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PERFORMANCE ANALYSIS OF A CDMA WIRELESS LOCAL LOOP SYSTEMS

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Electron Technology – Internet Journal
37/38
(2005/2006), 3, p. 1
−
7, Institute of Electron Technology, Warszawa
PERFORMANCE ANALYSIS OF A CDMA WIRELESS LOCAL LOOP SYSTEMS
E
MAD
S.
H
ASSAN
,
S
AMI
A.
E
L
-D
OLIL
,
M
OAWAD
I.
D
ESSOUKY
Department of Electronic and Electrical Communication Engineering, Faculty of Electronic Engineering, Menoufya University, Cairo, Egypt
Received March 31, 2006; accepted May 22, 2006; published May 31, 2006
A
BSTRACT
In this paper, the capacity of the Code Division Multiple Access Wireless Local Loop (CDMA WLL) system is analytically derived, and the capacity gain achieved in a CDMA WLL over a cellular mobile environment is calculated. The results show that the CDMA WLL system can support up to 36 % more users than CDMA cellular mobile system. The paper also propose a new approach to increase the reverse link capacity of the CDMA WLL system, which synchronize the reverse link so that signals transmitted from different subscriber units within the same cell are time aligned at the base station (BS). A theoretical analysis of the potential capacity gain of reverse link synchronous CDMA WLL is presented.
1. Introduction
The wireless local loop (WLL) system is a local telephone system without wireline connection. It is believed to be a fast and cost-effective means to provide local phone service in rural areas and third world countries. WLL system deploy access technologies based either on the existing standards (such as TDMA, GSM, IS-95 CDMA, etc.) or proprietary radio link technologies to provide reliable, and cost effective local telephone service [1], [2]. Major differences between the WLL and the mobile cellular environment include a usual strong line-of-sight (LOS) component and a stationary subscriber unit with a directional antenna. LOS channels and stationary users result in Rician-rather than Rayleigh-type of fading. The fading reduction leads to a substantial decrease in the link requirements and consequently an increase in system capacity [3]. In this paper ideal multiple-tier hexagonal cells are used to derive the capacity of a CDMA WLL system and comparing it with the capacity of CDMA cellular mobile system. The paper also propose a new approach to increase the reverse link capacity of the CDMA WLL system, where in CDMA WLL system, the ability to tolerate interference is used to allow other users to send their transmission on the same channel. Each of the other users also has a spreading code. It is important that each user has a different code and that the codes are orthogonal with each other. So whatever transmitted by the interferer and by the wanted user, the correlator produces the same result as if there were no interferer, more orthogonal interferers can be added without having any effect on the wanted signal. The only time this relationship does not hold is when the received signals are not synchronized [1], so that the transitions in the spreading sequences occur at different times. This would occur when the users were at different distances from the BS and so experiencing different propagation delays. This situation can be avoided through the use of timing advance commands from the BS to tell the user to change its internal clock by the propagation delay being experienced. This is one of the key differences between the use of CDMA for mobile and WLL purposes. In the mobile case, synchronization on the reverse link is almost difficult to achieve because of the movement of the mobile, resulting in variable propagation delays. Hence, the reverse link is designed to accept asynchronous input, resulting in a lower system capacity. But in WLL systems, there is no movement; hence, a synchronous system can be produced, so that signals transmitted from different users within the same cell are time aligned at the BS.
2. Reverse link capacity of a CDMA cellular mobile system
In this section the reverse link (MS to BS) capacity of a CDMA cellular mobile system is calculated, where in a multiple cell CDMA system,
Electron Technology – Internet Journal
37/38
(2005/2006), 3 (http://www.ite.waw.pl/etij/ )
2
an MS is power-controlled by the BS that sending the highest strength pilot signal to the MS. This BS is called the
home
BS of the given MS. The interference from subscribers within the same (
home
) cell is called intra-cell interference or self interference
I
self
and calculated as follows; since each user is power controlled by the same BS, it arrives with the same power
S
when active. Thus given
N
subscribers per cell, the total interference is never greater than (
N
−
1)
S
but on the average it is reduced by the voice activity factor,
α
. Subscribers in other cells, however are power controlled by other cell sites, so
I
self
=
α
(
N
−
1)
S
. (1) Figure 1 shows an ideal hexagonal cellular structure. The path loss
L
between the MS and the BS is described as
L
∝
r
−μ
10
ζ
/10
(2) where:
r
−
distance from an MS to a BS;
μ
−
path loss exponent;
−
attenuation in dB due to shadowing, which is a Gaussian random variable with standard deviation
σ
of 8 dB and zero mean
.
Fig. 1. A hexagonal cellular structure.
First, the reverse link interference from each tier to the center cell is calculated separately. Then, we can obtain the total other cell interference which is the interference produced by all users who are power-controlled by other BS’s. If the interfering subscriber in another cell is located at a distance
r
m
from its BS and
r
o
from the BS of the desired user, the other user when active, produces an interference to the desired user’s BS given by [4] .1101010),(
10/)(
40)10/(
440)10/(
0
00
≤⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ ==⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ ⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ =
−
mm
r r r r S r r I
mmm
ζ ζ ζ ζ
(3) Using a path loss exponent of 4, the first term is due to the attenuation caused by distance and blockage to the given BS, while the second term is the effect of power control to compensate for the corresponding attenuation to the BS of the out-of-cell interferer. For all values of the above parameters, the expression is less than unity, otherwise the subscriber would switch to the BS that makes it less than unity. Assuming
N
users uniformly distributed in a cir- cular cell of radius
R
, the user density is given by .
2
R N
π ρ
=
(4) To calculate the reverse link interference from each tier to the center cell, assuming a perfect power control so, the received power at the BS would be the same for each MS. Let
S
be the power of a CDMA mobile unit received at the BS of its own cell. Then, referring to Fig. 2 the total mobile power from a cell having
N
MSs uniformly distributed in it to a BS at distance
d
=
kR
is given by [5]
∫
⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ =
dAr r S d P
om
ρ α
4
)( (5) where the integration is over one cell area, and
r
0
is given by .cos2
220
θ
+++=
mm
dr r d r
(6)
d r
o
R dr
m
dA
MS
r
m
Fig. 2. CDMA interference calculation.
From Fig. 2 and using Eqs. (4) and (6), Eq. (5) becomes
θ ρ α
π
d dr r r r S d P
mm Rm
∫∫
⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ =
0040
2)(
or
( )
.cos22)(
022205
∫∫
++=
π
θ θ αρ
mmm Rm
dr r d d dr r S d P
(7) This integration can be evaluated analytically as follows. Let
( )( )
322220222
cos2)(
mmmmm
r d r d dr r d d r B
−+==++=
∫
π θ θ
π
(8) and
)(
05
m Rmm
r Bdr r A
∫
=
. (9) Thus,
( )
mmmm R
dr r d r r d A
3227520
−+=
∫
π
(10)
Electron Technology – Internet Journal
37/38
(2005/2006), 3 (http://www.ite.waw.pl/etij/ )
3
when
d = kR
, this integration becomes .)1(2
1641ln2
22242222
⎥⎥⎦⎤⎢⎢⎣⎡−+−−⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ −=
k k k k k k R A
π
(11) Finally,
⎥⎥⎦⎤⎢⎢⎣⎡−+−−⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ −=
2224222
)1(2
1641ln22)(
k k k k k k NS d P
α
(12) which is the total interference received at the
home
cell from an interfering cell
i
. Now consider the case when all CDMA cells are loaded with
N
active mobile units, the total interference power received at
home
BS from all mobiles in other cells is the sum of the interfering power from 6 ring-1 cells, 12 ring-2 cells and so on. Figure 3 shows that the distance between the BS of a ring-
n
cell and that of the cell under consideration is .2
22,
niin Rd
in
−+−
(13) The number of cells at the tier
n
facing one side of the reference cell is
n.
Thus the total number of cells in ring-
n
is 6
n
. Substituting from Eq. (13) into Eq. (12), the total other cell interference in the case of cellular mobile system,
I
occ
, for
N
tiers is given as follows
∑∑
= =
==
N nniinocc
d P I
11,
)(6
∑∑
= =
⎥⎦⎤⎢⎣⎡−+−−⎟ ⎠ ⎞⎜⎝ ⎛ −=
N nni
M M M M M M NS
1122
)1(2
1641ln212
α
(14) where:
M
= 4(
n
2
+
i
2
–
ni
) (15)
Fig. 3. Co-ordinates for inter-base station distance calculation.
For this system the reverse link capacity can be calculated by using [4]
( )
⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ −−××−=>
−−−=−−
∑
)/()/()1()10(
11013
S I Var S I E k
Q BER P
occocck N k N k N k r
δ α α
(16) where:
S N E RW dye xQ
obb x y
η δ π
−==
∫
∞−
//and21)(
)2/(
2
(17) and
W
is the frequency band assigned,
R
b
is the bit rate,
W/R
b
is the processing gain,
E
b
/N
o
is the energy per bit to interference density ratio,
η
is the back ground noise, and
E
(
I
occ
/S
) and
Var
(
I
occ
/S
) are the mean and variance of
I
occ
/S
respectively. The reverse link capacity
N
c
is defined as the maximum integer
N
satisfying
P
r
(
BER
> > 10
−
3
) < 0.01, and can be easily calculated using Eq. (16) when
E
(
I
occ
/S
) = 0.247x
N
and
Var
(
I
occ
/S
) = = 0.078x
N
, as given in [4]. This expression is plotted for
E
b
/N
o
= 7 dB,
W
=1.25 MHz,
R
b
= 8 Kbps,
α
= 3/8, and
/
S
=
−
1dB as shown in Fig. 4. This figure indicates that, the reverse link can support over 36 users/cell with 10
−
3
BER
. This number becomes 45 users/cell if the neighbouring cells are kept to half of this loading .The rightmost curve applies to a single cell without other cell interference (
I
occ
=
0).
n=2
n=1 n=4 n=3
n
i=1
i=2
d
2Rn 2Ri
i=3
i
Fig. 4. Reverse link capacity/cell.
3. The reverse link capacity of a CDMA WLL system
WLL is a fixed communication system, narrow beam antennas can be employed at both the base station and subscriber's side so that the propagation between base station and house is very close to free space propagation (20 dB/dec) [2], [9]. Applying the same model used in section 2, taking into account the major difference between the WLL and the mobile cellular environment which include
Electron Technology – Internet Journal
37/38
(2005/2006), 3 (http://www.ite.waw.pl/etij/ )
4
a usual
LOS
component and a stationary subscriber unit with a directional antenna, result in Rician type of fading. That leads to a substantial decrease in the link requirements and consequently an increase in system capacity. We will now present the derivation of an analytical formula for determining reverse link interference for a CDMA WLL system. Assuming
N
houses uniformly distributed in a circular cell of radius
R
so that the houses density as in Eq. (4). The transmitted power of the house with power control is directly proportional to
r
2
,
where
r
is the distance from the house to the BS.
3.1. Interference from a single cell
It is noticed that, not every house from another cell causes interference to the center cell. Only those whose transmitting antennas cover the center cell BS are interferers. Suppose the gain of a perfect house antenna with beam width
w
is given by, [2]
⎩⎨⎧ <<−=
otherwise,02/2/,1
)(
wwG
θ θ
. (18) The area with interfering houses is shown as a shadowed area in Fig. 5. If
w
<< 1 or
R
<<
D,
the interference area can be simplified as a perfect pie shape with angle span of .1
⎟ ⎠ ⎞⎜⎝ ⎛ +=
D RwW
(19)
Figure 5 shows the reference cell
C
o
,
and the interfering cell
C
i
.
Hence the interference received at the reference cell from a house in the interfering cell is .
21
⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛
o
r r S
α
(20)
Fig. 5. Interference from a single cell.
The total interference received at the reference cell from an interfering cell
C
i
is calculated by integrating the total interference power over the interference region in
C
i
, using (6) and (20).
∫ ∫
−
⋅++
RW W iii
rdr d r d r d
r S I
02/2/222
.cos2
θ θ αρ
(21) However, for narrow beam antennas,
W
<< 1 (in radian), the above integral can be approximated to,
∫ ∫
−
=⋅++=
RW W iii
rdr d r d r d
r S I
02/2/222
2
θ αρ
⎪⎪⎭⎪⎪⎬⎫⎪⎪⎩⎪⎪⎨⎧+−⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ ++−⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ =
iiiiiii
d Rd Rd Rd Rd Rd SW
11ln3221
22
αρ
(22) where
d
i
given in (13).
3.2. Total interference received from all cells
The number of cells at the tier
n
facing one side of the reference cell is
n.
Thus the total number of cells in ring-
n
is 6
n
. Hence, the total interference received from all cells at tier
n
is
∑
=
==
niin
ni I I
1
.,...,2,1,6 (23)
Thus
I
ocw
(total other cell interference in the case of CDMA WLL system) for
N
tiers will be
∑∑
= =
=
N nniiocw
I I
11
.6
.
(24) The capacity of this system can be calculated by using (16), when
E
(
I
ocw
/S
) and
Var
(
I
ocw
/S
) are given. Define the relative interference from all cells at tier
n
as
I
nr
=
I
n
/
I
self
. (25) Table 1 shows the results for relative interference from first 4 tiers.
Table 1. Relative interference
n
(tier umber)
I
nr
(relative interference) 1 0.10883 2 0.05890 3 0.03916 4 0.02922
The values of
E
(
I
ocw
/S
) and
Var
(
I
ocw
/S
) can be numerically obtained as,
E
(
I
ocw
/
S
)
≈
0.23611x
N
, and
Var
(
I
ocw
/
S
)
≈
0.03293x
N
. Figure 6 shows the reverse link capacity of CDMA WLL system for
E
b
/N
o
= 6 dB [6], the other parameters as in Fig. 4. According to this figure, the reverse link can support up to 49 users/cell with 10
−
3
BER
. This number becomes 60 users/cell when the neighboring cells kept to half of this loading. The rightmost curve applies to a single cell without other cell interference (
I
ocw
= 0).
Electron Technology – Internet Journal
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5
Fig. 6. Reverse link capacity/cell for CDMA WLL system.
Figure 7 represents a comparison between the obtained results and that from CDMA cellular mobile system. The figure shows that the CDMA WLL system can accommodate approximately 36% more users than CDMA cellular mobile system (when the surrounding cells are full).
Fig. 7. Reverse link capacity/cell for CDMA & CDMAWLL system.
4. Capacity gain of synchronous CDMA WLL system
In a conventional reverse link asynchronous direct-sequence CDMA system, each user is allocated a unique pseudonoise (PN) sequence; we will refer to the PN sequences as scrambling codes. In reverse link synchronized CDMA WLL, subscriber units within the same cell share the same scrambling code (the scrambling code is cell specific), while using different orthogonal channelization codes derived from the set of Walsh codes. The channelization codes are utilized to separate physical channels from subscriber units. Hence, the narrow-band signal from a subscriber unit is both multiplied by a channel- ization code (Walsh code) and a scrambling code (PN). The number of available channelization codes sets an upper limit of the maximum number of subscriber units per cell. However, this limitation can be lifted by introducing several scrambling code groups within a cell. This implies that a certain set of subscriber units are transmitted under one scrambling code while another set of subscriber units is transmitted under different scrambling codes [7]. The intro- duction of multiple scrambling codes within a cell eliminates the constraint on the maximum number of subscriber units due to channelization code shortage. However, this is obtained at the expense of an increased multiple-access interference (MAI), since signals transmitted under different scrambling codes are nonorthogonal. So the need to introduce an upper limit of the maximum number of scrambling code groups within a cell. The maximum cell capacity defined as the number of subscriber units that can be supported at a given noise rise (
NR
) at the BS. The
NR
at the BS is known to be a robust measure of the reverse link load of a CDMA system. The
NR
is defined as
noisetotal
P P NR
=
(26) where
P
total
is total average received power at the BS and
P
noise
is the power of the thermal noise at the BS. The reverse link load factor is defined as [8]
max
N N
=
η
(27) where
N
is the number of subscriber units within the cell and
N
max
is called the pole point and represent a theoretical maximum capacity that cannot be reached but serves as a useful reference point. The
NR
is related to the reverse link load factor as [7] .1
NR NR
−=
η
(28) Hence, the
NR
can be used to control how close the system is operated to the pole capacity. To derive an expression for the
NR
, assuming that there are
N
async
subscriber units in the cell of interest, which are transmitting asynchronously. In addition, there are
N
j sync
subscriber units in synchronous mode transmitting under scrambling code number
j
. Let us furthermore assume that the required
E
b
/N
o
is identical for all subscriber units. Under these assumptions, we can approximate the
E
b
/N
o
for the subscriber units operating in asynchronous mode as,
total async
P P G
=
ρ
(29) where
G
is the effective processing gain (ratio between the chip rate and the bit rate),
P
async
is the received power level at the BS from a subscriber unit in asynchronous mode, and
P
total
is the total received power. Similarly, we can express the
E
b
/N
o
for synchronous subscriber units under scrambling code number as

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