 4.2 shows the result when ESPRIT is applied to the same dataset as in paragraph 4.1.1.1. The DoA estimations together with their deviations from the true DoAs are shown in Table 4.2.

Figure 4.2: One-dimensional Model-Based DoA Estimation of four non-coherent sources. We apply ESPRIT.

Chapter 4. Results and Interpretation Real [◦ ] DoA1 DoA2 DoA3 DoA4

47

Estimation [◦ ] ESPRIT -43.2 -1.4 30.3 51.4 Mean Error [◦ ]

-50.7 0 25.3 45.2

Estimation error[◦ ] ESPRIT 7.5 1.4 5.0 6.2 4.33

Table 4.2: One-dimensional Spectral-Based DoA Estimation of four non-coherent sources. We apply ESPRIT. Both DoA estimations and estimation errors are shown. values in red and green denote resp. the max- and minimum estimation error for the DoA estimates.

ESPRIT shows a mean estimation error equal to 4.33◦ . This error is larger than the estimation errors of both MUSIC and Capon. In an ideal measurement situation, like we created for this experiment, we would expect ESPRIT to deliver the best results. The reason why ESPRIT does not, is the following. Usually, ESPRIT averages its DoA estimations over sequences of 50-100 tries, each consisting out of T samples. The estimation error that ESPRIT makes, decreases as the number of tries increases and eventually becomes close to zero. In our experiment, using a virtual UCA for which we had to manually displace the antenna element for each consecutive measurement, we only performed one try for practical reasons. This does not suffice for ESPRIT, as it needs averaging to decrease its estimation error. In the following measurements we will concentrate on spectral-based DoA estimation, i.e. we will only look at the results produced by Capon and MUSIC. 4.1.1.2

Two-dimensional DoA Estimation

After being able to successfully estimate the azimuthal angle of arrival of four non-coherent sources, we put up three non-coherent sources in the anechoic chamber at positions (φ, θ)

h

◦

◦

◦

◦

◦

◦

(−57 , 59 ) (0 , 0 ) (60 , −47.6 )

i

where φ is the azimuthal angle and θ is the elevation angle. Again, we are able to accurately determine the real azimuth angles. This is unfortunately not the case for the real elevation angles. We have to assume a possible error of up to 3◦ on the real elevation angles. This

Chapter 4. Results and Interpretation

48

causes the comparison of the estimations with the true DoAs to be less accurate. This has to be kept in mind when reading the estimation errors in this section. Spectral-Based DoA Estimation In Figure 4.4 we applied MUSIC to estimate the three DoAs. This time we scan not only the azimuth angle, but the elevation angle as well. Thus, instead of having to perform z calculations, we have to process z × z calculations. This places high demands on the processor unit. The execution time of the estimation algorithms will increase proportionately without taking the necessary steps. In order to save processing time, we institute an initial large scanning step. We chose for the azimuth and elevation scanning steps 4◦ and 2◦ respectively. When scanning the horizontal plane with a scanning step of 0.1◦ , we perform 3601 computations. With scanning steps 4◦ and 2◦ for the azimuth and elevation angle, we perform 8281 calculations. This is acceptable. Smaller scanning steps lead to excessive execution time. The UCA is parallel to the horizontal plane and we choose the radius of the circular array 0.148m. We use upwards-pointing monopoles for array elements. Figure 4.4 shows a two-dimensional contour-graph of the three-dimensional normalized MUSIC power spectrum. Peaks in the power spectrum are indicated by contour lines that lie very close together and by means of color, where red and blue denote the peaks and valleys respectively. The true DoAs are plotted as crosses in the contour graph. We see that MUSIC produces peaks in its power spectrum within the range of the true DoA. However, a critical shortcoming is that the power spectrum is mirrored around the XY -plane. This causes a broadened peak at (φ, θ) = (0◦ , 0◦ ) and two extra peaks around (−57◦ , −59◦ ) and (60◦ , 47.6◦ ) in the power spectrum. This ambiguity between DoAs above and under the XY -plane is due to the symmetry in the array configuration. Indeed, the horizontal plane is a plane of symmetry to the circular array. This can clearly be seen in Figure 4.4 at elevation angle 0◦ . We solve this by rotating the UCA and placing it perpendicular to the horizontal plane and parallel with the Y Z-plane, while keeping the origin in the same place. We then start over our measurement. This effectively moves the symmetry plane to the Y Z-plane and removes the ambiguity in elevation angle. However, it introduces an ambiguity in azimuthal angle. The plane of symmetry can distinctly be observed in Figure 4.5 at azimuth angles −90◦ and +90◦ . Note that, in theory, this configuration would not allow the visualization of the DoA at

Chapter 4. Results and Interpretation

49

position (φ, θ) = (0◦ , 0◦ ). The reason is clear. Since we assume plane waves, theoretically spoken the wave originated from (0◦ , 0◦ ) should arrive perpendicular to the UCA. This means that there is no possibility for the UCA to compare phase information of the wave since it arrives at the exact same time at all the different array elements. This would mean that we can not estimate the source of this wave. In a real life situation, it is impossible to align the transmitter so that the wave that it is transmitting arrives at the precise same time at all the array elements. Also, the assumption of plane waves is only an approximation. In a real measurement slightly spherical waves will fall into the receiver, especially in our situation since we are measuring in a anechoic chamber with restricted dimensions. In order to remove both ambiguities, we then multiply the two spectra obtained with the horizontally and vertically placed UCA. The result of this multiplication is shown in Figure 4.6. The outcome of this experiment is excellent. Not only does MUSIC succeed in estimating the true DoA correctly (within certain error margins), but also the few sidelobes present in the power spectrum do not rise above 10% of the maximum power.

Figure 4.3: A typical radiation pattern of a monopole, viewed in the vertical plane.

Next, the exact same test is repeated, only this time with Capon. The resulting power spectrum is depicted in Figure 4.7. As expected, the contour plot shows more sidelobes, plus sidelobes with higher power compared to the MUSIC spectrum. Overall, more spectral leakage is observed but Capon still remains successful in estimating the true DoAs, as it produces the highest peaks around the correct DoAs. We mentioned that the initial scanning steps for azimuthal and elevation angle were 4◦

Chapter 4. Results and Interpretation

50

and 2◦ respectively. This allows us to roughly single out the regions-of-interest (ROI) in the power spectra. In a next stage, we repeat the MUSIC and Capon algorithms, only this time we let them scan but the individual ROIs and we use smaller scanning steps. This greatly improves the execution time of the DoA estimation algorithms while also permitting an accurate estimation of the DoAs. The ROIs with MUSIC are shown in Figure 4.8. We considered a 10◦ interval around the initially determined DoAs for the ROIs. We then applied a azimuthal and elevation scanning step of 0.1◦ . The results, as resolved by the search algorithms from these power spectra, are displayed in Tables 4.3 and 4.4. Viewing these tables, it is clear that MUSIC and Capon show very similar results, as the mean estimation error only differs 0.1◦ . The estimated azimuth DoAs all lie within an acceptable range from the true azimuth DoAs. The maximum azimuth estimation error is 5.7◦ . Estimating the elevation angle, both MUSIC and Capon show a fairly large estimation error for the direction (φ, θ) = (59◦ , 20◦ ). This is because a circular array configuration can not offer a full elevation coverage. The coverage in elevation indeed depends on the radiation pattern of the array elements used (21). Recall that, for our measurements, we deployed a (virtual) array that consisted out of 90 monopoles. The typical radiation pattern of a 1/2 wavelength monopole is shown in Figure 4.3. From this graph, it is clear that a circular array composed out of monopoles, can only cover a range in elevation apprixomately equal to −60◦ , +60◦ . This is caused by the zeros in the element radiation pattern at elevation angles −90◦ and +90◦ . Clearly, the elevation angle 59◦ lies on the edge of what is detectable by the UCA we used.

Chapter 4. Results and Interpretation

51

Figure 4.4: Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. We apply MUSIC and use a horizontally aligned UCA.

Chapter 4. Results and Interpretation

52

Figure 4.5: Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. We apply MUSIC and use a vertically aligned UCA.

Chapter 4. Results and Interpretation

53

Figure 4.6: Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. We multiply the spectra obtained with MUSIC using (1) a vertically and (2) a horizontally aligned UCA.

Chapter 4. Results and Interpretation

54

Figure 4.7: Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. We multiply the spectra obtained with Capon using (1) a vertically and (2) a horizontally aligned UCA.

Chapter 4. Results and Interpretation

55

Figure 4.8: Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. In a first step we roughly determine the peaks in the power spectrum. Then we single the regions-of-interest (ROI) out and estimate them with more detail, in order to save processing power.

Chapter 4. Results and Interpretation Real [◦ ] DoA1 (φ) DoA2 (φ) DoA3 (φ)

-57 0 60

Estimation [◦ ] Capon MUSIC -59.7 -59.8 -2.1 -1.5 54.7 54.3 Mean Error [◦ ]

56 Estimation error[◦ ] Capon MUSIC 2.7 2.8 2.1 1.5 5.3 5.7 3.4 3.3

Table 4.3: Two-dimensional Spectral-Based DoA Estimation of three non-coherent sources. We compare MUSIC and Capon. Azimuth DoA estimations and errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values.

Real [◦ ] DoA1 (θ) DoA2 (θ) DoA3 (θ)

-47.6 0 59

Estimation [◦ ] Capon MUSIC -43.5 -43.6 8.3 8.5 38.4 38.6 Mean Error [◦ ]

Estimation error[◦ ] Capon MUSIC 4.1 4 8.3 8.5 20.6 20.4 8.3 8.2

Table 4.4: Two-dimensional Spectral-Based DoA Estimation of three non-coherent sources. We compare MUSIC and Capon. Elevation DoA estimations and errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values.

Chapter 4. Results and Interpretation

4.2

57

Outdoor Experiment

4.2.1

Virtual UCA with 90 elements

4.2.1.1

Direct Communication Link

In Figure 4.9 and Figure 4.10 we applied Capon and MUSIC respectively to estimate the DoAs of two non-coherent sources in an outdoor environment, described in Section 3.4.1. We used a UCA with radius 0.184m. We applied the same techniques as in the previous Section 4.1.1.2. I.e. we first used the measurement data gathered by a horizontally and a vertically aligned UCA and combined (multiplied the output spectra) these into one spectrum. Then we singled out the ROI to accurately determine the DoAs while keeping the execution time to a minimum. The estimated DoAs are shown in Tables 4.5 and 4.6. As there are high walls surrounding our test site, the transmitted signals will reflect against these walls and impinge together with the original signals on the receiver. This results in higher sidelobes as well as a higher number of sidelobes. This effect is clearly observed in both Figures 4.9 and 4.10. The spectrum obtained with MUSIC shows lower sidelobes and more prominent peaks, as expected. In this multipath environment, both Capon and MUSIC succeed in estimating the DoAs. Overall, they show good results, as the mean azimuth estimation errors are only 3.5◦ and 1.2◦ for MUSIC and Capon resp. The estimation errors in elevation total 3.5◦ and 4.9◦ for MUSIC and Capon resp. This result was expected, as the transmitters are in direct sight of the receiver and only a few meters away. Since MUSIC repeatedly shows the best results and, not unimportantly in a multipath environment, the lowest sidelobes, we will only display the results of MUSIC in our final measurement (Section 4.2.1.2).

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Figure 4.9: Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is a LoS between transmitter and receiver. We multiply the spectra obtained with Capon using (1) a vertically and (2) a horizontally aligned UCA.

Chapter 4. Results and Interpretation

59

Figure 4.10: Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is a LoS between transmitter and receiver. We multiply the spectra obtained with MUSIC using (1) a vertically and (2) a horizontally aligned UCA.

Real [◦ ] DoA1 (θ) DoA2 (θ)

-47 0

Estimation [◦ ] Capon MUSIC -53 -45.6 -1 -1 Mean Error [◦ ]

Estimation error[◦ ] Capon MUSIC 6.0 1.4 1.0 1.0 3.5 1.2

Table 4.5: Two-dimensional Spectral-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is a LoS between transmitter and receiver. We compare MUSIC and Capon. Azimuth DoA estimations and errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values.

Chapter 4. Results and Interpretation Real [◦ ] DoA1 (φ) DoA2 (φ)

6 22

Estimation [◦ ] Capon MUSIC 5 5 16.9 13.2 Mean Error [◦ ]

60 Estimation error[◦ ] Capon MUSIC 1.0 1.0 5.1 8.8 3.5 4.9

Table 4.6: Two-dimensional Spectral-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is a LoS between transmitter and receiver. We compare MUSIC and Capon. Elevation DoA estimations and errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values.

Chapter 4. Results and Interpretation 4.2.1.2

61

No Direct Communication Link

For these last tests, we were only able to measure with a horizontally aligned UCA. The estimations are thus ambigious in elevation angle. We apply MUSIC to the measured data. We use the ROI technique to accurately determine the DoAs. No Direct Communication Link Figure 4.12 shows the MUSIC spectrum after we applied spatial smoothing and a Chebyshev window. The DoA estimations are displayed in Table 4.7. As for the spatial smoothing, we averaged the correlation matrix over 37 subarrays each containing data from 53 array elements. The Chebyshev window suppresses the sidelobes to a -30dB level. The spectrum resulting from this, contains two distinctive peaks. Considering the ambiguity in elevation angle, we can not decide if the signal is arriving from under or above the horizontal plane. As we are transmitting from two non-coherent sources, we would suspect MUSIC to be able to differentiate between these two signals. The spectrum only shows one broad peak however. This is due to the Chebyshev window, that allows reduced sidelobes but causes a drop in resolution. Seen from the position of the receiver, the sources lie only 8◦ horizontally separated from each other. Clearly, this is not enough to make a distinction between the two sources. The transmitted RF signals are diffracted around the corner of the street and arrive at the receiver. MUSIC DoA1 DoA2

Azimuth [◦ ] 26.8 26.8

Elevation [◦ ] -40.7 35.3

Table 4.7: Two-dimensional Spectral-Based DoA Estimation of two non-coherent sources in an outdoor experiment, where there is no direct communication link.

No Direct Communication Link and Increased number of Reflections For our final test, we add a car to the test site, see Figure 3.12. This drastically increases the number of reflections and adds complexity to estimating the correct DoAs. We apply the same procedure (spatial smoothing combined with a Chebyshev window) as in the last experiment, in which there was no car present. The power spectrum can be seen in Figure 4.12, the estimated DoAs in Table 4.8. Interestingly enough, the same DoAs as in the previous experiment appear plus two more peaks. These new peaks indicate the presence of the car in the street. A birds eye view of the test site is shown in Figure 4.11.

Chapter 4. Results and Interpretation MUSIC DoA1 DoA2 DoA3 DoA4

Azimuth [â—Ś ] -21.2 -21.2 26.8 26.8

62 Elevation [â—Ś ] -34.4 29.6 -34.4 29.6

Table 4.8: Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is no LoS between transmitter and receiver and an increased number of reflections.

Figure 4.11: Birds eye view of the test site, as seen in Figure 3.12. T1 and T2 denote the two transmitters. At the origin of the coordinate system stands the receiver. The white space denotes the street which is surrounded by high buildings and passes under a bridge. There is a car parked in the outside corner of the street.

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63

Figure 4.12: Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is no LoS between transmitter and receiver.

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64

Figure 4.13: Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is no LoS between transmitter and receiver and an increased number of reflections.

Chapter 5 Summary 5.1

Summary

This thesis handles the subject of DoA estimation of RF signals, using virtual circular arrays. The first part represents a literature review of some available and well known techniques, such as Bartlett, Capon and MUSIC (spectral-based methods) and Root-MUSIC and ESPRIT (model-based). We also discuss the necessary preprocessing steps, such as spatial smoothing and model order estimation. After having built, simulated and compared the DoA estimation algorithms, we subject the most performant techniques of both spectral and model-based methods – Capon, MUSIC and ESPRIT – to a series of tests. The measurement setup is reported in detail. We start with the most basic case, after which we gradually increase the complexity of the experiments. The first experiments take place inside the anechoic chamber, Capon and MUSIC show very good results in estimating the DoAs of up to four non-coherent sources in one-dimensional estimation, and three sources in two-dimensional estimation – i.e. estimation of both azimuth and elevation angle of the DoA. We notice that the algorithms are limited in estimating the correct elevation angle. This is caused by the radiation pattern of the array elements we used, that show nulls at elevation angles +/ − 90◦ . The range in which proper estimation of elevation angle is possible, is approximately [−60◦ , +60◦ ]. Another problem that arises when estimating both azimuth and elevation angle, is that when using a horizontally aligned UCA, we can not tell a wave, arriving from under the horizontal plane, apart from a wave arriving from above the horizontal plane. We solve 65

Chapter 5. Summary

66

this by performing each measurement two times, once with the UCA horizontally aligned and once with a vertically aligned UCA. Hereafter we multiply both spectra, effectively removing the two ambiguities. In order to keep the execution time of the spectral-based methods as low as possible while accurately estimating the DoAs in azimuth and elevation, we work in two consecutive steps. In a first phase, we apply the algorithms with large scanning steps, to determine the regions-of-interest (ROI). Next we repeat the algorithms and we let them scan only the ROIs, this time with a smaller step. ESPRIT, even though simulations showed attractive performance results, is not considered further due to practical implications of the measurement setup that limit ESPRIT its efficacy. ESPRIT nevertheless showed acceptable results for the one-dimensional DoA estimation of four sources. Hence, in what follows we concentrate on Capon and MUSIC. In the next phase we conduct outdoor experiments, thus in an environment that is subject to fading and multipath propagation. We place both receiver and transmitters in a narrow street, surrounded by high walls. In the first test there exists a direct communication link between the transmitters and the receiver. MUSIC and Capon show very similar mean estimation errors for this measurement setup. Yet, the MUSIC spectrum displays considerably less spectral leakage than Capon. MUSIC thus receives our preference for the final experiment, in which we subject the MUSIC algorithm to the challenge of estimating the location of two transmitters in an outdoor environment and in absence of a direct communication link between transmitters and receiver. We learn that MUSIC looses a big part of its resolution, mainly caused by the extra techniques needed to render the results somewhat useable, such as spatial smoothing and a Chebyshev Window.

5.2

Future Work

Further works should emphasize primarily on the use of Root-MUSIC and ESPRIT. These algorithms, when used with a virtual array, provide both higher accuracy and resolution compared to the spectral-based methods, especially in the case of multipath propagation. Also, special attention should go to the performance of DoA estimation algorithms, when real arrays are used. Unwanted real array effects such as mutual coupling can severely influence the proper functioning of DoA finding programs. Lastly, it would be interesting to test the model order estimators extensively in a series of outdoor experiments.

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List of Figures 1.1

2.1 2.2 2.3 2.4 2.5 2.6

2.7

2.8

2.9

Number of the mobile cellular subscriptions from 2005 to 2010, according to the ITU [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Direction-of-Arrival Estimation Problem . . . . . . . . . . . . . . . . . Plane wave sl impinging from direction-of-arrival Φl on a M -element ULA Plane wave sl impinging from direction-of-arrival (φl , θl ) on a M1 xM2 -element UPA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plane wave sl impinging from direction-of-arrival (φl , θl ) on a M -element UCA Spectral-Based DoA Estimation . . . . . . . . . . . . . . . . . . . . . . . . Comparison of the resolution threshold of three spectral-based DoA estimation techniques, Bartlett (blue), Capon (black) and MUSIC (red), for a varying number of array elements. We assume uncorrelated sources and a ULA with half-wavelength inter-element spacing. Example for SNR = 15 dB and number of samples = 100. . . . . . . . . . . . . . . . . . . . . . . . Comparison of the resolution threshold of three spectral-based DoA estimation techniques, Bartlett (blue), Capon (black) and MUSIC (red), for varying signal-to-noise-ratio. We assume uncorrelated sources and a ULA with half-wavelength inter-element spacing. Example for number of array elements = 8 and number of samples = 100. . . . . . . . . . . . . . . . . . Comparison of the resolution threshold of three spectral-based DoA estimation techniques, Bartlett (blue), Capon (black) and MUSIC (red), for a varying number of samples taken. We assume uncorrelated sources and a ULA with half-wavelength inter-element spacing. Example for SNR = 15dB and number of array elements = 8. . . . . . . . . . . . . . . . . . . . . . . Dividing of ULA into two subarrays with maximum overlap . . . . . . . .

69

1 4 6 7 7 8

13

14

15 19

List of Figures 2.10 Estimation of the number of sources, for varying SNR. We set out the estimation error versus the SNR. Clearly AKIC performs better than the EDC or MDL estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11 Estimation of the number of sources, for varying number of samples. We set out the estimation error versus the number of samples. . . . . . . . . . 2.12 Forward and Backward smoothing applied to a ULA. . . . . . . . . . . . . 2.13 Example of the spatial smoothing effect, if applied to MUSIC. Four highly correlated signals arrive from four different DoA on a ULA. Both the MUSIC spectrum with and without spatial smoothing are shown. . . . . . . . . . . 2.14 MUSIC with and without spatial smoothing. . . . . . . . . . . . . . . . . . 2.15 Comparison of the mean estimation error. From left to right: Bartlett, Capon, MUSIC and ESPRIT. . . . . . . . . . . . . . . . . . . . . . . . . . 2.16 Comparison of the execution time. From left to right: Bartlett, Capon, MUSIC and ESPRIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.17 Mean estimation error versus SNR for Bartlett, Capon, MUSIC and ESPRIT. The mutual coupling effect illustrated for a circular array. Left the standalone radiation pattern of an array element, right the active element pattern of that same array element. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 DoA Estimation with mutual coupling. Simulation done with 4NEC2. . . . 3.3 Structure of the Anechoic Chamber. On the left we have the transmitting antenna (Tx ), on the right the receiving antenna (Rx ) . . . . . . . . . . . . 3.4 Coordinate system used throughout this thesis. . . . . . . . . . . . . . . . 3.5 An example of a received signal frame, when two sources are present. . . . 3.6 Schematic representation of the measurement setup for experiments in the anechoic chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Radiation patterns in the XY -plane of a monopole (left) and a dipole (right). 3.8 Virtual circular array, made from a monopole mounted on an arm, which is then rotated in the horizontal plane. . . . . . . . . . . . . . . . . . . . . . 3.9 The test environment: a lane located outside the university building, surrounded by high walls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 Direct communication link between transmitter and receiver. The two pictures left show the transmitters, the picture right the receiver. . . . . . . . 3.11 No direct communication link between transmitter and receiver. The picture left shows the transmitters, the picture right the receiver. . . . . . . . . . .

70

22 22 23

24 25 26 27 28

3.1

31 32 33 34 35 36 37 38 40 41 42

List of Figures 3.12 The test environment for the final experiment: a lane located outside the university building, surrounded by high walls and with a car placed nearby transmitter and receiver generating extra reflections. . . . . . . . . . . . . One-dimensional Spectral-Based DoA Estimation of four non-coherent sources. We apply MUSIC and Capon . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 One-dimensional Model-Based DoA Estimation of four non-coherent sources. We apply ESPRIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 A typical radiation pattern of a monopole, viewed in the vertical plane. . . 4.4 Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. We apply MUSIC and use a horizontally aligned UCA. . . . . . . . . . . . 4.5 Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. We apply MUSIC and use a vertically aligned UCA. . . . . . . . . . . . . . 4.6 Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. We multiply the spectra obtained with MUSIC using (1) a vertically and (2) a horizontally aligned UCA. . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. We multiply the spectra obtained with Capon using (1) a vertically and (2) a horizontally aligned UCA. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Two-Dimensional Model-Based DoA Estimation of three non-coherent sources. In a first step we roughly determine the peaks in the power spectrum. Then we single the regions-of-interest (ROI) out and estimate them with more detail, in order to save processing power. . . . . . . . . . . . . . . . . . . . 4.9 Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is a LoS between transmitter and receiver. We multiply the spectra obtained with Capon using (1) a vertically and (2) a horizontally aligned UCA. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is a LoS between transmitter and receiver. We multiply the spectra obtained with MUSIC using (1) a vertically and (2) a horizontally aligned UCA. . . . . . . . . . . . . . . . . . . . . . . . . 4.11 Birds eye view of the test site, as seen in Figure 3.12. T1 and T2 denote the two transmitters. At the origin of the coordinate system stands the receiver. The white space denotes the street which is surrounded by high buildings and passes under a bridge. There is a car parked in the outside corner of the street. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

43

4.1

45 46 49 51 52

53

54

55

58

59

62

List of Figures

72

4.12 Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is no LoS between transmitter and receiver. 63 4.13 Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is no LoS between transmitter and receiver and an increased number of reflections. . . . . . . . . . . . . . . . . . . . 64

List of Tables 3.1 3.2 3.3 4.1

4.2

4.3

4.4

4.5

The azimuthal and elevation coordinates of the transmitters in the anechoic chamber, for a 1-D DoA estimation experiment. . . . . . . . . . . . . . . . The azimuthal and elevation coordinates of the transmitters in the anechoic chamber, for a 2-D DoA estimation experiment. . . . . . . . . . . . . . . . The azimuthal and elevation coordinates of the transmitters in the lane. . .

39 39 41

One-dimensional Spectral-Based DoA Estimation of four non-coherent sources. We apply MUSIC and Capon. Both DoA estimations and estimation errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values. . . . . . . . . . . . . . . . . . . . . . . . . . 46 One-dimensional Spectral-Based DoA Estimation of four non-coherent sources. We apply ESPRIT. Both DoA estimations and estimation errors are shown. values in red and green denote resp. the max- and minimum estimation error for the DoA estimates. . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Two-dimensional Spectral-Based DoA Estimation of three non-coherent sources. We compare MUSIC and Capon. Azimuth DoA estimations and errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values. . . . . . . . . . . . . . . . . . . . . . . . . . 56 Two-dimensional Spectral-Based DoA Estimation of three non-coherent sources. We compare MUSIC and Capon. Elevation DoA estimations and errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values. . . . . . . . . . . . . . . . . . . . . . . . . . 56 Two-dimensional Spectral-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is a LoS between transmitter and receiver. We compare MUSIC and Capon. Azimuth DoA estimations and errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values. . . . . . . . . . . . . . . . . . . . . . . . . . 59 73

List of Tables 4.6

4.7 4.8

74

Two-dimensional Spectral-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is a LoS between transmitter and receiver. We compare MUSIC and Capon. Elevation DoA estimations and errors are shown. values in red and green denote resp. the maximum and minimum estimation error for all values. . . . . . . . . . . . . . . . . . . . . . . . . . 60 Two-dimensional Spectral-Based DoA Estimation of two non-coherent sources in an outdoor experiment, where there is no direct communication link. . . 61 Two-Dimensional Model-Based DoA Estimation of two non-coherent sources in an outdoor experiment. There is no LoS between transmitter and receiver and an increased number of reflections. . . . . . . . . . . . . . . . . . . . . 62

Direction-of-Arrival estimation of RF signals based on virtual circular arrays

Published on May 31, 2011

Wireless communication services have known an explosive growth in the last decade. To enable the necessary increase in channel throughput, r...

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