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ANALYSIS OF HANDOVER CHARACTERISTICS IN SHADOWED LEO SATELLITE COMMUNICATION NETWORKS YOUNG HOON KWON AND DAN KEUN SUNG Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology, 373-1, Kusong-dong, Yusong-gu, Taejon, 305-701, Korea
SUMMARY In the near future low earth orbit (LEO) satellite communication networks will partially substitute for fixed terrestrial multimedia networks especially in sparsely populated areas. Unlike fixed terrestrial networks, ongoing calls may be dropped if satellite channels are shadowed. Therefore, in most LEO satellite communication networks more than one satellite need to be simultaneously visible in order to hand over a call to an unshadowed satellite when the communicating satellite is shadowed. In this paper handover characteristics for fixed terminals (FTs) in LEO satellite communication networks are analyzed. The probability distribution of multiple satellite visibility is analytically obtained and the shadowing process of satellites for FTs are modelled. Using the proposed analysis model, shadowing effects on the traffic performance are evaluated in terms of the number of intersatellite and interbeam handovers during a call. KEY WORDS :
multiple satellite visibility; satellite channel shadowing; intersatellite handover; interbeam handover
1. INTRODUCTION In the emerging era of the International Mobile Telecommunications - 2000 (IMT-2000), LEO satellite communication networks are expected to coexist with terrestrial networks.1 Terrestrial regional telecommunication networks with diverse transfer modes and various protocols may suffer from internetworking and compatibility problems to provide global seamless multimedia communications. LEO satellite networks will be able to support end-to-end connections in the near future,2];[3 and thus, they will play both complementary and competitive roles compared with fixed telecommunication networks as well as cellular networks, and may partially substitute for fixed networks in sparsely populated areas where fixed telephony services are unavailable.4 LEO satellite channel characteristics affect the availability and the quality of services, depending on urban vs. suburban areas and satellite constellation parameters.5];[6];[7 When the quality of a satellite channel is degraded due to shadowing, an ongoing call may be dropped. Multiple satellite visibility is provided in most LEO satellite constellations to reduce this call dropping.8];[9 If ongoing calls are dropped only when all visible satellites are shadowed, service availability can be increased.
This study is partially supported by the Ministry of Science & Technology. Correspondence to: Prof. D. K. Sung, Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, Korea. E-mail: [email protected]
2
Shadowing of satellites for mobile terminals (MTs) is caused by two mobility factors. These are satellite mobility and user mobility. As an LEO satellite moves with a constant velocity the varying elevation angle of the satellite from an MT affects the shadowing parameters. Furthermore, the shadowing environment of an MT may vary with time because of the motion of the MT. For FTs with a fixed shadowing environment, shadowing of a satellite depends on the elevation angle of the satellite. Thus, if the elevation angle is sufficient to clear nearby obstacles a call can be connected to the satellite. Several previous studies5];[9];[10 have dealt with shadowing parameters of satellite availability and the received signal distribution in diverse environments. When a satellite which is communicating with an FT is shadowed or when the coverage area of the satellite moves out of the FT, an intersatellite handover occurs. Even within the coverage area of a satellite, interbeam handovers may occur in a multiple spot beam environment.11 The numbers of intersatellite handovers and interbeam handovers vary according to the shadowing environment of an FT. In this paper the handover characteristics of FTs in LEO satellite communication networks are analyzed. The shadowing process of satellites is modelled, and the numbers of intersatellite handovers and interbeam handovers are analytically obtained based on the shadowing model in a multiplesatellite-visible condition. The remaining part of this paper is organized as follows: Section 2 presents an analysis of the probability distribution of the multiple satellite visibility at an arbitrary latitude; Section 3 introduces a shadowing model and a multiple spot beam model; Section 4 shows an analysis of handover characteristics based on these system models; Section 5 shows numerical results; and Section 6 presents conclusions. 2. MULTIPLE SATELLITE VISIBILITY LEO satellite communication networks consist of multiple orbit planes and multiple satellites per orbit plane in order to realize global coverage. The candidate satellite to an FT is defined as a satellite whose elevation angle to the FT is greater than given minimum elevation angle. The number of candidate satellites,
NCS
varies according to constellation parameters, such as the number of satellites, the inclination angle of an orbit plane, and the altitude and the longitude of each satellite. The probability distribution of NCS at a latitude of
is now obtained.
3
Figure 1 shows the position of the i-th orbit plane to a reference point. If
i denotes the ascending node
right ascension of the i-th orbit plane, then i can be expressed as
i =
i ; NO 2
1
6 i 6 NO
(1)
where NO is the number of orbit planes. For an arbitrary point Q with a latitude and longitude of and , respectively, the distance between the point Q and the corresponding track on the earth’s surface of the i-th orbit plane is given by
li = RE sin
1
(sin
Æ cos sin( i
) + cos Æ sin )
(2)
where RE and Æ denote the radius of the earth and the inclination angle of each orbit plane, respectively. Figure 2 illustrates the coverage area of each satellite. The altitude and the minimum required elevation angle of a satellite are denoted by h and min , respectively. The radius of the coverage area of each satellite is then obtained as 12
Rs = RE
2
min
sin
1
RE
RE + h
cos
min
(3)
If the coverage area of each satellite is assumed to be a flat circle, as shown in Figure 3, the ground track distance of a satellite in the i-th orbit moved during the time the point Q is included in the coverage area of the satellite, (li ) can be expressed as
(li ) =
p
2
0
Rs 2 ;
li2 ;
6 li 6 Rs li > Rs 0
(4)
If the number of satellites in one orbit plane is denoted by NSO , the distance between adjacent sub-satellite points (SSPs) is given by
Ls =
RE NSO
2
(5)
The number of candidate satellites in the i-th orbit at the point Q, Mi depends on the relative position of the satellites to
(li ). An illustration for the case of (li )
= 5
and
Ls
= 2
is shown in Fig. 4. As shown in
this illustration, the number of candidate satellites in the i-th orbit at the point Q,
Mi is given by
j
(li ) Ls
k
or
4
j
(li ) Ls
k + 1,
where bxc denotes the greatest integer less than or equal to x. At an arbitrary time, the relative
position of the satellites has no correlation with the (li ), and thus, the probability qi (n; Q) that the number of candidate satellites in the i-th orbit is n at the point Q can be expressed as
qi(n; Q) =
8 > > < 1
(li )
> Ls > : 0
;
j
(li )
(li ) Ljs k Ls
(li ) Ls
k
j
k
; n = L(lsi ) j k n = L(lsi ) + 1
;
(6)
otherwise
The number of candidate satellites NCS at an arbitrary point Q can be obtained by summing the number of candidate satellites in the entire constellation. That is, the probability PCS (j ; Q) that NCS is j at the point Q is given by
PCS (j ; Q)
= =
fM
Pr 1 + j j X X n1 =0 n2 =0
M2 + + MNO
j X
nNO
j at the point Qg
=
qNO (j
n1 ; Q)qNO
n1
n2 ; Q)
1(
1 =0
q2(nNO
2
nNO
1;
Q)q1(nNO
1;
Q)
(7)
Therefore, the probability PCS (j ) that NCS is equal to j at a latitude of can be obtained as
PCS (j ) = N max X
R 2 0
PCS (j ; Q) d 2
PCS (j ) = 1
(8)
(9)
j =0
where
Nmax denotes the maximum number of candidate satellites. Then, the mean number of candidate
satellites E [NCS ] can be expressed as
E [NCS ] =
N max X
jPCS (j )
(10)
j =1
3. SYSTEM MODEL 3.1. Shadowing model Since LEO satellites move in their orbit plane the motion of each satellite relative to an FT can be modelled as a linear motion with a constant velocity. The satellite ground track speed VSSP depends on the altitude of
5
a satellite such that
VSSP where = 3 986 1014 m3 s
2
=
RE
r
(11)
RE + h RE + h
is the gravitational parameter.
From the viewpoint of an FT, satellites whose elevation angle is greater than the minimum required elevation angle
min can be connected if the communication channel between the FT and the satellite is not
shadowed. The service area for an FT is defined as the virtual area in which the SSP of a satellite with an elevation angle from the corresponding FT greater than
min can be located.13 If the coverage area of each
satellite is assumed to be a circle with a radius of Rs , the service area of an FT would also be a circle with a radius of Rs and each SSP inside the service area would move linearly with a constant velocity of VSSP . A communication channel is shadowed when the elevation angle of a satellite is lower than the required elevation angle. This can be caused by nearby obstacles, such as tall buildings, trees, and mountains. If the location of an FT is fixed the time variation of the shadowing is negligible. However, the shadowing process of satellite channels varies with time because each satellite moves with time. Thus, each satellite at an azimuth angle of
with respect to the reference direction of the FT, as shown in Figure 5, can be connected
to an FT if the elevation angle is greater than the minimum unshadowed elevation angle (
)
at an azimuth
angle of , where the minimum unshadowed elevation angle is a user-specific value which is determined by the shadowing environment of the MT. For mathematical simplicity it is assumed that the shadowing environment of an FT is omnidirectional, which implies that an FT has an identical minimum unshadowed elevation angle irrespective of the azimuth angle
(
) =
. The available area of an FT is defined as the area in which the SSP of unshadowed
satellites can be located. As the minimum unshadowed elevation angle is assumed to be omnidirectional, the available area of an FT can be modelled as a circle with a radius Ra , which is a function of . The probability distribution of with an elevation angle of
Ra can be obtained with the satellite availability PA () that one satellite
is available. PA() also implies the probability that exceeds the minimum
unshadowed elevation angle , that is,
PA () = Prf > g
(12)
6
Satellite availability has been extensively measured and analyzed in several previous studies.5];[10];[9 The probability that is less than equals to the probability that one satellite with an elevation angle of is available. Thus, the probability distribution function (PDF) of can be obtained as
f ()
= =
d Prf 6 g d d P () d A
(13)
where PA () satisfies two boundary conditions.
PA (0) = 0 PA ( 2 ) = 1
Similar to equation 3, the relationship between a radius ra and an elevation angle is given by
ra = RE
2
sin
1
RE
RE + h
cos
(14)
And, the maximum value of ra , Ra;max is obtained as
Ra;max = ra j=0 = RE cos
1
RE
(15)
RE + h
Therefore, the PDF of the radius of an available area fRa (ra ) can be expressed as
fRa (ra )
=
1
=
RE r sin ( Ra ) + E 2
in the range of 0 6 ra
dPA () d d dra
1 ra RE +h cos( RE )
n
r cos( Ra ) E
RE RE +h
o2
dPA () 0 d =tan @ 1
cos(
RE ra RE ) RE +h r sin( a ) RE
1 A
(16)
6 Ra;max.
Each FT has two independent virtual areas, a service area and an available area. As an FT has multiple number of candidate satellites, the FT may have several SSPs in a service area. If Ra is greater than Rs , all satellites in the service area are unshadowed and can be connected when a call is requested. However, if Ra is smaller than Rs , satellites outside of the available area within the service area may be shadowed, and thus, the number of available satellites is reduced. These two cases are shown in Figure 6. Therefore, an FT can connect a call to satellites in the circle with a radius of min(Rs ; Ra ).
7
3.2. Multiple spot beams In most LEO satellite constellations, the coverage area is partitioned into multiple spot beams.14 Use of multiple spot beams can increase system capacity, concentrate transmission power, and reduce FT antenna size and required transmission power. In this case an FT may experience interbeam handovers as well as intersatellite handovers. Intersatellite handovers occur between adjacent satellites. Thus, intersatellite handovers require message transfer to the earth station which controls both satellites, which causes a relatively high processing load and time delay. However, interbeam handovers occur between adjacent spot beams within a satellite. Therefore, these handover procedures can be controlled in a satellite and yield a relatively low processing load and time delay. Moreover, the next handover beam can be known a priori to the satellite controller. FTs covered by each spot beam may have different path losses according to the position of the spot beam within the coverage area of a satellite. This is due to an increase in slant range losses as the footprint moves farther from the SSP. This path loss is assumed to be compensated by increasing the spot beam antenna gain as the beam moves farther away. When an FT requests a call, the FT compares the received signal strengths from multiple satellites and connects to spot beam with the maximum received signal strength. Due to the compensation of path loss, each visible spot beam can be connected to this FT with equal probability. Thus, the position of the selected spot beam within a coverage area of the selected satellite is uniformly located. Therefore, the number of available satellites does not affect the residence time distribution in the coverage area of a satellite. The footprint of each spot beam inevitably overlaps its adjacent spot beams in order to provide seamless coverage. The overlap area is approximated to be a circle, as illustrated in Figure 7, where the radius of the beam footprint and the width of the overlap area are R and 2L, respectively. The distance between two adjacent spot beam centres is Lc . If the coverage area of a satellite consists of maximum Nb spot beams in a strip, R is related to Rs as follows
Rs
=
)R
=
R + (Nb Nb
(
R L)
1)(
Rs
1)(1
) + 1
(17)
8
=
where
=
Rs + (Nb Nb
1)
L
(18)
L=R is the normalized overlap width. Figure 8 illustrates the structure of spot beams in a satellite
coverage area with Nb
= 5.
It is assumed that an FT will be handed over only to the next beam in the same
strip. Then, the residence time in the transit spot beam is Lc =VSSP . 4. PERFORMANCE ANALYSIS 4.1. Residual distance of a satellite
D denotes the distance between an FT and an SSP inside the service area of the FT. The probability that D is less than or equal to r, PrfD
6 rg is given by 15 r fD 6 rg = R
2
Pr
2
s
=
r2 ; Rs2
0
6 r 6 Rs
;
0
(19)
Therefore, the PDF of D can then be expressed as
fD (r) = Under the condition that Ra
d PrfD 6 r g = dr
2r Rs2 0
;
6 r 6 Rs
(20)
otherwise
r
R ; ra ).
= a , available satellites for the FT can be located within a radius of min( s
If D0 denotes the distance between an FT and a candidate SSP within a radius of min(Rs ; ra ), the PDF of D0 is given by
fD0 (rjra )
=
fD (r) FD (ra )
where FD (ra ) is the cumulative distribution function (CDF) of D such that FD (ra ) = PrfD The residual distance of a satellite to an FT
(21)
6 ra g.
Xr is defined as the distance travelled of the SSP from the
beginning of a new/handover call to either the time that the SSP moves out of the service area or the time when the satellite is shadowed. When Ra
r and D0 = r, the CDF of the residual distance of a connected
= a
satellite to an FT is given by
FXr (xjr; ra )
fXr 6 xjD0 = r; Ra = rag
=
Pr
=
Pt (x; min(Rs ; ra ); r)
(22)
9
where Pt (x; r0 ; r) denotes the probability that a user whose distance from the centre of a circle with a radius of r0 is r, moves out of the circle when the FT moves a distance of x, such that 13
Pt (x; r0 ; r)
8 > < 0 =
;
1
cos > :
1
;
1
r02 r2 x2 2xr
6 x < r0 r ; r0 r 6 x 6 r0 + r 0
x > r0 + r
If equation 22 is unconditioned to D0 , FXr (xjra ) can be obtained as
FXr (xjra )
Z
min(Rs ;ra )
= 0
=
8 < 0
;
:
2! +sin 2!
;
1
FXr (xjr; ra )fD0 (rjra )dr ;
x 2 min(Rs ; ra )
(23)
where
! = sin
1
x 2 min(Rs ; ra )
Therefore, the CDF of Xr , FXr (x) can be obtained by unconditioning FXr (xjra ) on Ra .
FXr (x) =
Z Ra;max 0
FXr (xjra )fRa (ra )dra
(24)
4.2. Handover performance Let
TM denote the exponentially distributed call duration with a mean of T M . As each SSP moves with a
constant velocity, the distance mean of X M
=
XM that an SSP moves during a call is also exponentially distributed with a
VSSP T M . If the residual distance of the connected satellite Xr is shorter than XM an inter-
satellite handover occurs. Therefore, the probability PH jra that an FT with Ra
r requires an intersatellite
= a
handover can be obtained as
PH jra
=
fXM > Xr jRa = rag
Pr
Z
2 min(Rs ;ra )
= 0
e
x=X M
fXr (xjra )dx
(25)
The residual distance distribution of handed-over satellite to the FT is assumed to be identical to that of the original satellite. Thus, PH jra for new calls and handover calls is the same due to the memoryless property of
10
exponentially distributed call duration. The probability that the number of intersatellite handovers during a call Ksjra is n when Ra
r is given by
= a
Pr
Then, the CDF of Ks , PrfKs
fKsjra = kjRa = rag = (1
PH jra )PHk jra
(26)
6 kg can be expressed as
fKs 6 kg
Pr
Z Ra;max
fKsjra 6 kgfRa (ra)dra
=
Pr 0
=
Z Ra;max X k
(1
0
i=0
Z Ra;max =
(1 0
The mean number of intersatellite handovers when Ra
K sjra
=
1 X k=1
=
1 X k=1
=
PH jra )PHk jra fRa (ra )dra
PHk+1 jra )fRa (ra )dra
(27)
r K sjra can be obtained as
= a,
k PrfKsjra = kjRa = ra g k(1 PH jra )PHk jra
PH jra 1 PH jra
(28)
Thus, the mean number of intersatellite handovers during a call can be obtained by unconditioning K sjra on
Ra . Ks
Z Ra;max = 0
Z Ra;max = 0
K sjra fRa (ra )dra PH jra f (r )dr 1 PH jra Ra a a
To obtain the number of interbeam handovers during a call
(29)
KB , the shadowing condition of each spot
beam should be considered first. If the minimum unshadowed elevation angle for an FT is greater than the minimum elevation angle min (Rs
> Ra ), the spot beams located at the outer tier of a satellite coverage area
may be shadowed as shown in Figure 9. In this figure, Y denotes the length of the partly shadowed spot beam whose elevation angle is greater than , and can be obtained as
Y
8
Lc + L
(30)
11
Two integer random variables
Kb1 and Kb2 represent the number of interbeam handovers in one satellite
when the call is completed within a satellite and when an intersatellite handover occurs, respectively. When an interbeam handover occurs the residual distance of a handed over beam is Lc if this beam is not shadowed. Thus, the probabilities that Kb1jra and Kb2jra equal k when Ra
r are given by
= a
fKb jra = kg
Pr = =
1
XM > Xrjra Y b XrjLrac Y cLc + (k 1)LcjXM < Xrjra R 2 min(Rs ;ra ) FXM (x Y b xLcY cLc +(k 1)Lc) fXrjra (x)dx Y +(k 1)Lc FXM (x) 1 PH jra PrfKb2jra = k g Pr
L jXM > Xrjra g Y +(k 1)Lc F XM (x)fXrjra (x)dx = PH jra where F XM (x) is the complementary CDF of XM such that F XM (x) =
fXrjra > Y + (k
Pr
R 2 min(Rs ;ra )
(31)
1) c
(32) = 1
FXM (x)
= exp(
x=X M ). If
a call is completed within the first communicating satellite the number of interbeam handovers during a call
KB equals Kb1 . However, when an intersatellite handover occurs KB restarts at a transit satellite and is added to the number of interbeam handovers at the first satellite. Hence, KB jra when Ra
KBjra
r can be expressed as
= a
PH jra )Kb1jra + PH jra (KBjra + Kb2jra )
=
(1
=
PH jra K + Kb1jra 1 PH jra b2jra
(33)
The mean of KB jra , K B jra can then be obtained as
K Bjra
=
=
=
PH jra E [Kb2jra ] + E [Kb1jra ] 1 PH jra N b 1 X PH jra PrfKb2jra > k g + PrfKb1jra > k g 1 PH jra k=1 N b 1 X k=1
"
1 1
PH jra
Z
2 min(Rs ;ra )
Y +(k
1)Lc
F XM (x
Y
b xLcY cLc +(k
#
fXrjra (x)dx
1)Lc )
The mean of KB can be obtained by unconditioning K B jra on Ra .
KB
=
Z Ra;max NX b 1 0
k=1
PH jra PrfKb2jra > k g + PrfKb1jra > k g fRa (ra )dra 1 PH jra
(34)
12
Z Ra;max = 0
b 1 fRa (ra ) NX 1 PH jra k=1
Z
2 min(Rs ;ra )
Y +(k
1)Lc
F XM (x
Y
b xLcY cLc +(k
fXrjra (x)dxdra
1)Lc )
(35)
5. NUMERICAL RESULTS We consider two satellite constellations. Constellation 1 is a GLOBALSTAR-like constellation, and Constellation 2 is a typical inclined orbit LEO satellite constellation. The constellation parameters for both are shown in Table I. Analytical results can be obtained straightforwardly by simple numeric integrations with finite limits and sums with finite number of terms. Figure 10 shows the mean number of candidate satellites
E [NCS ] as a
function of latitude. In this figure, the proposed analytical results are compared with simulation results. In computer simulation, more than 20,000 samples are generated until their statistics converge. Each sample is generated at a randomly chosen longitude and time interval. In this case, shadowing of candidate satellites is not considered. As shown in this figure, the proposed analytical results agree well with simulation results. Since both Constellations 1 and 2 use inclined orbits,
E [NCS ] is high at medium latitude regions where the
user population is dense. Since Constellation 2 has twice as many satellites as Constellation 1, more satellites can be seen at low latitudes compared with Constellation 1. In high latitude regions beyond the inclination angle where no satellite passes over, the size of the coverage area affects E [NCS ], rather than the number of satellites in a constellation. The
E [NCS ] of Constellation 2, which has a lower altitude and more satellites,
decreases rapidly at latitudes higher than 50Æ . The probability distribution of NCS is applied to the shadowing models of an urban and a suburban areas. Measured data for shadowing model parameters are limited. Thus, the satellite availability
PA() cannot
be obtained directly from the measured data. Therefore, the curve-fitted data used by Karasawa et al.9 are modified to fit the boundary condition of equation 13 with a smooth transition. The satellite availabilities for both urban and suburban areas used here are
PA() =
1
( 2
(b1 2
a
)2
b2 )
;
6 6 2 ; 0 6 6 18
18
where
a
=
0 512
0 216
2 2
; for urban area ; for suburban area
(36)
13
b1
=
b2
=
825 06
a
208
a
376 182
98 484
Figure 11 illustrates the satellite availabilities for both areas. For numerical calculation the mean call duration
T M is set at 150 seconds. And, considered latitude is
35Æ north. Figure 12 shows the CDF of the residual distance of connected satellite of the number of interbeam handovers
fKs 6 kg.
Pr
FXr (x) and the CDF
Since Constellation 2 has smaller coverage area than
Constellation 1, it has shorter residual distance. And, because of heavy shadowing,
Xr for urban area is
shorter than for suburban area. Therefore, interbeam handovers occur more frequently in Constellation 2 than in Constellation 1, and more frequently in urban area than in suburban area. The mean number of intersatellite handovers for an FT with and 2 are shown in Figure 13. As
Ra
=
ra , K sjra for both Constellations 1
Ra increases, the probability that an intersatellite handover occurs due
to shadowing of a communicating satellite decreases, and thus, K sjra decreases. Throughout our numerical results, our analytical results are verified by computer simulation. In computer simulation, exponentially distributed call durations are generated and the number of intersatellite and interbeam handovers for both constellations are counted during each call. These calls are generated until handover statistics converge. As shown in this figure, our analytical results agree well with simulation results. Figure 14 shows the mean number of interbeam handovers with Ra
r K Bjra for Nb = 5 and 6. In both cases, is set at 0 1. As Ra increases, the residual distance of connected satellite increases, and thus, K B jra = a,
decreases. If Ra increases further and includes another boundary of spot beams, more interbeam handovers occur before the occurrence of an intersatellite handover. Therefore, KB jra has discontinuities at the boundary of spot beams. If Nb is an odd number, the nearest boundary of spot beams is located at Lc =2 from the center of the satellite coverage area. Therefore, if Ra is smaller than Lc =2, an intersatellite handover occurs at the spot beam that an FT requests a call and no interbeam handovers occur. However, if Nb is an even number, the boundary of spot beams exists at the center of satellite coverage area. Therefore,
KBjra increases as Ra
approaches 0. Figure 15 shows the mean number of intersatellite handovers and interbeam handovers for various values of
14
the minimum elevation angles min in suburban and urban areas. As min increases the service area is reduced and the residual distance of a satellite is shortened. Thus, the probability of requesting an intersatellite handover increases. An intersatellite handover occurs when a communicating satellite is shadowed or when the coverage area moves out of the FT. In urban areas, shadowing of visible satellites occurs more frequently because of poor satellite availability. Therefore, intersatellite handovers occur frequently in urban areas due to mainly the shadowing of communicating satellites, while movement of the coverage area is the primary reason for intersatellite handovers in suburban areas. Thus,
min affects K s more in suburban areas than
in urban areas. Comparing the average number of intersatellite handovers of Constellation 1 with that of Constellation 2, Constellation 2 has more intersatellite handovers. The altitude of the satellite can explain the reason for this. Because the altitude of a satellite in Constellation 2 is lower than that of the Constellation 1, the ground track speed of a satellite in the Constellation 2 is faster than that of Constellation 1. Therefore, Constellation 2 has more average number of both intersatellite handovers and interbeam handovers than the Constellation 1. As min increases, the number of interbeam handovers during a call
K B increases because
R is reduced and the residual distance of a spot beam is shortened. Compared with intersatellite handovers, interbeam handovers are not affected severely by shadowing environment. The geometry of spot beams significantly affects interbeam handovers. Figure 16 shows the effect of the maximum number of spot beams in a strip Nb , when min
= 10Æ .
In this case suburban areas are considered.
As Nb increases, R decreases and the residual distance of a spot beam decreases, which results in an increase of K B . 6. CONCLUSIONS Handover characteristics in LEO satellite communication networks with consideration of the shadowing of candidate satellites for an FT are analytically evaluated. The probability distribution of the number of candidate satellites at an arbitrary latitude is calculated and verified by simulation. For a given satellite availability the minimum unshadowed elevation angle to an FT is approximated to be omnidirectional. The residual distances of both a communicating satellite and a spot beam are obtained, and the traffic performance in urban and suburban environments is evaluated in terms of the mean number of intersatellite and interbeam
15
handovers during a call. Shadowing of communicating satellite causes frequent intersatellite handovers but yields a rather small effect on interbeam handovers. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
P. Dondl, ‘Standardization of the Satellite Component of the UMTS’, IEEE Personal Commun., 2(5), 68-74 (1995). J. V. Evans, ‘Satellite Systems for Personal Communications’, Proc. IEEE, 86(7), 1325-1341 (1998). G. Maral, J. J. De Ridder, B. G. Evans and M. Richharia, ‘Low Earth Orbit Satellite Systems for Communications’, Int. J. Satell. Commun., 9, 209-225 (1991). Y. F. Hu, R. E. Sheriff, E. D. Re, R. Fantacci and G. Giambene, ‘Satellite-UMTS Traffic Dimensioning and Resource Management Technique Analysis’, IEEE Trans. Vehic. Technol., VT-47, 1329-1341 (1998). E. Lutz, D. Cygan, M. Dippold, F. Dolainsky and W. Papke, ‘The Land Mobile Satellite Communication Channel - Recording, Statistics, and Channel Model’, IEEE Trans. Vehic. Technol., VT-40, 375-386 (1991). G. E. Corazza and F. Vatalaro, ‘A Statistical Model for Land Mobile Satellite Channels and Its Application ot Nongeostationary Orbit Systems’, IEEE Trans. Vehic. Technol., VT-43, 738-742 (1994). H. Bischl, M. Werner and E. Lutz, ‘Elevation-dependent Channel Model and Satellite Diversity for NGSO S-PCNs’, 46th Vehicular Technology Conf. (VTC ’96), Atlanta, GA, April 1996, pp. 1038-1042. W. Krewel and G. Maral, ‘Single and Multiple Satellite Visibility Statistics of First-Generation Non-GEO Constellations for Personal Communications’, Int. J. Satell. Commun., 16, 105-125 (1998). Y. Karasawa, K. Kimura and K. Minamisono, ‘Analysis of Availability Improvement in LMSS by Means of Satellite Diversity Based on Three-State Propagation Channel Model’, IEEE Trans. Vehic. Technol., VT-46, 1047-1056 (1997). F. Dosiere, G. Maral and J. -P. Boutes, ‘Shadowing Process Models for Mobile and Personal Satellite Systems’, GLOBECOM’95, Singapore, November 1995, pp. 536-540. P. Carter and M. A. Beach, ‘Evaluation of Handover Mechanisms in Shadowed Low Earth Orbit Land Mobile Satellite Systems’, Int. J. Satell. Commun., 13, 177-190 (1995). K. M. S. Murthy, ‘Mobile & Multimedia Satellite Systems’, International Conf. on Communications (ICC’96), Dallas, Texas, June 1996, Tutorial No. 15. Y. H. Kwon, J. Y. Yun and D. K. Sung, ‘Satellite Selection Scheme for Reducing Handover Attempts in LEO Satellite Communication Systems’, Int. J. Satell. Commun., 16, 197-208 (1998). B. Pattan, Satellite-Based Global Cellular Communications, McGraw-Hill Co., New York, 1998. Y. H. Kwon, J. Y. Yun and D. K. Sung, ‘A Novel Satellite-Selection Method in LEO Satellite Communication Systems’, Proc. 4th Int. Workshop on Mobile Multimedia Commun., Seoul, 1997, pp. 395-398. D. Hong and S. S. Rappaport, ‘Traffic Model and Performance Analysis for Cellular Mobile Radio Telephone Systems with Prioritized and Nonprioritized Handoff Procedures’, IEEE Trans. Vehic. Technol., VT-35, 77-92 (1986).
16
Table I. Constellation Parameters
Constellation 1 Constellation 2 Orbit plane 6 10 Satellites per orbit plane 8 10 Orbit altitude [km] 1410 1000 Minimum elevation angle [deg] 10 10 Inclination angle [deg] 52 50
17
Q( α , β ) β βi
li α δ
0 i -th orbit plane
Figure 1. Position of the i-th orbit plane
r
ato
equ
18
h min
Rs
RE
Figure 2. Elevation angle and coverage area
19
moving direction of the i -th orbit
Q coverage area of each satellite
Rs li Rs γ ( li )
Figure 3. (li ) in the coverage area
20
γ(l i) = 5 n=2 L s= 2
L s= 2
L s= 2
L s= 2 n=3
L s= 2
L s= 2
L s= 2
Figure 4. Illustration for the case of (li ) = 5 and Ls
=2
21
unshadowed shadowed
σ(ψ) ψ FT
reference direction Figure 5. Shadowing of a satellite
22
Ra > Rs
Ra < Rs
Ra Ra FT
FT Rs
Rs
available area
service area
available area
service area
: available SSP : shadowed SSP
Figure 6. Comparison of the service and available areas
23
Lc
R
R
2L
Figure 7. Circular assumptions for an overlapped area between adjacent spot beams
24
Nb = 5 (1−η) R
L
R
Lc + L
Lc
Lc
Lc
Lc + L
Rs
Figure 8. Structure of spot beams in a satellite coverage area
25
σ
Y Lc + L SHADOWED
Lc
Lc
Lc
2 Ra 2 Rs
Figure 9. Shadowing of edge spot beam
min
Lc + L SHADOWED
26
Mean number of candidate satellites
6
5
4
3
2 Constellation 1 Analysis Simulation
1
Constellation 2 Analysis Simulation
0 0
10
20
30
40
50
60
latitude [deg]
Figure 10. Mean number of candidate satellites, E [NCS ] at various latitudes
70
27
1
Satellite availability
0.8
suburban area
0.6
urban area
0.4
0.2
0 0
10
20
30
40
50
60
70
elevation angle [deg]
Figure 11. Satellite availability for urban and suburban areas
80
90
28
CDF of residual distance of a sat.
1
urban area
0.8
suburban area
0.6
0.4
0.2
Constellation 1 Constellation 2
0 0
1000
2000
3000
4000
5000
6000
7000
8000
x
a
( ) 1
CDF of interbeam handovers
0.8
urban area
0.6
suburban area
0.4
0.2
Constellation 1 Constellation 2
0 0
2
4
6
8
10
k
b
( )
Figure 12. CDF of residual distance of connected satellite FXr (x) and CDF of the number of interbeam handovers PrfKs (a) FXr (x); (b) PrfKs 6 k g
6 k g:
Mean number of intersatellite handovers when Ra = ra
29
16 Constellation 1 Analysis Simulation
14 12
Constellation 2 Analysis Simulation
10 8 6 4 2 0 0
0.2
0.4
0.6
0.8
1
1.2
r a /R s
Figure 13. Mean number of intersatellite handovers when Ra
=
ra , K sjra for both Constellations 1 and 2
Mean number of interbeam handovers when Ra = ra
30
6 Constellation 1 Analysis Simulation
5
Constellation 2 Analysis Simulation
4
3
2
1
0 0
0.2
0.4
0.6
0.8
1
1.2
r a /R s
a
Mean number of interbeam handovers when Ra = ra
( ) 6 Constellation 1 Analysis Simulation
5
Constellation 2 Analysis Simulation
4
3
2
1
0 0
0.2
0.4
0.6
0.8
1
1.2
r a /R s
b
( )
Figure 14. Mean number of interbeam handovers when Ra
=
ra , K B jra for Nb
=5
and 6 : (a) Nb
= 5;
(b) Nb
=6
31
Mean number of intersatellite handovers
1.4 1.2 urban area
1 0.8 0.6
suburban area
0.4 Constellation 1 Analysis Simulation
0.2
Constellation 2 Analysis Simulation
0 5
10
15
20
minimum elevation angle,
min
25
30
[deg]
a
( ) 1.8
Mean number of interbeam handovers
1.6 1.4 1.2 Constellation 2
1
Suburban area Analysis Simulation
0.8 0.6 Constellation 1
Urban area Analysis Simulation
0.4 0.2 0 5
10
15
20
minimum elevation angle,
min
25
30
[deg]
b
( )
Figure 15. Mean number of intersatellite handovers K s and mean number of interbeam handovers K B for various values of min : (a) K s ; (b) K B
32
Mean number of interbeam handovers
3.5 Constellation 1 Analysis Simulation
3 2.5
Constellation 2 Analysis Simulation
2 1.5 1 0.5 0 0
2
4
6
8
10
12
14
16
Nb
Figure 16. Mean number of interbeam handovers K B as a function of Nb with min
= 10Æ
SUMMARY In the near future low earth orbit (LEO) satellite communication networks will partially substitute for fixed terrestrial multimedia networks especially in sparsely populated areas. Unlike fixed terrestrial networks, ongoing calls may be dropped if satellite channels are shadowed. Therefore, in most LEO satellite communication networks more than one satellite need to be simultaneously visible in order to hand over a call to an unshadowed satellite when the communicating satellite is shadowed. In this paper handover characteristics for fixed terminals (FTs) in LEO satellite communication networks are analyzed. The probability distribution of multiple satellite visibility is analytically obtained and the shadowing process of satellites for FTs are modelled. Using the proposed analysis model, shadowing effects on the traffic performance are evaluated in terms of the number of intersatellite and interbeam handovers during a call. KEY WORDS :
multiple satellite visibility; satellite channel shadowing; intersatellite handover; interbeam handover
1. INTRODUCTION In the emerging era of the International Mobile Telecommunications - 2000 (IMT-2000), LEO satellite communication networks are expected to coexist with terrestrial networks.1 Terrestrial regional telecommunication networks with diverse transfer modes and various protocols may suffer from internetworking and compatibility problems to provide global seamless multimedia communications. LEO satellite networks will be able to support end-to-end connections in the near future,2];[3 and thus, they will play both complementary and competitive roles compared with fixed telecommunication networks as well as cellular networks, and may partially substitute for fixed networks in sparsely populated areas where fixed telephony services are unavailable.4 LEO satellite channel characteristics affect the availability and the quality of services, depending on urban vs. suburban areas and satellite constellation parameters.5];[6];[7 When the quality of a satellite channel is degraded due to shadowing, an ongoing call may be dropped. Multiple satellite visibility is provided in most LEO satellite constellations to reduce this call dropping.8];[9 If ongoing calls are dropped only when all visible satellites are shadowed, service availability can be increased.
This study is partially supported by the Ministry of Science & Technology. Correspondence to: Prof. D. K. Sung, Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, Korea. E-mail: [email protected]
2
Shadowing of satellites for mobile terminals (MTs) is caused by two mobility factors. These are satellite mobility and user mobility. As an LEO satellite moves with a constant velocity the varying elevation angle of the satellite from an MT affects the shadowing parameters. Furthermore, the shadowing environment of an MT may vary with time because of the motion of the MT. For FTs with a fixed shadowing environment, shadowing of a satellite depends on the elevation angle of the satellite. Thus, if the elevation angle is sufficient to clear nearby obstacles a call can be connected to the satellite. Several previous studies5];[9];[10 have dealt with shadowing parameters of satellite availability and the received signal distribution in diverse environments. When a satellite which is communicating with an FT is shadowed or when the coverage area of the satellite moves out of the FT, an intersatellite handover occurs. Even within the coverage area of a satellite, interbeam handovers may occur in a multiple spot beam environment.11 The numbers of intersatellite handovers and interbeam handovers vary according to the shadowing environment of an FT. In this paper the handover characteristics of FTs in LEO satellite communication networks are analyzed. The shadowing process of satellites is modelled, and the numbers of intersatellite handovers and interbeam handovers are analytically obtained based on the shadowing model in a multiplesatellite-visible condition. The remaining part of this paper is organized as follows: Section 2 presents an analysis of the probability distribution of the multiple satellite visibility at an arbitrary latitude; Section 3 introduces a shadowing model and a multiple spot beam model; Section 4 shows an analysis of handover characteristics based on these system models; Section 5 shows numerical results; and Section 6 presents conclusions. 2. MULTIPLE SATELLITE VISIBILITY LEO satellite communication networks consist of multiple orbit planes and multiple satellites per orbit plane in order to realize global coverage. The candidate satellite to an FT is defined as a satellite whose elevation angle to the FT is greater than given minimum elevation angle. The number of candidate satellites,
NCS
varies according to constellation parameters, such as the number of satellites, the inclination angle of an orbit plane, and the altitude and the longitude of each satellite. The probability distribution of NCS at a latitude of
is now obtained.
3
Figure 1 shows the position of the i-th orbit plane to a reference point. If
i denotes the ascending node
right ascension of the i-th orbit plane, then i can be expressed as
i =
i ; NO 2
1
6 i 6 NO
(1)
where NO is the number of orbit planes. For an arbitrary point Q with a latitude and longitude of and , respectively, the distance between the point Q and the corresponding track on the earth’s surface of the i-th orbit plane is given by
li = RE sin
1
(sin
Æ cos sin( i
) + cos Æ sin )
(2)
where RE and Æ denote the radius of the earth and the inclination angle of each orbit plane, respectively. Figure 2 illustrates the coverage area of each satellite. The altitude and the minimum required elevation angle of a satellite are denoted by h and min , respectively. The radius of the coverage area of each satellite is then obtained as 12
Rs = RE
2
min
sin
1
RE
RE + h
cos
min
(3)
If the coverage area of each satellite is assumed to be a flat circle, as shown in Figure 3, the ground track distance of a satellite in the i-th orbit moved during the time the point Q is included in the coverage area of the satellite, (li ) can be expressed as
(li ) =
p
2
0
Rs 2 ;
li2 ;
6 li 6 Rs li > Rs 0
(4)
If the number of satellites in one orbit plane is denoted by NSO , the distance between adjacent sub-satellite points (SSPs) is given by
Ls =
RE NSO
2
(5)
The number of candidate satellites in the i-th orbit at the point Q, Mi depends on the relative position of the satellites to
(li ). An illustration for the case of (li )
= 5
and
Ls
= 2
is shown in Fig. 4. As shown in
this illustration, the number of candidate satellites in the i-th orbit at the point Q,
Mi is given by
j
(li ) Ls
k
or
4
j
(li ) Ls
k + 1,
where bxc denotes the greatest integer less than or equal to x. At an arbitrary time, the relative
position of the satellites has no correlation with the (li ), and thus, the probability qi (n; Q) that the number of candidate satellites in the i-th orbit is n at the point Q can be expressed as
qi(n; Q) =
8 > > < 1
(li )
> Ls > : 0
;
j
(li )
(li ) Ljs k Ls
(li ) Ls
k
j
k
; n = L(lsi ) j k n = L(lsi ) + 1
;
(6)
otherwise
The number of candidate satellites NCS at an arbitrary point Q can be obtained by summing the number of candidate satellites in the entire constellation. That is, the probability PCS (j ; Q) that NCS is j at the point Q is given by
PCS (j ; Q)
= =
fM
Pr 1 + j j X X n1 =0 n2 =0
M2 + + MNO
j X
nNO
j at the point Qg
=
qNO (j
n1 ; Q)qNO
n1
n2 ; Q)
1(
1 =0
q2(nNO
2
nNO
1;
Q)q1(nNO
1;
Q)
(7)
Therefore, the probability PCS (j ) that NCS is equal to j at a latitude of can be obtained as
PCS (j ) = N max X
R 2 0
PCS (j ; Q) d 2
PCS (j ) = 1
(8)
(9)
j =0
where
Nmax denotes the maximum number of candidate satellites. Then, the mean number of candidate
satellites E [NCS ] can be expressed as
E [NCS ] =
N max X
jPCS (j )
(10)
j =1
3. SYSTEM MODEL 3.1. Shadowing model Since LEO satellites move in their orbit plane the motion of each satellite relative to an FT can be modelled as a linear motion with a constant velocity. The satellite ground track speed VSSP depends on the altitude of
5
a satellite such that
VSSP where = 3 986 1014 m3 s
2
=
RE
r
(11)
RE + h RE + h
is the gravitational parameter.
From the viewpoint of an FT, satellites whose elevation angle is greater than the minimum required elevation angle
min can be connected if the communication channel between the FT and the satellite is not
shadowed. The service area for an FT is defined as the virtual area in which the SSP of a satellite with an elevation angle from the corresponding FT greater than
min can be located.13 If the coverage area of each
satellite is assumed to be a circle with a radius of Rs , the service area of an FT would also be a circle with a radius of Rs and each SSP inside the service area would move linearly with a constant velocity of VSSP . A communication channel is shadowed when the elevation angle of a satellite is lower than the required elevation angle. This can be caused by nearby obstacles, such as tall buildings, trees, and mountains. If the location of an FT is fixed the time variation of the shadowing is negligible. However, the shadowing process of satellite channels varies with time because each satellite moves with time. Thus, each satellite at an azimuth angle of
with respect to the reference direction of the FT, as shown in Figure 5, can be connected
to an FT if the elevation angle is greater than the minimum unshadowed elevation angle (
)
at an azimuth
angle of , where the minimum unshadowed elevation angle is a user-specific value which is determined by the shadowing environment of the MT. For mathematical simplicity it is assumed that the shadowing environment of an FT is omnidirectional, which implies that an FT has an identical minimum unshadowed elevation angle irrespective of the azimuth angle
(
) =
. The available area of an FT is defined as the area in which the SSP of unshadowed
satellites can be located. As the minimum unshadowed elevation angle is assumed to be omnidirectional, the available area of an FT can be modelled as a circle with a radius Ra , which is a function of . The probability distribution of with an elevation angle of
Ra can be obtained with the satellite availability PA () that one satellite
is available. PA() also implies the probability that exceeds the minimum
unshadowed elevation angle , that is,
PA () = Prf > g
(12)
6
Satellite availability has been extensively measured and analyzed in several previous studies.5];[10];[9 The probability that is less than equals to the probability that one satellite with an elevation angle of is available. Thus, the probability distribution function (PDF) of can be obtained as
f ()
= =
d Prf 6 g d d P () d A
(13)
where PA () satisfies two boundary conditions.
PA (0) = 0 PA ( 2 ) = 1
Similar to equation 3, the relationship between a radius ra and an elevation angle is given by
ra = RE
2
sin
1
RE
RE + h
cos
(14)
And, the maximum value of ra , Ra;max is obtained as
Ra;max = ra j=0 = RE cos
1
RE
(15)
RE + h
Therefore, the PDF of the radius of an available area fRa (ra ) can be expressed as
fRa (ra )
=
1
=
RE r sin ( Ra ) + E 2
in the range of 0 6 ra
dPA () d d dra
1 ra RE +h cos( RE )
n
r cos( Ra ) E
RE RE +h
o2
dPA () 0 d =tan @ 1
cos(
RE ra RE ) RE +h r sin( a ) RE
1 A
(16)
6 Ra;max.
Each FT has two independent virtual areas, a service area and an available area. As an FT has multiple number of candidate satellites, the FT may have several SSPs in a service area. If Ra is greater than Rs , all satellites in the service area are unshadowed and can be connected when a call is requested. However, if Ra is smaller than Rs , satellites outside of the available area within the service area may be shadowed, and thus, the number of available satellites is reduced. These two cases are shown in Figure 6. Therefore, an FT can connect a call to satellites in the circle with a radius of min(Rs ; Ra ).
7
3.2. Multiple spot beams In most LEO satellite constellations, the coverage area is partitioned into multiple spot beams.14 Use of multiple spot beams can increase system capacity, concentrate transmission power, and reduce FT antenna size and required transmission power. In this case an FT may experience interbeam handovers as well as intersatellite handovers. Intersatellite handovers occur between adjacent satellites. Thus, intersatellite handovers require message transfer to the earth station which controls both satellites, which causes a relatively high processing load and time delay. However, interbeam handovers occur between adjacent spot beams within a satellite. Therefore, these handover procedures can be controlled in a satellite and yield a relatively low processing load and time delay. Moreover, the next handover beam can be known a priori to the satellite controller. FTs covered by each spot beam may have different path losses according to the position of the spot beam within the coverage area of a satellite. This is due to an increase in slant range losses as the footprint moves farther from the SSP. This path loss is assumed to be compensated by increasing the spot beam antenna gain as the beam moves farther away. When an FT requests a call, the FT compares the received signal strengths from multiple satellites and connects to spot beam with the maximum received signal strength. Due to the compensation of path loss, each visible spot beam can be connected to this FT with equal probability. Thus, the position of the selected spot beam within a coverage area of the selected satellite is uniformly located. Therefore, the number of available satellites does not affect the residence time distribution in the coverage area of a satellite. The footprint of each spot beam inevitably overlaps its adjacent spot beams in order to provide seamless coverage. The overlap area is approximated to be a circle, as illustrated in Figure 7, where the radius of the beam footprint and the width of the overlap area are R and 2L, respectively. The distance between two adjacent spot beam centres is Lc . If the coverage area of a satellite consists of maximum Nb spot beams in a strip, R is related to Rs as follows
Rs
=
)R
=
R + (Nb Nb
(
R L)
1)(
Rs
1)(1
) + 1
(17)
8
=
where
=
Rs + (Nb Nb
1)
L
(18)
L=R is the normalized overlap width. Figure 8 illustrates the structure of spot beams in a satellite
coverage area with Nb
= 5.
It is assumed that an FT will be handed over only to the next beam in the same
strip. Then, the residence time in the transit spot beam is Lc =VSSP . 4. PERFORMANCE ANALYSIS 4.1. Residual distance of a satellite
D denotes the distance between an FT and an SSP inside the service area of the FT. The probability that D is less than or equal to r, PrfD
6 rg is given by 15 r fD 6 rg = R
2
Pr
2
s
=
r2 ; Rs2
0
6 r 6 Rs
;
0
(19)
Therefore, the PDF of D can then be expressed as
fD (r) = Under the condition that Ra
d PrfD 6 r g = dr
2r Rs2 0
;
6 r 6 Rs
(20)
otherwise
r
R ; ra ).
= a , available satellites for the FT can be located within a radius of min( s
If D0 denotes the distance between an FT and a candidate SSP within a radius of min(Rs ; ra ), the PDF of D0 is given by
fD0 (rjra )
=
fD (r) FD (ra )
where FD (ra ) is the cumulative distribution function (CDF) of D such that FD (ra ) = PrfD The residual distance of a satellite to an FT
(21)
6 ra g.
Xr is defined as the distance travelled of the SSP from the
beginning of a new/handover call to either the time that the SSP moves out of the service area or the time when the satellite is shadowed. When Ra
r and D0 = r, the CDF of the residual distance of a connected
= a
satellite to an FT is given by
FXr (xjr; ra )
fXr 6 xjD0 = r; Ra = rag
=
Pr
=
Pt (x; min(Rs ; ra ); r)
(22)
9
where Pt (x; r0 ; r) denotes the probability that a user whose distance from the centre of a circle with a radius of r0 is r, moves out of the circle when the FT moves a distance of x, such that 13
Pt (x; r0 ; r)
8 > < 0 =
;
1
cos > :
1
;
1
r02 r2 x2 2xr
6 x < r0 r ; r0 r 6 x 6 r0 + r 0
x > r0 + r
If equation 22 is unconditioned to D0 , FXr (xjra ) can be obtained as
FXr (xjra )
Z
min(Rs ;ra )
= 0
=
8 < 0
;
:
2! +sin 2!
;
1
FXr (xjr; ra )fD0 (rjra )dr ;
x 2 min(Rs ; ra )
(23)
where
! = sin
1
x 2 min(Rs ; ra )
Therefore, the CDF of Xr , FXr (x) can be obtained by unconditioning FXr (xjra ) on Ra .
FXr (x) =
Z Ra;max 0
FXr (xjra )fRa (ra )dra
(24)
4.2. Handover performance Let
TM denote the exponentially distributed call duration with a mean of T M . As each SSP moves with a
constant velocity, the distance mean of X M
=
XM that an SSP moves during a call is also exponentially distributed with a
VSSP T M . If the residual distance of the connected satellite Xr is shorter than XM an inter-
satellite handover occurs. Therefore, the probability PH jra that an FT with Ra
r requires an intersatellite
= a
handover can be obtained as
PH jra
=
fXM > Xr jRa = rag
Pr
Z
2 min(Rs ;ra )
= 0
e
x=X M
fXr (xjra )dx
(25)
The residual distance distribution of handed-over satellite to the FT is assumed to be identical to that of the original satellite. Thus, PH jra for new calls and handover calls is the same due to the memoryless property of
10
exponentially distributed call duration. The probability that the number of intersatellite handovers during a call Ksjra is n when Ra
r is given by
= a
Pr
Then, the CDF of Ks , PrfKs
fKsjra = kjRa = rag = (1
PH jra )PHk jra
(26)
6 kg can be expressed as
fKs 6 kg
Pr
Z Ra;max
fKsjra 6 kgfRa (ra)dra
=
Pr 0
=
Z Ra;max X k
(1
0
i=0
Z Ra;max =
(1 0
The mean number of intersatellite handovers when Ra
K sjra
=
1 X k=1
=
1 X k=1
=
PH jra )PHk jra fRa (ra )dra
PHk+1 jra )fRa (ra )dra
(27)
r K sjra can be obtained as
= a,
k PrfKsjra = kjRa = ra g k(1 PH jra )PHk jra
PH jra 1 PH jra
(28)
Thus, the mean number of intersatellite handovers during a call can be obtained by unconditioning K sjra on
Ra . Ks
Z Ra;max = 0
Z Ra;max = 0
K sjra fRa (ra )dra PH jra f (r )dr 1 PH jra Ra a a
To obtain the number of interbeam handovers during a call
(29)
KB , the shadowing condition of each spot
beam should be considered first. If the minimum unshadowed elevation angle for an FT is greater than the minimum elevation angle min (Rs
> Ra ), the spot beams located at the outer tier of a satellite coverage area
may be shadowed as shown in Figure 9. In this figure, Y denotes the length of the partly shadowed spot beam whose elevation angle is greater than , and can be obtained as
Y
8
Lc + L
(30)
11
Two integer random variables
Kb1 and Kb2 represent the number of interbeam handovers in one satellite
when the call is completed within a satellite and when an intersatellite handover occurs, respectively. When an interbeam handover occurs the residual distance of a handed over beam is Lc if this beam is not shadowed. Thus, the probabilities that Kb1jra and Kb2jra equal k when Ra
r are given by
= a
fKb jra = kg
Pr = =
1
XM > Xrjra Y b XrjLrac Y cLc + (k 1)LcjXM < Xrjra R 2 min(Rs ;ra ) FXM (x Y b xLcY cLc +(k 1)Lc) fXrjra (x)dx Y +(k 1)Lc FXM (x) 1 PH jra PrfKb2jra = k g Pr
L jXM > Xrjra g Y +(k 1)Lc F XM (x)fXrjra (x)dx = PH jra where F XM (x) is the complementary CDF of XM such that F XM (x) =
fXrjra > Y + (k
Pr
R 2 min(Rs ;ra )
(31)
1) c
(32) = 1
FXM (x)
= exp(
x=X M ). If
a call is completed within the first communicating satellite the number of interbeam handovers during a call
KB equals Kb1 . However, when an intersatellite handover occurs KB restarts at a transit satellite and is added to the number of interbeam handovers at the first satellite. Hence, KB jra when Ra
KBjra
r can be expressed as
= a
PH jra )Kb1jra + PH jra (KBjra + Kb2jra )
=
(1
=
PH jra K + Kb1jra 1 PH jra b2jra
(33)
The mean of KB jra , K B jra can then be obtained as
K Bjra
=
=
=
PH jra E [Kb2jra ] + E [Kb1jra ] 1 PH jra N b 1 X PH jra PrfKb2jra > k g + PrfKb1jra > k g 1 PH jra k=1 N b 1 X k=1
"
1 1
PH jra
Z
2 min(Rs ;ra )
Y +(k
1)Lc
F XM (x
Y
b xLcY cLc +(k
#
fXrjra (x)dx
1)Lc )
The mean of KB can be obtained by unconditioning K B jra on Ra .
KB
=
Z Ra;max NX b 1 0
k=1
PH jra PrfKb2jra > k g + PrfKb1jra > k g fRa (ra )dra 1 PH jra
(34)
12
Z Ra;max = 0
b 1 fRa (ra ) NX 1 PH jra k=1
Z
2 min(Rs ;ra )
Y +(k
1)Lc
F XM (x
Y
b xLcY cLc +(k
fXrjra (x)dxdra
1)Lc )
(35)
5. NUMERICAL RESULTS We consider two satellite constellations. Constellation 1 is a GLOBALSTAR-like constellation, and Constellation 2 is a typical inclined orbit LEO satellite constellation. The constellation parameters for both are shown in Table I. Analytical results can be obtained straightforwardly by simple numeric integrations with finite limits and sums with finite number of terms. Figure 10 shows the mean number of candidate satellites
E [NCS ] as a
function of latitude. In this figure, the proposed analytical results are compared with simulation results. In computer simulation, more than 20,000 samples are generated until their statistics converge. Each sample is generated at a randomly chosen longitude and time interval. In this case, shadowing of candidate satellites is not considered. As shown in this figure, the proposed analytical results agree well with simulation results. Since both Constellations 1 and 2 use inclined orbits,
E [NCS ] is high at medium latitude regions where the
user population is dense. Since Constellation 2 has twice as many satellites as Constellation 1, more satellites can be seen at low latitudes compared with Constellation 1. In high latitude regions beyond the inclination angle where no satellite passes over, the size of the coverage area affects E [NCS ], rather than the number of satellites in a constellation. The
E [NCS ] of Constellation 2, which has a lower altitude and more satellites,
decreases rapidly at latitudes higher than 50Æ . The probability distribution of NCS is applied to the shadowing models of an urban and a suburban areas. Measured data for shadowing model parameters are limited. Thus, the satellite availability
PA() cannot
be obtained directly from the measured data. Therefore, the curve-fitted data used by Karasawa et al.9 are modified to fit the boundary condition of equation 13 with a smooth transition. The satellite availabilities for both urban and suburban areas used here are
PA() =
1
( 2
(b1 2
a
)2
b2 )
;
6 6 2 ; 0 6 6 18
18
where
a
=
0 512
0 216
2 2
; for urban area ; for suburban area
(36)
13
b1
=
b2
=
825 06
a
208
a
376 182
98 484
Figure 11 illustrates the satellite availabilities for both areas. For numerical calculation the mean call duration
T M is set at 150 seconds. And, considered latitude is
35Æ north. Figure 12 shows the CDF of the residual distance of connected satellite of the number of interbeam handovers
fKs 6 kg.
Pr
FXr (x) and the CDF
Since Constellation 2 has smaller coverage area than
Constellation 1, it has shorter residual distance. And, because of heavy shadowing,
Xr for urban area is
shorter than for suburban area. Therefore, interbeam handovers occur more frequently in Constellation 2 than in Constellation 1, and more frequently in urban area than in suburban area. The mean number of intersatellite handovers for an FT with and 2 are shown in Figure 13. As
Ra
=
ra , K sjra for both Constellations 1
Ra increases, the probability that an intersatellite handover occurs due
to shadowing of a communicating satellite decreases, and thus, K sjra decreases. Throughout our numerical results, our analytical results are verified by computer simulation. In computer simulation, exponentially distributed call durations are generated and the number of intersatellite and interbeam handovers for both constellations are counted during each call. These calls are generated until handover statistics converge. As shown in this figure, our analytical results agree well with simulation results. Figure 14 shows the mean number of interbeam handovers with Ra
r K Bjra for Nb = 5 and 6. In both cases, is set at 0 1. As Ra increases, the residual distance of connected satellite increases, and thus, K B jra = a,
decreases. If Ra increases further and includes another boundary of spot beams, more interbeam handovers occur before the occurrence of an intersatellite handover. Therefore, KB jra has discontinuities at the boundary of spot beams. If Nb is an odd number, the nearest boundary of spot beams is located at Lc =2 from the center of the satellite coverage area. Therefore, if Ra is smaller than Lc =2, an intersatellite handover occurs at the spot beam that an FT requests a call and no interbeam handovers occur. However, if Nb is an even number, the boundary of spot beams exists at the center of satellite coverage area. Therefore,
KBjra increases as Ra
approaches 0. Figure 15 shows the mean number of intersatellite handovers and interbeam handovers for various values of
14
the minimum elevation angles min in suburban and urban areas. As min increases the service area is reduced and the residual distance of a satellite is shortened. Thus, the probability of requesting an intersatellite handover increases. An intersatellite handover occurs when a communicating satellite is shadowed or when the coverage area moves out of the FT. In urban areas, shadowing of visible satellites occurs more frequently because of poor satellite availability. Therefore, intersatellite handovers occur frequently in urban areas due to mainly the shadowing of communicating satellites, while movement of the coverage area is the primary reason for intersatellite handovers in suburban areas. Thus,
min affects K s more in suburban areas than
in urban areas. Comparing the average number of intersatellite handovers of Constellation 1 with that of Constellation 2, Constellation 2 has more intersatellite handovers. The altitude of the satellite can explain the reason for this. Because the altitude of a satellite in Constellation 2 is lower than that of the Constellation 1, the ground track speed of a satellite in the Constellation 2 is faster than that of Constellation 1. Therefore, Constellation 2 has more average number of both intersatellite handovers and interbeam handovers than the Constellation 1. As min increases, the number of interbeam handovers during a call
K B increases because
R is reduced and the residual distance of a spot beam is shortened. Compared with intersatellite handovers, interbeam handovers are not affected severely by shadowing environment. The geometry of spot beams significantly affects interbeam handovers. Figure 16 shows the effect of the maximum number of spot beams in a strip Nb , when min
= 10Æ .
In this case suburban areas are considered.
As Nb increases, R decreases and the residual distance of a spot beam decreases, which results in an increase of K B . 6. CONCLUSIONS Handover characteristics in LEO satellite communication networks with consideration of the shadowing of candidate satellites for an FT are analytically evaluated. The probability distribution of the number of candidate satellites at an arbitrary latitude is calculated and verified by simulation. For a given satellite availability the minimum unshadowed elevation angle to an FT is approximated to be omnidirectional. The residual distances of both a communicating satellite and a spot beam are obtained, and the traffic performance in urban and suburban environments is evaluated in terms of the mean number of intersatellite and interbeam
15
handovers during a call. Shadowing of communicating satellite causes frequent intersatellite handovers but yields a rather small effect on interbeam handovers. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
P. Dondl, ‘Standardization of the Satellite Component of the UMTS’, IEEE Personal Commun., 2(5), 68-74 (1995). J. V. Evans, ‘Satellite Systems for Personal Communications’, Proc. IEEE, 86(7), 1325-1341 (1998). G. Maral, J. J. De Ridder, B. G. Evans and M. Richharia, ‘Low Earth Orbit Satellite Systems for Communications’, Int. J. Satell. Commun., 9, 209-225 (1991). Y. F. Hu, R. E. Sheriff, E. D. Re, R. Fantacci and G. Giambene, ‘Satellite-UMTS Traffic Dimensioning and Resource Management Technique Analysis’, IEEE Trans. Vehic. Technol., VT-47, 1329-1341 (1998). E. Lutz, D. Cygan, M. Dippold, F. Dolainsky and W. Papke, ‘The Land Mobile Satellite Communication Channel - Recording, Statistics, and Channel Model’, IEEE Trans. Vehic. Technol., VT-40, 375-386 (1991). G. E. Corazza and F. Vatalaro, ‘A Statistical Model for Land Mobile Satellite Channels and Its Application ot Nongeostationary Orbit Systems’, IEEE Trans. Vehic. Technol., VT-43, 738-742 (1994). H. Bischl, M. Werner and E. Lutz, ‘Elevation-dependent Channel Model and Satellite Diversity for NGSO S-PCNs’, 46th Vehicular Technology Conf. (VTC ’96), Atlanta, GA, April 1996, pp. 1038-1042. W. Krewel and G. Maral, ‘Single and Multiple Satellite Visibility Statistics of First-Generation Non-GEO Constellations for Personal Communications’, Int. J. Satell. Commun., 16, 105-125 (1998). Y. Karasawa, K. Kimura and K. Minamisono, ‘Analysis of Availability Improvement in LMSS by Means of Satellite Diversity Based on Three-State Propagation Channel Model’, IEEE Trans. Vehic. Technol., VT-46, 1047-1056 (1997). F. Dosiere, G. Maral and J. -P. Boutes, ‘Shadowing Process Models for Mobile and Personal Satellite Systems’, GLOBECOM’95, Singapore, November 1995, pp. 536-540. P. Carter and M. A. Beach, ‘Evaluation of Handover Mechanisms in Shadowed Low Earth Orbit Land Mobile Satellite Systems’, Int. J. Satell. Commun., 13, 177-190 (1995). K. M. S. Murthy, ‘Mobile & Multimedia Satellite Systems’, International Conf. on Communications (ICC’96), Dallas, Texas, June 1996, Tutorial No. 15. Y. H. Kwon, J. Y. Yun and D. K. Sung, ‘Satellite Selection Scheme for Reducing Handover Attempts in LEO Satellite Communication Systems’, Int. J. Satell. Commun., 16, 197-208 (1998). B. Pattan, Satellite-Based Global Cellular Communications, McGraw-Hill Co., New York, 1998. Y. H. Kwon, J. Y. Yun and D. K. Sung, ‘A Novel Satellite-Selection Method in LEO Satellite Communication Systems’, Proc. 4th Int. Workshop on Mobile Multimedia Commun., Seoul, 1997, pp. 395-398. D. Hong and S. S. Rappaport, ‘Traffic Model and Performance Analysis for Cellular Mobile Radio Telephone Systems with Prioritized and Nonprioritized Handoff Procedures’, IEEE Trans. Vehic. Technol., VT-35, 77-92 (1986).
16
Table I. Constellation Parameters
Constellation 1 Constellation 2 Orbit plane 6 10 Satellites per orbit plane 8 10 Orbit altitude [km] 1410 1000 Minimum elevation angle [deg] 10 10 Inclination angle [deg] 52 50
17
Q( α , β ) β βi
li α δ
0 i -th orbit plane
Figure 1. Position of the i-th orbit plane
r
ato
equ
18
h min
Rs
RE
Figure 2. Elevation angle and coverage area
19
moving direction of the i -th orbit
Q coverage area of each satellite
Rs li Rs γ ( li )
Figure 3. (li ) in the coverage area
20
γ(l i) = 5 n=2 L s= 2
L s= 2
L s= 2
L s= 2 n=3
L s= 2
L s= 2
L s= 2
Figure 4. Illustration for the case of (li ) = 5 and Ls
=2
21
unshadowed shadowed
σ(ψ) ψ FT
reference direction Figure 5. Shadowing of a satellite
22
Ra > Rs
Ra < Rs
Ra Ra FT
FT Rs
Rs
available area
service area
available area
service area
: available SSP : shadowed SSP
Figure 6. Comparison of the service and available areas
23
Lc
R
R
2L
Figure 7. Circular assumptions for an overlapped area between adjacent spot beams
24
Nb = 5 (1−η) R
L
R
Lc + L
Lc
Lc
Lc
Lc + L
Rs
Figure 8. Structure of spot beams in a satellite coverage area
25
σ
Y Lc + L SHADOWED
Lc
Lc
Lc
2 Ra 2 Rs
Figure 9. Shadowing of edge spot beam
min
Lc + L SHADOWED
26
Mean number of candidate satellites
6
5
4
3
2 Constellation 1 Analysis Simulation
1
Constellation 2 Analysis Simulation
0 0
10
20
30
40
50
60
latitude [deg]
Figure 10. Mean number of candidate satellites, E [NCS ] at various latitudes
70
27
1
Satellite availability
0.8
suburban area
0.6
urban area
0.4
0.2
0 0
10
20
30
40
50
60
70
elevation angle [deg]
Figure 11. Satellite availability for urban and suburban areas
80
90
28
CDF of residual distance of a sat.
1
urban area
0.8
suburban area
0.6
0.4
0.2
Constellation 1 Constellation 2
0 0
1000
2000
3000
4000
5000
6000
7000
8000
x
a
( ) 1
CDF of interbeam handovers
0.8
urban area
0.6
suburban area
0.4
0.2
Constellation 1 Constellation 2
0 0
2
4
6
8
10
k
b
( )
Figure 12. CDF of residual distance of connected satellite FXr (x) and CDF of the number of interbeam handovers PrfKs (a) FXr (x); (b) PrfKs 6 k g
6 k g:
Mean number of intersatellite handovers when Ra = ra
29
16 Constellation 1 Analysis Simulation
14 12
Constellation 2 Analysis Simulation
10 8 6 4 2 0 0
0.2
0.4
0.6
0.8
1
1.2
r a /R s
Figure 13. Mean number of intersatellite handovers when Ra
=
ra , K sjra for both Constellations 1 and 2
Mean number of interbeam handovers when Ra = ra
30
6 Constellation 1 Analysis Simulation
5
Constellation 2 Analysis Simulation
4
3
2
1
0 0
0.2
0.4
0.6
0.8
1
1.2
r a /R s
a
Mean number of interbeam handovers when Ra = ra
( ) 6 Constellation 1 Analysis Simulation
5
Constellation 2 Analysis Simulation
4
3
2
1
0 0
0.2
0.4
0.6
0.8
1
1.2
r a /R s
b
( )
Figure 14. Mean number of interbeam handovers when Ra
=
ra , K B jra for Nb
=5
and 6 : (a) Nb
= 5;
(b) Nb
=6
31
Mean number of intersatellite handovers
1.4 1.2 urban area
1 0.8 0.6
suburban area
0.4 Constellation 1 Analysis Simulation
0.2
Constellation 2 Analysis Simulation
0 5
10
15
20
minimum elevation angle,
min
25
30
[deg]
a
( ) 1.8
Mean number of interbeam handovers
1.6 1.4 1.2 Constellation 2
1
Suburban area Analysis Simulation
0.8 0.6 Constellation 1
Urban area Analysis Simulation
0.4 0.2 0 5
10
15
20
minimum elevation angle,
min
25
30
[deg]
b
( )
Figure 15. Mean number of intersatellite handovers K s and mean number of interbeam handovers K B for various values of min : (a) K s ; (b) K B
32
Mean number of interbeam handovers
3.5 Constellation 1 Analysis Simulation
3 2.5
Constellation 2 Analysis Simulation
2 1.5 1 0.5 0 0
2
4
6
8
10
12
14
16
Nb
Figure 16. Mean number of interbeam handovers K B as a function of Nb with min
= 10Æ
