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Sensitivity of Interference to Locations of Vehicle-Mounted Earth Stations Vijitha Weerackody The Johns Hopkins University, Applied Physics Laboratory 11100 Johns Hopkins Road, MD 20723 Email: [email protected] Abstract—Adjacent satellite interference from a satellite ter- minal depends on its location. Vehicle-mounted Earth stations (VMES) are mobile terminals and in many applications the locations of the VMES may be available only as approximate values. In this paper we investigate the effect on the adjacent satellite interference when the locations of the VMES are given by approximate values. I. I NTRODUCTION AND BACKGROUND Vehicle-Mounted Earth Stations (VMES) are new ter- minals with applications in both commercial and military sectors. These are mobile terminals that use small aperture antennas and may operate using time- or frequency-division multiple access schemes. To facilitate the use of VMES new regulations and standards are currently being established [1], [2], [3]. Because these terminals may operate in shared frequency bands with existing satellite and terrestrial ser- vices, satellite operators and regulators are concerned about potential interference from these terminals. To alleviate such concerns rules are currently being adopted that may require accurate determination and storage of the location of the VMES terminal. These requirements are necessary to confirm that the VMES is operating in compliance with the applicable regulations and without harmful interference. Moreover, location information of the VMES are necessary to determine the interference levels at a victim receiver. In this paper we investigate in detail the effect of the location accuracy of the VMES terminal on the interference to adjacent satellites. This analysis is very useful because accurate location recording requirements add to the cost and complexity of the VMES network. Because accurate locations of the VMES may not be available in some applications, it is useful to estimate the interference when the locations of the VMES are specified as approximate values rather than actual values. In this paper a methodology is given to estimate the interference resulting from VMES located at these approximate locations. In cases when it is necessary to estimate the actual interference, it is shown that the estimated interference obtained using approximated locations can be modified by adding an error term to give the actual interference. Also, we examine the impact of the equivalent isotropically radiated power (EIRP) level of the VMES on the interference level and demonstrate that the VMES may operate at slightly reduced EIRP levels so that the actual interference is less than the estimate interference using the approximated locations for most of the time. In general, because of factors such as mobility of the terminals, multiple access protocol and antenna pointing er- rors, interference from VMES terminals is a random process. Therefore, in this analysis we use statistical measures to quantify the sensitivity of the interference to the location of the terminal. The specific approach to this analysis is described in Section II. II. OVERVIEW OF ANALYSIS In this paper we carry out a statistical analysis of the interference power spectral density (PSD) that is received at a victim receiver of an adjacent satellite network. It is assumed that all link parameters necessary to compute this interference PSD are available. However, the actual locations of the terminals are not available but they are approximated by a set of predetermined grid points as described below. The location error of a terminal is given by the difference between the actual location of the terminal and its approximated value. The interference PSD computed using these approximated location data of the terminals could be more or less than its actual value resulting in, respectively, overestimation or underestimation of the inter- ference PSD. The difference in interference PSD when the actual and approximated location data are used is computed and its cumulative distribution function (CDF) obtained as a function of the location error of the terminals. Furthermore the error in the interference PSD, which is the difference between the interference PSDs when they are computed using the actual locations and their approximated values, is analyzed as a function of the distance between adjacent grid points and the EIRP of the terminals. The specific steps used in this analysis are described as follows. Step 1. Compute the interference PSD to a victim receiver in an adjacent satellite network and estimate its cumulative distribution function (CDF). This step makes use of the actual locations of the terminals and the relevant link parameters of the satellite networks. Step 2. In this step the interference PSD is estimated using the approximated locations of the terminals. Quantize the spatial region where the terminals are 2013 IEEE Military Communications Conference 978-0-7695-5124-1/13 $31.00 © 2013 IEEE DOI 10.1109/MILCOM.2013.309 1832 2013 IEEE Military Communications Conference 978-0-7695-5124-1/13 $31.00 © 2013 IEEE DOI 10.1109/MILCOM.2013.309 1832

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Page 1: [IEEE MILCOM 2013 - 2013 IEEE Military Communications Conference - San Diego, CA, USA (2013.11.18-2013.11.20)] MILCOM 2013 - 2013 IEEE Military Communications Conference - Sensitivity

Sensitivity of Interference to Locations of Vehicle-Mounted Earth Stations

Vijitha Weerackody

The Johns Hopkins University, Applied Physics Laboratory

11100 Johns Hopkins Road, MD 20723

Email: [email protected]

Abstract—Adjacent satellite interference from a satellite ter-minal depends on its location. Vehicle-mounted Earth stations(VMES) are mobile terminals and in many applications thelocations of the VMES may be available only as approximatevalues. In this paper we investigate the effect on the adjacentsatellite interference when the locations of the VMES are givenby approximate values.

I. INTRODUCTION AND BACKGROUND

Vehicle-Mounted Earth Stations (VMES) are new ter-

minals with applications in both commercial and military

sectors. These are mobile terminals that use small aperture

antennas and may operate using time- or frequency-division

multiple access schemes. To facilitate the use of VMES new

regulations and standards are currently being established

[1], [2], [3]. Because these terminals may operate in shared

frequency bands with existing satellite and terrestrial ser-

vices, satellite operators and regulators are concerned about

potential interference from these terminals. To alleviate

such concerns rules are currently being adopted that may

require accurate determination and storage of the location

of the VMES terminal. These requirements are necessary

to confirm that the VMES is operating in compliance with

the applicable regulations and without harmful interference.

Moreover, location information of the VMES are necessary

to determine the interference levels at a victim receiver.

In this paper we investigate in detail the effect of the

location accuracy of the VMES terminal on the interference

to adjacent satellites. This analysis is very useful because

accurate location recording requirements add to the cost and

complexity of the VMES network.

Because accurate locations of the VMES may not be

available in some applications, it is useful to estimate the

interference when the locations of the VMES are specified

as approximate values rather than actual values. In this paper

a methodology is given to estimate the interference resulting

from VMES located at these approximate locations. In cases

when it is necessary to estimate the actual interference,

it is shown that the estimated interference obtained using

approximated locations can be modified by adding an error

term to give the actual interference. Also, we examine the

impact of the equivalent isotropically radiated power (EIRP)

level of the VMES on the interference level and demonstrate

that the VMES may operate at slightly reduced EIRP levels

so that the actual interference is less than the estimate

interference using the approximated locations for most of

the time.

In general, because of factors such as mobility of the

terminals, multiple access protocol and antenna pointing er-

rors, interference from VMES terminals is a random process.

Therefore, in this analysis we use statistical measures to

quantify the sensitivity of the interference to the location

of the terminal. The specific approach to this analysis is

described in Section II.

II. OVERVIEW OF ANALYSIS

In this paper we carry out a statistical analysis of the

interference power spectral density (PSD) that is received

at a victim receiver of an adjacent satellite network. It

is assumed that all link parameters necessary to compute

this interference PSD are available. However, the actual

locations of the terminals are not available but they are

approximated by a set of predetermined grid points as

described below. The location error of a terminal is given

by the difference between the actual location of the terminal

and its approximated value. The interference PSD computed

using these approximated location data of the terminals

could be more or less than its actual value resulting in,

respectively, overestimation or underestimation of the inter-

ference PSD. The difference in interference PSD when the

actual and approximated location data are used is computed

and its cumulative distribution function (CDF) obtained as a

function of the location error of the terminals. Furthermore

the error in the interference PSD, which is the difference

between the interference PSDs when they are computed

using the actual locations and their approximated values,

is analyzed as a function of the distance between adjacent

grid points and the EIRP of the terminals.

The specific steps used in this analysis are described as

follows.

• Step 1. Compute the interference PSD to a victim

receiver in an adjacent satellite network and estimate

its cumulative distribution function (CDF). This step

makes use of the actual locations of the terminals and

the relevant link parameters of the satellite networks.

• Step 2. In this step the interference PSD is estimated

using the approximated locations of the terminals.

Quantize the spatial region where the terminals are

2013 IEEE Military Communications Conference

978-0-7695-5124-1/13 $31.00 © 2013 IEEE

DOI 10.1109/MILCOM.2013.309

1832

2013 IEEE Military Communications Conference

978-0-7695-5124-1/13 $31.00 © 2013 IEEE

DOI 10.1109/MILCOM.2013.309

1832

Page 2: [IEEE MILCOM 2013 - 2013 IEEE Military Communications Conference - San Diego, CA, USA (2013.11.18-2013.11.20)] MILCOM 2013 - 2013 IEEE Military Communications Conference - Sensitivity

operating to a finite set of grid points. These grid points

may be determined apriori and the spacings between

adjacent points determine the accuracy of the location

of the terminal.

– Step 2 (a). Approximate the location of each termi-

nal to one of the grid points, preferably the nearest.

The location error in this case is the difference

between the actual location of the VMES and its

approximated location to this grid point.

– Step 2 (b). Estimate the interference PSD and its

CDF assuming that the locations of the terminals

are given by these approximated grid points.

• Step 3. Determine the difference in the interference

PSDs obtained when using the actual locations of the

terminals and their approximated locations. This is the

error in the interference PSD. Determine its statistics

and the CDF.

A. Application of the Analysis

As noted in Section I this analysis could be used in the

following two approaches. In both approaches the locations

of VMES are specified by their approximate grid points and

this information is stored in the network for future reference.

In the first approach the interference PSD is estimated

using these approximate grid points and this estimate is

made available for any interference assessments by adjacent

satellite operators. Additionally, a statistical variable that

corresponds to the error in the interference PSD is provided.

Satellite operators could use this error term to modify the

estimated interference PSD in order to obtain the actual

interference PSD.

In the second approach the EIRP of the VMES are

reduced by a predetermined level. This can ensure that the

interference PSD estimated using the approximated locations

is less than its actual interference PSD only for a small

fraction of time.

III. SYSTEM MODEL

Figure 1 shows the terminals from the interfering and

the victim satellite networks. The transmit terminals of the

interfering network are denoted by Ti as shown here. This

figure also shows the victim and interfering satellites, Sv

and Si, wanted (victim) transmit terminal Tv , and victim

receive terminals Rv . The spatial location of the Terminal

Ti is denoted by the variable r, which is in general a three-

dimensional variable corresponding to the spatial coordi-

nates of that location. The interfering terminals are operating

in a time-division multiple access manner with only a single

terminal transmitting at a particular time instant in a narrow

frequency band of interest. In Figure 1 it is assumed that the

Satellites Sv and Si employ the same frequency translation

from the uplink to the downlink. If this is not the case the

downlinks from Si and Sv to Rv correspond to terminals

from different interfering networks.

Ci�

SV – Victim satellite

RV – Victim receiver Ti – Interfering

transmitter

Wanted signal

Si – Interfering satellite

ψr,v

ηiβi,r

r rv

Cv�

O Ti

Ti

TV – Wanted (victim) transmitter

ψv,i

βv,r

ηV

Figure 1. Interference paths from Terminal Ti to the victim receiver Rv ,via Satellites Si and Sv . Ci and Cv denote the beam centers of Si andSv on the Earth surface; O is the origin from which the distances to theterminal locations are measured.

Further details of this interference model and methodolo-

gies to assess the interference are given in Recommendation

ITU-R S. 2029 [3]. As stated in the preceding section, the

focus of this work is on investigating the effect on the

interference when it is estimated assuming that the locations

of the interfering terminals are approximated by a set of

quantized values of r.

A. Interference Power Spectral Density at the Victim Re-ceiver

In this problem the interfering terminals are transmitting

in a random manner, and in a given time instant only a

single terminal located at r is sending data. Therefore, the

time instant at which a particular interfering terminal is

transmitting can be represented by the location-dependent

random variable, r, and the probability density function

(PDF) of this random variable is denoted by pr. When

all the interfering terminals are in a Region R, it follows

that∫R pr(r)dr = 1. For illustrative purposes, suppose

the spatial locations at which the terminals are transmitting

are denoted by rTn, n = 1, 2, . . . . Then this PDF can be

expressed as the following pr(r) =∑

n pn,rδ(r − rTn),where pn,r is the probability of transmitting at location

r = rTnwith

∑n pn,r = 1, and δ(x) is the Direc delta

function with∫xδ(x)dx = 1 and δ(x) = 0, x �= 0. Note

that this summation encompasses all the interfering terminals

in the region of interest R. It should be stated that we

are interested in only on the terminal that transmits at a

particular time instant and the location of this terminal is

represented by r; the terminals in the network that do not

transmit at this time instant are not of interest from an

interference standpoint.

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Page 3: [IEEE MILCOM 2013 - 2013 IEEE Military Communications Conference - San Diego, CA, USA (2013.11.18-2013.11.20)] MILCOM 2013 - 2013 IEEE Military Communications Conference - Sensitivity

For small aperture terminals, because of off-axis emission

limits, the EIRP spectral density (ESD) in the boresight1

direction depends on the aperture size of the terminal’s

antenna. Let us consider a network of terminals consisting

of a finite set of antenna aperture sizes that are distributed

randomly. Then the distribution of the boresight ESD can be

represented by a discrete probability distribution with values

from the set {E1, E2, . . . , EnE}. The conditional PDF of the

ESD, conditioned on the specific location of the terminal,

can now be expressed as

pEr|r(E) =

nE∑n=1

pn,Erδ(E − En) (1)

where pn,Er is the probability of occurrence of the ESD

level En at location r and∑nE

n=1 pn,Er = 1. Note that this

shows that there can be more than one ESD level at a single

spatial location r. Since pEr|r(E) is a PDF, it follows that∫pEr|r(E)dE = 1, where the integral is over all possible

values of E. In some cases it can be assumed that the EIRP

level is not dependent on the specific location. In such cases

pE(E) =∑nE

n=1 pn,Eδ(E − En) where pn,E is now the

probability of occurrence of the ESD level En in the entire

region of interest and∑nE

n=1 pn,E = 1.The signal paths from the interfering terminals to the

victim receiver via the interfering and victim satellites are

shown Figure 1. The interference power spectral densities

at the victim receiver, via Satellites Sv and Si, due to the

interfering terminal Ti at r are denoted by Iv(r) and Ii(r),respectively. These can be expressed in terms of the satellite

link parameters and γx, x = v, i, which are defined as the

transmission gains from the output of the receive antenna at

Satellite Sx, x = v, i, to the output of the receive antenna

at Rv . Note that the downlink path transmission gains from

the satellites are not functions of the specific locations of

the interfering terminals. Therefore, the values of γv and γido not change when interference is evaluated by assuming

that the locations of the transmit terminals are approximated

by a set of quantized values of the location variable.Before determining the interference power spectral den-

sities it is necessary to define the following satellite link

parameters: Er(ψ), ESD in an off-axis direction ψ at Ti

located at r; Gsr,x, x = v, i, receive antenna gain pattern at

Sx; Lu,r, uplink loss from Ti at r; βx,r, x = v, i, angle at

Sx between SxCx and SxTi; and ψr,v angle at Ti between

TiSi and TiSv .Using the above satellite link parameters the interference

power spectral densities are expressed as

Iv(r) =Er(ψr,v)G

sr,v(βv,r)

Lu,rγv

Ii(r) =ErG

sr,i(βi,r)

Lu,rγi. (2)

1The antenna boresight direction is the direction of the maximum antennagain.

In the above it is assumed that the orbital separation between

the satellites is close so that the uplink path losses to the

satellites are the same. Observe that, by definition, γv and

γi do not depend on the specific location of the interfering

terminal and the values of these can be determined using

the downlink satellite link parameters [3].

IV. INTERFERENCE COMPUTED USING QUANTIZED

SPATIAL LOCATIONS

In this section the locations of the interfering terminals

are quantized to a set of points rk and the interference

is computed by approximating the actual location of the

terminal to its representative point rk. An illustrative quanti-

zation scheme for the locations of the interfering terminals is

shown in Figure 2. Here the quantized regions are denoted

by Rk, k = 1, 2, . . . ,K, and the corresponding locations

of the interfering terminals are represented by the points on

the grid rk, k = 1, 2, . . . ,K. The K quantized regions,

R1,R2, . . . ,RK , are disjoint and encompass the entire

region of interest R, that is, R1 ∪ R2 · · · ∪ RK = R.

Note that although this figure shows a regular pattern for

the quantized regions, in general, they may take the shape

of some conveniently chosen predetermined pattern. In this

figure the actual locations of the interfering terminals are

shown as ‘o’ and these terminal locations are quantized to

one of the points rk, k = 1, 2, . . . ,K, using the nearest-

neighbor quantization rule. Specifically, denote the distance

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Figure 2. Quantization of Region R to Regions Rk, k = 1, 2, . . . ,K.Representative center of Rk is shown as rk . The points ‘o’ denote thespecific locations of the interfering terminals and En, n = 1, 2, . . . , nE ,denote the boresight EIRP levels at these terminals.

metric between the interfering terminal located at r and a

quantized point rk as d(r, rk). Then this terminal is located

in Region Rk and represented by the grid point rk when the

following is satisfied

r ∈ Rk if d(r, rk) ≤ d(r, rk′), rk �= rk′ . (3)

In this work we will use the Euclidean distance metric for the

distance between points x1 and x2 defined as d(x1, x2) =||x1 − x2||.

18341834

Page 4: [IEEE MILCOM 2013 - 2013 IEEE Military Communications Conference - San Diego, CA, USA (2013.11.18-2013.11.20)] MILCOM 2013 - 2013 IEEE Military Communications Conference - Sensitivity

The interference is now computed assuming that the

interfering terminals are located at the representative points

rk rather than at their actual locations r. So the resulting

interference PSDs for the paths TiSvRv and TiSiRv can be

written similar to (2) as

Iv,q(rk) =Erk(ψrk,v)G

srk,v

(βv,rk)

Lu,rk

γv

Ii,q(rk) =ErkG

srk,i

(βi,rk)

Lu,rk

γi. (4)

Observe that the link parameters on the right side of the

above are with respect to the quantized locations rk, and in

the following we will discuss the process of obtaining these

values. The loss terms and the satellite antenna gains, Lu,rk ,

Gsrk,v

(βv,rk) and Gsrk,i

(βi,rk), can be computed by using

the respective values at the grid point, rk. The technique for

computing Erk is given below.

Observe that Erk is a discrete random variable from the

sample space {E1, E2, . . . , EnE}. Therefore, in order to

define Erk we need to determine its PDF. Let us first obtain

the PDF of rk. Denote by prk = Pr{r ∈ Rk}, which is the

probability that the transmit terminal is in the Region Rk.

This probability can be expressed as prk =∫r∈Rk

pr(r) dr.

Observe that∑K

k=1 prk = 1. When the PDF pr(r) is known

apriori these probabilities can be determined for a given

set of quantization regions. On the other hand, if pr(r) is

not available, the required probabilities can be estimated

using the method of relative frequency of occurrence of

the terminals in the respective quantization regions. For

example, suppose tk is the total time interval the transmit

terminals are observed in the Region Rk, then

prk ≈ tk∑Ki=1 ti

. (5)

Next, Erk represents the ESD of all the terminals that

are in the Region Rk in the observation period of interest.

Notice that only a single terminal is active at a given

time instant and the terminal at r transmits at ESD level

En, n = 1, 2, . . . , nE , with probability pn,Er . Because the

distribution of the terminals in Rk is according to the PDF

pr(r) with r constrained so that r ∈ Rk, we have for the

conditional PDF of Erk given that r ∈ Rk as

pErk|r∈Rk

(E) =

1∫r∈Rk

pr(r)dr

∫r∈Rk

nE∑n=1

pn,Erδ(E − En)pr(r)dr. (6)

When the probability distributions of r and Er are available

the conditional probability of Erk can be computed as shown

above. Alternatively, in the absence of these distributions,

the above probability can be estimated using the following

relative frequency of occurrence of method. This method

requires tabulating the time duration of occurrence of each

ESD level at each RegionRk in the desired observation time

interval. Denote by tn,k the time duration for which the ESD

level En was used in the Region Rk. Then the desired PDF

is estimated as

pErk|r∈Rk

(E) ≈∑n

tn,k∑nE

i=1 ti,kδ(E − En). (7)

The off-axis ESD Erk(ψrk,v) at rk used in (4) can be

estimated using Erk estimated as above and assuming that

ψr,v has very little variations in Region Rk. In this case

ψrk,v may be used for all values of ψr,v , r ∈ Rk. The PDF

of this can be estimated using the frequency of occurrence

method similar to (7) with En replaced by En(ψrk,v).

V. STATISTICS OF THE INTERFERENCE POWER

SPECTRAL DENSITY

One of the key objectives of this work is to evaluate the

statistics of the excess interference resulting from quantizing

the actual locations of the transmit terminals. To accomplish

this in the following we derive the PDFs of the interference

PSD when it is computed using the actual and approximated

locations.

A. PDF of Interference When Using Actual and QuantizedLocations

The total interference PSD from a terminal located at ris I0(r) = Iv(r) + Ii(r) and using (2) this is expressed as

I0(r) =Er(ψr,v)G

sr,v(βv,r)

Lu,rγv +

ErGsr,i(βi,r)

Lu,rγi. (8)

The random variables here are the location variable rand the ESD variable Er. The PDFs of these vari-

ables were obtained in Section III-A. The gain patterns

of the receive antennas at the satellites, Gsv(βv,r) and

Gsv(βv,r), are deterministic functions of the location vari-

able r. So for a given r, the interference PSD takes the

value(

En(ψr,v)Gsr,v(βv,r)γv

Lu,r+

EnGsr,i(βi,r)γi

Lu,r

)with probabil-

ity pn,Er . So the marginal PDF of I0(r) can be determined

using these.When quantized locations are used the total interference

from representative point rk is denoted by Iq(rk). Combin-

ing the expressions given in (4), the total interference PSD

from terminals represented by rk is

Iq(rk) =Erk(ψrk,v)G

srk,v

(βv,rk)

Lu,rk

γv +ErkG

srk,i

(βi,rk)

Lu,rk

γi.

(9)

The random variables here are rk and Erk and their PDFs

were given obtained in the preceding section. For a given

quantized location rk and ESD level En the interference

PSD takes the value

In,k =(

En(ψrk,v)Gsrk,v(βv,rk

)

Lu,rkγv +

EnGsrk,i(βi,rk

)

Lu,rkγi

)with

probability pn,k =∫Rk

pn,Erpr(r). Observe that pn,k is the

probability of occurrence of the terminals with ESD En in

the Region Rk and it follows that∑K

k=1

∑nE

n=1 pn,k = 1.

Using these the PDF and the CDF of Iq can be determined.

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Page 5: [IEEE MILCOM 2013 - 2013 IEEE Military Communications Conference - San Diego, CA, USA (2013.11.18-2013.11.20)] MILCOM 2013 - 2013 IEEE Military Communications Conference - Sensitivity

B. Error in the Interference PSD

The error in the interference PSD is because the actual

locations of the terminals are approximated by the grid

points. In order to determine this error, first consider a

terminal with an ESD level En at r. The corresponding

interference PSD is

I0,n(r) =En(ψr,v)G

sr,v(βv,r)

Lu,rγv +

EnGsr,i(βi,r)

Lu,rγi

and this occurs with probability pn,Er. The location of this

terminal is now quantized to the grid point rk and the

corresponding interference PSD is

Iq,n(r) =En(ψrk,v)G

srk,v

(βv,rk)

Lu,rk

γv +EnG

srk,i

(βi,rk)

Lu,rk

γi.

The error in the interference PSD is the difference between

these two terms and occurs with probability pn,Er . This error

term, denoted by Ie(n, r) is

Ie(n, r) = I0,n(r)− Iq,n(r). (10)

The PDF and CDF of Ie(n, r) can be computed using the

PDFs of Er and r. Observe that the actual interference is

given by the addition of the error term to the estimated

interference PSD using the approximated locations. There-

fore, knowledge of the estimated interference PSD and the

statistics of the error term are sufficient to reconstruct the

actual interference PSD. This is one approach for using this

analysis as stated in Section II-A. In the simulations given

in the next section we estimate the CDF of Ie(n, r) using

Monte-Carlo simulations. Note the following two cases:

Ie(n, r) > 0, in such cases the interference PSD estimated

using the approximated locations is less than the actual in-

terference PSD and it underestimates the actual interference

PSD; Ie(n, r) < 0, the interference PSD estimated using the

approximated locations is more than the actual interference

PSD and it overestimates the actual interference PSD.

VI. SIMULATION RESULTS

The relevant link parameters used in the simulations are

given in Table I. The beam centers of Satellites Sv and Si

are co-located at Harrisburg, PA and the 6-dB contour of the

antenna pattern of Sv is shown in Figure 3. The distribution

of the interfering terminals are shown in the paths in this

figure. The grid points are chosen along the paths of the

terminal distributions and the distances between adjacent

grid points are uniform and separated by dgrid. In these

simulations the variations in Iq and Ie are examined for

different values of dgrid and the ESD level of the terminals

as described next.

The interfering terminals are assumed to satisfy the

ESD Mask: (KaMask − Ered) (dB(W/Hz)), where KaMask

(dB(W/Hz)) is the ESD Mask established in ITU-R Recom-

mendation S. 524-9 and Ered (dB) is a small value to reduce

the ESD levels to accommodate the error in the interference

Uplink frequency 28.75 GHzAperture diameters uniformly distributed inof Ti [0.2 0.25 0.3 0.35 0.4] mLocations of Ti uniformly distributed in segments:

New Haven, RI to Washington, DCNew York City, NY to Albany, NYNew York City, NY to Harrisburg, PAWashington, DC to Hagerstown, MDBaltimore, MD to Harrisburg, PA

Longitudes at 102.8◦ W and (102.8◦ − 2◦) WSatellites Sv , Si

Satellite beam centers, (41.27◦N, 76.88◦W). Harrisburg, PACv and Ci, (latitude, longitude)Receive antennas at satellites 1.4 m diameter aperture

with parabolic illumination

Table ISATELLITE LINK PARAMETERS USED IN SIMULATIONS.

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@2011 Google

Figure 3. Distribution of Terminals Ti and the 6-dB beam pattern ofSatellite Sv . Here the beam center of Sv is at Harrisburg, PA.

PSD. This error term decreases for larger values of Ered

and this behavior is examined in the simulations. Also, for

these simulations consider a large antenna aperture for Rv .

Because of this the interference received via Satellite Si can

be neglected. In order to normalize the interference PSDs

we consider a terminal located at the beam centers of Sv

and Si and it is assumed that this terminal is transmitting

at its maximum off-axis emission level given in KaMask,

which is (19− 25 log10(ψr,v)) dB(W/40 kHz) where ψr,v

is in degrees and 2◦ ≤ ψr,v ≤ 7◦. Interference PSD from

this terminal is denoted by Icenter. Note that Icenter is the

maximum value of the interference PSD for any terminal

location and any antenna aperture size.

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Figure 4. CDF of the error in the interference PSD for the terminaldistribution shown in Table I. Legend shows dgrid and Ered.

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Page 6: [IEEE MILCOM 2013 - 2013 IEEE Military Communications Conference - San Diego, CA, USA (2013.11.18-2013.11.20)] MILCOM 2013 - 2013 IEEE Military Communications Conference - Sensitivity

For these simulations it was observed that there is very lit-

tle difference in the CDFs of I0Icenter

andIq

Icenter. Figure 4 shows

the CDF of the error in the interference PSD normalized

with respect to Icenter, that is, IeIcenter

, where Ie = (I0−Iq) and

follows from (10). For these results dgrid = 10, 20 and 50 km

and Ered = 0 and 0.2 dB. These curves show a discernible

difference in the results for the cases considered. It should

be noted that when Ered = 0 dB, Ie may take both positive

and negative values with approximately the same probability.

That is, the interference estimated using the grid points may

underestimate or overestimate the actual interference with

approximately the same probability. On the other hand, when

Ered = 0.2 dB, the error in the interference PSD is mostly

negative and the estimated interference PSD overestimates

the actual interference PSD most of the time. To see the

effect of the distance between the adjacent grid points on

the error in the interference PSD, consider the error levelIe

Icenter= 0.01 with Ered = 0 dB in Figure 4. It can be seen

that Pr{Ie < 0.01 × Icenter} = 0.99 for dgrid = 10 km and

this decreases to 0.93 and 0.78 when dgrid is increased to 20

and 50 km, respectively. This shows that, as expected, the

error in the interference PSD increases when the distance

between adjacent grid points are increased.

0 0.05 0.1 0.15 0.20.5

0.6

0.7

0.8

0.9

1

Reduction in ESD, Ered

(dB)

Pr{I e/I cen

ter<

0}

20 km50 km

Figure 5. Pr{Ie/Icenter < 0 } as a function of the reduction of ESDlevel.

The effect of the ESD of the terminals on the error in

the interference PSD is examined in the results presented in

Figure 5. Here the values of Pr{

IeIcenter

< 0}

are plotted for

various values of Ered. As expected this probability increases

for large values of Ered. Observe that when Ie/Icenter = 0dB the estimated interference PSD using the approximated

grid points is the same as its actual value. Therefore, with

dgrid = 50 km, it can be seen that the estimated interference

PSD is more than its actual value for 53% of the time when

Ered = 0 dB and this increases to 92% of the time when

Ered = 0.2 dB. It can be seen that the ESD of the VMES can

be reduced to satisfy a criterion that requires the estimated

interference to be less than its actual value only for a small

fraction of time, which may be given.

VII. DISCUSSION AND CONCLUSIONS

Interference from a VMES terminal depends on its loca-

tion and in this contribution a sensitivity analysis of the

interference to the location of the VMES terminal was

carried out. Because of practical and operational reasons

the exact locations from which the VMES terminals are

transmitting may not be available. In these cases the exact lo-

cations may be conveniently represented by suitably spaced

grid points in the region of interest. Then, for interference

estimation purposes, the actual location of the transmit

terminal may be approximated by a suitably chosen grid

point. The interference estimated using these approximated

locations is different than its actual value. In many situations

it is necessary to obtain the actual interference levels when

the estimated interference levels are available only with

respect to a set of grid points. It was shown that a random

variable representing the error can be added to the estimated

interference PSD to obtain the actual interference PSD.

Alternatively, it was shown that the ESD of the terminals

can be reduced slightly to satisfy a criterion that requires

the error in the interference PSD not to exceed a given value

for a certain time fraction.

REFERENCES

[1] Federal Communications Commission. FCC 09-64, Report andOrder, §25.226 Blanket Licensing Provisions for Domestic,U.S. Vehicle-Mounted Earth Stations (VMESs) Receiving in the10.95-11.2 GHz (Space-to-Earth), 11.45-11.7 GHz (Space-to-Earth), and 11.7-12.2 GHz (Space-to-Earth) Frequency Bandsand Transmitting in the 14.0-14.5 GHz (Earth-to-Space) Fre-quency Band, Operation with Geostationary Satellites in theFixed-Satellite Service. July 31, 2009.

[2] European Telecommunications Standards Institute. Final DraftETSI EN 303 978 V1.1.1, Harmonized EN for Earth Stationson Mobile Platforms (ESOMP) transmitting towards satellitesin geostationary orbit in the 27,5 GHz to 30,0 GHz frequencybands covering essential requirements under article 3.2 of theR&TTE Directive, 2012.

[3] International Telecommunication Union. RecommendationITU-R S.2029, Statistical methodology to assess time-varyinginterference produced by a network of small earth stations op-erating with TDMA schemes onto geostationary fixed-satelliteservice networks. Dec. 2012.

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