White Paper - Understanding Diversity

SSiiggmmaa WWiirreelleessss TTeecchhnnoollooggiieessMMccKKeeee AAvveennuuee FFiinnggllaass,,DDuubblliinn 1111.. IIrreellaannddPPhhoonnee:: ++ 335533 11 88114422005500FFaaxx:: ++ 335533 11 88114422005511EEmmaaiill:: iinnffoo@@ssiiggmmaa..iieewwwwww..ssiiggmmaawwiirreelleessss..iiee

UUNNDDEERRSSTTAANNDDIINNGG AANNDD

MMAAXXIIMMIISSIINNGG SSPPAACCEE DDIIVVEERRSSIITTYY

GGAAIINN AATT 440000 MMHHZZ

.

© Sigma Wireless Technologies Page 2 of 39 April 2001

Contents

1 INTRODUCTION .............................................................................................................................................. 4

1.1 SUBJECT OF PAPER............................................................................................................................................ 4

1.2 GENERAL INFORMATION ON DIVERSITY ........................................................................................................... 5

1.2.1 Diversity Gain Explained ........................................................................................................................ 61.2.2 Experimental Results ............................................................................................................................... 61.2.3 Different Diversity Schemes Described ................................................................................................... 71.2.4 How does Space Diversity work? ............................................................................................................ 8

2 LAND MOBILE PROPAGATION................................................................................................................... 9

2.1 A THEORETICAL MODEL FOR PATH LOSS ........................................................................................................ 9

2.1.1 Two Correct Facts in Basic Theoretical Model..................................................................................... 102.1.2 Two Weak Points in Basic Theoretical Model....................................................................................... 10

2.2 A TWO-WAVE MODEL ON FLAT GROUND ...................................................................................................... 10

2.3 OKUMURA MODEL.......................................................................................................................................... 12

2.4 EFFECTIVE ANTENNA HEIGHT ........................................................................................................................ 13

2.4.1 Non-Obstructive Propagation ............................................................................................................... 132.4.2 Reflection Points on a Non-Flat Ground............................................................................................... 14

3 FACTORS AFFECTING SPACE DIVERSITY GAIN ................................................................................ 15

3.1 GENERAL ........................................................................................................................................................ 15

3.1.1 Introducing Correlation Coefficient ...................................................................................................... 153.1.2 Correlation Coefficient Defined ............................................................................................................ 16

3.2 DEPENDENCY OF DIVERSITY GAIN ON ANTENNA ORIENTATION TO MOBILES ............................................... 16

3.3 ANTENNA HEIGHT / SEPARATION DEPENDENCY............................................................................................. 17

3.3.1 Frequency Dependence of Factor η ...................................................................................................... 193.3.2 Why Use a Correlation Coefficient of 0.7? ........................................................................................... 20

3.4 DIFFERENCE IN GAIN BETWEEN ANTENNAS.................................................................................................... 22

3.4.1 Relationship between Correlation Coefficient and Diversity Gain ....................................................... 233.4.2 Different Diversity Techniques. ............................................................................................................. 233.4.3 Measurement Results and Formulas ..................................................................................................... 24

3.5 APERTURE GAIN EXPLAINED .......................................................................................................................... 26

3.6 OTHER PHYSICAL CONSIDERATIONS............................................................................................................... 27

3.6.1 Physical Considerations in Horizontal Separation ............................................................................... 283.6.2 Effective Antenna Height ....................................................................................................................... 31

4 A PRACTICAL GUIDE TO DIVERSITY..................................................................................................... 32

4.1 APERTURE GAIN (NUMBER OF ANTENNAS) .................................................................................................... 33

4.2 ANTENNA GAIN / PATTERN DIFFERENCES ...................................................................................................... 33

4.3 ANTENNA HEIGHT AND SEPARATION.............................................................................................................. 34

4.4 ORIENTATION OF ANTENNAS TO MOBILES...................................................................................................... 36

5 PRIORITISED DIVERSITY GAIN FACTORS ........................................................................................... 37

.


Figures

FIGURE 1 - OVERVIEW OF FACTORS AFFECTING DIVERSITY GAIN........................................................................................4

FIGURE 2 - VARIABILITY OF THE SIGNAL STRENGTH COMING FROM A MOBILE TRANSMITTER OVER TIME...........................5

FIGURE 3- ILLUSTRATION OF DUAL POLARISATION DIVERSITY ...........................................................................................8

FIGURE 4 - A TWO - WAVE PROPAGATION MODEL ...........................................................................................................11

FIGURE 5 - MULTIPATH PROPAGATION ..............................................................................................................................12

FIGURE 6 - IDENTIFICATION OF SPECULAR REFLECTION POINTS: (A)MULTIPLE; (B)CASE I; (C) CASE II. ...........................14

FIGURE 7 – CHANGE OF EFFECTIVE ANTENNA HEIGHT WITH VEHICLE POSITION..............................................................15

FIGURE 8 - ANTENNA ORIENTATION AT BASE STATION.....................................................................................................17

FIGURE 9 - CORRELATION VERSUS PARAMETER η FOR TWO ANTENNAS IN DIFFERENT ORIENTATIONS ............................18

FIGURE 10 - THREE DIMENSIONAL REPRESENTATION OF CORRELATION VS PARAMETER η AT 850MHZ..........................19

FIGURE 11 - SIGNAL LEVEL DB WITH RESPECT TO RMS VALUE .......................................................................................22

FIGURE 12 - DIVERSITY GAIN FOR VARIOUS COMBINER TYPES.........................................................................................26

FIGURE 13 - ANTENNA PATTERN WHEN THREE 6DB ANTENNAS MOUNTED AT SAME HEIGHT .........................................29

FIGURE 14 - PATTERNS OF OMNI ANTENNAS ON TRIANGULAR TOWERS ...........................................................................30

FIGURE 15 – PATTERNS OF ANTENNAS ON A 600MM TOWER SPACED AT 1500MM.............................................................31

FIGURE 16 - GRAPH OF GAIN VS η FOR DIFFERENT DIVERSITY COMBINING TYPES AT 405MHZ.......................................36

Tables

TABLE 1 - DIVERSITY GAIN AS A FUNCTION OF OPERATING ENVIRONMENT .......................................................................7

TABLE 2 – ‘OPTIMUM’ SPACING VS ANTENNA HEIGHT FOR SPACE DIVERSITY AT 405MHZ ............................................20

TABLE 3 - EFFECT OF CLOSELY SPACED ANTENNAS..........................................................................................................29

TABLE 4 – INDICATIVE DIVERSITY GAIN FOR DIFFERING ANTENNA GAINS.......................................................................33

TABLE 5 – INDICATIVE GAIN (DB) FOR DIFFERENT ANTENNA HEIGHTS AND SPACING USING MAX-RATIO......................35

TABLE 6 – INDICATIVE GAIN (DB) FOR DIFFERENT ANTENNA HEIGHTS AND SPACING USING EQUAL-GAIN ....................35

TABLE 7- INDICATIVE GAIN (DB) FOR DIFFERENT VALUES OF η, FOR THE THREE DIVERSITY TYPES. ..............................35

TABLE 8 – INDICATIVE GAIN (DB) FOR VARIOUS ANGLES AT DIFFERENT ANTENNA SPACING ON 30M TOWER.................37

.


1 Introduction

1.1 Subject of Paper

The paper describes how to evaluate the level of diversity gain which can be achieved using Two

Horizontally Spaced antennas at 400MHz. It assumes that Digital PMR applications are the main area of

interest for diversity gain at this frequency. It explores the factors involved in achieving diversity gain, and

provides insight into how much of the achievable diversity gain is affected by each factor. The term aperture

gain is introduced to illustrate from an antenna designer’s perspective how different diversity schemes

operate. A model is generated from other published work to describe diversity gain in terms of antenna

height, spacing, mobile orientation and difference in antenna gains in specific directions. It notes that

antennas located at the same level can distort each other’s azimuth radiation patterns, as can towers.

The outcome of this research is a series of tables, which a systems Planning Engineer can use in a practical

manner to optimise the Coverage Plan.

Figure 1 below illustrates the results in graphical form. It lists the elements which the system designer has

control over and shows the other items considered during the course of the discussion. The item with most

effect on the final diversity gain is on the left and the one with least effect is on the right.

AntennaGain

Difference

Aperture Gain(Number ofAntennas)

Diversity Gain

CorrelationCoefficient

AntennaOrientation

Diversity Type

Factors over which SystemDesigner has Control arePresented in this colour

Factor η

EffectiveHeight

AntennaSpacing

AntennaHeight Frequency

Figure 1 - Overview of factors affecting Diversity Gain

.


1.2 General Information on Diversity

The descriptions of diversity given in this section are those given in Sigma's "Antenna System Design"

paper. Each statement is in itself correct, but the information presented here will change the emphasis placed

on the factors involved. It is presented as an evolving understanding of the subject of diversity.

Figure 2 illustrates the variability of the strength of a received signal coming from a mobile transmitter over

time into two vertically polarised antennas. Signals usually arrive at the receiver via multiple paths (see

below). This receiver diversity can be used to enhance systems performance. This is particularly useful

when the system requires talkback from low powered handheld devices. This technique ensures that the

network receives the same signal at least twice (dual receiver mode) which is then manipulated either by an

additive or a selective process to ensure a better net received signal to noise ratio.

Signal Strength In Dual Polar Antenna with Distance Travelled

-120

-100

-80

-60

-40

-20

0

Time Travelling

Sig

nal

Str

eng

th

Left Polar

Right Polar

Figure 2 - Variability of the Signal Strength coming from a mobile transmitter over time

Quoting from referencei may help to understand the complexities of propagation in the mobile radio

environment: - "Radio wave propagation in the mobile radio environment is described by dispersive multi-

path caused by reflection, diffraction and scattering. Different paths may exist between a BS and a MS due

to large distant reflectors and/or scatterers and due to scattering in the vicinity of the mobile, giving rise to a

number of partial waves arriving with different amplitudes and delays. Since the mobile will be moving, a

Doppler shift is associated with each partial wave, depending on the mobile's velocity and the angle of

incidence. The delayed and Doppler shifted partial waves interfere at the receiver causing frequency and time

selective fading on the transmitted signal."

.


The available antenna diversity options are: - Space -Vertical.

Space - Horizontal

Polarisation (Usually dual polarisation)

The principle is the same for each, in that the receiving base station has a choice of two signals on the

incoming path. The process on average yields a ‘gain’ on the receive path.

1.2.1 Diversity Gain Explained

Diversity gain only operates on the up-link (Mobile Station to Base Station). It is required because portables

usually have one watt transmit power towards the base, but bases can be up to 40-Watts back to the mobile.

The measurement test involves a mobile and a base station with special test software in it.

A typical test route is driven: the mean bit-error rate is measured at the base, using a vertically polarised

antenna of equivalent gain to the antenna under test. The route is then driven again using either two

vertically polarised antennas spaced apart, or the two halves of a cross polarised antenna (as two separate

tests) each being fed into separate receivers. The mobile transmit power is reduced in steps until the same bit

error rate is achieved at the base as was measured in the reference drive. The amount by which the power is

reduced is the equivalent Diversity Gain of the base antenna configuration chosen for the test.

1.2.2 Experimental Results

During Sigma’s initial Digital PMR antenna development work, tests were performed to determine if

diversity gain existed in the 400MHz band. From these experimental results, we know that the diversity gain

of a cross-polarised antenna in a suburban environment is about 4dB. The diversity gain of two vertically

polarised antennas horizontally spaced at 5.5 metres is about 4.5dB. We also know that in a high-density

urban environment the gains are increased by a further 1dB. In open countryside there is some small gain

improvement (over a single antenna) for both configurations. For three antenna diversity, it is possible to

assume that there is at least a 1.5dB improvement over two-antenna diversity. Thus, the diversity gain of a

particular antenna configuration will also depend on the type of environment in which it is being used.

(See also section 3 below).

Over the years most cellular operators have carried out experiments to assess the gain obtained with different

diversity schemes, some have published their results. The findings are generally similar, but never identical.

One set of results is given here ii.

.


Area Type Estimated DiversityGain with 45

Slanted Antenna

Estimated DiversityGain with Space

Diversity

Urban, Indoor 3.7 dB 5.0 dB

Urban, Outdoor 4.7 dB 3.3 dB

Suburban, Indoor 4.0 dB 3.7 dB

Suburban, Outdoor 5.7 dB 4.7 dB

Rural 2.7 dB 5.3 dB

Table 1 - Diversity Gain as a Function of Operating Environment

1.2.3 Different Diversity Schemes Described

• Horizontal space diversity requires that two antennas are separated horizontally by approximately 5.5

meters. Reducing this space reduces the gain. The final gain obtained depends on the antenna height

above surrounding terrain as well as the spacing between the antennas. This is the optimum situation

electrically, but in reality, access to the required space is limited. The greater the antenna separation, the

less likely that fades will occur in both antennas simultaneously. If optimum diversity techniques are

used in the base station, expect a minimum of 3dB diversity gain for two antennas and 4.7dB gain from

three antennas.

• Vertical space diversity can be easier to implement, but again the requirement is for approximately 10

metres vertical separation between two antennas to give the best improvement over a single antenna

(similar to that given by horizontal spacing). Most of the diversity advantage is lost at four metres. One

reason for this failure is that the coverage area of the two antenna systems is very different at this

spacing. This will cause many problems trying to balance the signal quality received at the base with that

received at the mobile / portable. Another disadvantage of this type of diversity is that the two received

signal are not the same strength at the antenna, causing a reduction in diversity gain.

• Dual-polar diversity is achieved using a single antenna structure with two sets of dipoles positioned at

+/- 45 degrees to each other. The dipoles positioned in this way typically produce 2 to 4dB better than a

single vertically polarised antenna of similar dimensions. The gain of these antennas is usually specified

as Co-Polar gain i.e. the gain measured at +/-45 Degrees. The 2 to 4dB gain improvement is relative to

this gain. If, however, you measure the antenna gain vertically polarised, it will be 3dB less than that

measured at +/-45o . The vertical space occupied by a dual polarised antenna of a given Co-Polar gain is

the same as for a vertically polarised antenna of the same gain.

.


R e dF e e d

B lu eF e e d

Figure 3- Illustration of Dual Polarisation Diversity

1.2.4 How does Space Diversity work?

To achieve diversity at least two receivers are required. These will receive signals from diverse sources -

two antennas. These antennas will provide a separate signal to each receiver but this signal comes from the

same original source, the portable / mobile (called a mobile in the following discussion), but via different

paths. These antennas will need to be positioned on a mast in a suitable position to allow them to appear as

two separate diverse sources of the same signal. The greater the distance between the antennas horizontally,

the less likely that a signal fade (received from a moving mobile) from one antenna will occur at the same

time as a signal fade from the other antenna. Thus, the diversity gain (reducing the effect of these fades)

increases as the separation increases and relies on the concept that the strength of the two signals should on

average be nearly equal. On average, if the two signal strengths are not equal, then the full diversity gain

cannot be achieved. At 900 MHz, antennas are generally regarded as being at optimum separation at 2.75

metres. At 400 MHz, this optimum is generally regarded as occurring at 5.5Metres, which is often difficult

to achieve in practical situations. This is the subject of the rest of this paper.

The correlation coefficient between the amplitude envelope of the received signals depends on the antenna

spacing. To give an adequately low coefficient (0.7), the antennas should be at the same height and spaced at

least 5.5 metres apart. In other words, the long-term correlation between the amplitude of the received

signals should be high, but the instantaneous value of the correlation should be very low. (The lowest short

term correlation coefficient achievable with two antennas is approximately 0.7, which is adequate to achieve

expected diversity gain. The lower the short-term correlation coefficient, the better the diversity gain). If

these criteria are met by the antenna system, and the receivers receive equal amplitude signals on average in

the long term, the gain achieved by two receivers over one is up to 5 dB, and by three receivers is up to 7dB.

.


2 Land Mobile Propagation

As already mentioned, the propagation mechanism of radio waves in mobile environment is a vital aspect of

system design. In mobile radio environment, there are five unique factorsiii: -

• Natural terrain configurations such as, flat ground, hills, water, mountains, valley, desert;

• Manmade structures, such as open areas, suburban and urban areas and metropolitan areas;

• Manmade noise such as automotive ignition noise and machine noise;

• Moving medium brought about by the mobility of the mobile and portable units;

• Dispersive medium causing frequency selective fading and time-delay spread.

The above five factors are made significant because the mobile antenna is close to the ground. When the

mobile antenna is between 1.5m to 3m above the ground, the signal received by the mobile unit comprises a

direct path signal and a strong reflective wave due to the closeness of the ground. These two waves, when

combined, result in the excessive path loss at the mobile reception. In addition, because the mobile antenna

is close to the manmade structures and manmade noise sources then the path losses, multi-path fading, and

interference will have profound effects.

Why is a prediction model so important? The value of the prediction model is to save manpower, cost, and

time. Before planning a radio network, selecting the base station locations for signal coverage that are

mutually interference-free is a big task. Without prediction tools, the only way is to use cut-and-try methods,

which are very costly. With an accurate prediction tool and computer manipulation we can easily pick the

optimum base station site locations.

There are very few theoretical propagation models, but there are many empirical models. We will first

illustrate two theoretical models; one will be used to illustrate dependence on antenna height, and the second

will illustrate a two-wave theory of propagation (an understanding of which is required for effective antenna

height). We will then give the Okimura model to provide a more complete picture. This will be followed by

an illustration of effective antenna height, which is needed for full consideration of diversity gain.

2.1 A Theoretical Model for Path Loss iv

This theoretical model if useful for analysing path-loss predictions and not for multi-path fading. The

equation is as follows: -

Equation 12

221

=

d

hhPr

.


where Pr is the received power from both a direct wave and a reflected wave. The height of the base antenna

is h1, and of the mobile antenna is h2, and d is the distance between the transmitting and receiving antennas.

2.1.1 Two Correct Facts in Basic Theoretical Model

1. The equation shows the path loss of 40dB/decade (∼ d-4) or 12dB/Octave. This has been verified

from experimental data.

2. The equation shows a 6dB per octave (∼ h12) for antenna height gain at the base station. Experiments

show that (in flat terrain) doubling the antenna height at the base gains 6dB. In fact there is a

relationship between base station antenna height and signal strength at receiver given as: -

Equation 21

1

1020)(h

hLogLossghtGainAntennaHei =

where h1 is the new antenna height and h1 is the Base Antenna height.

2.1.2 Two Weak Points in Basic Theoretical Model

1. The frequency or the wavelength is missing in Equation 1. However, measured data shows that the

empirical loss formula is a function of frequency as: -

Equation 3 Pr ∝∝∝∝ f -n where 2 ≤≤≤≤ n ≤≤≤≤ 3

2. The equation shows a 6 dB/octave (∼ h22) for antenna height at the mobile. This is not true. From

experimentation, for a mobile antenna height of three metres, cutting its height by one-half results in a 3dB

loss of signal.

2.2 A Two-Wave Model on Flat Ground

The received power at a mobile antenna is obtained by summing up two waves - a Direct wave and a

Reflected wave from a direct path and a reflected path, respectively, as shown in Figure 4 below.

When all the mathematics are completed on this model, we get the following formula for the received power

at the mobile: -

Equation 4

2

2

=

d

hhGGPP mb

mbtr

.


Where Pt = Transmitted Power, Gb = Gain of Cell Site Antenna; Gm = Gain Mobile Antenna; hb, hm = antenna

height of the cell site and the mobile unit respectively. Other, more sophisticated, versions of this equation

exist which vary the power to which hm is raised to take into account the different effects caused by

manmade environments immediately around the mobile. Additionally, a factor could be included to reduce

the received signal due to the total environment through which the signal propagates from the base antenna to

the mobile.

Image

d

φ1 φ2

φ1 = φ2

Reflection Point φ1 = Incident Angle φ2 = Reflected Angle

Figure 4 - A Two - Wave Propagation Model

This 4th power law is known as the plane earth propagation equation. This equation is used as the basis for

calculating received signal strength in mobile communications systems. The propagation loss is given by: -

Equation 5 L = 40 Log10 d - 20 Log10hb - 20Log10hm dB

This means that the loss increases by 40dB each time the distance is multiplied by 10 (one decade). It should

be noted that the equation is not dependent on the carrier frequency. If the surface is undulating a correction

factor, which is frequency dependent, must be included. It should be noted that significant variations may be

observed in practice.

Equation 5 gives the mean loss as a function of distance. However, it is important to realise that the radio

channel is subject to Fading. Fading occurs as a result of multi-path propagation as illustrated in Figure 5

below. There is no direct path from the base station to the mobile. Two paths are illustrated. In real

situations many such paths would exist.

.


Diffracted Wave Reflected Wave

Figure 5 - Multipath Propagation

If the phase difference between the diffracted wave and the reflected wave is a whole number of wavelengths

then the two waveforms arriving at the mobile will reinforce each other and the amplitude at the mobile

antenna will (approximately) double. If the phase difference is an odd number of wavelengths then the two

waveforms will cancel producing a null.

As the mobile moves there are substantial amplitude variations in the received signal known as fast fading.

This is also accompanied by slower variation in signal strength known as slow fading or shadow fading. Fast

fading is observed over distances of about half a wavelength and can produce signal strength variations of up

to 30dB. Movement over much longer distances produces slow fading, sufficient to produce gross variations

in the overall path between base station and mobile. It should be noted that at 400MHz moving at 50 km/h

the path will experience several fast fades in one second as the mobile is travelling at 18 wavelengths per

second.

2.3 Okumura Model

Equation 5 gives the underlying 4th power relationship between path loss and distance. In the Digital PMR

environment the base station antenna is likely to be above the surrounding buildings while the mobile

antenna is at street level. Thus, it is unlikely that there is a line of sight path, as assumed for the 4th power

relationship.

Mathematical models may be derived and are dependent on the relative heights of buildings and base station

antennas. The Okumurav model, which is often used, was formed from averaging measured data in Japan.

Hata subsequently derived parametric fits to the large-scale measurements reported by Okimura. The

resulting propagation loss is expressed as a statistical average as follows:

Equation 6 ( )mhbb ARhhFL −−+−+= 10101010 loglog5.659.44log82.13log16.2655.69

.


Where

L = Path Loss from base station to the mobile unit;

F = Carrier Frequency in MHz;

hb = Base Station Antenna height in metres above the ground level in the range 3-10km from the base station;

hb may therefore vary slightly with the direction of the mobile from the base;

R = Distance between base station and mobile in kilometres;

( ) ( );8.0log56.17.0log1.1 1010 −−−= FhFA mhm

hm = mobile antenna height in metres.

Different versions of this model have been formulated for urban, suburban and open areas. The loss is

calculated on a grid basis taking into account the 'clutter' around the mobile located in each separate grid

location. This allows the tool to predict the 'coverage' of a particular site. Most other empirical propagation

models are based on similar modelling techniques and most coverage-planning tools use this as the basis for

their modelling. Other models include the COST231-Hata model, The Lee Model and The Ibrahim and

Parsons Model.

2.4 Effective Antenna Height

Antenna height would intuitively appear to affect the diversity gain. One of the models listed at the end of

section 2.3 (The Lee Model) has a specific method of dealing with Effective antenna height. This base

antenna height is different from the height used by the Okimura Hata model.

2.4.1 Non-Obstructive Propagation

In a non-obstructive propagation environment, the signal is not totally obstructed by hills or mountains.

Although the signals are blocked by buildings or homes they can still reach the mobile or portable units from

multiple reflected waves. We call this wave path a direct-wave path. The direct-wave path is distinguished

from the line-of-site path, along which the cell site antenna can be seen from the mobile unit. It is also

distinguished from the obstructed path where the signal is obstructed and the signal only reaches it’s

destination by diffraction or the destination is close enough to the source to overcome the additional

attenuation of the obstruction.

.


When the ground is not flat, it not only creates a direct wave path but also more than one reflected wave path,

as shown in Figure 6 (a). A two-reflection ground situation can be illustrated by either the cell site antenna

located on top of a hill as illustrated in Figure 6 (b) (Case I), or at the base of a hill as illustrated in (c) (Case

II). Based on the wave theory, there are two reflection points corresponding to two reflected waves on two

reflected grounds, as shown in Figure 6 (b, c). The closest one to the mobile unit is called the specular

reflection point, and the one away from the mobile is called the diffuse reflection point. The specular

reflection point is the point from which the reflected wave that can deliver the most energy to the mobile

unit. Therefore, in reality, there is always one reflected wave dominating the reflected energy and the others

can be neglected.

ha

ha

ha

he

he

Diffuse Reflecti on Point

Diffuse Reflecti on Point

Specular Reflecti on Point


(a) (b) (c)

Diffuse Reflecti on Points


Figure 6 - Identification of specular reflection points: (a)Multiple; (b)Case I; (c) Case II.

2.4.2 Reflection Points on a Non-Flat Ground

To illustrate the reflected waves on a drawing (See Figure 7), the vertical and horizontal scale usually have a

difference of two orders of magnitude; that is the vertical scale is usually in metres and the horizontal scale is

usually in kilometres. These scales are used to make the illustration fit on a page and still have a visible

slope on hills. Nevertheless, the readers’ perception could be misled. The slope of the hills, as shown on

drawings, is always large.

The specular reflection point occurring on a non-flat ground would be used to measure the effective antenna

height. The effective antenna height is measured at the cell site antenna location from an extended ground

plane where the specular reflection point is. The effective antenna height he is different from the actual

antenna height ha. The antenna height gain can be expressed as shown in Equation 7, which is a re-written

version of Equation 2.

Equation 7a

ee h

hLogG 1020=

The antenna height gain Ge will be changed as the mobile travels from place to place because the effective

antenna heights heA and heB and heC are changing as shown in Figure 7.

.


C

HeA

HeB

HeC

He

B A

Figure 7 – Change of Effective Antenna Height with Vehicle Position.

3 Factors Affecting Space Diversity Gain

3.1 General

Space diversity depends on many factors. The one which first springs to mind is spacing between the

antennas. The other factors that come into play are:

• Orientation of Antennas Relative to mobile unit.

• Antenna Height

• Antenna Separation

• Difference in gain between Antennas (This usually this varies as mobiles go around the tower)

• The number of antennas used (Aperture Gain)

• Other Physical Considerations

These items will be discussed in detail in this section. New concepts and methods will be introduced as

necessary during the discussion.

3.1.1 Introducing Correlation Coefficient

Since diversity signal fading in the mobile radio environment causes severe reception problems, diversity

techniques are used to reduce fading effects. Usually diversity is used at the base receiving site. The

diversity performance of the base station / antenna system (gain) is dependent on the number of branches, the

diversity scheme implemented in the receiver and the correlation coefficient between the branches.

.


Usually the two-branch signals are somewhat correlated, because the required separation of the two antennas

cannot be physically wide enough to achieve uncorrelated condition between the two signals. The best

performance of a diversity receiver is achieved by trying to make the correlation coefficient (ρ) of the two

signals approach zero. (ρ = 0 => no correlation, ρ = 1 => full correlation).

3.1.2 Correlation Coefficient Defined

Correlation is frequently used in the assessment of antenna diversity. Correlation measures the relationship

between two sets of data that are scaled to be independent of the unit of measurement and is used to

determine whether two ranges of data are moving together. A positive coefficient indicates that large values

of one set are associated with large values of the other. A negative coefficient indicates that small values of

one set are associated with large values of the other. A near zero value indicates that values in both sets are

unrelated. The larger the coefficient, the more the two sets are alike. The smaller the coefficient, the less the

two sets are alike. Normally the value of the coefficient lies between zero and one. As a mobile moves

around its environment, the signal received at the base antenna will vary considerably as illustrated in Figure

2 on page 5. The long-term correlation between the amplitude of the received signals should be high, but the

instantaneous value of the correlation should be very low to generate diversity gain.

3.2 Dependency of Diversity Gain on Antenna Orientation to Mobiles vi

Waves transmitted from a mobile unit at a large distance away will arrive at the two base station antennas at

an angle α as illustrated in Figure 8. The angle α is the angle between a line which is drawn perpendicular to

the line joining the two antennas and a line drawn from the mobile and the centre of the antennas on the mast.

The angle α = 00 occurs when the mobile is broadside to the antennas and the angle α = 900 occurs when the

mobile is in-line with the antennas.

The radio signal travelling along the path from the mobile will be take a direct route through any electrically

transparent objects to the base antennas. It will also be reflected from different scatterers along the route

before arriving at the base antennas. The terrain configuration usually dominates the propagation path loss

and the local scatterers surrounding the mobile unit will cause short-term fading (See Figure 8). The local

scatterers are so named if two requirements are met: (1) the size of the scatterers is greater than the operating

wavelength (approximately 0.75metres at 400MHz). (2) the heights of the scatterers are higher than the

mobile / portable antenna height. Naturally the surrounding houses and buildings around the mobile unit

meet these two requirements and are local scatterers. It has been determined experimentally that the radius

of the local scatterers (i.e. the distance from the mobile unit to the predominant scatterers, which will

primarily be positioned on the circumference of a circle) vi is given as: -

.


Equation 8 r =50λλλλ to 100λλλλ (Suburban area).

or for a frequency of 400MHz it is 37 to 75 metres. The secondary reflections due to the houses or buildings

further away than this distance do not interfere with the signal received at the base antenna.

Vehicle

EffectiveLocalScatters

Radius of localscatterers.

DBase

Station

Antennas

α=00

α=900

Figure 8 - Antenna Orientation at Base Station

The difference in correlation coefficient between the two fading signals depends on the separation between

the two antennas and on the angle α. Intuitive logic reasons a lower value of correlation coefficient would be

obtained for the broadside case than for the in line case for a given antenna separation. This is because the

amplitude envelope of the two received signals will tend to be the same in the inline case. The fading signals

received at the two base-station antennas will arrive at the first antenna through the same propagation path as

the signal arriving at the second antenna. The only factor involved in lowering the correlation coefficient

between the two signals is the extra distance travelled in the antenna separation, and the ‘filling-in’ of very

narrow fades, which will not be very effective. In the broadside case, the two received signals will travel

through different paths and reflect from different local scatterers before arriving at the base antennas.

3.3 Antenna Height / Separation Dependency

Designing an antenna diversity scheme is based on the parameter η (proposed by Lee), which dependsvii on

the real antenna height (h), and the antenna separation (d):

Equation 9d

h

arationAntennaSep

ghtAntennaHei ==η

.


It has been determined experimentally that the value most frequently used for η, at 850MHz, is 11 for

horizontal antenna separation. For example, when the antenna height ‘h’ is 33 metres, the optimum ‘d’ is

3Metres at 850MHz – the frequency at which the measurements were made. (See 3.3.1 on page 19 for more

information on this factor at 405MHz). Therefore, the higher the antenna, the more separation will be needed

for optimum diversity gain.

This is based on the plot given in Figure 9, which plots the correlation coefficient in suburban area for

different orientation angles of the base antennas to the mobile unit. The data in Figure 9 is derived from

many thousands of measurements, from which the empirical curves shown for each angle of orientation are

derived. The correlation coefficient shown for a particular orientation case will occur more than 90% of the

time for the given ratio of height-to-distance (η = h / d).

Some think that Lee may have come to the wrong conclusion from his measured results. He assumed that it

was antenna height that impacted ρ but, if you look at his drive routes, the sites with higher antennas have

larger coverage areas and data was collected at a greater distance from the antenna. It is believed that it is the

distance from the antenna that affects ρ. The measured results of others illustrate this clearly for a fixed

antenna height. As will be seen in section 5 this factor is one that has less effect than might be understood

from this discussion.

α

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Cor

rela

tion

ρ ρρρ

1 2 5 10 20 50 100

ηηηη=h/d

Data below these Lineswith high Probability

6666 4 4 44 4 44 4 44 4 4 7777 4 4 44 4 44 4 44 4 4 8888

αααα= 900

600

450

00 &300

Empirical Curves

d Base StationAntennas

00

α= 00

300

450

600

900

(Broadside)

h: Antenna Heightd: Antenna Spacing

0.5 1 2.4 4.8 9.5 23.8 47.6

At 850MHz

At 405MHz

Figure 9 - Correlation versus Parameter ηηηη for two Antennas in Different Orientations viii

.


Figure 10 - Three Dimensional Representation of Correlation Vs Parameter ηηηη at 850MHz

For a given η the correlation coefficient values are always smaller in the broadside case (α = 00) than in any

other case. The highest values of correlation coefficients are in the inline case (α = 900) i.e. the diversity

gain is least at this orientation. The experimental correlation coefficients in an urban area, with respect to the

parameter η, would be smaller than those in a suburban area and smaller again in a rural environment. This

is because more scatterers exist along the path between the mobile unit and the base station in the urban area.

Thus the diversity gain tends to be higher in suburban areas than in rural areas.

3.3.1 Frequency Dependence of Factor ηηηη

In designing and calculating antenna spacing for space diversity in a mobile radio environment, the same

experimental curves used for a frequency of 850MHz can be used to compute the antenna separation for

other frequenciesviii

Equation 10

=

11 850

fdd

where f1 is the new frequency in MHz. The formula is valid for f ≥ 30 MHz.

.


Another method of viewing this is to adjust the value of η accordingly. Therefore at 380MHz the optimum

value is 4.9 and at 430MHz it is 5.56. Thus, for Equation 9, the optimum value for ηηηη, is 5.25 for

horizontal antenna separation at 405MHz.

As stated in 1.2.2 on page 6 the diversity gain achieved using vertically polarised panel antennas at a height

of 30 metres and a horizontal spacing of 5.5 metres, was found to be the same as that which had been

achieved at 900MHz. It may be possible that the diversity gain at 405MHz would be slightly lower than at

1800MHz, as the radius of local scatterers (See Section 3.2 on page 16 and especially Equation 8 on page 17)

will mean that the signal is more attenuated than at 1800MHz. On the other hand, the attenuation in free

space (this is because the local scatterers are local and would not have any obstructions between them and

the moving mobile) will be the same, as the distance to local scatterers is between 50λ and 100λ and not

absolute distance. Thus, on balance it is considered that the model will still hold at these frequencies.

Some examples are given in section 3.6.2 on page 31 which illustrate this in more detail. The table below is

an example of some optimum antenna spacing for different antenna heights.

Antenna Height OptimumSeparation

Antenna Height OptimumSeparation

10 1.9 25 4.8

15 2.9 30 5.7

20 3.8 35 6.7

Table 2 – ‘Optimum’ Spacing Vs Antenna Height for Space Diversity at 405MHz

3.3.2 Why Use a Correlation Coefficient of 0.7?

When measurements are taken for a travelling mobile (an example is shown in Figure 2 on page 5) the signal

varies significantly during the measurement process (because the mobile is moving) and many hundreds of

thousands of individual measurements may be made. The results can be divided into ranges and the number

of results which fall below each range are counted. From the same signal fading we count N1 sample points

below a certain level L1. The percentage N1/N is obtained for level L1, where N is the total number of

samples. The percentage of sample points below other levels, e.g. L2, L3,..Ln, can also be easily obtained by

counting the number of samples below each level. The plot of percentages versus the levels is called

Cumulative Probability Distribution (CPD). This can be plotted on Rayleigh paper, as illustrated in Figure

11 on page 22. The Rayleigh paper gets its name from the fact that the Rayleigh curve drawn on this paper is

a straight line. Various theoretical CPD can be used to describe the mobile radio environment and the

Rayleigh curve is frequently used.

.


Rayleigh fading can be used to examine the signal reception in a single antenna. The results plotted in Figure

11 are experimental and are plotted on Rayleigh paper to give a comparative reference. The correlation

coefficient of up to 0.7 between two maximal-ratio diversity branches, achieves a large reduction of signal

fading. The performance of ρ = 0.7 compared to other values of ρ is shown in Figure 11. The percentage

shown in Figure 11 means the percentage of the signal below its corresponding dB level.

Now we will examine the curves more closely. At a level of –10dB , with respect to the RMS value, the

fading reduction is from 9.5% at ρ = 1.0 (no diversity condition, single Rayleigh channel on chart) to 1.3% at

ρ = 0.7 and then to 0.5% at ρ = 0. This observation encourages us to use ρ = 0.7. Since great improvement

in performance is shown from ρ = 1.0 to ρ = 0.7, then a relatively slight improvement is shown from ρ = 0.7

to ρ = 0. This ρ = 0.7 is chosen for its cost effectiveness in realising physical antenna spacing, as is shown in

the following example for 405MHz (using data derived also from Figure 9): -

• ρ = 0.7, then η = 5.25

• ρ = 0.3, then η = 1.667

Both examples are for the broadside case. With a given antenna height of 30 m, but different values of η, the

antenna spacing can be determined: -

Equation 11 7.525.5

30 ===ηh

d (ρρρρ=0.7)

Equation 12 18667.1

30 ===ηh

d (ρρρρ=0.3)

From this example it is clear that an antenna spacing of 5.7m for ρ = 0.7 and 18m for ρ = 0.3 is required.

Therefore, lowering the value of η widens the antenna spacing d. From Figure 11, the percentage of a signal

below –10dB is 1.3% at ρ = 0.7, and about 0.5% at ρ = 0.4. Combining the information observed from

Figure 9 and Figure 11, we found that at a given antenna height h = 30 m 1.3% of the signal will be below a

–10dB level if the antenna spacing is 5.7metres. About 0.5% of total signal will be below a –10dB level if

antenna spacing is 18metres. It is obvious that while increasing the antenna separation from 5.7m to 18m

requires a big effort, the improvement is not significant. Therefore, a separation of 5.7m at an antenna height

of 30m is suggested. This example will be examined further in section 3.6.2 on page 31.

.


0.01

4.0

6.0

1.0

0.1

99.99

99.9

99.0

96.0

94.0

90.0

80.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

95.0

96.0

99.0

99.5

99.99

99.98

99.95

99.9

70.0

60.0

50.0

40.0

30.0

20.0

10.0

5.0

4.0

1.0

0.5

0.2 99.8

0.1

0.05

0.02

0.01

ρρρρ = 0.9

ρρρρ = 0.7

ρρρρ = 0.5

ρρρρ = 0.3

ρρρρ = 0.1

ρρρρ = 0

Sing

le R

ayle

igh

Chan

nel

Tw

oRay

leig

h Ch

anne

ls (

ρρρρ =

1.0)

PE

RC

EN

T P

RO

BA

BIL

ITY

THAT

AM

PLI

TUD

E <

AB

SC

ISS

A

PE

RC

EN

T P

RO

BA

BIL

ITY

THAT

AM

PLI

TUD

E >

AB

SC

ISS

A

-40 -35 -30 -25 -20 -15 -10 -5 0 5 10

Signal Level dB With Respect to RMS Value

Figure 11 - Signal Level dB with respect to RMS Value

3.4 Difference in Gain between Antennas

For Digital PMR systems there is a requirement to achieve omni coverage from cell sites. High traffic

density leads to sectorisation of GSM systems, while Digital PMR systems tend to use omni sites in the

majority of cases. Thus, the need for omni coverage from sites without sectoring is much more of a

requirement for Digital PMR than at GSM. If omni antennas are placed close to other structures, the pattern

becomes distorted. The effects are minimal for panel antennas, provided all other metal structures (such as

other antennas) are kept out of the field of view of the antenna under consideration. To introduce the effect

of this distortion on diversity gain other factors (Relationship between Correlation Coefficient and Diversity

Gain and Aperture Gain) must be understood. The full effect of this distortion will be dealt with in more

detail in section 3.6.1 on page 28.

.


3.4.1 Relationship between Correlation Coefficient and Diversity Gain

Most of the previous statements about diversity are based upon consideration of correlation coefficient.

However, most working engineers are more interested in the equivalent antenna gain achieved with diversity

as planning tools will use this gain rather than anything else. An experimental study was completed on this

subject ix, and the results are presented here. Although the study was done at 1800MHz, there is a good

correlation between results obtained and those obtained in more limited tests at 400MHz. The results of the

study produced a relationship between correlation coefficient and diversity gain. The same study also

produced a relationship between difference in gain between antennas and the resulting diversity gain. Before

presenting the results of the study, it is necessary to understand different diversity techniques.

3.4.2 Different Diversity Techniques.

To assess the signal improvements in signal statistics through diversity combining, the system designer needs

to know which type of combining technique are used in the Digital PMR base stations being used on his

system. The three types are: -

1. Two / three branch selection

2. Equal gain combining

3. Maximal Ratio Combining

If the signals are designated v1(t) and v2(t) and the resultant signal envelope is represented as vc(t) then the

output of the combiner of specified type, assuming equal noise levels on both branches, is given as: -

Vc(t) = Max[v1(t),v2(t)] for selection

2

)()()( 21 tvtv

tvc

+= for equal-gain

)()()( 22

21 tvtvtvc += for maximal ratio combining

All variables in this equation are expressed in volts.

Selection is not a very good method, as the signal from only one antenna is used at any one time. However,

implementation is easy for the base station designer.

Equal-Gain doesn't work very well when the signals from the two branches are significantly different in

strength (or the antennas have different gains). When the signals received by the base station from both

.


antennas are the same, both arms contribute equal signal (thus the name). The output Signal-to-Noise-Ratio

(SNR) is dependent on the SNR of the received signal of each arm of the combiner, meaning that the

combiner operates well under this circumstance. When the signals are unequal, the noisy branch (the one

with the lower signal level) will simply contribute additional noise (and very little signal) when combined

with the less noisy branch. In other words, it will increase the noise power substantially, but will contribute

very little signal to the final output, decreasing the overall effective SNR.

Maximal Ratio is the best technique, because it assumes that each of the inputs is weighed by the incoming

signal’s C/N before being correctly phased and combined. It gets most signal and least noise from the

incoming signals to combine them in an optimum manner.

3.4.3 Measurement Results and Formulas

The cited experiments ix were performed at five different base station locations in four different types of

environments namely: urban, sub-urban, rural and motorway areas. At each base station, a total of 15

routes, radial or transverse with respect to the base site, were chosen. Altogether, a total of 924 runs were

made covering the different combinations of diversity type. The results allowed the authors to generate an

empirical relationship relating the diversity gain to the mean signal level difference and the correlation of the

signals. Below are the resulting equations for selection, equal-gain and maximal-ratio combining: -

Equation 13 G= 5.71exp(-0.87ρρρρ-0.16∆∆∆∆) for Selection

Equation 14 G= -8.98+15.22exp(-0.20ρρρρ-0.04∆∆∆∆) for Equal-Gain

Equation 15 G= 7.14exp(-0.59ρρρρ-0.11∆∆∆∆) for Maximal Ratio

where G represents the diversity gain at 90% signal reliability in dB, ∆ represents the mean signal level

difference and ρ represents the cross-correlation coefficient between the signals.

Figure 12 plots these equations and shows the diversity gain as a function of envelope cross-correlation and

mean signal level between branches for the stated combiner types. As expected, maximal-ratio combining

offers the largest improvement and the maximum diversity gain is obtained for a signal difference of 0dB and

a correlation of less than zero (when small amplitudes in one antenna correlate with large amplitudes in the

other). All of these results include the Aperture Gain of the antennas. (See 3.5 on page 26 for a discussion

about Aperture Gain).

As far as the author is aware, most modern base stations use Maximal ratio Combining for diversity. If the

system designer is in doubt, it is best to contact the original manufacturer of the equipment being deployed,

as this element of the base station’s design can affect the coverage achievable by the overall system.

Selection is almost never used any more, and Equal-Gain is being phased out in newer base station designs.

.


From the graphs in Figure 12 (which are Equation 13, Equation 14 and Equation 15 represented graphically),

it is clear that the Selection combining technique performs least well. At a correlation coefficient of 1.0, the

diversity gain is 3.4dB with no gain difference between the two antenna gains. Even with a difference of

3dB the gain is down to 1.5dB, which is less than the Aperture Gain. The maximum gain with no difference

between the antennas, and a correlation coefficient of zero, the gain is 5.7dB (which would never be

achievable in a real-world situation). For the Equal Gain combining technique at a correlation coefficient of

1.0, the diversity gain is 3.5dB with no difference between the two antenna gains and with a difference of

3dB, the diversity gain is 2dB. The maximum gain with no gain difference between the antennas, and a

correlation coefficient of zero, the gain is 6.7dB. (which would never be achievable in a real world situation).

For the Max Ratio combining technique at a correlation coefficient of 1.0, the diversity gain is 3.9dB with

no difference between the two antenna gains and with a difference of 3dB, the gain is 2.9dB. The maximum

gain with no gain difference between the antennas, and a correlation coefficient of zero, the gain is 7.9dB

(which would never be achievable in a real-world situation). Obviously, the situation of zero correlation

coefficient would never be achieved, so the diversity gain values given for this situation are mathematical

constructs.

In the graphs below, the gains are split into bands of 2dB with the colours for each band being the same in all

three graphs. It can be seen that the diversity gain of Selection is only significant when the gains of the two

antennas are very close. For Equal Gain, the diversity gain keeps reducing as the difference between the

antennas increases, and even becomes negative below 10dB at one end of the correlation range (ρ = 1.0) and

at 15dB difference at the other end (ρ = -0.2). For Max Ratio, the diversity gain stays above the Aperture

Gain at ρ = 1.0 for a difference of 2.5dB, and at ρ = 0 at 7.5dB difference.

.


-0.200.00

0.200.40

0.600.80

1.00

25

20

15

10

5

0

-4

-2

0

2

4

6

8

10

Div

ersi

ty G

ain

(d

B)

Cross-Correlation

Difference in Signal (dB)

Selection of Strongest Signal Diversity Gain

8.00-10.00

6.00-8.00

4.00-6.00

2.00-4.00

0.00-2.00

-2.00-0.00

-4.00--2.00

Gain Range

-0.200.00

0.200.40

0.600.80

1.00

25

20

15

10

5

0

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

Div

ers

ity

Ga

in (

dB

)

Cross Correlation

Difference in Signal (dB)

Equal-Gain Diversity Plot

8.00-10.00

6.00-8.00

4.00-6.00

2.00-4.00

0.00-2.00

-2.00-0.00

-4.00--2.00

Gain Range

-0.200.00

0.200.40

0.600.80

1.00

25

20

15

10

5

0

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

Div

ersi

ty G

ain

(d

B)

Cross-Correlation

Difference Signal (dB)

Maximal-Ratio Diversity gain

8.00-10.00

6.00-8.00

4.00-6.00

2.00-4.00

0.00-2.00

-2.00-0.00

-4.00--2.00

Gain Range

Figure 12 - Diversity Gain for Various Combiner Types

3.5 Aperture Gain Explained

From an antenna designer’s perspective, the use of two antennas will give 3dB extra gain in the same way as

using a phasing harness with two antennas, or doubling the antenna’s length, will give a gain of 3dB. This

extra gain is obtained from adding the field strengths (as volts per metre) of the antennas together as voltages

and then converting that sum back to power. Thus, the gain for two antennas will be represented as

22

211020 vvLogG += and for three antennas will be 2

322

211020 vvvLogG ++= giving 3dB and 4.8dB

respectively where v1, v2 and v3 are all equal in amplitude. Another way to view this is that there is twice (or

three times) as much antenna aperture to collect the signal. In this discussion, we will refer to this gain as the

aperture gain. The method of processing the received signals (and the correlation coefficient between the

signals) will then determine the final gain of the total antenna and receiver system.

.


The more antennas used in a system, the greater the aperture gain the system will provide. The formulas

given in section 3.4.3 on page 24 include the aperture gain; it is not obvious that it is included in them. The

author has never seen anyone report less gain than the aperture gain illustrated here for any systems with

equal antenna gains.

The difference between Equal Gain and Max Ratio is not how they treat the aperture gain achieved by the

antennas, but how they acquire the additional gain from the two (or three) signals received. Everything is

fine for the Equal Gain method if both branches of the signal are equal. It performs almost as well as

Maximal Ratio. When the signals are unequal the problem arises, as one arm will add more noise to the

final signal than the other will. See Figure 12 on page 26 to see the comparison under all circumstances. In

fact, negative diversity gain is achieved by the Equal Gain combining technique when the difference

between the signals is more than 10dB, and below the full aperture gain (of two equal gain antennas i.e.

3dB) at 2 to 3dB signal differences. Max Ratio obtains the full aperture gain (of 3dB) up to a signal

difference of 4dB. It is worth noting that when gain of the two antennas are different, the aperture gain will

also reduce. Therefore, this not a good or fair comparison. Table 4 on Page 33 shows that the equivalent

aperture gain is always achieved by the Max Ratio combining technique, whatever the gain differences

between the antennas. However, for Equal Gain the equivalent aperture gain is only achieved up to a signal

difference of 8dB.

Selection switches between the two antennas, so only one signal is used by the base receiver system at any

one time, leading to the poor performance of this diversity technique, only achieving 3dB gain when the two

signal are identical in amplitude.

Aperture gain could also be used to illustrate the operation of dual-slant polarised diversity. Here, there are

two separate antennas which are orthogonal to each other, and each picks up a different component of the

received signal. The fact that these two components are travelling through the same space at the same time,

but the reception of these components is little affected by the other half of the same antenna is the major

attractiveness of this antenna type.

3.6 Other Physical Considerations

In planning a network, we must be aware of other limitations placed on the models we use by physical

considerations. These include the effect antennas have on one another when placed in close proximity to

each other, or a tower and what happens to diversity gain when the effective antenna height changes. These

are considered next.

.


3.6.1 Physical Considerations in Horizontal Separation

Antenna separation can be determined based upon the parameter η = 5.25 (at 405MHz), as mentioned

previously in section 3.3.1 on page 19. If h = 30 metres, then d = 5.7metres and if h = 15m, then d = 2.8m.

However, the physical separation of either 5.7m or 2.8m may cause a severe ripple effect on the two base-

station antenna patterns, depending on the antenna length.

The discussion which follows refers to omni antennas. The effects described are minimal for panel antennas,

provided all other metal structures (such as other antennas) are kept out of the field of view of the antenna

under consideration. For a 6-dB gain (with respect to a dipole) antenna, its physical length is two

wavelengths. At 405MHz, two wavelengths equal approximately 1575mm. This is the actual length of the

internal metal parts of the antenna. The external length of such an antenna would be approximately

2.2metres. Then the far field distance of this antenna is: -

Equation 16( )

mmL

D 6615750

157522 22

===λ

3.6.1.1 Antennas on Top of Tower

If we mount two 1.5m long antennas above the top of a tower and separate them by 2.5m, then one antenna is

in the other’s near field and causes the ripple effect. This effect is even larger for a three-antenna

configuration.

Three omni antenna patterns above the top of a tower, altered by the ripple effect, are shown in Figure 13. It

must be remembered that the patterns of the three antennas will be the same, but they will be mounted around

the top of the tower with different relative orientations, so the ripples from in one antenna pattern will not

coincide with the ripple in the others. The antenna patterns for three configurations are illustrated with the

antennas spaced at 2, 3.5 and 5.5metres. The three full patterns are illustrated in Figure 13A (in different

colours, as well as an ideal pattern undisturbed by anything nearby is shown in black). The difference

between the actual pattern and an ideal pattern is illustrated in Figure 13B. Figure 13B is illustrated over

±600 from the main beam, to keep the illustration from becoming overcrowded. The ripple effect is caused by

having three 1.5m long omni antennas in a triangular configuration with separations of 2, 3.5 and 5.5metres

while operating at 405MHz. The maximum variation of the ripples is given in Table 3. Since the two

diversity signals are received by a difference of less than 2dB (most of the time), we can still have good

diversity gain. The ripple effect will occur on each of the three antenna patterns around the tower, and the

ripple differences will have an effect in proportion to this difference. The table shows the worst possible

case, as the diversity gains given relate to the largest deviations from an ideal omni antenna.

.


Worst Antenna Gain Difference (dB)

Relative to an OmniDiversity Gain (dB)Antenna

SpacingMax. Pos. Max. Neg. Total Max Ratio Equal Gain Selection

2.0m 1.7 -2.4 4.1 2.5 1.6 1.2

3.5m 1.4 -1.7 3.1 2.8 2.0 1.5

5.5m 1.1 -1.2 2.3 3.0 2.4 1.7

Table 3 - Effect of Closely Spaced Antennas

0 -3 -6 -10

-15

dB

0

90

180

270

(A)-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 2.0

3.5

5.5

(B)

Figure 13 - Antenna Pattern when Three 6dB Antennas Mounted at Same Height

3.6.1.2 Antennas off the Side of a Tower

Figure 14 below illustrates the ripple which occurs when omni antennas are mounted at the same level on the

tower. The pattern illustrated Figure 14A shows an antenna placed at 2.3m from two different sized towers –

1m and 1.5m. The difference between the maximum and minimum of the radiation pattern is up to 6.9dB for

the 1m tower (and 5.5dB for the 1.5m tower) and the diversity gain in that direction will be reduced to as

little as 1.8dB (2.2dB) for Max Ratio and 1.5dB (1.0dB) for Equal Gain. The situation could even be as bad

as is illustrated in Figure 14B where the black pattern is an ideal omni and the blue pattern is an omni placed

at 1.6metres from a 1metre triangular tower. This case gives a gain difference between antennas of up to

7.5dB, which could lead to a diversity gain of as little as 1.7dB for Max Ratio, and 0.25 for Equal Gain.

However, this is not a realistic assessment, as the maximum of one antenna pattern coincident with the

minimum of the other will never occur at more than a few points around the tower.

A more accurate method of calculating the diversity gain is required. This is achieved by calculating the

diversity gain at each angle, in steps of one degree around the two (or three) antenna patterns. This allows a

composite plot of the diversity gain of the antennas to be made.

.


0 -3 -6 -10

-15-20

dB

0

90

180

270

(A) Three omnis at 2.3m from Different SizedTriangular Towers

0 -3 -6 -10

-15-20

dB

0

90

180

270

(B) Three omnis on 1 Metre Triangular TowerSpaced at 1.6Metres

Figure 14 - Patterns of Omni Antennas on Triangular Towers

The pattern distortion caused by towers is treated in more detail in separate a paper entitled “Achieving Omni

Antenna Patterns from Towers at 400MHz”. Now we will look in more detail at the effect this factor has on

the resulting diversity pattern of antennas on towers.

The plot in Figure 15A shows the patterns of two antennas mounted at different places around a tower (red

pattern for the red antenna, blue pattern for the blue antenna), as well as the resulting pattern (in green) after

the diversity calculations have been applied. The large null in the pattern of the red pattern (at zero degrees)

is ‘filled in’ by the blue pattern. At 240 degrees, however, there is a null in both antenna patterns, giving rise

to low diversity gain at that point. For the two-antenna situation there is still much pattern distortion and the

resulting pattern is close to the omni pattern shown in black (within 0.55dB at 240 degrees). There is also

6.12dB of ripple in the diversity pattern.

A third antenna is required to fill in this null. This then leaves a near omni pattern on receive which is at least

5dB above the omni, as is normally assumed. The three-antenna diversity is illustrated in Figure 15B. The

resulting composite diversity pattern has 3.25dB ripple on it. However, the distortion of the single transmit

antenna still holds for the transmit path, leading an illusory system imbalance in certain directions. This may

be blamed on the radio technology, rather than on not using the proper antenna patterns.

.


0 -3 -6 -10

-15

d

0

9

18

Omni

Blue Antenna

Red Antenna

Diversity Composite

Antennas2M Spacing at 20M Height

(A) Two Antennas

0 -3 -6 -10

-15

dB

0

90

180

27090

Red Antenna

Omni

Blue Antenna

Green Antenna

1.5M from 0.6M Tower

Diversity Composite

Antennas3M Spacing at 10M Height

(B) Three Antennas

Figure 15 – Patterns of Antennas on a 600mm Tower spaced at 1500mm

3.6.2 Effective Antenna Height

As mobiles move around the coverage area of a base station, the effective height of the base antenna system

is continually changing as the terrain height changes and the relative slope of the terrain changes (see 2.4 on

page 13). We need to consider what effect these changes have on the diversity gain, as most propagation

software takes into account the effective antenna height, but not changes in the diversity gain. Only

Propagation models using the Lee methodology will be affected by this factor, but it is worth examining the

effect of Effective Height when considered separately from the Propagation model.

Let us again take the example from section 3.3.2 on page 20 to see how this changes the effective antenna

height. (Antenna Height of 30metres, spacing of 5.7metres). We have already calculated η = 5.25 for this

configuration, equivalent to a correlation coefficient of 0.7. Using Equation 15 for Max Ratio Diversity on

page 24 will give a diversity gain of 4.66dB (and Equation 14 for Equal Gain will give a gain of 4.19dB) for

this configuration. What would happen if the effective antenna height was halved? At this point, we use

Equation 7 to calculate the new effective gain. This will give us an antenna height gain

dBLogGe 615

3020 −== . For this change in height, the factor η will have changed from 5.25 at 30 metres

to 2.6 at 15metres. This will lead to an increase in gain from 4.66dB to 5.37dB for Max Ratio (and from

4.19dB to 4.84dB for Equal Gain), giving an increase of 0.71dB gain for Max ratio (and 0.65 for Equal

Gain). Thus, while 6dB of gain is lost, only 0.7dB is obtained back from the change in effective antenna

height. All coverage software will take into account the change in antenna height, but will not be able to take

the change in diversity gain into account. However, the diversity gain change is very small compared to the

gain change due to change in antenna height.

.


4 A Practical Guide to Diversity

At the beginning of section 3 the following factors were listed as potentially affecting the diversity gain of a

system: -

• Orientation of Antennas Relative to mobile unit.

• Antenna Height

• Antenna Separation

• Difference in gain between Antennas (usually this varies as mobile goes around tower)

• The number of antennas used (Aperture Gain)

• Other Physical Considerations

Orientation of antennas relative to mobiles is dealt with as a separate item. Antenna Height and separation

are combined into the single factor η. The number of antennas used is not dealt with separately in section 3,

and we do not yet have any formulas for dealing with any number other than two, so all discussions are in

relation to two antennas. Other physical considerations have been dealt with in section 3.6 on page 27.

(Another, larger, physical factor (proximity of tower to antennas) is introduced at the end of section 5, during

the discussion of item 2 about difference in antenna gains on page 37). After consideration of the effect of

these factors and re-arrangement, they can be reduced to:

• Aperture Gain

• Antenna Gain / Pattern Differences

• Antenna Height and Separation

• Orientation of antennas to mobiles

These are ranked in order of importance in the above list.

We have shown that there is an equation which can relate the gain to the correlation coefficient and the

difference in gain between any two antennas (Equation 13, Equation 14 and Equation 15). The correlation

coefficient in these equations depends upon the antenna height, spacing and orientation of the mobile to the

diversity antennas (Figure 9).

It should be emphasised that the gains obtained here are only indicative, as the experiments which gave rise

to these equations were conducted in four different types of environment, and the resulting equations were

taken from a composite of these measurements. The different gains obtained in different environments will

vary somewhat (please refer to Table 1 on Page 7) and this should be considered by the system designer. All

practical examples given in this paper are frequency adjusted to 405MHz using Equation 10 on page 19,

unless specifically otherwise stated.

.


4.1 Aperture Gain (Number of Antennas)

Aperture Gain is always present for all types of diversity combining. This is 3dB for two antennas and 4.7dB

for three antennas. It is inherent in the formulas presented in section 3.4. It is in fact a hidden factor not

discussed by authors of papers on the subject of diversity gain and is included in all the discussions that

follow.

4.2 Antenna Gain / Pattern Differences

Table 4 represents, in tabular form, the variation of Diversity gain with differences in signal level from two

antennas for the three different diversity combining types. Also presented in the table is the Aperture Gain

of this situation showing that the only diversity combining technique to exceed this theoretical minimum

under all circumstances is the Max Ratio combining system. Aperture Gain is calculated using the formula

+=

1010 10110

Diff

LogG , where Diff is the difference in power received from the antennas expressed in

dB (antenna gain is always expressed as dB or relative power received). The power received from the

antenna with higher gain is taken to be unity, and the second then depends on the absolute ratio of one gain to

the other. If the two gains are equal, the total gain will be 10Log10(2), which is 3dB. See also 3.5 on page 26

for a fuller discussion on Aperture Gain. We do not consider here what would happen if more than two

antennas are used for the diversity gain, but it is obvious that a third antenna would add more gain. The

Aperture Gain is 4.7dB when three antennas have equal gains.

Antenna Signal Differences (dB) 0 1 2 3 4 5 6 7

Aperture Gain 3.01 2.54 2.12 1.76 1.46 1.19 0.97 0.79

Max Ratio 4.66 4.18 3.74 3.35 3.00 2.69 2.41 2.16

Equal Gain 4.19 3.68 3.18 2.70 2.25 1.81 1.38 0.98

Selection 3.05 2.60 2.21 1.89 1.61 1.37 1.17 0.99

Antenna Signal Differences (dB) 8 9 10 15 20 25 30 40

Aperture Gain 0.64 0.51 0.41 0.14 0.04 0.01 0.00 0.00

Max Ratio 1.93 1.73 1.55 0.90 0.52 0.30 0.17 0.06

Equal Gain 0.59 0.21 -0.15 -1.75 -3.06 -4.13 -5.01 -6.32

Selection 0.85 0.72 0.62 0.28 0.12 0.06 0.03 0.01

Table 4 – Indicative Diversity Gain for Differing Antenna Gains.

.


4.3 Antenna Height and Separation

We will use the example from section 3.3.2 on page 20 to see how the diversity gain can be derived for

different antenna spacings at a height of 30m. Firstly we will examine the gain obtained for the spacing

given in Equation 11 on page 21 (ρ = 0.7, d = 5.7metres). We have already calculated η = h / d = 30 / 5.7 =

5.25 for this configuration. As observed previously this is equivalent to a correlation coefficient of 0.7.

Using Equation 15 for Max Ratio Diversity on page 24 will give a diversity gain of 4.66dB (and Equation 14

for Equal Gain will give a gain of 4.19dB) for this configuration. If we increase the spacing to 18m, the

correlation coefficient will be 0.3 and the gain using the same equations will be 5.4dB and 6.0dB

respectively. In both of these cases, only 1dB in gain is obtained for an impossible increase in antenna

spacing. It should also be remembered that the gains given are two decimal places, they are only indicative

of the gains achievable with these configurations.

Table 5 and Table 6 (on page 35) are the results of applying the above methodology to many different

combinations of height and separation, using the two different base-station diversity types. Table 7 (on page

35) shows how the gain varies with η, and Figure 16 (on page 36) shows this variation graphically. These

results are for 405MHz, zero degrees orientation and equal signal in both antennas. It is worth noting that: -

• When η ≤ 10 (highlighted in grey in both Table 5 and Table 6) there is no change in gain. This is

because there is a minimum gain in both of these types of diversity types.

• When the signals from each antenna are the same, the Max Ratio type gives approximately 0.5dB more

gain throughout the differing values of η.

• If we examine Figure 16 on page 36 closely we will see that when the antennas are infinitely spaced (η =

0) there is a maximum gain. When η = 10 the gain reaches a certain minimum and the value chosen for

optimum η in section 3.3.1 on page 19 gives about half of the difference between the two extremes of

gain. This is also the maximum spacing achievable in practice.

• At the stated ‘Optimum’ Spacing (η = 5.25) there is a diversity gain of 4.66dB for Max Ratio, 4.19dB

for Equal Gain (and 3.04dB for Selection) which is 1.66dB, 1.19dB (and 0.04) respectively over the

Aperture Gain of the two-antenna configuration. It illustrates that this is not necessarily the only spacing

to achieve diversity gain, and the information presented here should be sufficient to allow the system

designer to make informed choices.

.


Spacing = d (Metres)

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

10 3.98 4.45 4.73 4.95 5.15 5.32 5.48 5.61 5.74 5.81 5.97

15 3.96 3.98 4.35 4.55 4.73 4.89 5.01 5.15 5.23 5.37 5.48

20 3.96 3.96 3.98 4.25 4.45 4.59 4.73 4.84 4.95 5.04 5.15

25 3.96 3.96 3.96 3.98 4.22 4.40 4.51 4.61 4.73 4.81 4.92

30 3.96 3.96 3.96 3.96 3.98 4.18 4.35 4.45 4.55 4.63 4.73

35 3.96 3.96 3.96 3.96 3.96 3.98 4.15 4.29 4.41 4.49 4.57Hei

ght

= h

(M

etre

s)

40 3.96 3.96 3.96 3.96 3.96 3.96 3.98 4.13 4.25 4.36 4.45

Table 5 – Indicative Gain (dB) for Different Antenna Heights and Spacing Using Max-Ratio

Spacing = d (Metres)

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

10 3.50 3.99 4.26 4.47 4.64 4.79 4.94 5.04 5.15 5.21 5.35

15 3.48 3.50 3.88 4.08 4.26 4.41 4.52 4.64 4.72 4.84 4.94

20 3.48 3.48 3.50 3.79 3.99 4.12 4.26 4.36 4.47 4.55 4.64

25 3.48 3.48 3.48 3.50 3.75 3.94 4.05 4.14 4.26 4.33 4.44

30 3.48 3.48 3.48 3.48 3.50 3.72 3.88 3.99 4.08 4.17 4.26

35 3.48 3.48 3.48 3.48 3.48 3.50 3.68 3.83 3.95 4.03 4.11Hei

ght

= h

(m

etre

s)

40 3.48 3.48 3.48 3.48 3.48 3.48 3.50 3.66 3.79 3.90 3.99

Table 6 – Indicative Gain (dB) for Different Antenna Heights and Spacing Using Equal-Gain

ηηηη = h/d

1.00 2.00 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75

Max Ratio 6.49 5.74 5.23 5.15 5.08 5.01 4.95 4.89 4.84 4.78

Equal Gain 5.76 5.15 4.72 4.64 4.58 4.52 4.47 4.41 4.36 4.30

Selection 4.96 4.14 3.61 3.52 3.45 3.39 3.33 3.27 3.22 3.16

ηηηη = h/d

5.00 5.25 5.50 5.75 6 6.5 7 10 15 20

Max Ratio 4.73 4.66 4.61 4.57 4.55 4.47 4.41 3.98 3.96 3.96

Equal Gain 4.26 4.19 4.14 4.11 4.08 4.01 3.95 3.50 3.48 3.48

Div

ersi

ty T

ype

Selection 3.11 3.04 3.00 2.96 2.93 2.87 2.81 2.41 2.39 2.39

Table 7- Indicative Gain (dB) for Different Values of ηηηη, for the Three Diversity Types.

.


Diversity Gain Vs Factor ηηηη

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.00 5.00 10.00 15.00 20.00 25.00

ηηηη = h / d

Div

ers

ity

Gai

n (

dB

)

Max Ratio

Equal Gain

Selection

d=∞ d=0

Figure 16 - Graph of Gain Vs ηηηη for different Diversity Combining Types at 405MHz

4.4 Orientation of Antennas to Mobiles

Table 8 illustrates how Max Ratio combining gain varies with angle when an antenna is positioned at 30m

for various antenna spacings. It again shows that there is a minimum gain of 3.9dB, which illustrates the

principle of Aperture Gain. As previously discussed in 3.2 on page 16, the correlation coefficient is

consistent up to 450 and falls rapidly from 600 to 900. However, it must be noted that the angle of orientation

only has a significant effect when the factor η is in the range 1 to 5 at 405MHz (See Figure 9 on page 18). It

does have with some small effect up to a maximum η at a value of 9, from which point it has no effect

whatsoever. At the ideal separation (η = 5.25) the decrease in diversity gain is 0.7dB from α = 00 to α = 900.

In Table 8, the cases highlighted in grey indicate those that are at the bottom of the possible gain range.

.


Orientation Angle αααα (Degrees)

ηηηη 0 10 20 30 40 50 60 70 80 90

2.0 15.00 3.96 3.96 3.96 3.96 3.96 3.96 3.96 3.96 3.96 3.96

2.5 12.00 3.96 3.96 3.96 3.96 3.96 3.96 3.96 3.96 3.96 3.96

3.0 10.00 3.98 3.98 3.98 3.98 3.98 3.96 3.96 3.96 3.96 3.96

3.5 8.57 4.18 4.18 4.18 4.18 4.10 4.05 3.96 3.96 3.96 3.96

4.0 7.50 4.35 4.35 4.35 4.35 4.25 4.15 3.96 3.96 3.96 3.96

4.5 6.67 4.45 4.45 4.45 4.45 4.35 4.20 4.00 3.99 3.97 3.96

5.0 6.00 4.55 4.55 4.55 4.55 4.42 4.27 4.07 4.04 4.01 3.96

5.5 5.45 4.63 4.63 4.63 4.63 4.52 4.36 4.16 4.10 4.04 3.96

6.0 5.00 4.73 4.73 4.73 4.73 4.61 4.44 4.25 4.17 4.07 3.96

6.5 4.62 4.81 4.81 4.81 4.81 4.68 4.52 4.32 4.21 4.09 3.96

7.0 4.29 4.89 4.89 4.89 4.89 4.76 4.60 4.40 4.25 4.10 3.96

An

ten

na

Sp

acin

g (M

etre

s)

7.5 4.00 4.95 4.95 4.95 4.95 4.82 4.65 4.47 4.31 4.15 3.98

Table 8 – Indicative Gain (dB) for various Angles at different Antenna Spacing on 30m Tower

5 Prioritised Diversity Gain Factors

From the results obtained in Section 4, it is possible to rank the differing factors according to how much they

affect the overall diversity gain as follows: -

1. Aperture Gain is always present for all types of diversity combining. This is 3dB for two antennas

and 4.7dB for three antennas. This gain is there when you use either Max Ratio or Equal Gain

combining techniques.

2. Difference between Antenna gains. This factor can reduce the diversity gain in specific directions

down to near zero – below the aperture gain. In typical cases, two or three antennas will be placed

at a distance from the tower, at the same level, in an attempt to maximise the diversity gain and

minimise pattern distortion. The resultant typical antenna patterns are illustrated in Figure 15on

page 31. In fact, the pattern distortion of the transmit antenna (created by the presence of the tower

close to the antenna) is much more important than the distortion of the diversity pattern in the

overall coverage requirements. The pattern distortion caused by towers is treated in more detail in

separate a paper entitled “Achieving Omni Antenna Patterns from Towers at 400MHz”.

.


3. Antenna Height and Separation could have a maximum effect of 1.8dB, depending on separation.

The minimum spacing, which a system designer would typically be able to achieve, would be

2.5metres, which could yield a diversity gain as low as 4dB for Max Ratio and 3.5dB for Equal

Gain. The maximum practical spacing would be 5 metres, which would yield a maximum gain of

5.9dB and 5.3dB respectively (on 10m towers). A more typical range of gains would be 1dB to

0.5dB over the Aperture Gain (assume a typical practical spacing of 3.5m, and antenna height range

from 20 to 40 metres).

4. Orientation of Antennas relative to mobile unit has a lot less effect than might be suggested in

section 3.2 on page 16. If the typical range for η is taken to be 3.5 to 5.5, then the typical effect of

orientation might be as low as 0.2dB at η = 3.5 to 0.6dB at η = 5.5.

However, it must be remembered that for these analyses the factors have all been isolated from each other.

In a real situation, they will all interact. It is best, however to examine them all individually so that the

effects can be observed separately, and the system designer can then make value judgements as to the

applicability of each factor, and adjust his antenna patterns or diversity gains in the models accordingly.

i ETS 300-392-2 First Edition, March 1996 Section 6.6.3.1

ii Jaana Laiho Steffens, Jukka Lempeiainen et al., “Experimental Evaluation of Polarisation Diversity Gain at

Base Station End in GSM900 Network”, IEE Transactions, Vehicular Technology 0-7803-4320-4/98 Pages

16-20.

iii Bullington K., “Radio Propagation for Vehicular Communications”, IEE Transactions, Vehicular

Technology, Volume T-26 Number 4, Pages 295-308.

iv Attwood, S.S., ed., “The propagation of Radio Waves through the Standard Atmosphere” Summary

technical Report of the Committee on Propagation 3 (Washington, DC, Reports and Documents 1946):250

v Okumura, Y., E. Ohmori, T. Kohono, and K. Fukuda, “Field strength and Its Variability in VHF and UHF

Land-Mobile Radio Service”, Rev. Elec. Comm. Lab., Volume 16, No. 9-10, 1968 pp.825-873

vi Lee, W.C.Y. “Mobile Communications Design Fundamentals”, Second Edition Wiley Series in

Telecommunications, Pages 157 to 159.

vii Lee, W.C.Y. “Mobile Radio Signal Correlation Vs Antenna Height and Spacing”, IEE Trans. Vehicular

Technology,, August 1997, pp290-292.

.


viii Lee, W.C.Y. “Mobile Communications Design Fundamentals”, Second Edition Wiley Series in

Telecommunications, Pages 199 to 211.

ix A.M.D. Turkmani, A.A.Arojolu, A.Jefford and C.J. Kellet, “An Experimental Evaluation of the

Performance of Two-Branch Space and Polarisation Diversity Schemes at 1800MHz IEE Transactions,

Vehicular Technology, Volume 44 Number 2, Pages 318-326.

Copyright

This document was written by John Reilly and it is the property of Sigma Wireless Technologies. All rights

reserved. No part of this publication may be reproduced, or transmitted in any form by any means,

electronic, mechanical, photocopying, recording or otherwise, without prior permission of Sigma Wireless

Technologies.