Thesis

Submitted in partial fulfilment of the requirements of

BITS C421T/422T Thesis

BY

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI

Under the Supervision of

Asst. Professor, School of Computer Science & Statistics

AT

Trinity College Dublin, College Green, Dublin 2

December 2012

Submitted in partial fulfilment of the requirements of

BITS C421T/422T Thesis

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI

Under the Supervision of

Asst. Professor, School of Computer Science & Statistics

AT

Trinity College Dublin, College Green, Dublin 2

(August - December 2012)

Trinity College Dublin, College Green, Dublin 2

CERTIFICATE This is to certify that the Thesis entitled “Calculating Electromagnetic Field Coverage over Terrain using an Integral Equation Method in order to enable Coexistence in Cognitive Radio” is a bonafide work of KARTIC BHARGAV K.R, ID No. 2009A3TS170P in partial fulfilment of the requirement of BITS C421T/422T Thesis embodies the work done by him under my guidance & supervision at the School of Computer Science & Statistics, Trinity College Dublin from 02/08/2012 to 08/12/2012.

Date: Signature of the Supervisor Name

Designation

ACKNOWLEDGEMENTS

I am deeply indebted to my Thesis supervisor and mentor Dr. Eamonn O’Nuallain. Without his expert

guidance and support, no part of this beautiful venture would have been possible. The lessons

imparted and knowledge gained were priceless and meant more than just an academic programme.

Needless to say I am confident that these sparks have kindled a powerful flame of commitment and

dedication.

I sincerely thank Prof. Jeremy Jones, Head of SCSS for well coordinating the Thesis Programme and

for aiding the project to develop by equipping it with the necessary fuel and mileage for it to

proceed in the right direction.

I also thank Dr. Hitesh Tiwari of the School of Computer Science & Statistics for having agreed to set

aside his valuable time to tutor me.

I express my gratitude to the Administration, Treasurers’ Office and the Management of SCSS for

promptly helping me through various formalities and paperwork.

I would also like to extend my heartfelt thanks to all the people associated, directly or indirectly with

this project for their valuable suggestions and constant motivation throughout the project.

Never the least, come my alma mater(s) BITS Pilani and Trinity College Dublin which gave me such a

wonderful opportunity and a memorable life experience.

Kartic Bhargav K.R

Thesis Abstract

Thesis Title: Calculating Electromagnetic Field Coverage over Terrain using an Integral

Equation Method in order to enable Coexistence in Cognitive Radio.

Supervisor: Dr. Eamonn O’Nuallain

Semester: First

Name of Student: Kartic Bhargav K.R ID No: 2009A3TS170P

Abstract

Basic Objective: To calculate the Electromagnetic Field coverage over terrain using a

Propagation Modelling based Electric Field Integral Equation (EFIE) Method and its variants

in order to enable coexistence in Cognitive Radio.

Previous methods of computing electromagnetic field coverage use Path-loss methods and

Ray–Tracing. Both of these however are either too simple or are computationally too

intensive. Initially, a glance through the history and background of Cognitive Radio

Technology is done. Following this, an appreciation of radio wave propagation and Radio

Environment Mapping is given as it applies to Cognitive Radio. Also a study into the

different existing methods of localization and position awareness in Cognitive Radio is done.

Next, the Electric Field Integral Equation Method is implemented for rural and urban profiles

taking into account forward scattering. Then, a reference Solution is generated for the EFIE

using Gauss-Jordan Elimination & LU Decomposition. Finally, both forward and backward

scattering were taken into account in order to investigate the Electromagnetic Field

Coverage on the German profile using the standard values of frequency of propagation and

transmitter height.

Table of Contents

Thesis Abstract 4

Introduction 6

1. History & Background of Cognitive Radio Technology 7

2. Cognitive Techniques - Position Awareness 9

2.1 Global Position Awareness (GPS) 9

2.2 Time of Arrival (ToA) 10

2.3 Time Difference of Arrival (TDoA) 10

2.4 Angle Of Arrival (AoA) 10

2.5 Very high frequency Omnidirectional Ranging (VOR) 11

2.6 Received Signal Strength (RSS) 11

3. Network Support - REM 12

4. The EFIE Method (Forward Scattering) 16

4.1 Synopsis of the EFIE 16

4.2 Program Implementation 18

4.3 Testing and Observations 18

4.4 Danish Profile Testing 23

5. The Reference Solution Generation 24

6. The Forward Backward Solution 26

6.1 Background Study of the EFIE Solution with Backward Sweep 26

6.2 Programming Methodology 27

7. Conclusion 28

8. Future Scope for Extension 29

9. Bibliography/ References 30

INTRODUCTION

Cognitive Radio (CR) is a radio technology that refers to the ability of a radio

device to sense/learn the communication parameters of its environment and to adapt its

transmissions accordingly. The ability of a radio device to do this with sufficient

sophistication will enable such devices to transmit in underutilized licensed bands without

affecting the communications of the licensee. The Shared Spectrum Company, who famously

measured over 80% underutilization of the spectrum (30-2900MHz) in New York during the

Republican Convention in 2004 and dispelled the myth that the spectrum is ‘crowded’, has

measured similar underutilization in other locations since then.

The value of CR technology is enormous since it opens up large portions of the

valuable communications spectrum for use by such devices – much of it with good

propagation characteristics. CR technology will enable the continuing worldwide exponential

growth and innovation in wireless communications. It is a technology currently in its nascent

stage with the FCC very recently making available a 16MHz portion of the analogue TV

spectrum at 700Mz for, among other purposes, CR. Though there is currently a fast growing

body of literature on the topic it is currently somewhat speculative and consensus on how

technical challenges relating to the deployment of CR ought to be addressed has not been

reached though the current draft IEEE 802.11 WRAN standard and the recent FCC auction

has served to bring these issues into focus.

There are however specific technical challenges that must be overcome for CR to be

feasible. Chief among these is the ability of the cognitive radio to adapt its transmissions

with sufficient agility so as not to adversely affect the communications if the incumbent

licensees or Primary Users (PUs). There are a number of proposals which aim to detect PU

transmission even at very low power and on that basis avoid CR transmission in that band

(matched filter detection, cyclostationary feature detection etc.). Apart from adding

complexity to the cognitive device however, none have explicitly solved the ‘Hidden Node’

problem. This is the presence of a PU receiver in the region covered by the CR transmission.

The CR not has detected the PU signal because of its low power. The result is unwanted

interference at the PU receiver.

The ‘Hidden Node’ problem must be overcome to guarantee non-interference with

PU signals. Furthermore, the chosen link must be stable for effective CR communications.

This requires a means with which to predict link stability based on spectrum usage patterns

such that the scenario of the CR initiating transmission only to be shortly afterward forced to

terminate due to the sudden presence of a PU signal is avoided. It is proposed to address the

‘Hidden Node’ problem through Radio Environment Mapping (REM).

1. History & Background of Cognitive Radio Technology

A Smart Radio should have the ability to think for itself. More like predicting what

the user needs and providing for it without him explicitly asking for it. With conservation of

spectrum becoming a national priority, there arises a need for devices that can efficiently

optimize Spectrum Management. In addition to this, the device should also be able to

perform beneficial tasks that aid the user and should be able to interface with a wide variety

of networks thereby interacting with them in their preferred protocols. Thus a Cognitive

Radio, an SDR in its advanced stage – is basically a combination of many pagers, PDAs, cell

phones and various other present-day gadgets.

Now, the progression of the Basic SDR onto the Cognitive Radio can be visualized to consist

of the development of various threads such as improvement in radio communication

performance by the semiconductor industry, advancement in DSP techniques that replaced

the conventional analog functions (implemented with large discrete components) with

digital functions (implemented in Silicon) and of course, the machine learning and related

methods for improved machine behaviour.

A basic SDR includes an RF-front end, a modem, a cryptographic security function and the

application end. In order to allow the radio to provide network services and to be connected

with the local Ethernet, usually support for the network devices is provided on the plain text

side or the modem side of the radio. The modem on the other hand, is responsible for

processing the received signal or synthesizing the transmitted signal on a full-duplex radio.

The computational processing resources in an SDR usually consist of the GPPs, DSPs and

FPGAs. While speech & video applications run on a DSP processor, text and web browsing

are supported typically by the GPP processor. FPGAs on the other hand are now capable of

providing tremendous amounts of multiply accumulating operations on a single chip. By

defining the on-chip interconnect of many gates, more than 100 multiply accumulators are

arranged to process frequencies of more than 200MHz. All these computational resources

demand significant amount of off-chip memory.

Common Measurements such as the SNR, frequency offset, timing offset, or equaliser taps

can be read by Java reflection. By examining these radio properties, the receiver can

determine what changes at the transmitter will improve the important objectives of

communication (like battery life, interference etc). From the Java reflection, the receiver

formulates a message onto the reverse link and multiplexes it on the channel and observes if

the transmitter gives an improved performance after making the changes.

Smart Antennas and efficient spectrum management are other essential qualities of a

cognitive radio. A smart antenna basically tells a smart radio what its key capabilities are. A

smart transmit antenna can form a beam to focus the transmitted energy in the direction of

the intended receiver while a smart receive antenna can synthesize a main lobe in the

appropriate direction of the transmitter as well as synthesize a deep null in the direction of

interfering transmitters thereby enabling coexistence.

2. Cognitive Techniques - Position Awareness

Position and time are essential elements to a Cognitive radio. From these, a radio can

1. Calculate the Antenna Pointing angle that best connects to another member of the

network.

2. Precisely Place a transmit packet in the air at the right instant so that it is received by a

node of another network with minimum interference using minimal energy (short

hops) and low latency (directional propagation).

3. Guide the user in his daily tasks to achieve his objectives.

Furthermore, from position and time, the velocity and acceleration can be inferred

too, giving the radio some more idea about its environment. Applications such as spatially

aware routing, boundary aware policy deployment, spatially variant advertisement and space

& time dependent scheduling of tasks are enabled by the Geolocation technologies. Some of

the widely known radio geolocation services are the GPS, VOR (VHF Omnidirectional ranging)

transmitters used by aircrafts, geolocation by WLAN IP Address and more recently TV

broadcasts for frequency, position and time.

From the geolocation knowledge the radio users would be able to:

flirt or reject flirtation

recognize when someone nearby is either desirable to meet or should be avoided

recognize individuals with common or special interests who are nearby

identify individuals with common or special interests who are nearby

identify individuals with limited time budgets

identify released criminals who might pose a serious threat to the environment

2.1 Global Position Awareness (GPS)

The GPS System is divided into 3 segments – space, control and user. In the

space segment, there are 24 active GPS satellites evenly distributed in 6 orbital planes (with

60-degree separation between each of the four satellites in each plane) and having an orbital

period of 12 hours. An LOS view of 4 or more satellites is needed to process the signals and

calculate location. Ground tracking stations are positioned worldwide in the Control segment

to monitor and operate the constellation of GPS satellites. The GPS receivers and their

operators form the user segment. The receivers process the signals from four or more

satellites into 3-D position and time.

The GPS receiver correlates the known coarse acquisition spreading codes (which are very

short and can be generated or stored in memory) from the received signal of each of the GPS

satellites. Though each satellite uses a different spreading code, when the receiver has a peak

correlation, it knows which satellite sent the signal. The full power signal after dispreading is

tracked using a PLL and the 50Hz navigation message is demodulated from each satellite. ToA

information is extracted when the correlation peak is measured. Given the ToA information

and the GPS time, the range to each satellite in view can be estimated and the intersection of

multiple range spheres determines where the receiver is located. The positional estimates are

in ECF (Earth Centred fixed) Coordinates which are then converted to latitude, longitude and

height. The position n accuracy can be improved by employing differential GPS.

2.2 Time of Arrival (ToA)

The ToA approach is centred on the ability to time tag a transmitted signal and

measure the time to propagate to the receiver at the speed of light. This time, assuming LOS

propagation is a direct measure of the propagation distance. This provides a receiver with a

iso-range sphere for a given transmitted and received signal. With a set of four receivers, using

the intersection of multiple iso-range spheres, the transmitter’s location can be estimated. A

similar method goes to locate the position of a receiver with time-tagged transmitted signals

from four different transmitters.

2.3 Time Difference of Arrival (TDoA)

The ability to measure the time difference between the receptions of the same signal

at two different locations leads us to use the TDoA approach. Again, propagation time,

at the speed of light is assumed to provide a direct measure of the LOS propagation distance.

The constant time difference recorded provides a hyperboloid surface with the foci at the two

receivers. Then, with the intersection of multiple iso-range hyperboloids (atleast three pairs)

constructed from multiple pairs of receivers at known locations, the location of the transmitter

can be determined. Other places where the TDoA approach can be extended include the

LORAN, TV Broadcast etc.

2.4 Angle Of Arrival (AoA)

The AoA Approach requires an antenna array at the receivers. Multiple

receivers estimate the AoA of a signal. Combining the bearing to the signal with the known

location of multiple receivers yields an intersection with the transmitter.

2.5 Very high frequency Omnidirectional Ranging (VOR)

Aircrafts navigation is aided by their transmitters transmitting an AM signal through a

series of antennas located sequentially in a circle. The energy is swept electronically such that

it introduces a FM Doppler onto each. Thus each receiver antenna perceives the phase angle

as that uniquely relative to it and a further conversion is done by the VOR receivers. By

locating 2 or more such transmitters, the receiver estimates its location.

2.6 Received Signal Strength (RSS)

If the transmitted power is accurately known, the patterns of the transmitter and

receiver gain are also known accurately and hence the receiver is also able to measure the

RSS. With this a propagation model can be created where the distance to the transmitter can

be estimated from the RSS value measured. The next part of the location approach, similar to

the ToA uses the intersection of four iso-range spheres to determine the exact positioning of

the transmitter. The physical environment is a key factor to the realistic channel models which

take into account terrain, foliage and building. The setting may also be a lookup table as a

function of rural, suburban or urban environments and frequency.

3. Network Support - REM

Network Support is a crucial area for the development of cognitive radio since the

requirements on CR user equipment could be significantly relaxed as many computation

intensive functions can be realised at the network side itself. Also, network support is very

important to the evolution of wireless communications from the legacy radio to the

cognitive radio. The radio environment map (REM) is essentially an integrated

spatiotemporal database with an abstraction of real world radio scenarios. It characterizes

the radio environment in multiple domains including geographical features, regulations,

policy, RF emissions, radio equipment capability profile etc.

The network support is divided on basis of function into internal and external network

support. While the internal network refers to the radio network with which the CR is

associated, external network refers to other outside networks (which can be a legacy

network or other cognitive radio networks) that can provide meaningful knowledge to aid

the functioning of the cognitive radio. Also this network support can be realised through a

global or a local REM. The global REM maintained at the network level keeps an overview of

the radio environment while the local REMs maintained at the users’ terminal equipments

present more specific views thereby reducing the memory footprint and the communication

overload. The global and local REMs may also exchange information in a timely manner so as

to keep the database at different entities current.

The REM can provide both current and historic radio environment information, so that most

cognitive functionalities can be realised in a cost-efficient way. For example, by leveraging

the REM, the Cognitive Radio can conduct spectrum sensing with prior knowledge rather

than blindly scanning the whole spectrum. By combining reasoning and decision making

with the data mining in an REM, network intelligence directly enables cognitive capabilities

for its network nodes irrespective of whether the subscriber radios are cognitive or not.

The basic techniques to support an REM include database design and management,

database transactions (query, search, update etc.) and data mining. In order to implement

and exploit the REM, various technologies must be employed such as AI, detection and

estimation, pattern classification, cross-layer optimization, database management and data

mining, site-specific propagation prediction and network based ontology. Radio propagation

simulation tools too can predict many important parameters such as path loss, SINR.

Compared to the empirical channel model-based prediction, the advanced site specific radio

propagation techniques and software tools using 3-D terrain maps have been successfully

employed. This makes it possible to embed several contours on the REM such as the service

contour, the blind zone, the interference region, which will enable cognitive radios to make

decisions and adaptations that will overcome most common user complaints.

Situation Awareness (SA) is of utmost importance to cognitive radios. By being

aware of their situations, the radios observe the environment, make in situ decisions

according to their observations, anticipations and experiences; and then execute intelligent

adaptations to reach their goals. They thereby evolve by a spiral leaning process – also called

as the cognition cycle. Thus SA means that the radio knows its current scenario, intent of the

user and the regulations to which it must comply. Thus SA may include the following:

Location awareness

Geographical environment awareness

RF environment and waveform awareness

Mobility and trajectory awareness

Power supply and energy awareness

Regulations and Policy Awareness

Capability Awareness

Mission, context and background awareness

Priority awareness

Language awareness

Past Experience Awareness

A cognitive radio can obtain SA through

Direct Observation

Inference from Network support

Analysis of local terrain propagation models combined with existing database

structures defining known communication systems.

With channel awareness, planning becomes easy for a cognitive radio. With the awareness

of fading and shadowing characteristics, cognitive radio may adopt the appropriate

waveform to adapt or take advantage of propagation characteristics. Or in a multipath

environment, a CR can choose to apply its MIMO techniques to improve performance. A

simple radio with limited cognition capability can become more capable by leveraging REM-

based network support.

An REM based network support fits into the core of the CR functional architecture

and is independent from the specific network topology. Also it is always compatible with

hybrid node technology and intelligence. The centralized global REM can pay an important

role in many infrastructure based radio systems, such as the IEEE 802.22 – Wireless Regional

Area Network (composed of WRAN Base Stations, repeaters and Consumer premise

equipment). With an REM maintained, the WRAN BS can know the antenna height, transmit

power, local terrain, the forbidden part of the spectrum meant for public safety use etc.

Local REMs can be used in ad hoc mesh networks that consist of cognitive radios. By sharing

and exchanging the local REMs, cognitive radios may learn to match the right routing

protocol, either proactively or reactively. Master nodes may be selected to be responsible

for collecting the distributed local REMs and combining them into a complete REM for the

network. Such a complete map can be accessed by each individual node, in a role similar to

the routing table for an ad hoc network.

Essentially the REM is a database that stores information utilized in the decision process of a

cognitive network. However, various elements including the learning, reasoning and

decision-making algorithms are necessary to work in conjunction to create the network. This

reasoning, data mining and query capability that can furnish information for the REM is

called the self-informing system (SIS).Decision making outside the SIS is the key to

integrating heterogeneous networks or even dissimilar radios within a homogeneous

network. Given the information produced by the SIS, a radio with its own decision making

capability can make decisions relevant to the radio and/or the network capabilities and the

supporting application. Even for non-cognitive radios, a cognitive network can be achieved

by interfacing the SIS with the network radio management system.

Complicated learning and reasoning techniques are practically implemented on the network

rather than on an individual cognitive radio. Data mining can be used for extracting hidden

information and for predicting future events. Two basic optimization approaches that are

employed to optimize complex parameters are:

The Classical optimization method based on the properties of the objective function.

These include the cyclic coordinate method, steepest descent method and the quasi-

Newton and conjugate-gradient method.

Heuristic Optimization which includes genetic algorithm, simulated annealing, ant

colony optimization, Tabu search, neural network etc.

Hidden Markov Models (HMMs) can be used for radio scene classification, case recognition

and for making meaningful predictions based on past experience captured into the training

data. AI techniques are useful to fully exploit the REM to obtain SA and to enable reasoning,

decision making, and self learning. Thus as a vehicle to providing network support to

cognitive radios, REM is proposed to be an integrated database consisting of multi domain

information such as geographical features, available services, spectral regulations, locations

& activities of radios, policies of the user and/or service provider and past experience.

An REM can be exploited by a cognitive engine to enhance or achieve most cognitive

functionalities such as SA, reasoning, learning, planning and decision support. Leveraging

both internal and external network support through global and local REMs presents a

sensible way to implement Cognitive radios in a reliable, flexible, cost-effective way.

Considering the dynamic nature of spectral regulation and policy making an REM based

cognitive radio is flexible and future proof since it allows the regulators or service provider

to modify their rules/policies simply by updating their REMs accordingly.

4. The EFIE Method (Forward Scattering)

4.1 Synopsis of the EFIE

The Integral Equation based method in question is also referred to as the Field

Extrapolation Method (FEXM) [3]. The FEXM yields values for the large-scale fading signal

(incl. path-loss) – the small-scale fading signal must be treated separately. The problem is

treated as two-dimensional TMz, the surface is taken to be a perfect electrical conductor

(PEC) and forward scattering is assumed – that is, all radiation is taken to propagate away

from the transmitter. The latter two assumptions are justifiable in the case of grazing

incidence of transmitter radiation which is predominantly the case for the terrain profiles

examined here. All are simplifying and not limiting assumptions.

The surface is impinged by a monochromatic TMZ polarized cylindrical wave of wave number

β emanating from an infinite, unit current carrying wire of negligible cross-section, placed a

distance above and transverse to the terrain profile. A time variation of e jwt

is assumed and

suppressed. An electric current J is induced on the surface, which satisfies the Electric Field

Integral Equation (EFIE):

E(r) = βη/4 ∫s J(r’)Ho (2) β(|r-r’|)dr’

Here, r and r' are vectors whose end-points are respectively the scattering and receiving

points s Є S. E(r) is the source electric field incident on the surface at the point given by r. η is

the wave impedance of the medium through which the radiation propagates and Ho (2) is a

zero order Hankel function of the second kind which is the Green’s function for the problem.

The surface is discretized into N equal sized sampling intervals of length Δs with centre-

points indicated by the vectors ri and rj depending on whether they are scattering or

receiving intervals respectively. Using the Method of Moments with unit pulse basis

functions and Dirac delta weighting functions we get the following matrix relation:

E = ZJ

where

Ei = E(ri)

(1)

(2)

Jj = J(rj)

E and J are column vectors of length N. Z, known as the impedance matrix, is N x N and

symmetric. The elements in the strictly lower triangle of Z correspond to forward scattering

and those in the strictly upper triangle to backscattering. The diagonal elements correspond

to the self interaction of the sampling intervals. On the assumption of forward scattering,

which is equivalent to setting the strictly upper triangular elements of Z to zero, J is

determined by forward substitution:

The order of complexity of determining J is O(N 2). The total field at points above the surface

is then the sum of the field from the source and the field scattered by the surface. The

surface is divided into groups each containing M sampling intervals. There are then N /M

such groups.

The following is assumed a-priori:

a) The surface current envelope over a group (e.g.Rayleigh distributed)

b) The phase shift associated with the surface current for each group can be forced to zero.

Equation (3) can then be manipulated such that the following equation ensues:

where

This quantity is approximately constant for all groups and consequently needs only to be

evaluated once thereby obviating the need for time-consuming group-specific aggregation

(3)

(4)

or disaggregation stages. Equation (4) takes the form of (3) and use of the latter over the

former results in a reduction in the complexity from O (N) 2 to O (N /M) 2 and a reduction in

memory requirements from O(N) to O(N/M) .

4.2 Program Implementation

The above method was programmed in C in several progressive steps. Considering

an appropriately hilly semi-urban German profile, the accurately recorded values of the

terrain coordinates were stored & read from the file X.04. The whole surface terrain was

divided into several individual strips (referred to as Line subs in the program). Each of these

were of width DeltaX (= Lambda/4).

Initially affixing a seed value for the surface current J at the location of the transmitter, the

successive surface currents J were accordingly calculated for each strip for the total of N Line

Subdivisions. This was accordingly done by forward substitution also taking into account the

surface currents induced by the transmitter. Once the surface currents were calculated for

all the points on the terrain, the Electric Field E for points at a uniform height of 2.4m from

the terrain was now calculated. Both J and E across the terrain were individually plotted.

Primarily, the program was implemented for a transmitter placed at a height of 52m from

the ground (which resulted in a total of 442m from sea-level) and for a wave frequency of

970 MHz. The results were matched to the German.exact plot.

4.3 Testing and Observations

On the given semi-urban German Profile, The Electric Field Coverage initially due to

forward scattering alone was plotted for different variations of the Transmitter height (20m,

52m, 80m and 140m above the starting point of the terrain) and the Propagation Frequency

(50MHz, 470MHz, 970MHz). After execution of each of these programs, the results of E & J

were computed, stored and accordingly plotted.

The plots of Electric Field coverage (E) variation across the terrain for different parameters

are as shown:

Fig. 1,2,3,4 || Propagation Frequency: 50MHz|| Transmitter Heights – 410, 442, 470, 530m|| Semi-Urban FS

Fig. 5,6,7,8|| Propagation Frequency: 470MHz|| Transmitter Heights – 410, 442, 470, 530m|| Semi-Urban FS

Fig. 9,10,11,12||Propagation Frequency: 970MHz||Transmitter Heights – 410, 442, 470, 530m||Semi-Urban FS

Figure 13. German.Exact

The following results were inferred from the plots after comparing with the original

German.exact plot which had the transmitter at 52m with 970MHz propagation frequency.

Keeping the transmitter height constant, varying the frequency resulted in a directly

proportional variance in fading. Compared to 50MHz, the small scale fading at 970MHz was

considerably higher which is expected since the wavelength of the latter is much lesser and

hence the wave would certainly encounter much more obstacles in its path with dimensions

comparable to its own λ and hence more reflectors => More constructive and destructive

interference. In these cases of larger frequencies the Doppler spread of the channel

becomes relatively greater as the coherence path becomes small compared to the delay

constraint. Different paths have different Doppler shifts and hence overall, a large Doppler

spread. The greater rate of fading at higher frequencies can also be justified by the presence

of lower diffraction. At lower frequencies, since there is higher diffraction, the incident wave

bends around corners rather than being reflected alone. This in turn leads to comparatively

lesser reflection and hence lesser interference => lesser fading.

Fig.13|| Propagation Frequency: 970MHz|| Transmitter Height – 442|| German.Exact|| Semi-Urban FS

However the rate of large scale fading/ shadowing over the parts of the terrain remains

nearly the same at all 3 frequencies. Also an increase in frequency does show a considerable

increase in the initial Electric Field Strength – this might be the constructive interference due

to the presence of a large number of reflectors at high frequencies.

With the frequency remaining constant, on increasing the transmitter height, the

rate of small scale fading again showed an increase at the initial region of 500 – 1000m.

Hence in this region, the plot is comparatively much smoother at the 20m height, since the

field recorded at the receivers (at a height of 10.4m above the terrain throughout) would be

primarily due to the directly incident waves from the source rather than due to interference

from reflecting surfaces. Now, observing the nature of the terrain can lead us to infer that at

a low height of 20m, the amount of reflection is relatively lesser than at 140m. Moreover,

uniformly in all plots there exist specific regions around 1.8 to 2.0 km & 2.8 to 3.1 km on the

terrain where the field strength shows a dip. These can be concluded at apparent points of

high destructive interference thereby resulting in Electric Field Nulls.

4.4 Danish Profile Testing

The EFIE program under consideration was also tested for the Danish Profile. A rural

terrain sample belonging to the region of Hjorring in Denmark was focussed for analysis.

However there were a few marked differences to be applied to this profile whose values

were stored and accordingly read from hjorring.dhm. The transmitter was positioned at a

height of 10.4m initially (as contrasted to the 52m in the case of German profile). The Step

size was taken to be 50m with 220 steps in total for hence a total of 11 Km of terrain.

Otherwise proceeding in a similar manner, the program was tested and the results were

compared and contrasted with the actual measurements (recorded with the aid of naval

instruments in the file mhjo970.10m). The results were found to closely resemble the

measured solution.

5. The Reference Solution Generation

With the German and Danish Profiles analysed by the EFIE method, the next progressive

step was to generate a reference solution to the given problems in question by highly

reliable methods such as the Gauss Jordan and LU Decomposition. The sole purpose of

producing the reference solution was to ensure consistency and accuracy among all the

ingenious methods to follow like the forward – backward, the fast EFIE etc. This was due to

the simple fact that the Gauss Jordan/ The LU Decomposition generated the required

solution from first principles and were certainly reliable though slow. As a result, the

solution obtained could only be preserved for cross-checking & validation purposes but not

for testing the terrain with varying parameters.

Both Gauss Jordan and the LU Decomposition followed the basic steps for the calculation of

the surface current J by employing matrix inversion in the equation E = Z*J. While gauss

Jordan applied it directly, the LU decomposition split the J matrix down into forward (the

upper triangular matrix), backward (the lower triangular matrix) and the self terms (along

the main diagonal). Naturally the LU decomposition resulted in a relatively faster, yet

accurate solution. On comparing, the solutions yielded by both the methods were found to

be exceedingly similar due to the employment of the same basic root method.

The solution for the German Profile at a wave frequency of 970MHz and for a transmitter

height of 442m is as shown below. The solution when plotted along with the result of EFIE

method is shown next. As can be observed, both the plots tend to match in most of the

circumstances, thereby validating the existence and effectiveness of the EFIE method. Time

of execution is a crucial point of difference here. While the LU decomposition takes nearly 4

hours to run, the EFIE plots almost the same solution within 45 minutes.

Figure 14. Propagation modelling of the semi-urban profile at 970MHz, 442m with LU Decomposition

6. The Forward Backward Solution

6.1 Background Study of the EFIE Solution with Backward Sweep

The highly oscillatory nature of the surface current necessitates one to adopt a high

sample rate (typically around ten basis functions per wavelength) and means that for

problems of practical size it becomes impossible to store, let alone invert, the

impedance matrix Z. Instead, the matrix equation is typically solved using an iterative

procedure such as the method of conjugate gradients.

Recently, there has been much interest in the concept of physically inspired iterative

solvers. These solve for the unknown basis function amplitudes I in a manner that

attempts to mimic the physical processes that create the current and can often yield

useful results in a reduced number of iterations. Specifically, a current marching

algorithm involves decomposing the scatterer into M sub-regions and “marching” a

solution for the current along the scatterer surface from sub region to sub region. The

solution at processed sub regions is used to set up the problem to be solved at the next

sub region, and so on. Mathematically, the algorithm involves decomposing the Z matrix

into blocks, the Z ij block containing the interactions between basis functions residing in

the ith and jth sub regions on the scatterer.

Each iteration of a forward/backward algorithm involves solving two equations. The first

equation is solved for the sub regions i = 1. . .M in turn and is termed the forward sweep

where V i and I i are the appropriate sub vectors of V and I, respectively. The above

equation is a matrix equation for the kth estimate of the currents on sub region i. Note

that the right-hand side incident fields have been modified by including the effects of

the most up to date current estimates available for the other subregions. As it involves a

matrix of relatively low order (3) can be efficiently solved using a conjugate gradient

solver.

The second equation is solved for i = M . . . 1 in turn and corresponds to a backward

sweep:

Being of low order, the above equation can be efficiently solved using a conjugate

gradient solver. For the purposes of clarity in discussing the presented numerical results

we deem an iteration to be one complete forward sweep followed by a complete

backward sweep.

6.2 Programming Methodology

Once the reference solution was generated, the next task at hand was to generate

the EFIE solution including Backward Sweep also. For this purpose, buffer regions were

considered at the beginning and the end of the terrain profile and the forward backward

method was analysed.

The buffer regions were taken to be of 200m in length. The program was proceeded

over in several consecutive sweeps first forward and then backward. The first sweep ran

forward from the transmitter to the final point of the terrain under consideration. The

2nd sweep (forward too) ran from the transmitter to the initial starting point. Next came

the first backward sweep from the final point to the transmitter followed finally by the

sweep from the starting point to the transmitter.

Figure 15. Plot of EFIE with forward-backward

Since the changes produced as a result of employing the backward sweep were very

minimal, the solution was expected to approximately resemble the solution produced

by the EFIE forward scattering program.

7. Conclusion

Initially after a brief introduction to the relevance and importance of Cognitive

Radios, a glance through the history and background of Cognitive Radio Technology was

done. This dealt with the significance and evolution of Software Defined radio (SDR).

Following this, a study into the different existing methods of localization and position

awareness in Cognitive Radio was carried out. This section gave a detailed outlook on the

importance and execution of GPS, ToA, TDoA, AoA, VOR & RSS methods of localization in

Cognitive Radio.

Also an appreciation of radio wave propagation and Radio Environment Mapping was given

as it applies to Cognitive Radio. This clearly described the importance of Situation awareness

where the radio knows its current scenario, intent of the user and the regulations to which it

must comply, hence outlining the dire need for Radios to achieve Situation Awareness.

Moving on, Radio Environment Mapping (REM) in a nutshell, is essentially an integrated

spatiotemporal database with an abstraction of real world radio scenarios. The uses of REM

as well as the various techniques to support it, the types of optimization methods and

Markov models that prove highly instrumental were also studied.

Next, the Electric Field Integral Equation Method was implemented for rural and semi-urban

profiles taking into account forward scattering alone for different wave propagation

frequencies and variations of transmitter heights. The results were contrasted relatively.

A reference Solution was generated for the EFIE using Gauss-Jordan Elimination & LU

Decomposition from first principles. The results were certainly reliable though slow and

thus, the solution obtained could only be preserved for cross-checking & validation purposes

but not for testing the terrain with varying parameters.

Finally, both forward and backward scattering were taken into account in order to

investigate the Electromagnetic Field Coverage on the German profile using the standard

values of frequency of propagation and transmitter height. For this purpose, buffer regions

were considered at the beginning and the end of the terrain profile and the forward

backward method was analysed.

To summarize, in a nutshell, the primary objective of calculating the Electromagnetic Field

coverage over rural & semi urban types of terrain in order to enable coexistence in Cognitive

Radio was done using a Propagation Modelling based Electric Field Integral Equation (EFIE)

Method and its variants.

8. Future Scope for Extension

The present working EFIE program for the forward backward sweeps can be further

extended to suit the Fast EFIE method (FEM) which has an added benefit of saving

substantial computation time thereby proving considerably more efficient. This hence can

be used to easily test different terrain profiles for various variations of the usual parameters

of transmitter height and frequency of propagation.

Since as of present, the measurements for only the Danish profile of Hjorring is available, the

Fast EFIE Method can be cast into implementation after incorporating the backward sweeps

as well. The existence and validity of such a solution can also be verified by comparing it with

its counterpart generated by the LU Decomposition/ Gauss Jordan Elimination on the same

Hjorring profile.

Testing can now be done for the urban profile of Dublin and all the methods can be now

employed with the reference solution being generated by the LU Decomposition/ Gauss

Jordan Elimination as always. All of EFIE (forward), Forward-Backward and FEM can be

readily put to use by execution to determine which suits best for an urban profile.

Accordingly modifications can be done to each of these methods to adapt to their respective

compatibilities for the urban profile.

With measurements for the semi-urban German profile and the urban Dublin profile,

significant progress can be made into establishing the Electromagnetic Field coverage across

terrain and hence accordingly individual analysis can be done into the behavioural pattern of

each propagation model. Further research would prove instrumental in minimising the

primary user interference in all three kinds of profiles in order to ultimately enable co-

existence in Cognitive Radio.

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