Proposal for Volume II of the Handbook



|[pic] | |ACP/WGF 26/WP XX |

| |International Civil Aviation Organization | |

| | | |

| |WORKING PAPER | |

| | | |

AERONAUTICAL COMMUNICATIONS PANEL (ACP)

26TH MEETING OF THE WORKING GROUP F

Montreal, Canada, 21 – 30 March 2012

|Agenda Item 4 : |Review, update and development of the ICAO Frequency Spectrum Handbook |

Proposal for Volume II of the Handbook

(Presented by the John Mettrop)

|SUMMARY |

|This paper proposes an alternative structure and revised generic methodology for Volume II of the ICAO |

|Frequency Spectrum Handbook. |

|ACTION |

|The meeting is invited to consider this proposed structure and generic methodology as the basis for |

|further work on volume II ICAO Frequency Spectrum Handbook |

INTRODUCTION

Working Group F agreed to the development of a second volume of the Frequency Spectrum Handbook at it’s 18th meeting in 2008. Since then a number of proposals for text on a generic compatibility methodology , the planning of VHF communications frequencies and associated background material have been received, the latest being to this meeting.

discussion

Reviewing the proposal for sections of volume II of the Frequency Spectrum Handbook, I would support the general principles behind the work. Recommendation ITU-R SM.337 is a sound model to use for assessing compatibility and there has been a lot of good work on the rest of the document. I do however have a number of observations on that document, the more substantive ones being listed below:-

1) The document appears to focus on the planning of aeronautical systems however my understanding was that this section should provide more technical information not only on the planning of aeronautical systems but also the protection of aeronautical systems from interference from non-aeronautical systems.

2) The general methodology should be a stand-alone section and not include information on VHF communications planning as it should be applied universally rather than to the specifics of VHF.

3) The methodology contained in ITU-R SM.337 is complex and hard to apply.

4) Translation of the 14 and 20 dB desired to undesired ratios in to distance ratios only applies when the transmit powers of the wanted and unwanted are the same. This, in my experience, is rarely the case. It would be better to use the generic planning criteria and then provide a simplification using the distance ratio’s with the relevant caveats.

5) When considering area services there appears to be a mis-understanding of how the radio horizon criteria is applied.

Whilst I support the general approach taken and think that the work is valuable, I would suggest that it could be structured slightly better keeping each section distinct, that the generic methodology is made stand-alone and simplified, and that there is a section on protection of aeronautical systems from other systems. To this end I attaché the work I have completed so far on an alternative structure to the Volume II that uses the simpler net filter discrimination methodology as the generic compatibility methodology for consideration. The net filter discrimination is based on ITU-R SM.337 but simplies the model to use the equipment RF masks.

ACTION BY THE MEETING

The ACP WGF is invited to consider the attachment as a potential structure and draft content for Volume II of the ICAO Frequency Spectrum Handbook.

Attachment

Table of Contents

1 Chapter 1 General Methodology for Compatibility Analysis

1.1 Introduction

This chapter describes a general methodology, base on ITU-R Recommendation SM.337, which can be used in the analysis of interference between and within radio systems. The methodology contained in ITU-R SM.337 calculates the distance and frequency separation required for an acceptable level of interference, based on the measured transmit spectral masks of the transmitters and receivers.

The methodology described rather than using the measured spectral masks uses the transmitted spectrum density mask and receiver selectivity mask defined for the systems being considered and is commonly referred to as net filter discrimination.

1.2 Methodology

1.2.1 Introduction

The electromagnetic compatibility of radio equipment should be calculated by the following method:

Step 1: determine the desired signal level at the victim receiver front end;

Step 2: determine the resulting level of interference at the victim receiver’s front end taking into account the Receiver selectivity mask;

Step 3: determine the required separation distance for a given frequency offset to ensure that any interference received by the victim receiver is permissible;

Step 4: determine, if necessary, the relationship between frequency offset and separation distance for a range of offset values.

The diagram below illustrates the scenario to be considered.

[pic]

Figure 1: Schematic diagram of the Scenario to be Analysed

Where:-

Fd: feeder loss for the desired transmitter (dB)

Fr: feeder loss of the receiver (dB)

Fu: feeder loss for the undesired transmitter (dB)

Gd: gain of the desired antenna (dBi)

Gr: gain of he receive antenna (dBi)

Gu: gain of the undesired antenna (dBi)

Ld: propagation loss for the desired signal (dB)

Lu: propagation loss for the undesired signal (dB)

NFDd: net filter discrimination of the desired signal due to receiver filtering (dB)

NFDu: net filter discrimination of the undesired signal due to receiver filtering (dB)

PTd: output power of the desired transmitter (dBW)

PTu : output power of the undesired transmitter (dBW)

In certain circumstances the minimum signal level of the wanted signal at the antenna of the receiver may be described. Where this is the case and it is legitimate to consider the worst case scenario, such as when protecting an aeronautical service then the scenario can be simplified as shown below and the analysis is based on the minimum desired signal at the receive antenna (PTdm):

[pic]

Figure 2: Schematic diagram of the Simplified Scenario to be Analysed

1.2.2 Calculation of the Desired Signal at the Victim Receiver

The following diagram illustrates the scenario to be analysed.

[pic]

Figure 3: Schematic diagram of the Desired Signal Path to be Analysed

The received power at the output of the RF discriminator (Pd) can be calculated by summing the various powers, gains and losses as indicated in the formula below:-

[pic]

Where:-

Fd: feeder loss for the desired transmitter (dB)

Fr: feeder loss of the receiver (dB)

Gd: gain of the desired antenna (dBi)

Gr: gain of he receive antenna (dBi)

Ld: propagation loss for the desired signal (dB)

NFDd: net filter discrimination of the desired signal (dB)[1]

PTd: output power of the desired transmitter (dBW)

The propagation loss is calculated in accordance with one of the various propagation models developed by the ITU. See section 1.3 for further guidance on the relevant ITU propagation models and how to use then to calculate the path loss. Section 1.4.2 provides guidance on the calculation of the net filter discrimination. Where the minimum desired signal at the receive antenna is used then the equation above can be simplified as shown below:-

[pic]

1.2.3 Calculation of the Undesired signal at the Victim Receiver for a given frequency offset

The following diagram illustrates the undesired signal path to be analysed.

[pic]

Figure 1: Schematic diagram of the Undesired Signal Path to be Analysed

The received power at the output of the RF discriminator (Pd) can be calculated by summing the various powers, gains and losses as indicated in the formula below and should be expressed in terms of a separation distance :-

[pic]

Where:-

Fu: feeder loss for the undesired transmitter (dB)

Fr: feeder loss of the receiver (dB)

Gu: gain of the undesired antenna (dBi)

Gr: gain of he receive antenna (dBi)

Lu: propagation loss for the undesired signal (dB)

NFDu: net filter discrimination of the undesired signal (dB)

PTu: output power of the desired transmitter (dBW)

Pu: power of the undesired signal (dBW)

The propagation loss is calculated in accordance with one of the various propagation models developed by the ITU. See section 1.3 for further guidance on the relevant ITU propagation models and how to use then to calculate the path loss. Section 1.4 provides guidance on the calculation of the net filter discrimination.

1.2.3 Calculation of the Required Separation Distance for a given Frequency Offset

The power from the desired signal and that of the undesired signal at the receiver’s detector are obtained from sections 1.2.2 and 1.2.3 with the undesired signal strength being expressed in terms of a separation distance. Knowing the minimum required protection ratio then the maximum power of the undesired signal can be determined by taking the required protection ratio from the desired signal.

[pic]

Where:-

Pu: power of the undesired signal at the receiver detector (dBW)

Pd: power of the desired signal at the receiver detector (dBW)

PR: Protection ratio (dB)

Equating the Pu calculated above for the Pu calculated in section 1.2.2 expressed in terms of a separation distance and resolving the equation gives the minimum separation distance required.

Note: if this process is being used for determining compatibility between an aeronautical system and a non-aeronautical system then a 6dB safety margin should be added

If a curve of separation distance vs frequency offset is required then the process should be repeated for the desired number of points and the results plotted and used in the study.

1.3 Propagation modelling

1.3.1 Introduction

The ITU has developed a number of propagation models some of which are applicable to the study of the planning criteria for aeronautical systems and the protection of those systems from interference from other radio systems that are either sharing the frequency band or operating in adjacent frequency band.

The common propagation models used in aeronautical spectrum studies are described in sections 1.3.2 – 1.3.4 and their applicability including the advantages and disadvantages are described in section 1.3.5.

1.3.2 Free – Space Propagation Model

The free space propagation model as defined in Recommendation ITU-R P.525 assumes an ideal propagation path where the antennas are replaced by isotropic antennas located in a perfectly dielectric, homogeneous, isotropic and unlimited environment with no obstructions.

[pic]

where:

Lbf : free-space basic transmission loss (dB)

d : distance

( : wavelength

Noting that d and ( are expressed in the same unit.

The same equation can be re-written using the frequency instead of the wavelength.

[pic]

where:

f : frequency (MHz)

d : distance (km).

or

[pic]

where:

f : frequency (MHz)

d : distance (NM)

It should be noted that the propagation of radio waves, typical VHF and UHF frequencies, is subject to a number of conditions, compare to the free space propagation. Refraction and ducting as described below as described below can extend the range over which this propagation model is applicable:

Refraction – refraction of radio waves in the atmosphere along the Earth’s surface bend slightly towards the Earth. The effect is that radio waves can propagate beyond the physical horizon to what is commonly referred to as the radio horizon with no other (significant) loss than the free space loss. This phenomenon is corrected in radio propagation by using a 4/3 Earth radius. The radio horizon is calculated using a 4/3 Earth radius.

Ducting – Unusual weather conditions (or other phenomena such as sand storms) can bend the radio waves more than normal and VHF or UHF radio frequencies can be received without significant attenuation over longer distances. In aeronautical frequency assignment planning this phenomenon is not normally taken into account.

As a result of these two conditions this propagation model is applicable within the radio horizon as defined using 4/3 Earth radius rather than the physical horizon. The radio horizon can therefore be calculated using the following formula:-

[pic]

where

dRH: the distance of the station to the radio horizon (NM)

hTx: the height of the transmitter above the Earth’s surface (feet)

Applying this to the transmitter and receiver then you get the following equation for the radio horizon separation distance between the transmitter and receiver:-

[pic]

where

SD: the radio horizon separation distance between the transmitter and receiver (NM)

hTx: the height of the transmitter above the Earth’s surface (feet)

hRx: the height of the receiver above the Earth’s surface (feet)

1.3.3 Aeronautical standard propagation model

The aeronautical standard propagation model is contained in Recommendation ITU-R P.528 “propagation curves for aeronautical mobile and radionavigation services using the VHF, UHF and SHF bands”. This propagation model is based on empirical data for 5%, 50% and 95% time availability. Within the radio horizon this propagation model is consistent with free-space path loss allowing for a dB offset to account for the various time availability percentages.

The model however is also valid where the propagation path extends beyond the radio horizon for propagation beyond the radio horizon. The curves from ITU-R P.528 are contained in appendix X .

A Windows version of this model is contained in the ICAO frequency assignment planning program FREQUENCY FINDER and can be used for assessing more precise signal parameters. Normally, for radio paths up to the radio horizon, aeronautical frequency assignment planning is based on free space propagation. Applying the IF-77 model may result in a more accurate prediction of the actual radio wave propagation characteristics.

For propagation over the horizon and based on ITU-R P.528 curves for 125 MHz, 1 200 MHz and 5 100MHz the following path losses per nautical mile (a) can be used to simply estimate the path loss beyond the radio horizon.

in the band 108 – 137 MHz a is 0.5 dB/NM

in the band 960 – 1215 MHz a is 1.6 dB/NM

in the band 5030 – 5091 MHz a is 2.7 dB/NM

Where

d ≤ SD, (i.e. the receiver is within direct radio line of sight of the transmitter) the basic transmission (or propagation) loss between the transmitter Tx and the receiver Rx is

[pic]

d > SD, (i.e. the receiver is within direct radio line of sight of the transmitter)the basic transmission loss between the transmitter Tx and the receiver Rx is

[pic]

1.3.3 Microwave interference for stations located on the earth’s surface

Description of ITU-R P.452

1.3.4 Applicability of propagation models

1.4 Net filter discrimination

1.4.1 Introduction

Net filter discrimination calculates the rejection of the received signal, whether that is the desired or undesired, resulting from the filtering in the receiver. The method is based on that described in ITU-R SM.337 but instead of using the measured mask it uses the regulatory mask. By using the regulatory mask the results will underestimate the rejection and hence be pessimistic although this will err on the safe side.

1.4.2 Masks Discrimination – MD

The Masks Discrimination (MD) expresses the reduction (in dB) of the signal power caused by the filter shape of the transmitter spectrum density mask and the receiver selectivity mask.

MD is calculated as follows :

MD = 10 log (TX area/ overlapping area at co-channel)

1.4.2.1 Calculation of the TX area

An example of a transmitter spectrum density mask is given in Figure 1. The mask can be split up into different elements. The areas of these elements are relative power portions to the transmitter power. The area within the entire mask represents the TX area.

[pic]

Figure

Flat elements have to be calculated using formula 2.1 with ri= 0 (see below), slope elements have to be calculated using formula 2.2 with ri= 0 (see below).

1.4.2.2 Calculation of the overlapping area at co-channel

An example of the overlapping area at co channel between transmitter spectrum density mask and receiver selectivity mask is given in Figure 2.

[pic]

Figure  

The common frequency range at co channel has to be split into flat and slope partial elements. Flat element (F) is a partial element where both masks are flat. Slope element (S) is a partial element where at least in one partial element a slope is detected.

Flat elements have to be calculated using formula 2.1; slope elements have to be calculated using formula 2.2.

The overlapping area is the sum of all partial elements calculated using formulas 2.1 and 2.2 in the common frequency range at co channel.

1.4.3 Net Filter Discrimination - NFD

The Net Filter Discrimination (NFD) expresses the reduction (in dB) of the signal power if the transmitter and receiver frequencies are different.

The NFD value can be determined by measurement or by calculation.

1.4.3.1 Calculation method

The NFD is defined as:

[pic]

Where:

Pc: the total power received after co-channel RF, IF and base band filtering.

Pa: he total power received after offset RF, IF and base band filtering.

For calculation of the power ratio (Pc/Pa) in the common frequency case the overlapping area is considered only.

For the calculation of Pc and Pa the same transmitter power is used and therefore the formula for NFD can be

NFD = 10 log (overlapping area at co-channel / overlapping area at frequency offset)

Pc is calculated taking the overlapping area of TX spectrum density mask and RX selectivity mask at same operational frequency

An example of the overlapping area at co channel between transmitter spectrum density mask and receiver selectivity mask is given in Figure 5.

[pic]

Figure X

The calculation method is based on integration of the spectrum density of the transmitter spectrum density mask and the receiver selectivity mask in the common frequency range at co channel.

The common frequency range at co channel has to be split into flat and slope partial elements. Flat element (F) is a partial element where both masks are flat, Slope element (S) is an partial element where at least in one partial element a slope is detected.

Flat elements have to be calculated using formula 2.1, slope elements have to be calculated using formula 2.2.

The overlapping area at co channel is the sum of all partial elements calculated using formulas 2.1 and 2.2 in the common frequency range of both masks.

Pa is calculated taking the overlapping area of TX spectrum density mask and RX selectivity mask with the frequency offset:

The common frequency range is the part where both masks are overlapping each other.

An example of the common frequency range at frequency offset between transmitter spectrum density mask and receiver selectivity mask is given in Figure 6.

[pic]

Figure 6

The calculation method is based on integration of the spectrum density of the transmitter spectrum density mask and the receiver selectivity mask in the common frequency range.

The common frequency range has to be split into flat and slope partial elements. Flat element (F) is a partial element where both masks are flat, Slope element (S) is an partial element where at least in one partial element a slope is detected.

Flat elements have to be calculated using formula 2.1, slope elements have to be calculated using formula 2.2.

The overlapping area is the sum of all partial elements calculated using formulas 2.1 and 2.2 in the common frequency range of both masks.

Flat element areas (F) can be calculated according to following formula:

[pic] (2.1)

Where:

For the element F

[pic] [pic]

With [pic]

Where

b: sum of the attenuation of the transmitter ([pic]) and receiver ([pic]) masks at the beginning or at the end of an element (dB),

fi+1: frequency at the end of the element (MHz),

fi: frequency at the beginning of the element (MHz),

fc: bandwidth of the element (MHz),

F: partial elements areas under the spectrum masks in the common frequency range.

Slope element areas (S) can be calculated according to following formula:

[pic] (2.2)

Note: this is only true if a does not equal 0

For the element F

[pic] [pic] [pic]

With [pic]

If the two corresponding elements of the masks represent inverted inclinations, the parameter a may turns to 0. When a=0, the formula (2.1) shall be applied.

Where:

b: sum of the attenuation of the transmitter (ti) and receiver (ri) masks at the end of an element (dB),

ti: transmitter mask attenuation at the beginning of an element (dB),

ri: receiver selectivity mask attenuation at the beginning of the element (dB),

fi: frequency at the beginning of the element (MHz),

fc: bandwidth of the element (MHz),

S: partial elements areas under the spectrum masks in the common frequency range.

ti+1: transmitter mask attenuation at the end of the element (dB),

ri+1: receiver selectivity mask attenuation at the end of the element (dB),

fi+1: frequency at the end of the element (MHz),

[pic] (2.1)

|where: | | | |

| |for the element F |[pic] |[pic] |

|where: |

|b |sum of the attenuation of the transmitter ([pic]) and receiver ([pic]) masks at the beginning of an element |

| |(dB), |

| | |

| | |

|fi |frequency at the beginning and at the end of the element (MHz), |

|fc |bandwidth of the element (MHz), |

|F |partial elements areas under the spectrum masks in the common frequency range. |

Slope element areas (S) can be calculated according to following formula:

|[pic] | |

| | |

| |(2.2) |

| | | | | |

| |for the element S |[pic] |[pic] |[pic] |

|where: |

|b |sum of the attenuation of the transmitter and receiver masks at the beginning of an element (dB), |

|ti |transmitter mask attenuation at the beginning and at the end of an element (dB), |

|ri |receiver selectivity mask attenuation at the beginning and at the end of the element (dB), |

|fi |frequency at the beginning and at the end of the element (MHz), |

|fc |bandwidth of the element (MHz), |

|S |partial elements areas under the spectrum masks in the common frequency range. |

1.4.4 Necessary data for the calculation of mask discrimination and net filter discrimination

Transmitter spectrum density masks: For the calculation, the real spectrum density mask shall be used and described in Paragraph 3.3.1. If this mask is not available, the relevant transmitter masks shall be used.

Receiver selectivity mask: For the calculation, the real receiver selectivity mask shall be used and described in Paragraph 3.3.1. If this mask is not available, the relevant transmitter mask of the accompanying transmitter can be used as receiver selectivity mask.

Necessary data for the data exchange procedure: At least two points of each, the transmitter spectrum density mask and the receiver selectivity mask, have to be provided (see Figure 7).

• Each point is defined by its frequency (MHz) and its attenuation (dB).

• The first point (which is not a part of the data exchange procedure) is automatically defined as 0 MHz and 0 dB.

• The last point must be set for the attenuation of ( 40 dB.

The NFD values for the first adjacent channel, named NFD 1 (+ 1 channel spacing), and the second adjacent channel, named NFD 2 (+ 2 channels spacing), shall be derived from measured data, if available.

In order to use NFD1 and NFD2 values, the following conditions must be fulfilled:

• the interferer and interfered equipment must be produced by the same supplier, and have the same identification;

• the interferer and interfered frequencies must belong to the same frequency plan;

• the capacities (Mbit/s) of the interferer and interfered equipment must be the same.

[pic]

2 Chapter 2 Planning of Aeronautical Systems

2.1 Non-Directional Beacons (130 – 535 kHz)

2.2 HF Air Ground Communications (2 850 – 22 000 kHz)

2.3 Instrument Landing System (74.8 – 75.2, 108 – 112 & 328.6 – 335.4 MHz)

2.4 VHF Omni-direction Ranging (108 – 117.975 MHz)

2.5 Ground Based Augmentation System (108 – 117.975 MHz)

2.6 VHF Air Ground Communications (112 – 137 MHz)

2.7 Emergency Locator Transmitters (406 – 406.1 MHz)

2.8 Distance Measuring Equipment (960 – 1 215 MHz)

2.9 Universal Access Transceiver (977 MHz)

2.10 Secondary Surveillance Radar (1 030 & 1 090 MHz)

2.11 Airborne Collision Avoidance System (1 030 & 1 090 MHz)

2.12 Satellite Navigation (1 164 – 1 215 & 1 559 – 1 626.5 MHz)

2.13 Satellite Communications (1 525 – 1 559, 1 626.5 – 1 660.& 5 000 – 5 150 MHz)

2.14 Ground Based Primary Surveillance Radar

2.14.1 L-Band (1 215 – 1 400 MHz)

2.14.2 S-Band (2 700 – 3 300 MHz)

2.14.3 X-Band (9 000 -9 500 MHz)

2.14.4 Ku/K/Ka-Band (15.4 – 15.7, 24.25 – 24.65 & 31.8 – 33.4 GHz)

2.15 Radio Altimeters (4 200 – 4 400 MHz)

2.16 Microwave Landing Systems (5 000 – 5 250 MHz)

2.17 Airport Surface Communications (5 091 – 5 150 MHz)

2.18 Airborne Weather Radar (5 350 – 5 470 MHz, 9 000 – 9 500 MHz, 13.25 – 13.4 GHz, 15.4 – 15.7 GHz)

2.19 Airborne Doppler Radar (8 750 – 8 850 MHz)

3 Chapter 3 Protection of Aeronautical Systems

3.1 Non-Directional Beacons (130 – 535 kHz)

3.2 HF Air Ground Communications (2 850 – 22 000 kHz)

3.3 Instrument Landing System (74.8 – 75.2, 108 – 112 & 328.6 – 335.4 MHz)

3.4 VHF Omni-direction Ranging (108 – 117.975 MHz)

3.5 Ground Based Augmentation System (108 – 117.975 MHz)

3.6 VHF Air Ground Communications (112 – 137 MHz)

3.7 Emergency Locator Transmitters (406 – 406.1 MHz)

2.8 Distance Measuring Equipment (960 – 1 215 MHz)

2.9 Universal Access Transceiver (977 MHz)

2.10 Secondary Surveillance Radar (1 030 & 1 090 MHz)

2.11 Airborne Collision Avoidance System (1 030 & 1 090 MHz)

2.12 Satellite Navigation (1 164 – 1 215 & 1 559 – 1 626.5 MHz)

2.13 Satellite Communications (1 525 – 1 559, 1 626.5 – 1 660.& 5 000 – 5 150 MHz)

2.14 Ground Based Primary Surveillance Radar

2.14.1 L-Band (1 215 – 1 400 MHz)

2.14.2 S-Band (2 700 – 3 300 MHz)

2.14.3 X-Band (9 000 -9 500 MHz)

2.14.4 Ku/K/Ka-Band (15.4 – 15.7, 24.25 – 24.65 & 31.8 – 33.4 GHz)

2.15 Radio Altimeters (4 200 – 4 400 MHz)

2.16 Microwave Landing Systems (5 000 – 5 250 MHz)

2.17 Airport Surface Communications (5 091 – 5 150 MHz)

2.18 Airborne Weather Radar (5 350 – 5 470 MHz, 9 000 – 9 500 MHz, 13.25 – 13.4 GHz, 15.4 – 15.7 GHz)

2.19 Airborne Doppler Radar (8 750 – 8 850 MHz)

-----------------------

[1] Since we can assume that the desired signal will be co-channel with the receiver the simpler form of net filter discrimination, mask discrimination can be used.

-----------------------

f0 f1 f2 f3 f4 f5

t4

Freq.

Common frequency range at co channel

t7

t5

t0,1,2,3=0

r4,5

r2,3

f0 f1 f2 f3 f4 f5 f7

a5

a4

a2,3

a0,1= 0

Calc. Point

ai = ti + ri

S

S S

F

r0,1=0 F

F

S

S

S

Freq.

RX Atten.

Calc. Point

ri, ti

Freq.

TX Atten.

S

Overlapping area at co channel

Atten.

f0 f1 f2 f3 f4 f5

t4

Freq.

Common frequency range at co channel

t7

t5

t0,1,2,3=0

r4,5

r2,3

f0 f1 f2 f3 f4 f5 f7

a5

a4

a2,3

a0,1= 0

Calc. Point

ai = ti + ri

S

S S

F

r0,1=0 F

F

S

S

S

Freq.

RX Atten.

Calc. Point

ri, ti

Freq.

TX Atten.

S

Overlapping area at co channel

Atten.

F = flat area element

S = slope area element

S

S

S

F

F

F

F

S

S

S

S

F

f0 f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12

r9,10,11,12

a5,6,7

S

S

S

f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12

r9,10,11,12

a5,6,7

S

S

S

S

S

S

S

F

F

F

t2,3,9,10

a0,1

Calc. Point

ai = ti + ri

r8

r3

r5, 6,7

r0,1,2

t4,5,6,7

Freq.

Tx Atten. ti

Rx Atten. ri

Calc. Point

ri , ti

Δ

f

Freq.

Common frequency range with frequency offset

Overlapping area with frequency offset

t0,1,11,12

f0 f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12

a11,12

a3

a8

a4

0

a2

F

a9,10

Freq.

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