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Effect of sectoring on the capacity of CDMA multi-hop
communication network
Kshipra Yadav
1, Dr.Manish Rai
2 1 2Department of Electronics and Communication Engineering 1 Galgotias College of Engineering and Technology, Greater Noida, (UP)-India
2 Faculty of Engineering and Technology, MJP Rohilkhand University, Bareilly, (UP)-India
1ykshipra@yahoo.com ,2manishrai1968@gmail.com
Abstract—Sectoring is one of the widely accepted techniques to increase the capacity of a cellular system. It considerably increases the capacity of cellular CDMA. On the other hand multi-hopping is also seen to increase the capacity in cellular networks. Although both the techniques reduce interference, the increment in capacity due to sectoring is very large as compared to that of multi-hopping. Multi-hopping alone shows an increment of 10% in the capacity whereas a 3-sectored cell shows an increment of 200%. This paper explores the effect on CDMA capacity if sectoring is also applied on a multi-hopping scheme. If we use this technique of sectoring on multi-hopping scheme, it is seen that the capacity increases to 141.68% as opposed to 10% with multi-hopping only. So this paper explores the tremendous effect which sectoring can impose on multi-hopping.
Index Terms— capacity, CDMA, interference, multi-hopping, sectorization.
I. INTRODUCTION
CDMA exhibits a soft-limit on the capacity of the cellular system. This means there is always a scope of adding one more user at the expense of an increased noise floor. An additional user will cause an increase in the interference of the system. Whereas in the case of TDMA and FDMA, time slots and frequency band respectively are the decision factor on the upper limit of the number of users, in the case of CDMA it is decided by the tolerance limit to interference. Hence, any reduction in the interference will result in linear increase in the capacity of the CDMA system.
In Multi-hopping, relaying mobile terminals are used to send the signal in multiple-hops to the base station and back to the mobile terminals. Different multi-hop proposals could be found in [1]-[3] and that the multi-hop can increase the capacity is shown in [3], [4]. The capacity increase associated with multi-hopping and the use of formulas in calculating the interference in this paper is derived from [7]. This interference is calculated at the base station during the reverse link and no specific channel assignment is assumed.
In sectorization, an omnidirectional antenna at the cell-site is replaced by the sectored antenna. Mainly 3 or 6 sectors are used. A 3-sectored antenna reduces the interference to one-third and the corresponding increase in capacity is three times or 200% [8].
In this paper, the effects in the reduction of interference is seen when sectorization is applied on a multi-hopping communication network. The relaying mobile terminals are different than mobile terminals sending their own data. This gives the worst case scenario since this increase the total interference and hence the capacity increase is shown in the worst case. Power control is assumed only in the innermost disc.
Section II contains the network model. The use of formulas in calculating interference is shown in section III. In section IV, numerical results are presented and discussed. Section V concludes the paper.
II. NETWORK STRUCTURE
In the case of multi-hopping, a cell is divided into k concentric discs around the base station. The innermost disc is numbered 0 and the outermost disc is k [7]. In order to see the effects of sectoring on multi-hopping, the omnidirectional antenna at the cell site is replaced by the three directional antennas, each of beam width 120° as shown in fig. 1. Only the mobile terminals of the innermost disc are under the power control of these directional antennas. The signals from these mobile terminals are received at each antenna with power SR. All other mobile terminals transmit with constant power STR and they relay their signals through the
Figure1. A cell with sectoring imposed on multi-hopping
III. INTERFERENCE CALCULATION
Interference is calculated at the base station during an uplink slot. The interference produced is composed of intra-cell interference which results from inside the cell and inter-cell interference which is due to the neighboring cells. The directional antennas are used instead of omnidirectional antenna and the power control is exhibited only in the innermost disc. Thus, while calculating the interference, the intra-cell interference from the innermost disc is reduced to one-third. This is because the use of 120° beamwidth sectors in place of an omnidirectional antenna causes the interference to reduce to one-third at the cell-site[8]. Similar approach is applied while determining the inter-cell interference i.e. the interference only due to the innermost disc from the neighboring cells is reduced to one-third.
A. Intra-cell interference at the base station
The intra-cell interference at the base station is calculated using the formulas derived in [7], which is given by
= + , 10ξ ƒ ,
!
1
(1)
Where N0 is the number of mobile terminals transmitting in disc 0, SR is the constant strength with which the signals are
received at the mobile terminal, STR is constant transmission power of the mobile terminals outside the innermost disc, Ni is the
number of mobile terminals transmitting in disc i, d(x,y) is the distance from any point (x,y) inside the cell to BS, m is the path loss exponent, ξ is the shadowing effect, ƒ(x,y) is the distribution function of mobile terminals inside disc i and A(i) is the area of disc i.
The first term’N0SR’ in (1) gives the interference from the innermost disc. This is the case when no sectoring is applied.
Now, due to the application of sectoring, this term is reduced to N0SR/3.
After changing the Cartesian co-ordinates into polar co-ordinates (since the cells are assumed to be circular[6]) and simplifying the integral, the common term for intra-cell interference is found out as
= 3 + $%& '
(
)π
* + - + + 1 +.1 + 2+ (/ !
2
Where NT is the total number of calls in each cell, Rs is the radius of the circle circumscribing the cell, k is the number of
concentric discs in which the cell is divided.
B. Intercell interference at the base station
Because signals from mobile terminals reach the Base station in multiple hops, therefore their transmission power is limited, so only first tier cells are considered. Since all the neighboring base stations are equidistant from the base station of concern, therefore interference from one cell is calculated then multiplied by six.
The term for calculating inter-cell interference at base station as derived in [7] is given by
0 1 = )
,
2 , / 10
3ξ4 ξ56⁄
ƒ , + 8 , 10ξ⁄ ƒ ,
!
(3) Where di(x,y) and ξi are the distance and shadowing effect from mobile terminalto its own BS and dj(x,y) and ξj are the
distance and shadowing effect from mobile terminal to the BS where the interference is calculated. The first term in the above formula gives the intercell interference from the innermost disc. While considering the sectoring effect, this term reduces to one-third. The second term gives the interference due to outer discs.
Applying polar co-ordinates, the first term of the above equation reduces to
0 , !9= 1/3
; <
=36 &(
0.8270 B
C 1 + (
1 − ( E
.C(C
F G
H 4
The above term gives the inter-cell interference from all the six neighboring cells where ‘n=0’ signifies the innermost disc. The second term of equation (3) which gives the inter-cell interference from the outer discs can be simplified to
0 , ! 9 =4% J( $
%K
& '
L π
* +
!
B 1 −1 +( E(
.C(C M
.C(C
5
Where Rc is the radius of the hexagonal cell and Rs is the radius of the circle circumscribing the cell.
Due to the use of sectorization, the intra-cell and inter-cell interference from the innermost discs is reduced to one-third which is shown in eq. (2) and (4) respectively.
IV. Numerical results and discussion
In order to find out the numerical results, polar co-ordinates are used since the integration is done over circular cells [6].The
term Ni which is the number of mobile terminals transmitting in disc ‘i’ is given by= * O* + +α * P
! M
Q 6
Where NT is the total number of calls in each cell. AT is the cell area, α is 1 which implies that active mobile terminals
cannot relay other mobile’s data [7]
I
T_BS=C
kN
TS
R(7)
Where Ck is the numerical value which depends on the number of discs and is defined as the average interference caused per
original call.
Now comparing the values of Ck in hopping case to the case where sectoring is also applied together with
multi-hopping, there is a considerable decrease in the values of Ck as simulated results show in fig. 2. It can be seen that the values
almost reduce to half with sectorization. Table 1 shows the comparative study of the reduction in average interference per original call between multi-hopping case and the case where sectoring is also applied on multi-hopping.
Table 1. Comparative study of the reduction in average interference per original call
No. of discs ’k’
Average interference per original call(dB)
Multi-hopping
Multi-hopping+sectoring
k=1 1.3796 1.3796
k=2 1.2453 0.5708
k=3 1.2451 0.5860
k=4 1.2650 0.5979
k=5 1.2721 0.6052
k=6 1.2766 0.6099
k=7 1.2797 0.6130
k=8 1.2818 0.6151
k=9 1.2833 0.6166
k=10 1.2844 0.6178
Figure 2.Comparison of average interference (Ck) per original
Call between simple multi-hopping case and the case where sectoring is also applied.
Based on the values of Ck, the maximum number of simultaneous calls that can be accommodated are calculated using the
formula as given in [11].
=R ST MU
V
(8)
Where W is the RF bandwidth which is 1.22 MHz, R is data rate which is 9.6 kbps and τ is the threshold value for Eb/I0 which should be above 5 (7 dB). The cell radius Rc considered here is 500m.
Using the formulas above, the percentage increase in the number of calls can be plotted. The two plots are compared as shown fig. 3. Table 2 shows the comparative study of the increase in the number of simultaneous calls and Table 3 contains
1 2 3 4 5 6 7 8 9 10
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
Number of discs
comparative study of the percentage increase between the cell which uses multi-hopping only and the cell which also uses sectoring upon multi-hopping.
Figure 3
.
Comparison of percentage increase in the number ofsimultaneous calls.
Table 2. Comparative study of the increase in the number of simultaneous calls
No. of discs ’k’ Maximum number of simultaneous calls
Multi-hopping
Multi-hopping+sectoring
k=1 13.8847 13.8847
k=2 15.3815 33.5563
k=3 15.2740 32.6852
k=4 15.1422 32.0365
k=5 15.0579 31.6484
k=6 15.0042 31.4076
k=7 14.9686 31.2498
k=8 14.9438 31.1413
k=9 14.9260 31.0636
k=10 14.9128 31.0063
Table 3. Comparative study of the percentage increase in the number of simultaneous calls
No. of discs ’k’ Percentage increase in the number of simultaneous calls
Multi-hopping
Multi-hopping+sectoring
k=1 0 0
k=2 10.7803 141.6774
k=3 10.0058 135.4034
k=4 9.0570 130.7314
k=5 8.4499 127.9367
k=6 8.0630 126.2021
1 2 3 4 5 6 7 8 9 10
0 50 100 150
Number of discs
P
e
rc
e
n
ta
g
e
i
n
c
re
a
s
e
k=7 7.8060 125.0654
k=8 7.6279 124.2840
k=9 7.4998 123.7250
k=10 7.4048 123.3119
V. Conclusions
In this paper, a combined effect of sectoring and multi-hopping is shown on the capacity of cellular CDMA. It is seen that the interference values almost decrease to half. Due to this the percentage increase in capacity as compared to a cell which does not employ any sectoring or multi-hopping goes up to 141.68% whereas for a cell which employs multi-hopping this percentage increase is only 10%. Such increment can be attributed to the fact that a 3-sectored cell as opposed to an omnidirectional antenna sees capacity increase to 200%. So, when this sectoring approach is applied on a cell with multi-hopping scheme then the intra-cell and inter-intra-cell interference from the innermost disc is reduced to one-third and correspondingly there is an increase in the capacity.
The findings of this paper could be beneficial in the areas of high density of users which demand high throughput rates. Further research in this topic can be done by the use of adaptive antennas and by the use of new centrality based power control in multi-hopping network[8].
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