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Digital Indoor Transmission System in 60GHz

Band Using Adaptive Beamforming

Marcin Dabrowski

ii

Streszczenie

W pracy zbadano celowosc oraz mozliwosci budowy nowych szerokopasmowych

systemów transmisji danych wewnatrz budynków w pasmie nielicencjonowanym

60GHz. W zwiazku z tym autor przeanalizował własciwosci kanału radiowego w tym

pasmie oraz własnosci liniowych szyków antenowych przy załozeniu adaptacyjnego

formowania wiazki. Praca zawiera krytyczny przeglad mozliwych do zastosowa-

nia algorytmów adaptacyjnych wraz z analiza rozwiazan konstrukcji nadajników

i odbiorników. Autor zaproponował takze szczegółowe rozwiazania techniczne doty-

czace realizacji warstwy fizycznej.

W celu przeprowadzenia eksperymentów symulacyjnych, autor opracował pakiet

oprogramowania w srodowisku M��, które umozliwia symulacje transmisji da-

nych w rozpatrywanym systemie z terminalami ruchomymi. Praca zawiera wyniki

przeprowadzonych badan. W pełni potwierdzaja one przydatnosc algorytmu LMS

do adaptacyjnego formowania wiazki w pasmie 60GHz.

Abstract

Usefulness and possibilities of realization of new broadband indoor transmission

systems in an unlicensed band near 60GHz have been examined in this thesis. To

this end the author has analyzed radio channel characteristics in 60GHz band and

properties of uniform linear arrays of antennas using adaptive beamforming. The

thesis consists of a critical review of possible adaptive algorithms for the considered

application together with the analysis of possible structures of transmitters and

receivers. The author has suggested detailed technical solutions for the realization

of the physical layer.

In order to perform simulation experiments, the author has developed a software

package in M�� environment, which is capable of simulating data transmission

in the proposed system with mobile terminals. The thesis contains results of the

experiments carried out by the author. They fully confirm usefulness of the LMS

algorithm for adaptive beamforming in 60GHz band.

Contents

Glossary xi

1 Introduction 1

1.1 Need for High Speed Wireless Transmission Systems . . . . . . . . . . 1

1.2 Thesis Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Aim and Scope of the Work . . . . . . . . . . . . . . . . . . . 3

1.2.2 Tasks for Further Study and Implementation . . . . . . . . . . 4

2 Transmission in 60GHz Band 5

2.1 Relationship Between Frequency and Wavelength . . . . . . . . . . . 5

2.2 Antenna Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Antenna Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.1 Directivity and Gain . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.2 EIRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Friss Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.5 Atmosphere Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.6 Material Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.7 Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.7.1 Multipath Channel Model . . . . . . . . . . . . . . . . . . . . 14

2.7.2 Modified Saleh-Valenzuela Model . . . . . . . . . . . . . . . . 15

2.7.3 Doppler Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.7.4 Example of Channel Properties . . . . . . . . . . . . . . . . . 18

2.8 Legal Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

iii

iv CONTENTS

3 Antenna Arrays 21

3.1 Uniform Linear Array (ULA) . . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 Directional Ambiguity . . . . . . . . . . . . . . . . . . . . . . 23

3.1.2 Example of Patterns . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.3 Element Spacing . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.4 Directivity and Gain . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Principle of Pattern Multiplication . . . . . . . . . . . . . . . . . . . 26

3.3 Rectangular Planar Array . . . . . . . . . . . . . . . . . . . . . . . . 26

4 Array Steering and Adaptive Algorithms 31

4.1 Direct Array Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2 Mean Square Error (MSE) . . . . . . . . . . . . . . . . . . . . . . . . 33

4.3 Correlation Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4 Steepest Descent Method . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.5 Least Mean Square (LMS) Algorithm . . . . . . . . . . . . . . . . . . 38

4.6 Sample Covariance Matrix Inversion (SCMI) . . . . . . . . . . . . . . 40

4.7 MUSIC algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.8 ESPRIT Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5 System Architecture Concepts 55

5.1 Architecture Functionality and Concepts . . . . . . . . . . . . . . . . 55

5.1.1 Broadway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.1.2 IEEE P802.15 Draft Proposal . . . . . . . . . . . . . . . . . . 56

5.1.3 Integrated Mobile Broadband Mobile System (IBMS) . . . . . 58

5.1.4 Wireless Gigabit With Advanced Multimedia Support (WIG-

WAM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.2 Selected Hardware Concepts . . . . . . . . . . . . . . . . . . . . . . . 60

5.2.1 Remarks on the Number of Elements in Arrays . . . . . . . . 60

5.2.2 RF Front-End Technologies . . . . . . . . . . . . . . . . . . . 61

CONTENTS v

5.2.3 Phase Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2.4 DOA Estimation Through Sub-band Sampling . . . . . . . . . 66

6 System Proposal and Simulation Experiments 69

6.1 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.2 Phase Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.3 Terminal Addressing and Packet Structure . . . . . . . . . . . . . . . 72

6.4 Connection States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.5 Adaptive Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.6 Developed Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.6.1 Simulation Environment . . . . . . . . . . . . . . . . . . . . . 77

6.6.2 Illustration Scripts . . . . . . . . . . . . . . . . . . . . . . . . 78

7 Final Conclusions 81

vi CONTENTS

List of Figures

2.1 Free space loss at 60GHz . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Broad attenuation peak near 60GHz . . . . . . . . . . . . . . . . . . 13

2.3 Saleh-Valenzuela clusters and rays illustration, [24] . . . . . . . . . . 16

2.4 Laplacian distribution, µ = 0, σ = 1. . . . . . . . . . . . . . . . . . . 17

2.5 Total received power as a function of the distance from the access

point, simulation results from [25] . . . . . . . . . . . . . . . . . . . . 18

2.6 Frequency allocations for 60GHz bands . . . . . . . . . . . . . . . . . 19

3.1 ULA containing N = 6 elements . . . . . . . . . . . . . . . . . . . . . 22

3.2 Wavefront run length differences between antennas in ULA . . . . . . 22

3.3 Example of ULA pattern with N = 2, θ0 = π/6, β = 0. . . . . . . . . 24



3.6 Example of influence of ULA element spacing on its directional char-

acteristic, d = λ/4, N = 4, θ0 = π/6, β = 0. . . . . . . . . . . . . . . 27


acteristic, d = λ/2, N = 4, θ0 = π/6, β = 0. . . . . . . . . . . . . . . 27


acteristic, d = λ, N = 4, θ0 = π/6, β = 0. A pair of grating lobes

present. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

vii

viii LIST OF FIGURES


acteristic, d = 2λ, N = 4, θ0 = π/6, β = 0. Three pairs of grating

lobes present. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.10 Rectangular planar array . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.11 Example of a rectangular planar array pattern with dx = dy = λ/2,

θ0 = 0, φ0 = 0, Nx = Ny = 8, [37] . . . . . . . . . . . . . . . . . . . . 29

4.1 Desired signal and intereference signal impinge an array . . . . . . . . 32

4.2 Model for an unknown system . . . . . . . . . . . . . . . . . . . . . . 33

4.3 Unknown system identification . . . . . . . . . . . . . . . . . . . . . . 35

4.4 An example of MSE surface . . . . . . . . . . . . . . . . . . . . . . . 36

4.5 Applying weights to antenna outputs used for receiving the desired

signal from the desired direction . . . . . . . . . . . . . . . . . . . . . 40

4.6 Matrix inversion issue, above: two examples of |R|, white color showsmaximum values, below: patterns obtained by R, a) R close to iden-

tity, b) R close to singular . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1 Pilot and data subcarriers in IEEE 802.15 draft proposal for 60GHz

OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.2 User groups channel allocation . . . . . . . . . . . . . . . . . . . . . . 57

5.3 WIGWAM demonstrator receiver, [64] . . . . . . . . . . . . . . . . . 59

5.4 WIGWAM demonstrator receiver parts, [64] . . . . . . . . . . . . . . 60

5.5 Virtual increase of the number of elements, [34] . . . . . . . . . . . . 60

5.6 Example of ULA with patch antennas . . . . . . . . . . . . . . . . . . 61

5.7 A GaAs MESFET transistor current and power gains as functions of

frequency, [59] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.8 Receiver design, [57] . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.9 CMOS receiver details, [57] . . . . . . . . . . . . . . . . . . . . . . . 63

5.10 CMOS receiver die photograph, [57] . . . . . . . . . . . . . . . . . . . 64

5.11 Modulator-type phase shifter . . . . . . . . . . . . . . . . . . . . . . . 64

ACKNOWLEDGEMENT ix

5.12 PIC as a phase shifter . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.13 Transmitter with MEMS phase shifters, [36] . . . . . . . . . . . . . . 65

5.14 3-bit MEMS phase shifter frequency-dependent operation, [36] . . . . 66

5.15 ULA containing eight boards with IF beamformers and patch anten-

nas, [33] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.16 Down-conversion and subband sampling in order to estimate DOA, [33] 68

5.17 System with sub-band sampling in order to estimate DOA, [33] . . . 68

6.1 BPSK baseband and passband signals . . . . . . . . . . . . . . . . . . 71

6.2 Average BPSK baseband signal spectrum . . . . . . . . . . . . . . . . 72

6.3 PSDU scrambler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.4 Physical layer block diagram applied in simulation of the transmitter 75

6.5 Recevier block diagram with per frame LMS part . . . . . . . . . . . 76

6.6 Simulation window screenshots from M�� . . . . . . . . . . . . . 79

6.7 beamformLms.m window part screenshot . . . . . . . . . . . . . . . . . 80

x ACKNOWLEDGEMENT

Acknowledgement

I would like to thank my supervisor Professor Krzysztof Wesołowski

for suggesting the fascinating field of adaptive beamforming.

I also appreciate his stimulation, consultation, and the literature support.

Glossary

2-D two-dimensional

3-D three-dimensional

A/D Analog/Digital

AFE Analog Front-End

AOA Angle of Arrival

AP Access Point

AWGN Additive White Gaussian Noise

BiCMOS Integration of BJT and CMOS technologies into a single device

BJT Bipolar Junction Transistor

BPF Band Pass Filter

BPSK Binary Phase Shift Keying

CEPT European Conference of Postal and Telecommunications Administrations

CMOS Complementary-symmetry Metal Oxide Semiconductor

D/A Digital/Analog

DBF Digital Beam Forming (Former)

DOA Direction of Arrival

xi

xii GLOSSARY

EIRP Effective (Equivalent) Isotropic Radiation Power

ESPRIT Estimation of Signal Parameters via Rotational Invariance Techniques

FCC Federal Communications Commission

FPGA Field Programmable Gate Array

FSL Free Space Loss

GaAs Gallium Arsenide

GMSK Gaussian Minimum Shift Keying

HEMPT High Electron Mobility Pseudomorphic Transistor

HPA High-Power Amplifiers

IBMS Integrated Broadband Mobile System

IC Integrated Circuit

IEEE Institute of Electrical and Electronics Engineers

IF Intermediate Frequency

ISM Industrial Scientific Medical

IST Information Society Technologies

ITU International Telecommunication Union

LDPC Low Density Parity Code

LMS Least Mean Square

LNA Low-Noise Amplifier

LO Local Oscillator

LOS Line of Sight

LPF Low Pass Filter

MAC Medium Access Control

MMIC Monolithic Microwave Integrated Circuit

MMW Millimeter Wave

MSE Mean Square Error

MUSIC Multiple Signal Classification

OFDM Orthogonal Frequency Division Modulation

xiii

PAN Personal Area Network

PDF Probability Density Function

PHY Physical layer

PIC Pass Invert Cancel

PLL Phase Locked Loop

PPDU Physical layer Protocol Data Unit

PSD Power Spectrum Density

PSDU Physical layer Service Data Unit

QAM Quadrature Amplitude Modulation

QMMIC Quasi-Monolithic Microwave Integrated Circuit

QoS Quality of Service

QPSK Quadrature Phase Shift Keying

RF Radio Frequency

RMS Root Mean Square

SCMI Sample Covariance Matrix Inversion

SiGe Silicon Germanium

SiGe:C Blend of Silicon Germanium and Carbon

ULA Uniform Linear Array

UWB Ultra Wideband

VCO Voltage Controlled Oscillator

WARC World Administrative Radio Conference

WIGWAM Wireless Gigabit with Advanced Multimedia

WLAN Wireless Local Area Network

WPAN Wireless Personal Area Network

xiv GLOSSARY

Chapter 1

Introduction

1.1 Need for High Speed Wireless Transmission

Systems

A success of digital wireless transmission solutions in unlicensed bands can be ob-

served in recent years. Equipment such as WiFi access points, antennas, and radio

cables are now commonly available. Radio unlicensed access to the Internet is to-

day an efficient alternative to the offer of big and inert telecommunication compa-

nies, which typically do not provide broadband access in rural areas. The practice

of recent years has shown that networks such as WiFi are reasonable for indoor

point-multipoint access as well as long distance point-point wireless bridges. How-

ever, systems defined by IEEE 802.11, Hiperlan, and WiMax standards have several

limitations among which the most significant is the effective throughput from the

end-user point of view. Even if we consider a WiFi wireless bridge operation mode

and transmission only between two terminals in indoor environment, the maximum

physical layer rate is 54 Mbit/s, which is much less than capacities of current cable

solutions, nor it can cover today needs. This is because the throughput of this level is

not sufficient for such applications as e.g. real time digital video transmission. The

present-day Personal Area Networks (PANs) were designed for short-range trans-

mission between devices like mobile phones and external microphone sets and are

1

2 CHAPTER 1. INTRODUCTION

not satisfying the growing throughput demands.

Due to above mentioned limitations of existing systems, a need for higher data

rate wireless solutions emerges. 60GHz band gives an opportunity for building a

new standard of PANs, which would allow much higher transfer rates. The new

system would be exploited in the following indoor applications:

• wireless access to 4G networks and the Internet, media supply in public areas

such as trains and busses,

• communication between mobile data terminals,

• image acquisition from digital cameras to storage devices, e.g. downloading

JPEG images from camera into laptop,

• real time video signal transmission from camera to storage device, e.g. DVD

recorder,

• raw video signal transmission from decoder to displaying device, e.g. operation

as a wireless interface between LCD screen and DVB-T STB (set-top box) or

a DVD player.

Example: Consider real time communication between a typical video camera and

a DVD recorder. Assume raw digital video signal transmitted, thus the required

throughput should be

T = (768 columns× 576 lines) /frame× (1.1)

24 bits/pixel× 25 frames/s ≈ 265Mbits/s

None of present-day indoor wireless systems working in 2.4GHz, 5.4GHz, 5.8GHz,

or other bands can satisfy (1.1).

A broad air absorption band near 60GHz gives a place for yet another unlicensed

digital transmission system. The highest specific attenuation in that band is about

17.5 dB/km. However the most significant attenuation is due to free space loss

(FSL) at 60GHz, which at the distance 100m away from the transmitter reaches

1.2. THESIS DESCRIPTION 3

100 dB. Millimeter waves are strongly attenuated by walls and other materials, thus

access points should be located in every room. In real indoor environments, strong

multipath fading is observed. Because of high attenuation, in order to build inexpen-

sive receivers using circuits with average gain and noise characteristics, directional

antennas should be used. Furthermore, as the terminals are assumed mobile, adap-

tive beamforming must be applied. These two observations are motivation for this

thesis.

1.2 Thesis Description

1.2.1 Aim and Scope of the Work

The aim of this thesis consists in examination of usefulness and possibilities of

realization of new broadband indoor transmission systems in unlicensed bands near

60GHz. The thesis describes the most important issues emerging with the advent

of 60GHz systems. The discussed fields include such topics as:

• Propagation environment at 60GHz and channel models used in indoor trans-

mission (Chapter 2),

• Properties of antenna arrays, particularly uniform linear arrays (Chapter 3);

in this work mainly 2-D models were discussed, however, a rectangular planar

array with 3-D pattern has been also briefly described,

• Mathematical basis for selected methods of adaptive beamforming (Chapter 4),

• A selection of architecture, functionality and hardware issues has been pre-

sented in Chapter 5, as the field of 60GHz mobile demonstrator systems is

now being intensively discussed and investigated by many research teams.

The experimental part of this work described in Chapter 6 consisted in proposing

and testing a system for transmission between mobile terminals. The physical layer

of such a system has been proposed and simulated by the author. A system with two

4 CHAPTER 1. INTRODUCTION

mobile terminals with uniform linear arrays (ULAs) has been developed inM��.

An adaptive LMS algorithm per frame has been proposed and tested. Performed

simulations confirm that the implemented version of LMS leads to the optimal beam

shape within satisfactory time. Channel models used in indoor transmission have

been described in this thesis, however, they have not been used in simulations.

A collection of M�� scripts developed by the author, which is a part of this

project, is capable of simulating data transmission in the proposed, experimental

broadband transmission system with mobile terminals operating in an unlicensed

band near 60GHz.

1.2.2 Tasks for Further Study and Implementation

The developed software includes or may straightforwardly be extended in order to

include:

• different propagation environments, real channel models described in further

course may be used instead of an anechoic chamber,

• noise, e.g. the thermal noise,

• non-isotropic array elements,

• 3-D space, planar arrays,

• different adaptive algorithms, not only the LMS.

Error analysis of adaptive algorithms may be elaborated. A future cooperation

with RF circuitry and antenna design teams would be valuable. Thus, the sim-

ulations would assume real antenna patterns and data flow between stages such

baseband processors, the IF and RF blocks of the devices.

Chapter 2

Transmission in 60GHz Band

2.1 Relationship Between Frequency and Wave-

length

The speed of the electromagnetic wave in vacuum equals c ≈ 2.99792458 · 108m/ s.In further course we assume that sinusoidal wave velocity as well as group velocity

in atmosphere is c ≈ 3 · 108m/ s. A sinusoidal wave of frequency f0 = 60GHz =

6 · 1010Hz has the wavelength equal to

λ0 =c

f0≈ 3 · 108

6 · 1010 m = 0.5 · 10−2m = 5mm

Thus a band near 60GHz is referred to as millimeter wavelength (MMW) band.

The range of frequencies 40—70GHz is called the V-band.

2.2 Antenna Fields

Consider a transmitting antenna located close to the origin of a 3-D coordinate sys-

tem. Let the vector r = 1rr be the location of an observation point. Electromagnetic

field radiated by antenna in far-field region (r → ∞) can be expressed as propor-

tional to general complex amplitude vector A(k), where k is the wave propagation

5

6 CHAPTER 2. TRANSMISSION IN 60GHZ BAND

vector defined as

k = 1kk = 1k2π

λ

where λ is the wavelength and 1k is the unit vector towards the direction of the

wave propagation. The electric and magnetic fields may expressed as

E(r) ∼ A(k)e−jkr

r

H(r) ∼ [1k ×A(k)]e−jkr

r

As far-field is considered, the location vector r and propagation vector k have the

same directions, and they are equal

1r = 1k

thus kr = kr. The complex amplitude vector is defined in such a manner, that

|A(k)|2 has the unit [W/ sr] (watts per steradian). It can be decomposed into two

components

A(k) = uA(k,u) + vA(k,v)

where

A(k,u) = A(k)u∗

A(k,v) = A(k)v∗

The u and v vectors are orthogonal unitary vectors lying on the plane tangent to

k, thus they satisfy

u = v = 1

uv∗ = vu∗ = 0

uk = vk = 0

The pairs (k,u) and (k,v) are referred to as polarization states of the considered

wave. In far-field region the field intensity in state (k,u) is defined by

Iu(k) = |A(k,u)|2

The total radiation intensity for both polarization states takes the form

I(k) = |A(k)|2= |A(k,u)|2+ |A(k,v)|2 (2.1)

2.3. ANTENNA PROPERTIES 7

2.3 Antenna Properties

2.3.1 Directivity and Gain

Consider a generator producing a signal of power Pgen and feeding the transmitter

antenna. Because of impedance mismatch between the antenna and its feeder, the

power accepted by the antenna is

Pacc = (1− |Γ|2)Pgen (2.2)

where Γ is the amplitude reflection coefficient. Due to material loss, the antenna

radiates only a part of its accepted power

Prad = ηPacc (2.3)

where η is the antenna efficiency. The directivity of a given antenna towards the

direction k is defined by

D(k) =4π

PradI(k)

where I(k) is defined by (2.1). The gain (in [38] referred to as realized gain) is

defined as

G(k) =4π

Pgen

I(k) (2.4)

Using (2.2) and (2.3), the relationship between the directivity and the gain takes

the form

G(k) = η(1− |Γ|2)D(k)

Note that G(k) ≤ D(k).

2.3.2 EIRP

Consider an ideal isotropic antenna, which has the gain equal to

Giso(k) = 1


Assume we observe the field intensity I(k) in some direction k. This field could be

produced by an isotropic antenna as well as by a real antenna with gain G(k):

I(k) =

=1︷︸︸︷Giso(k) · EIRP(k)

4π=G(k) · Pgen

4π(2.5)

where EIRP (Effective (Equivalent) Isotropic Radiated Power) is the power fed to

the hypothetical ideal isotropic antenna. Simplifying (2.5) we get

EIRP(k) = G(k) · Pgen

It may be defined also for the maximum radiation direction

EIRP = maxk

{G(k)} · Pgen

Example: According to recommendations, the power of a data transmission device

at 60GHz may be at most 100mW (EIRP). Calculate how much power we can feed

to each antenna of four element (N = 4) uniform linear array (ULA) with isotropic

elements. Neglect the material loss and the impedance mismatch. Solution: Using

formula (3.6), which will be discussed in the chapter Antenna Arrays, a ULA with

isotropic elements has the maximum gain GULA = N2 = 16. The power per element

is therefore EIRP /GULA = 100mW/16 ≈ 6.25mW.

2.4 Friss Formula

Consider communication between two terminals in free space and assume that they

are located in far-fields of each other. Let the power produced by the generator in

terminal 1 equal P1 and the power passed to the receiver in terminal 2 equal P2.

The relationship between these powers is given by

P2 = P1

(λ

4πR

)2pG1(k1)G2(−k1)

where R is the distance between terminals, k1 is the propagation vector of the

transmitting antenna, and p is the polarization efficiency defined by

p = |u1u2|2

2.5. ATMOSPHERE LOSS 9

where u1 and u2 are the polarization vectors of the transmitting and the receiving

antenna. In case of the perfect polarization match

u2 = u∗1

We take the conjugate because of opposite propagation directions of the antennas

[38]. Therefore

p = |u1u∗1|2 = 1 (2.6)

Using (2.6) we finally obtain the so-called Friss transmission formula

P2P1

=

(λ

4πR

)2G1(k1)G2(−k1) (2.7)

Free-space loss (FSL) factor is defined by:

FSL =

(4πR

λ

)2

One may notice that the lower the wavelength, the higher is the loss, which is the

reason of limiting millimeter wavelength systems to indoor applications. Figure

2.1 shows free space loss in dB (10 log10 (FSL)) as a function of distance from the

transmitter, which radiates a sinusoidal wave at f0 = 60GHz.

A proof of the Friss formula, showing particularly that the FSL factor is a func-

tion of λ is beyond the scope of this work. It may be found in [38], where the

reciprocity principle was used in the form presented in [11].

2.5 Atmosphere Loss

ITU-R Recommendation P.676-5 [52] presents methods for estimating gaseous atten-

uation in different propagation conditions determined by wave frequency, altitude,

air pressure, and other factors. The document includes formulas for estimating the

attenuation due to dry air and water vapor near 60GHz. The given formulas are

valid for altitudes from the sea level to 5 km.


0 10 20 30 40 50 60 70 80 90 100

20

40

60

80

100

Distance from the transmitter [m]

Free sp

ace loss [dB]

Figure 2.1: Free space loss at 60GHz

The specific attenuation due to dry air for f between 54GHz and 66GHz can be

estimated by

γo [dB / km] = exp

(54−N ln (γ0 (54)) (f − 57) (f − 60) (f − 63) (f − 66) /1944−−57−N ln (γ0 (57)) (f − 54) (f − 60) (f − 63) (f − 66) /486+

+60−N ln (γ0 (60)) (f − 54) (f − 57) (f − 63) (f − 66) /324−−63−N ln (γ0 (63)) (f − 54) (f − 57) (f − 60) (f − 66) /486+

+66−N ln (γ0 (66)) (f − 54) (f − 57) (f − 60) (f − 63) /1944)fN

(2.8)

2.5. ATMOSPHERE LOSS 11

where

N = 0 for f ≤ 60GHz, N = −15 for f > 60GHz

γo (54) = 2.136r1.4975p r−1.5852t exp (−2.5196(1− rt))

γo (57) = 9.984r0.9313p r2.6732t exp (0.8563(1− rt))

γo (60) = 15.42r0.8595p r3.6178t exp (1.1521(1− rt))

γo (63) = 10.63r0.9298p r2.3284t exp (0.6287(1− rt))

γo (66) = 1.935r1.6657p r−3.3714t exp (−4.1612(1− rt))

rp = p/1013

rt = 288/(273 + t)

The user given parameters are:

f [ GHz] frequency,

p [hPa] pressure,

t [ ◦C] temperature.

The water vapor specific attenuation is estimated for f < 350GHz by

γw [dB / km] = (2.9)

=

(3.13 · 10−2rpr2t + 1.76 · 10−3ρr8.5t + r2.5t

(3.84ξw1g22 exp (2.23 (1− rt))(f − 22.234)2 + 9.42ξ2w1

+

+10.48ξw2 exp (0.7 (1− rt))(f − 183.31)2 + 9.48ξ2w2

+0.078ξw3 exp (6.4385 (1− rt))(f − 321.226)2 + 6.29ξ2w3

+

+3.76ξw4 exp (1.6 (1− rt))(f − 325.153)2 + 9.22ξ2w4

+26.36ξw5 exp (1.09 (1− rt))

(f − 380)2+

+17.87ξw5 exp (1.46 (1− rt))

(f − 448)2+883.7ξw5g557 exp (0.17 (1− rt))

(f − 557)2+

+302.6ξw5g752 exp (0.41 (1− rt))

(f − 752)2

))f 2ρ · 10−4


where

ξw1 = 0.9544rpr0.69t + 0.0061ρ

ξw2 = 0.95rpr0.64t + 0.0067ρ

ξw3 = 0.9561rpr0.67t + 0.0059ρ

ξw4 = 0.9543rpr0.68t + 0.0061ρ

ξw5 = 0.955rpr0.68t + 0.006ρ

g22 = 1 + (f − 22.235)2 / (f + 22.235)2

g557 = 1 + (f − 557)2 / (f + 557)2

g752 = 1 + (f − 752)2 / (f + 752)2

rp = p/1013

rt = 288/(273 + t)

The user given parameters are:

f [ GHz] frequency,

p [hPa] pressure,

t [ ◦C] temperature,

ρ [ g/m3] water vapor density.

The total attenuation of the path is

A [dB] = (γo + γw) r0 (2.10)

where γo and γw are defined by (2.8) and (2.9), r0 [ km] is the path length.

A broad attenuation peak can be observed near 60GHz, the recommendation

says many oxygen absorption lines merge in that band. This is the reason for which

the band has been assigned to unlicensed transmission. The specific attenuations

γo and γw and the total specific attenuation γo + γw are shown in Figure 2.2 with

p = 1013 hPa, t = 20 ◦C, ρ = 7.5 g/m3. In the range 54GHz — 66GHz the formulas

(2.8) and (2.9) are to be used. The recommendation contains formulas for frequencies

below 54GHz and above 66GHz, which were used as well.

2.6. MATERIAL LOSSES 13

f[GHz]10

010

110

210

310

-4

10-3

10-2

10-1

100

101

102

f[GHz]

γo, γ

w [d

B/k

m]

50 55 60 65 700

5

10

15

20

γo+γw [dB/k

m]

γo

γw

60GHz

Figure 2.2: Broad attenuation peak near 60GHz

2.6 Material Losses

Millimeter wave attenuation strongly depends on the kind of material it impinges

on. High frequency implies high reflection and attenuation in materials such as

concrete and wood. A 15 cm thick concrete wall attenuates up to 36 dB, whereas

a glass slab attenuates from 3 to 7 dB. Thus floors and concrete walls determine

the cell boundaries. Assuming wireless access scenario, the access points should be

located in every room and corridor. Thanks to relatively small cells, echo paths are

shorter than those at lower frequencies.

2.7 Channel Models

Channel at 60GHz is strongly multipath. Millimeter waves rather reflect from walls

than travel through them. We can neglect wall penetrating waves, thus e.g. mul-

tiwall models, commonly used for 2.4GHz band are not to be applied in this case.

Atmosphere absorption given by (2.10) may be neglected in indoor channel simula-

tions.


2.7.1 Multipath Channel Model

Let a terminal transmit a signal

s(t) = u(t)ej2πfct

where u(t) is the baseband signal and fc is the carrier frequency. The signal at the

receiving terminal equals

r(t) =

L(t)−1∑

i=0

ri(t)

It is a sum of rays coming from L(t) dominant paths, which appear as a result of

reflection, diffraction, and scattering. Our channel model assumes that the com-

ponents ri(t) undergo additional local scattering in the vicinity of the receiving

terminal, thus they take the form

ri(t) =∞∑

j=0

rij(t) =∞∑

j=0

αiju(t− τ ij)ej2πfc(t−τ ij) ≈ (2.11)

≈ u(t− 〈τ i〉)ej2πfct∞∑

j=0

αije−j2πfcτ ij

where αij and τ ij are random attenuations and random delays introduced by the

j-th locally scattered ray of the i-th ray, 〈τ i〉 = E {τ ij} is the expected value of the

delays. We assume that the period of u(t) is much longer than the ray delays, thus

we approximate delays of the baseband signal by the delay expected value. Using

(2.11), the received signal may be expressed in the form

r(t) =

L(t)−1∑

i=0

ri(t) =

L(t)−1∑

i=0

u(t− 〈τ i〉)ej2πfct∞∑

j=0

αije−j2πfcτ ij = (2.12)

=

L(t)−1∑

i=0

u(t− 〈τ i〉)∞∑

j=0

αije−j2πfcτ ij

ej2πfct =

Substituting

ci(t) =∞∑

j=0

αije−j2πfcτ ij (2.13)

into (2.12) we obtain a brief form

r(t) =

L(t)−1∑

i=0

u(t− 〈τ i〉)ci(t)

ej2πfct = ur(t)ej2πfct (2.14)

2.7. CHANNEL MODELS 15

where ur(t) is the baseband signal at the receiver. Equation (2.14) leads to the

conclusion that the impulse response of the channel equals at instant t:

h(τ ) =

L(t)−1∑

i=0

ci(t)δ (τ − 〈τ i〉) (2.15)

The RMS delay spread τRMS is defined as the variance of 〈τ i〉, where the probabilisticmeasure (the weight set) are the variances σ2i = E

{|ci(t)|2

}, which represent powers

of the paths:

τRMS =

∑L(t)−1i=0 σ2i 〈τ i〉2∑L(t)−1

i=0 σ2i

Note that in (2.15) the coefficients ci(t) take values with respect to the long-term

time variable t whereas τ is used as the short-term time variable. Thus the coef-

ficients ci(t) may be considered constant in (2.15). The in-phase and quadrature

components of ci(t) can be obtained from (2.13):

cIi (t) =∞∑

j=0

αij cos(2πfcτ ij)

cQi (t) =∞∑

j=0

αij sin(2πfcτ ij)

Due to infinite sums of functions of random variables αij and τ ij, the components

cIi (t) and cQi (t) have both Gaussian distribution. Note that they have zero mean

and equal variances as well. Thus the absolute values (i.e. envelopes) |ci(t)| =∣∣∣cIi (t) + jcQi (t)∣∣∣ have Rayleigh distribution. Let us now introduce the modification

of (2.15), which may be used for uniform linear antenna arrays:

h(τ ) =

L(t)−1∑

i=0

ci(t)v(θl)δ (τ − 〈τ i〉)

where v(θl) is the array propagation vector.

2.7.2 Modified Saleh-Valenzuela Model

The model used for simulating indoor environments [20] is a multipath channel

model based on the clustering phenomenon. Rays arrive at the receiver in groups


referred to as clusters. Both entire clusters and the rays within clusters change their

amplitudes in time (figure 2.3).

Figure 2.3: Saleh-Valenzuela clusters and rays illustration, [24]

The impulse response of the channel is given by

h(t) =∞∑

i=0

∞∑

j=0

cijδ (t− Ti − τ ij)

where i is the cluster index and j counts the rays within clusters, Ti is the i-th

cluster arrival time and τ ij is the j-th ray arrival times within the i-th cluster. The

absolute values of the weights cij are Rayleigh distributed and the weight variance

is

E{c2ij}= E

{c200}e−GTi−gτ ij

where G and γ constants are referred to as the cluster and ray time decay factors.

The modification of the Saleh-Valenzuela model assumes that the channel impulse

response may be decomposed into statistically independent components of time and

angle of arrival:

h(t, θ) = h(t)h(θ)

2.7. CHANNEL MODELS 17

where the angular impulse response h(θ) is given by

h(θ) =∞∑

i=0

∞∑

j=0

cijδ (θ −Θi − ωij)

and Θi is the i-th cluster angle of arrival, which is a random variable with uniform

distribution over 〈0, 2π). The random variable ωij is the j-th ray angle relative to

the direction of the i-th cluster. It has Laplacian distribution

PDF(ωij) =1√2σe−

∣∣∣∣

√2ωij

σ

∣∣∣∣

of zero mean and standard deviation σ.It has a strong peak at ωij = 0, which means

rays within a cluster are concentrated close to the main cluster direction.

-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

ωij

PD

F( ω

ij)

Figure 2.4: Laplacian distribution, µ = 0, σ = 1.

2.7.3 Doppler Shift

The maximum Doppler frequency shift is given by

∆fmax = fcv

c(2.16)


where fc is the carrier frequency, v is the mobile terminal velocity and c is the speed

of the light. As indoor application is considered, we assume the terminals move due

to walking with v = 1m/ s. Substituting fc = 60GHz and v = 1m/ s into (2.16) we

have ∆fmax = 200Hz. Calculation done in [25] for OFDM with 1024 sub-carriers

show that the Doppler shift has no significant influence on performance of systems

at 60GHz. Thus the terminal motion can be neglected in the indoor scenario.

2.7.4 Example of Channel Properties

Objects in line of sight (LOS) between terminals cause that shadowmargin should be

taken into consideration, which is assumed 10 dB on average. Simulations described

in [25] show the received power rapidly changes along the path. A plot of the total

received power as a function of the distance from the access point is shown in figure

2.5. Saleh-Valenzuela model was used in the simulation. RMS delay spread τRMS

Figure 2.5: Total received power as a function of the distance from the access point,

simulation results from [25]

2.8. LEGAL ISSUES 19

fell between 18 and 20 ns in the given example. However it can reach even 100 ns if

omnidirectional antennas are used in APs and large areas are covered [61].

2.8 Legal Issues

The band 54-60GHz has been internationally adjusted by ITU for unlicensed data

transmission [51]. Transmitter power has been limited to 100mW EIRP [49]. Ac-

cording to recommendations, the band near 60GHz has been allocated for that pur-

pose in many countries. Japan has allocated quite a broad range between 59GHz

and 66GHz. FCC granted the scope 59-64GHz in the USA. In Europe the unlicensed

band is expected to be finally allocated in the range 59-62GHz. A comparison of

both licensed and unlicensed frequency allocations is shown in figure 2.6.

54 55 56 57 58 59 60 61 62 63 64 65 66

ITU ISM

54 60 61 61.5

Europe59 62

59 66

Japan

59 64

USA

GHz

Figure 2.6: Frequency allocations for 60GHz bands

According to WARC 1979 regulations for Region 2, ITU assigned 60GHz band

for radar operation. The V-band is used for mostly short-range tracking [5], however,

such coexistence will not cause interference thanks to high FSL and air attenuation.

In Poland unlicensed transmission issues are regulated by the governmental edict

[53]. So far the band 61.0−61.5GHz has been allocated as general purpose band for

ISM devices and video signal transmission. The maximum power is 100mW EIRP.


60GHz band has not been assigned for unlicensed broadband data transmission.

For this purpose the only bands allocated in Poland are enumerated in Table 2.1.

Table 2.1: Unlicensed data transmission bands in Poland, excerpt from [53].

Frequency range Radiated power Remarks

2400.0− 2483.5MHz 100mW (EIRP)

5150− 5250MHz 200mW (EIRP) indoor use only

5250− 5350MHz 200mW (EIRP) indoor use only

5470− 5725MHz 1000mW (EIRP)

17.1− 17.3GHz 100mW (EIRP)

Note that band allocations differ considerably in the above-mentioned countries.

We should expect that this situation will undergo some further discussion and better

uniformity as a result. There are different bandwidths assigned, according to the

table:

Japan USA Europe ITU

6GHz

7GHz 6GHz 3GHz (only 1GHz overlapping

with Japan, USA and Europe)

Design of universal devices forces the assumption of the most restrictive options

for the bandwidth. For instance in the research project [50], 3GHz bandwidth has

been assumed for early design and simulations.

Chapter 3

Antenna Arrays

3.1 Uniform Linear Array (ULA)

Consider an array consisting of N isotropic antennas distributed along a line with

uniform element spacing d. The angle measurement convention used in this work

is shown in Figure 3.1. The angle θ denotes the incident wave direction and it

is the terminal radiation pattern variable. It is calculated relative to the terminal

diagonal. The angle β is the entire terminal rotation. Note that if we change β by

∆β, we must add −∆β to the incident wave direction θ at the same time, having

assumed the wave source a has constant position. The author decided to consider

counterclockwise angles positive, as it is often done in the elementary mathematics.

However, in literature of the field of beamforming the opposite convention is widely

adopted, e.g. in [37]. In examples of polar plots of array patterns it is assumed that

the ULA is directed as in Figure 3.1.

Signal delays or phase shifts in case of sinusoidal signals are observed between

adjacent array elements. If a signal is incoming from direction θ, the phase difference

between the elements of indices i and i+ 1 is equal to

∆ϕ = 2πd

λsin θ (3.1)

We easily obtain (3.1) using wavefront run length difference shown in Figure 3.2.

Every i-th antenna output is multiplied by a complex weight wi. Assume a plane

21

22 CHAPTER 3. ANTENNA ARRAYS

θ>0

12

34

56

d

β>0

Figure 3.1: ULA containing N = 6 elements

θ

d

i i+1

θ

. d sinθ

Figure 3.2: Wavefront run length differences between antennas in ULA

wave of the form Aej2πfct impinges on the array at angle θ. The array output takes

the form

y(t) = Aej2πfct(w∗1 + w

∗2e

j∆ϕ + w∗3ej2∆ϕ + . . .+ w∗Ne

j(N−1)∆ϕ)=

= Aej2πfct(w∗1 + w

∗2e

j2π dλsin θ + w∗3e

j2π2 dλsin θ + . . .+ w∗Ne

j2π(N−1) dλsin θ)=

= Aej2πfctF (θ)

where F (θ) is referred to as the array factor or the array pattern. Conjuctions are

taken to obtain a regular scalar product in (3.3). Let us introduce the weight vector

3.1. UNIFORM LINEAR ARRAY (ULA) 23

as

wT = [w1, w2, . . . , wN ]

and the array propagation vector as

vT =[1, ej

2πλd sin θ, ej

2πλ2d sin θ, . . . ej

2πλ(N−1)d sin θ

](3.2)

Now the array factor may be written in the form

F (θ) = wHv (3.3)

and it has the interpretation of far field radiation array pattern. We can steer the

array pattern through the weight vector v, a ULA is optimally steered towards the

angle θ0 if the weight is in the form

wT =[1, ej

2πλd sin θ0, ej

2πλ2d sin θ0, . . . ej

2πλ(N−1)d sin θ0

](3.4)

Using (3.4), the pattern peak will appear at the angle θ0:

F (θ0) =[1, e−j

2πλd sin θ0 , e−j

2πλ2d sin θ0 , . . . e−j

2πλ(N−1)d sin θ0

]

1

ej2πλd sin θ0

...

ej2πλ(N−1)d sin θ0

=

= N

3.1.1 Directional Ambiguity

Note that a ULA consisting of isotropic antennas steered towards θ0 will have addi-

tional pattern maximum at π − θ0. Indeed,

sin θ0 = sin (π − θ0)

thus using π − θ0 instead of θ0 in (3.4) will effect

F (θ0) = F (π − θ0) (3.5)

which can be observed for instance in Figures 3.3 and 3.4.


3.1.2 Example of Patterns

ULA patterns F (θ) with N ∈ {2, 4, 8}, d = λ2, θ0 = π/6, β = 0 are shown in Figures

3.3, 3.4 and 3.5. The absolute |F (θ)| values are presented as polar plots as well as

in the form

10 log(|F (θ)|2 /maxθ|F (θ)|2) = 10 log(|F (θ)|2 /N2) = 20 log(|F (θ)| /N)

in rectangular coordinates. The phases of the patterns are shown as arg {F (θ)}plots. Thin straight lines indicate values of θ0.

-100 0 100-50

-40

-30

-20

-10

0

θ [°]

|F|/m

ax(|

F|)

[dB

]

-100 0 100

-3

-2

-1

0

1

2

3

θ [°]

arg

(F)

[rad

]

Figure 3.3: Example of ULA pattern with N = 2, θ0 = π/6, β = 0.

3.1.3 Element Spacing

In most cases the element spacing d = λ2is used. If the distances between antennas

are larger, additional main lobes called the grating lobes are observed. Patterns

computed for N = 4, θ0 = π/6 and four different values of d ∈ {λ/4, λ/2, λ, 2λ} areshown in figures 3.6 - 3.9. Note the value of d is a trade-off between the angular

width of the main lobe and the number of grating lobes. The choice d = λ2is

3.1. UNIFORM LINEAR ARRAY (ULA) 25

-100 0 100-50

-40

-30

-20

-10

0

θ [°]

|F|/m

ax(|

F|)

[dB

]

-100 0 100

-3

-2

-1

0

1

2

3

θ [°]

arg

(F)

[rad

]


optimal in the meaning it gives the narrowest main lobes if the smallest number of

main lobes including grating lobes (equal 2) is assumed.

3.1.4 Directivity and Gain

The array factor F (θ) describes how the complex amplitude of the radiated wave

changes around the array. If each element in a ULA has directivity D(k) = D(θ)

and gain G(k) = G(θ) then the array gain is

DULA(θ) = |F (θ)|2D(θ)

GULA(θ) = |F (θ)|2G(θ)

If ULA consists of isotropic elements, the maximum array gain equals

GULA = GULA(θ0) = |F (θ0)|2 = N2 (3.6)


-100 0 100-50

-40

-30

-20

-10

0

θ [°]

|F|/m

ax(|

F|)

[dB

]

-100 0 100

-3

-2

-1

0

1

2

3

θ [°]

arg

(F)

[ra

d]


3.2 Principle of Pattern Multiplication

So far examples of arrays with isotropic elements have been presented. However,

more accurate results can be obtained with the assumption that the elements are

non-isotropic and have patterns f(θ). Then the total array pattern results from the

principle of pattern multiplication:

K(θ) = f(θ)F (θ) (3.7)

This principle is also useful for planar array calculations, where we can use the 3-D

version:

K(θ, φ) = f(θ, φ)F (θ, φ) (3.8)

3.3 Rectangular Planar Array

A rectangular planar array consists of Nx×Ny isotropic elements distributed over a

rectangular grid with element spacing dx and dy (Figure 3.10). In order to find the

array pattern we consider the rectangular array as a linear array of linear arrays.

3.3. RECTANGULAR PLANAR ARRAY 27

-100 0 100-50

-40

-30

-20

-10

0

θ [°]

|F|/m

ax(|

F|)

[dB

]

Figure 3.6: Example of influence of ULA element spacing on its directional charac-

teristic, d = λ/4, N = 4, θ0 = π/6, β = 0.

-100 0 100-50

-40

-30

-20

-10

0

θ [°]

|F|/m

ax(|

F|)

[dB

]

Figure 3.7: Example of influence of ULA element spacing on its directional charac-

teristic, d = λ/2, N = 4, θ0 = π/6, β = 0.

We assume that the arrays parallel to x-axis are ULAs with isotropic elements.

According to (3.3), the array factors of them will take the form

Fx(θ) = wHx vx

where

vx =[1, ej

2πλdx sin θ, ej

2πλ2dx sin θ, . . . ej

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