New ECC Report Style

CEPT
SE21(16)xx
ECC
Electronic Communications Committee
Project Team SE21
96st Meeting ECC PT SE21
4-5 July 2016, Copenhagen, Denmark
Date issued:
Source:
1 July 2016
SE21_19 Work Item Convener
Subject: Unwanted Emissions – Guidance and Methodologies when using typical
equipment performance in sharing and compatibility studies
Group membership required to read? (Y/N): N
Summary:
To provide a starting template for the draft new recommendation / report ‘Unwanted Emissions – Guidance
and Methodologies when using typical equipment performance in sharing and compatibility studies’
Proposal:
SE21 to consider adopting this document as a starting point
Background:
In April 2016 CEPT Working Group Spectrum Engineering (WGSE) approved ECC Report 249 ‘Unwanted
emissions of common radio systems: measurements and use in sharing/compatibility studies’ for publication.
WGSE also discussed and approved the new work item SE21_19 and requested that SE21 to further its work
on unwanted emissions. This new deliverable is a ECC Report / Recommendation on Unwanted Emissions –
Guidance and methodologies when using typical equipment performance in sharing/compatibility studies
ECC Recommendation
/ Report <No>
Unwanted Emissions – Guidance and methodologies
when using typical equipment performance in
sharing/compatibility studies
approved DD Month YYYY (Arial 9)
[last updated: DD Month YYYY] (Arial 9)
0 EXECUTIVE SUMMARY (STYLE: ECC HEADING 1)
Body text (style: ECC Paragraph)1
(advice: the Executive Summary should provide a short and concise explanation on the purpose of the
respective ECC Report and should clearly indicate the covered subjects to which it applies. In addition, it
should clearly explain the application of the document.)
1
Example of Footnote
TABLE OF CONTENTS
0
EXECUTIVE SUMMARY (STYLE: ECC HEADING 1) ............................................................................... 3
1
INTRODUCTION ......................................................................................................................................... 7
2
DEFINITIONS (OPTIONAL SECTION) ....................................................................................................... 8
3
HEADING (STYLE: ECC HEADING 1) ...................................................................................................... 9
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3.3 Example of numbered lists ................................................................ Error! Bookmark not defined.
3.4 Example of lettered lists ..................................................................... Error! Bookmark not defined.
3.5 Examples of figures and tables.......................................................... Error! Bookmark not defined.
4
CONCLUSIONS ........................................................................................................................................ 22
ANNEX 1: HEADING (STYLE: ECC ANNEX - HEADING1) ............... ERROR! BOOKMARK NOT DEFINED.
ANNEX 2: HEADING (STYLE: ECC ANNEX - HEADING1) ............... ERROR! BOOKMARK NOT DEFINED.
ANNEX 3: LIST OF REFERENCE .................................................................................................................. 24
Note on the Table of Contents (delete after reading)
This is automatically styled and compiled from the headings,
subheadings and page numbers from the document that
follows. To update the Table of Contents move cursor within
the table and press F9.
LIST OF ABBREVIATIONS
Editor's Note 1:
Abbreviations coppied from ECC report 249 - these need review
Abbreviation
Explanation
3GPP
3rd Generation Partnership Project
AM
Amplitude Modulation
BCCH
Broadcast Control Channel
BS
Base Station
BW
Bandwidth
CEPT
European Conference of Postal and Telecommunications Administrations
CQPSK
Complementary Quadrature Phase Shift Keying
D/A
Digital to Analogue
DAB
Digital Audio Broadcasting
DECT
Digital Enhanced Cordless Telecommunications
DSP
Digital Signal Processor
DSSS
Direct-Sequence Spread Spectrum
DVB-T
Digital Video Broadcasting – Terrestrial
ECC
Electronic Communications Committee
ERC
European Radiocommunications Committee
e.i.r.p.
Equivalent Isotropically Radiated Power
e.r.p.
Effective Radiated Power
ETSI
European Telecommunications Standards Institute
E-UTRA
Evolved Universal Terrestrial Radio Access
FDD
Frequency Division Duplex
FM
Frequency Modulation
FS
Fixed Service
FSK
Frequency Shift Keying
GMSK
Gaussian Minimum Shift Keying
GSM
Global System for Mobile Communications
G-TEM
Gigahertz Transverse Electromagnetic
IEEE
Institute of Electrical and Electronics Engineers
IMT
International Mobile Telecommunications
ITU
International Telecommunication Union
ITU-R
International Telecommunication Union - Radiocommunication Sector
I/Q
In-phase/Quadrature
Abbreviation
Explanation
LTE
Long Term Evolution
MSR
Multi Standard Radio
OFDM
Orthogonal Frequency-Division Multiplexing
OoB
Out-of-Band
PCS
Personal Communications System
PEP
Peak Envelope Power
PSD
Power Spectral Density
PMR
Private Mobile Radio
QAM
Quadrature Amplitude Modulation
QPSK
Quadrature Phase Shift Keying
RAT
Radio Access Technology
RB
Resource Block
RF
Radio Frequency
RLAN
Radio Local Area Network
RMS
Root Mean Square
RR
ITU Radio Regulations
Rx
Receiver
SC-FDMA
Single Carrier Frequency Division Multiple Access
SEAMCAT
Spectrum Engineering Advanced Monte Carlo Analysis Tool
SEM
Spectrum Emission Mask
SRD
Short Range Devices
SSB
Single-Sideband Modulation
TDD
Time Division Duplex
TDMA
Time Division Multiple Access
TETRA
Terrestrial Trunked Radio
TFES
TC MSG / TC ERM Task Force for the production of Harmonised Standards under
the R&TTE Directive for the IMT family
Tx
Transmitter
UE
User Equipment
UMTS
Universal Mobile Telecommunications System
UTRA
Universal Terrestrial Radio Access
VHF
Very High Frequency
W-CDMA
Wideband Code Division Multiple Access
WiMAX
Worldwide Interoperability for Microwave Access
WLAN
Wireless Local Area Network
WRC
World Radio Conference
1
INTRODUCTION
Editor's Note 2:
Introduction needed
2
DEFINITIONS (OPTIONAL SECTION)
Editor's Note 3:
Abbreviations coppied from ECC report 249 - these need review
Term
Definition
Emission (1.138)
Radiation produced, or the production of radiation, by a radio transmitting
station.
Out-of-band
emission (1.144)
Emission on a frequency or frequencies immediately outside the necessary
bandwidth which results from the modulation process, but excluding spurious
emissions.
Spurious emission
(1.145)
Emission on a frequency or frequencies which are outside the necessary
bandwidth and the level of which may be reduced without affecting the
corresponding transmission of information. Spurious emissions include harmonic
emissions, parasitic emissions, intermodulation products and frequency
conversion products, but exclude out-of-band emissions.
Unwanted
emissions (1.146)
Consist of spurious emissions and out-of-band emissions.
Out-of-band
domain
(of
an
emission) (1.146A)
The frequency range, immediately outside the necessary bandwidth but
excluding the spurious domain, in which out-of-band emissions generally
predominate. Out-of-band emissions, defined based on their source, occur in the
out-of-band domain and, to a lesser extent, in the spurious domain. Spurious
emissions likewise may occur in the out-of-band domain as well as in the
spurious domain. (WRC-03)
Spurious domain
(of an emission)
(1.146B)
The frequency range beyond the out-of-band domain in which spurious
emissions generally predominate. (WRC-03)
Necessary
bandwidth (1.152)
For a given class of emission (RR 1.139), the width of the frequency band which
is just sufficient to ensure the transmission of information at the rate and with the
quality required under specified conditions.
Occupied
bandwidth (1.153)
The width of a frequency band such that, below the lower and above the upper
frequency limits, the mean powers emitted are each equal to a specified
percentage β/2 of the total mean power of a given emission.
Unless otherwise specified in an ITU-R Recommendation for the appropriate
class of emission, the value of β /2 should be taken as 0.5%.
Frequency
assignment (1.18)
Assignment (of a radio frequency or radio frequency channel): authorization
given by an administration for a radio station to use a radio frequency or radio
frequency channel under specified conditions.
Conducted power
Power of wanted and/or unwanted emissions measured at the transmitter output
or antenna feed
Radiated power
Power of wanted and/or unwanted emissions radiated from the transmitting
antenna. This power is determined through calculation based on field strength
measurement off air and the formula for free space attenuation.
1
Numbers in brackets refer to paragraph numbers in the ITU Radio Regulations [4]
3
SCOPE
Editor's Note 4:
Taken from the scope of the SE21_19 work item / deleliverable
Deliverable: ECC Recomendation / Report
a) To be used by other CEPT / ECC groups when conducting sharing/compatibility studies
b) To provide clear guidance on the use of the typical performance of equipment in
sharing/compatibility studies in addition to limits e.g. those set in ECC Recommendation (02)05,
ERC Recommendation 74-01 or European Harmonised Standards.

Further investigate and provide methodologies on the use of typical performance in
sharing/compatibility studies. This may include:

Guidance on defining typical performance of the equipment through measurements;
Defining a methodology for developing the distribution of values for typical performance of
equipment, for sharing/compatibility studies, this may include a guidance on determining an
‘average’ level of spurious emissions.

Defining a methodology to introduce power distribution in sharing/compatibility studies.

Guidance on use of a sensitivity analysis.

Provide guidance on how the boundary between the Out of Band domain and the Spurious
domain based on the 250% rule relates to the discontinuity of typical unwanted emissions in
the Out-of-band and Spurious domains.

Look for any baseline assumptions that can be defined for the typical performance of
equipment
that
can
be
used
in
sharing/compatibility
studies.
c) Changing limits in ERC Recommendation 74-01 is outside the scope of this work. However,
developing an informative annex to 74-01 could be within scope.
d) Liaise with other SE project teams and ETSI where appropriate.
e) Use ECC report 249 as a basis for this work. Other work references could include ECC Report
207 and ERC Report 065 which give examples of previous studies where performance better than
the limits were used.
4
METHODOLOGIES FOR USING TYPICAL EQUIPMENT PERFOMANCE IN SHARING STUDIES
Editor's Note 5:
Further investigate and provide methodologies on the use of typical performance in
sharing/compatibility studies. This may include:
5
GUIDANCE FOR DEFINING TYPICAL PERFOMANCE OF EQUIPMENT
Editor's Note 6:
Guidance on defining typical performance of the equipment through measurements;
Defining a methodology for developing the distribution of values for typical performance
of equipment, for sharing/compatibility studies, this may include a guidance on
determining an ‘average’ level of spurious emissions.
6
METHODOLOGIES FOR USING POWER DISTRIBUIONS
Editor's Note 7:
Defining a methodology to introduce power distribution in sharing/compatibility studies.
Editor's Note 8:
Input document SE21(16)07 Introduction of varible Power in Deterministic Studies France:
6.1
INTRODUCTION
Usually, in deterministic compatibility studies could use propagation model defining losses on the
considered path in terms of percentage of time. Some of these models are provided by ITU-R, especially
ITU-R P.2001, ITU-R P.452 and ITU-R P.1812. In order to protect the interfered receiver from the
interferer transmitter, the percentage of time introduce in the propagation model is often the percentage of
time of the permissive interference in the receiver (i.e. 2% for RAS, see ITU-R RA.769). For most
compatibility studies (depending of services) the interferer transmitter is considered as transmitting
constant and uniform power (or median power) in direction of the interfered receiver (The e.i.r.p could
change - in function of transmitter gain - but the power in unchanged). The presented methodology could
only be applied if emitted power and losses are totally independent. It’s important to notice that some
services present an emitted power fluctuation function of time in order to compensate the loss evolution.
In this particular case, this methodology would be totally inefficient. Today, new solution of power
representation are proposed and especially in terms of unwanted emission (particularly in spurious
domain). Some focuses are made on the development/building of probability distribution function in the
spurious domain in order to create representation as realistic as possible. In other terms, the idea is to
consider some floor values (-X dBm) during long percentage of time and to admit that spikes with higher
power could appear in some sporadic situation with a low percentage of time.
As described above, the introduction in compatibility studies of the emitter power variability is not trivial if
deterministic studies are expected. For dynamic or statistic studies, the situation is different and really
simple, by using random variable and/or Monte Carlo simulation. In a deterministic study, the convolution
has to be introduced. This contribution tries to give some methodology and guidance in order to
implement, if necessary, convolution in compatibility studies. Methodology is required due to the fact that
some propagation models are limited in terms of percentage of times (i.e. ITU-R P.452 and ITU-R
P.1812) and in this case convolutions have to be evaluated considering minimum assumptions.
6.2
THE CONVOLUTION PRODUCT
6.2.1 Generality
In probability theory, convolutions arise when we consider the distribution of sums of independent random
variables (RV). To see this, suppose that X and Y are independent, continuous random variables with
f X x and fY  y  . Let Z=g(X,Y) be a continuous random
variable obtained as a function of X and Y. Let us denote by FZ z  and f Z z  the cumulative
respective probability densityy functions (PDF)
distribution function (CDF) and resp. the PDF of Z. By definition the CDF of a RV is given by the following
equation:
 
FZ z   Pr Z  z 
Where Pr A is the probability of the event
the PDF of a RV is given as follows:
FZ z   Pr Z  z  
(1)
A . It is well known that the relation between the CDF and
dF z 
 f u du  f z   dz
z
Z
Z
Z

Let
DZ be a geometrical domain in the plane of X,Y defined by the following equation:
Z  g  X ,Y   z   X ,Y  Dz
Based on equations (2) and (3), we can write the following equation:
(2)
(3)
FZ z   Pr Z  z   Pr  X , Y  Dz  
z
 f u du   f x, y dxdy
Z
X ,Y

Here
f X ,Y x, y 
Dz
(4)
stands for the joint pdf of X and Y. Using equations (2) and (4), we can write the
dF  z 
f Z z   Z

dz
d  f X ,Y x, y dxdy
Dz
dz
following equation:
(5)
We should notice that equation (5) can be applied for any regular function g(X,Y). In the case of g(X,Y) is
reduced to the sum of these two variables, then equation (5) can be simplified:
Z  X  Y  z   X ,Y  Dz  Y , X X  z  Y 
 z  y
dF z 
f Z z   Z

dz
d
  f x, y dxdy
z y

X ,Y
 
dz



d
 f x, y dx

X ,Y

dz
dy 
 f z  y, y dy
X ,Y

(6)
Equation (6) can be simplified in the case of two independent RV X and Y. In fact, if X and Y are two
independent RV, then their joint PDF becomes the simple product of their marginal PDF:
indep
f X ,Y x, y   f X x  fY  y 
(7)
Based on equations (6) and (7); we can find the PDF of the sum of two independent RV:
f Z z  
dFZ z 
  f X z  y  fY  y dy  f X z  * fY z 
dz


(8)
Where * in the above equation defined the convolution product between two functions. For discrete RV,
equation (8) can be written as follows:
𝑃(𝑍 = 𝑧) = ∑𝑧−𝛿
(9)
𝑘=−𝛿 𝑃 (𝑋 = 𝑘) 𝑃( 𝑌 = 𝑧 − 𝑘)
Due to the mathematical intractability in implementing the discrete convolution formula, for certain no
identically distributed random variables [e.g., X ~ Poisson (λ), Y ~ geometric (p)] and the inefficiency in
making computations with this formula for random variables with arbitrary supports (e.g., X with support {216, -57, 23, 81} and Y with support {-1002, -15, 2, 62, 211} (the support values are the values of X or Y
corresponding to a non-zero probability), only certain convolutions can or should be computed using this
formula . For random variables with arbitrary supports, the discrete convolution formula can be used, but
it is often inefficient because one or both of the random variables have support values ranging over a
large domain of non adjacent integer values (see example 2 in [1]).
In others terms, to provide accurate convolution between random variables, it is better to use the same
interval in the support values of X and Y in order to be preserved to any difficulty
6.2.2 PDF versus CDF
The convolution product is made on the basis of the probability density function (PDF) of two
independent, continuous random variables. As mentioned after, in compatibility study, most of the input
parameters depending of the time are given in terms of cumulative distribution function (CDF). The CDF
FX x  of a continuous random variable 𝑋 can be simply expressed as the integral of its probability
density function f X x  as follows:
𝑥
𝐹𝑋 (𝑥) = ∫ 𝑓𝑋 (𝑡) 𝑑𝑡
−∞
In other word, the PDF is the derivative of the CDF and could be expressed as
d
𝑓𝑋 (𝑥) =
𝐹 (𝑥)
𝑑𝑥 𝑋
6.3
APPLICATION OF THE CONVOLUTION IN DETERMINIST COMPATIBILTY STUDIES
6.3.1 Usual Methodology of received power calculation
Usually, in deterministic studies, considering the emitter producing constant and uniform power, the
equation ruling the power at the input of the interfered receiver could be summarizing as:
Pr( p)  Pt  Gt  L ( p)  Gr
(1)
Where:
𝑃𝑡: Maximum available transmitting power level (dBW) in the reference bandwidth at the terminals of the
antenna of a transmitting interferer. Power is always considered as constant and uniform or as median.
𝑃𝑟(𝑝): Permissible interference power of an interfering emission (dBW) in the reference bandwidth to be
exceeded for no more than 𝑝% of the time at the terminals of the antenna of an interfered receiver
𝐺𝑡: Maximum antenna gain of the transmitter in direction of the receiver (dBi)
𝐺𝑟: The horizon gain of the receiver antenna in direction of the transmitter (dBi)
𝐿(𝑝): The minimum required propagation loss (dB) for 𝑝% of the time
In this equation, no convolution is necessary and the percentage of time to introduce in the propagation
model is the time percentage of the permissible interference. In this model, if convolution have to be
introduced in this equation, it would be easy to say that the probability distribution function of power in this
case could be represented by a Dirac, with a percentage value equal to 1 (or 100%) and centred on the
constant power value.
6.3.2 Introduction of variable emitted power
First of all, in most of compatibility studies between different services, it is totally possible to consider that
emission distribution is totally independent of the evolution of the propagation losses. In fact, in
propagation model, the time fluctuation of losses is linked to considerations of atmosphere evolution,
particularly function of weather change. The emitted power generated by the interferer is not dependant
to this evolution. So, the independence between propagation losses and power variables could be
reached and the emitted power and propagation losses can be assumed as independent, continuous
random variables. In this case, Eq. (1) could be expressed as:
Pr( p)  Pt ( p1 )  L( p2 )  Gt  Gr
(2)
Where
𝑃𝑡(𝑝1 ): Power level (dBW) in the reference bandwidth at the terminals of the antenna of a transmitting
interferer not exceeded for 𝑝1 % of the time. The CDF of emitted power is described by 𝐹𝑃
𝐿 (𝑝2 ): The minimum required propagation loss (dB) not exceeded for 𝑝2 % of the time. The CDF of losses
are described by 𝐹𝐿
𝑃𝑟 (𝑝): Permissible interference power of an interfering emission (dBW) in the reference bandwidth to be
exceeded for no more than 𝑝% of the time at the terminals of the antenna of an interfered receiver
𝐺𝑡: Maximum antenna gain of the transmitter in direction of the receiver (dBi)
𝐺𝑟: The horizon gain of the receiver antenna in direction of the transmitter (dBi)
For some particular services, this independence between emitted power and losses is not respected
because power from emitted is adjusted in order to offset the propagation losses enabling a constant
received power in the receiver. In this particular case, the following methodology could not be applied..
As describe in section 2, the PDF of two independent random variablescould be obtained as the
convolution product of two marginal PDF. The losses given by propagation model developed by ITU-R
Study Group 3 are given in terms of CDF. As described above, there is no correlation between the PDFs
of Pt and L. Let us suppose that the variables 𝑃𝑡 and 𝐿 could be associated in a variable 𝑃𝐿 presenting
support values equal to the addition of all values supported by 𝑃𝑡 and 𝐿. At this new range of support
values could match a probability density function 𝑓𝑃𝐿 built on the convolution between the PDF of emitted
power 𝑓𝑃 and the PDF of 𝑓𝐿 . In this case the expression (2) could be expressed as:
Pr ( p)  PL ( p)  Gt  Gr
The proposed methodology is based on the fact that 𝐹𝑃 and 𝐹𝐿 are described between 0 to 100% of the
time. Several time dependant propagation models enable to evaluate the losses between two fixed points
(emitter and receiver). The most relevant models are described in ITU-R Recommendation:
-- ITU-R P.2001: This Recommendation contains a general purpose wide-range model for terrestrial
propagation which predicts path loss due to both signal enhancements and fading over effectively the
range 𝑝 from 0% to 100% of an average year. This makes the model particularly suitable for Monte-Carlo
methods, and studies in which it is desirable to use the same propagation model, with no discontinuities
in its output, for signals which may be either wanted or potentially interfering. The model covers the
frequency range from 30 MHz to 50 GHz, and distances from 3 km to at least 1 000 km. Noting that the
method is symmetrical.
-- ITU-R P.452: This Recommendation contains a prediction method for the evaluation of interference
between stations on the surface of the Earth at frequencies from about 0.1 GHz to 50 GHz, accounting for
both clear-air and hydrometeor scattering interference mechanisms. The models within Recommendation
ITU-R P.452 are designed to calculate propagation losses not exceeded for time percentages over the
range 0.001% ≤ 𝑝 ≤ 50%. This assumption does not imply the maximum loss will be at 𝑝 = 50%.
-- ITU-R P.1812: This Recommendation describes a propagation prediction method suitable for terrestrial
point-to-area services in the frequency range 30 MHz to 3 GHz for the detailed evaluation of signal levels
exceeded for a given percentage of time, 𝑝%, in the range 1% ≤ 𝑝 ≤ 50% and a given percentage of
locations, 𝑝𝐿 , in the range 1% ≤ 𝑝𝐿 ≤ 99%. The method provides detailed analysis based on the terrain
profile. The method is suitable for predictions for radio communication systems utilizing terrestrial circuits
having path lengths from 0.25 km up to about 3 000 km distance, with both terminals within approximately
3 km height above ground. It is not suitable for propagation predictions on either air-ground or spaceEarth radio circuits.
As described at the end of section 2.1, it’s better to use the same interval of support values in the random
variables. In other terms, the step between each support values of emitted power have to be identical as
it is for the loss values. For example, if the PDF of losses (𝐿) are described every 1dB, the PDF of emitted
power (𝑃𝑡) have to be described every 1dBm. At the end the support value of PL are linked to a kind of
“an emitted power closed to the receiver” (losses are subtracted) and are expressed in dBm. The support
values of losses have to express negatively.
6.3.3 The Convolution with ITU-R P.2001
The ITU-R P.2001 contains a general purpose wide-range model for terrestrial propagation which predicts
path loss due to both signal enhancements and fading over effectively the range 𝑝 from 0% to 100% of an
average year. This recommendation is particularly useful if convolution between losses and others terms
of the propagation equation is required.
As shown in Figure 1, The ITU-R P.2001 model provides the result of losses in terms of CDF. The
following steps explain the process to obtain first of all the CFD, the PDF of losses and finally the
convolution product between random variables 𝐿 and 𝑃𝑡.
Figure 1 : Evolution of the path AB losses in function time percentage. CDF is iven by ITU-R
P.2001 algorithm. PDF is derivated from CDF. Others curves are interpolation of PDF.
2
10
Derivated PDF
Calculated CDF by ITU-R P.2001
PDF (Cubic) interpolation every 1dB
PDF (Linear) interpolation every 1dB
1
10
0
Percentage of time
10
-1
10
-2
10
-3
10
-4
10
-5
10
120
140
160
180
200
Loss values (dB) between A and B
220
240
6.3.3.1
CDF acquisition & Discussion
In ITU-R P.2001, the percentage of time for which the basic transmission loss are not exceeded on the
path, have to be introduced as input. Unfortunately, to obtain useful CDF, some constraints have to be
considered. The most significant constraint is linked to the choice of the iterative step of time percentage.
In fact a calculation on a particular path for every 1% of the time (1%, 2%, 3%…10%…20%…100%)
would be inefficient du to the fact that the low percentage of time (0.001%...0.01%... 0.1%) would not be
considered, leading to a real lack of accuracy. The most powerful solution resides in a manual creation of
the time percentage for which losses have to be evaluated.
On a particular propagation path, different propagation mechanisms could appear. Usually for low terrain
elevation on a trans horizon path, it is common to evaluate the losses respectively for low and high
percentage of time as associated to ducting propagation and troposcatter.
As shown in Figure 2 in most case, it is possible to assess the middle of the CDF as something relatively
linear whereas the beginning and the end of the curves is totally nonlinear. In most test cases, simulation
provides same results as shown in Figure 2. So, globally the CDF curves of ITU-R P.2001 could be built
with several values in low and high time percentage and few values between approximatively 10 and
90%. The first proposed time percentage vector is 0.0001, 0.0005, 0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 1, 2,
3, 4, 5, 6, 7 8, 9, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 95, 99, 99.9, 99.99, 99.999 and 99.9999. This
vector could be reduced (see curves with yellow square and blue circle) as 0.0001, 0.001, 0.01, 0.1, 0.5,
1, 5, 10, 30, 50, 70, 90, 95, 99, 99.9, 99.99, 99.999, and 99.9999 and could pass from 31 to 17 values
(dimension n).
Figure 2 : Evolution of the losses CDF for different propagation path.
100
90
80
Percentage of time
70
60
50
40
30
Propagation path between A
Propagation path between A
Propagation path between A
Propagation path between A
20
10
0
120
140
160
and B - long vector
and C - long vector
and B - short vector
and D - long vector
180
200
220
240
Propagation losses (dB) between differents points
260
280
300
6.3.3.2
CDF and PDF acquisition
The second step is the derivation of the CDF in order to obtain the PDF. Figure 3 shows the result of the
direct discrete derivation (by difference) of the CDF for the path AB (loss CDF representation on Figure
(2)). The obtained PDF has a dimension of n-1. As shown the step between support values of losses PDF
is totally random and linked to the model (ITU-R P.2001) calculation for each percentage of time. As
described in section 2.1 and 3.2, for a relevant and efficient calculation of the convolution, it is preferable
to use a fixed interval between support values. In others terms, the losses PDF have to be interpolated.
The process is simple and only assumes to know the maximum and minimum value of calculated losses.
The interpolation of the PDF is made on the new support values from the minimum to the maximum of L
by step of 1dB.
Figure 3: Evolution of the losses PDF and CDF / PDF interpolation
2
10
1
10
0
Percentage of time
10
-1
10
-2
10
CDF of ITU-R P.2001
PDF from CDF derivation
PDF interpolation every 1dB
-3
10
-4
10
-5
10
-240
-220
-200
-180
Losses in dB
-160
-140
-120
The Figure 3 presents the losses in term of attenuation (in comparison of Figure 1). The step between
each support value could be lower and equal to 0.1 dB or less, but, as it will be presented in a following
section, in this case the “conventional” convolution algorithm generally based on the value indexes have
to be modified.
6.3.3.3
Emitted power PDF
If convolution is introduced in compatibility studies, the PDF of emitted power (the PDF shape) seems to
be an important factor. In fact, the emitted power could be expressed by a well-known probability
distribution shape. It could be made for example by a Normal distribution. In this contribution to provide
example and in order to be rational with the Report on characteristic emission of unwanted emission, a
Normal distribution is assumed and the emitted power is approximated presenting support values from 90 dBm to -30 dBm centred on -60 dBm (this representation is totally fictive). Figure 4 presents the
distribution of emitted power.
Figure 4: Shape of emitted power distribution
4
3.5
Percentage of time (%)
3
2.5
2
1.5
1
0.5
0
-90
-80
-70
-60
Emitted Power (dBm)
-50
-40
-30
As described in the previous section, the step between each support value of emitted power has to be
identical as it is for the losses PDF. In the presented figure, the step is equal to 1dBm.
6.3.3.4
The global convolution of Pt and L
At the end, the losses and emitted power PDFs are known and the support values sampling of each of
them is similar (1dB). The convolution could be reached.
On Figure 5, the convolution of L by Pt (named PL) is presented in terms of PDF and CDF. In order to
verify the given results, some approximation could be done. For example at 2% of the time, on the path
AB, the losses are equal to around 145 dB (see Figure 1). The median emitted power is -60 dBm (Figure
4). At the end, the association of ¨emitted power and losses at 2% of the time have to reach a value
closed to -205 dBm and the real convolution gives -220 dBm.
Figure 5 : Evolution of the PDF of PL by convolution of L and Pt. Representation of the CDF of PL
by integration
2
10
1
10
0
Percentage of time (%)
10
-1
10
-2
10
-3
10
Emitted Power Pt - PDF
Losses L - PDF
Convolution PL - PDF
Convolution PL - CDF
-4
10
-350
-300
-250
-200
-150
Values of Pt , PL (dBm) and L(dB)
-100
-50
0
6.3.4
The Convolution with ITU-R P.452 and P.1812
As described in section 3.2, the Recommendation ITU-R P.452 and P.1812 are limited in terms of time
percentage range: from 0.001% to 50 % for P.452 and from 1% to 50% for P.1812.
In the case of each border, the only solution consist in the prediction of the missed time percentage for
example, it could be done by saturation. In this case the support values of all the time percentage above
50 % would be the value at 50% exactly. The same process could be made for the lower border.
Unfortunately this process is not exact and could only approximate the real convolution.
7
GUIDANCE ON USE OF A SENSITIVITY ANALYSIS
Editor's Note 9:
Guidance on use of a sensitivity analysis
8
BOUNDRY BETWEEN OUT OF BAND AND SPRUIOUS DOMAINS FOR UNWANTED EMISSIONS
Editor's Note 10: Provide guidance on how the boundary between the Out of Band domain and the
Spurious domain based on the 250% rule relates to the discontinuity of typical
unwanted emissions in the Out-of-band and Spurious domains.
9
BASELINE ASSUMPTIONS FOR USE IN SHARING STUDIES
Editor's Note 11: Look for any baseline assumptions that can be defined for the typical performance of
equipment that can be used in sharing/compatibility studies.
10 CONCLUSIONS
Editor's Note 12: To be drafted
ANNEX 1:
ANNEX 2: LIST OF REFERENCE
Editor's Note 13: To be reviewed and added to
[1] ECC Report 249 Unwanted emissions of common radio systems: measurements and use in
sharing/compatibility studies
[2] ERC Recommendation 74-01 (Siófok 98, Nice 99, Sesimbra 02, Hradec Kralove 05, Cardiff 11)
‘Unwanted emissions in the spurious domain’.
[3] Recommendation ITU-R SM.329 ‘Unwanted emissions in the spurious domain’.
[4] ITU Radio Regulations, Edition of 2012.
[5] Recommendation ITU-R SM.1539 ‘Variation of the boundary between the out-of-band and spurious
domains required for the application of Recommendations ITU-R SM.1541 and ITU-R SM.329’.