Impact of the line transmission rate on the upstream capacity of
the S-CDMA-HFC system with integrated traffic
Huifang Chen, Lei Xie and Peiliang Qiu
Dept. of Information Science and Electronic Engineering,
Yuquan Campus, Zhejiang Univ., 310027, China
chenhf@isee.zju.edu.cn
Abstract: In the S-CDMA-HFC system with integrated traffic, the source rates of the traffic types are
different. We always choose a line transmission rate to transmit the integrated traffic for the system
simplicity. In this paper, the architecture of an S-CDMA-HFC system is introduced. The impact of
the line transmission rate choice on the upstream capacity of the system with different traffic types is
analyzed, and the numerical results and conclusions are given.
Keywords: Line Transmission Rate, S-CDMA-HFC System, Integrated Traffic
Introduction
For the bad transmission condition of the
upstream channel of the HFC networks,
Synchronous Code Division Multiple Access
(S-CDMA) is a good method to cancel and
oppose the noise of the upstream channels [1].
S-CDMA based HFC is the new generation of the
HFC system. Supporting the integrated traffic is
one of the common goals of the broadband access
networks. The design of the S-CDMA-HFC
system is primarily concerned with the greatly
varying information bit rates and communication
quality requirements of various traffic types. It
is necessary to analyze the performance of the
S-CDMA-HFC system with integrated traffic.
There are three traffic types considered in this
paper: voice, data and video. Different types of
traffic may have different source rates, different
quality requirements and different Activity
Factors (ACF). CDMA is an auto-interference
system [2]. Normally, the different traffic types
received at a receiver have different power levels.
Since different traffic types will also mutually
interfere with each other, their power levels affect
the overall capacity. Suitable power levels,
which should be assigned to different traffic
types, need to be determined.
There are two methods to transmit different types
of traffic on the same CDMA channel [3]: one is
the use of the line transmission rate. A line
transmission rate is the actual bit transmission
rate through a channel. If the source rate of a
traffic type is lower than the line transmission
rate, it is increased to the fixed line transmission
rate with a correspondingly reduced activity
factor. If the source rate of a traffic type is
higher than the line transmission rate, it is
subdivided into several parallel streams
transmitting at the fixed line transmission rate.
Another is the use of the spread sequences with
different processing gain for different traffic
types. If the source rate of a traffic type is low,
the processing gain of the spread sequence is
large. If the source rate of a traffic type is high,
the processing gain of the spread sequence is
small. This method will increase the hardware
implementation difficulty of the receivers and the
transmitters. In the S-CDMA-HFC system with
integrated traffic, different traffic types may have
different source rates.
To simplify system
design, one or a limited number of line
transmission rates can be employed to transmit
the traffic in a wide range of source rates [3]. The
number and value of the line transmission rates
are determined by many factors, such as capacity,
complexity and the other problems that need to be
considered [4-5].
In this paper, we give a brief introduction of the
model of the S-CDMA-HFC system with
integrated traffic, then analyze the impact of the
choice of the line transmission rate on the
upstream capacity. This paper is organized as
follows. Section II outlines the model of the
S-CDMA-HFC system with integrated traffic.
In section III, the impact of the line transmission
rate choice on the upstream capacity is analyzed.
183
The numerical results and analysis are given in
section IV. Section V presents conclusions.
Model of the S-CDMA-HFC system with
intergrated traffic
Fig.1 shows the architecture of a bi-directional
HFC transmission system based on S-CDMA.
At the head-end, the Head Network Adapter
(HNA) is composed of the backbone network
terminal module, the downstream channel
transmitter module (64QAM modulation) and the
upstream
channel
receiver
module
(S-CDMA-QPSK
or
S-CDMA-16QAM
modulation).
The downstream channels are
Local M essage
Service
shared by many Optical Network Terminators
(ONTs) in the network, or are dedicated to a
specific ONT, depending on the bandwidth
demand of the users connected to an ONT. For
the upstream direction, one separate receiver is
available at the head-end for each group of
CDMA Terminators that are sharing the same
time and frequency resources. Such a group of
modem is also referred to as a MAC domain.
One receiver can handle a lot of CDMA
terminators. At the subscribers’ premises, a
CDMA terminator is available which is composed
of a downstream 64-QAM demodulator and an
upstream S-CDMA modulator.
Headend
Network
Adaptor
CDM A
Termination
User
Equipments
ONT
Fiber
O/E
Backbone Network
e.g. ATM -SDH
Cable
E/O
Network
Adaptor
CDM A
Termination
Gateway to
other networks
User
Equipments
Figure 1: Architecture of the bi-directional HFC transmission system based on S-CDMA
In a MAC domain, dispersed voice, data and
video transmit to the head-end through a common
upstream channel.
An user, who want to
establish a connection, must carry out an
initialization process, then send a connection
request message to the head-end. This message
always includes the requirements of service.
According to the current upstream resource usage
condition and the quality requirements of current
request, the head-end decides whether to accept
this request or not. If the connection is allowed
to set up, the power control and regulation
process is needed to carry out. After the
connection is set up, user can send the data
regularly.
Impact of the choice of the line transmission
rate on the upstream capacity of the
S-CDMA-HFC system with integrated traffic
provided users in the given time under given
quality of service (includes precision and
requirement of supported service).
In the
S-CDMA-HFC system, all upstream CDMA
terminators in a single MAC domain are allowed
to use the full time and frequency resources
simultaneously. Figure 2 shows that a CATV
network is power limited. The power resources
are distributed over the transmitters that are
allowed by the system. The more the CDMA
signals are present, the higher the resulting power
in the trunk cable will be. The power of a
CDMA channel depends on the required signal to
noise ratio of the cable distribution network and
required quality of service. The number of
allowed CDMA carriers on a single frequency
channel depends on the maximal signal to noise
ratio that can be achieved (without causing a
disturbance of the system resulting from a too
high transmit power).
The upstream capacity of the S-CDMA-HFC
system is the average number of the service
184
Maximum P ower Level
Channel 1
Channel 2
Channel 3
Channel Noise
Frequency Spect rum
W
Figure 2: Usable power budget in upstream channel of the S-CDMA-HFC system
The following conditions are assumed for further
analysis [2,6]:
(1) The ith type of traffic arrives randomly and
Poisson distributed. The arrival rate is λ i
calls/s.
The service time is exponential
distribution. The average call time interval is
1/μi s/call. According to the Erlang formula,
the number of active call of ith traffic type is a
Poisson random variable with mean
i   i 
(1.)
i
Different types of traffic in a MAC domain are
independent.
(2) The activity factor of the ith type of traffic is
 i .  i , a binary random variable, means that
the ith user is active or not in an arbitrary
instance. When user is active,  i =1; when
user is inactive,  i =0. Meanwhile,
(2.)
 i  Pr ( i  1)  1  Pr ( i  0)
(3) Users in a MAC domain are well
distributed. While the other MAC domains
cannot share the frequency channel, there is no
problem of the effect of other MAC domains.
Total spread-spectrum bandwidth of a MAC
domain with integrated traffic is WHz. The
background noise is N0xW. The bit energy under
the perfect power control is Ebi. Suppose that
the users’ arrival and active processes are stable,
the total power of the trunk cable is
Total channel power 
m
ni
 
i , j Ebi Ri
 N0 xW
(3.)
by the ath MAC domain is IaW, and the sum of all
CDMA channels’ power is smaller than ImW, the
maximum allowed power. Therefore, (3.) can be
written as
m
ni
 
Ebi Ri  N 0aW  I aW  N 0aW  I mW
(4.)
We confine the ratio of the maximum allowed
power and the background noise (ImW/N0xW)
within a necessary limit.
Im
1

N 0a 
(5.)
Therefore,
m
ni
 
i, j
(4.) can
be written as
Ebi Ri  ( I m  N 0a )W  I mW (1  )
(6.)
i 1 j 1
The low-rate users are the users whose source
rates are lower than or equal to the line
transmission rate. Since a line transmission rate
is the actual data transmission rate involved in
direct-sequence (DS) spreading and de-spreading.
Both processing gain (PG) and activity factor
(ACF) are determined by the value of the line
transmission rate. Given that total spreading
bandwidth is fixed, a lower line transmission rate
results in a larger PG and larger ACF, while a
higher line transmission rate results in a smaller
PG and smaller ACF. The impact of the line
transmission rate on PG and ACF is shown in (7.)
and (8.).
i 1 j 1
PGl 
Where, there are m types of traffic in a MAC
domain. The number of users of every type of
traffic is ni.  i , j means the activity factor of jth
user of ith type of traffic (i=1,2,…,m; j=1,2,…,ni).
Total receiving power is the sum of noise,
interference and signal power. If the usable
power budget of the frequency channel occupied
i, j
i 1 j 1
Rc Rc Ri
R


 PGi  i
Rl
Ri Rl
Rl
(7.)
Where
PGl processing gain when data are transmitted
at the line transmission rate;
Rc
spreading chip rate;
Rl
line transmission rate;
Ri
source rate of the ith type of low-rate traffic;
185
PGi processing
gain
when
the
data
transmissions rate is the source rate.
If the rate of a traffic type is lower than the line
transmission rate, when transmitting at the line
transmission rate, its activity factor is reduced as
 l ,i   i 
m1
(8.)
i 1 j 1
The high-rate users are the users whose source
rates are higher than the line transmission rate.
If the rate of a traffic type is higher than the line
transmission rate, when transmitting at the line
transmission rate, it will be split into L parallel
streams. The activity factor of L-1 streams
keeps unchanged, and the last stream’s ACF is the
same or smaller than the original ACF. The
stream number with unchanged ACF after split is
l
E bi
E
, ri   bi
E b1
E b1
m1

ri
i 1
(13.)
ni
m2
ni
j 1
i 1
j 1
  l ,i , j   ri'  ( k i' , j   'l ,i , j )

(1  ) W R
E b1
(14.)
l
Im
If
ui 
ni

ui 
l ,i , j
j 1
ni
 ( k
'
i, j
  'l ,i , j )
(15.)
j 1
m1
m2
i 1
i 1
x   ri ui   ri ' ui
(16.)
W
(9.)
Rl
Eb1
Im
(17.)
then, (14.) can be written as
Where, Ri’ is the source rate of the i type of
high-rate traffic;  x  means an integer operation.
ACF of the last stream is
th
Ri  kRl
Rl
We assume that the power control of the upstream
channel is perfect and the power received at the
head-end controller from the active reference user
is normalized to one.
m2
i 1
i 1
(18.)
Pout  Pr ( x  K )
(19.)
When integrated traffic type is transmitted in the
system, the outage probability relates to the
distribution of x. The distribution function of x
relates to ui and u’i and ni, ni is a Poisson
distributed variable (see suppose 1), its arrival
probability function is can be defined by its
moment-generating function.
If there are m1 low-rate traffic types and m2
high-rate traffic types (m=m1+m2), (6.) can be
resolved as
m2
m1
x   ri ui   ri ' ui  K (1  )  K 
The upstream channel’s outage probability of the
system with integrated traffic is
(10.)
where  i is the original activity factor of the ith
type of high-rate traffic. ACF of the other
streams is equal to the original ACF.
Pr (ni  n) 
i n
n!
e   , Pr (ni  n) 
i
 in 
n !
e  
i
(20.)
The probability value of ui and u’i is shown in
(2.), the distribution of ui and ui can be defined by
its moment-generating function.
ni
   i , j E bi Ri     i' , j E bi' Ri'  I m (1  )W (11.)
i 1 j 1
(12.)
then, (12.) can be written as
K
 R 
k i
 Rl 
ni
i 1 j 1
 I m (1  ) W R
ri 
Where
activity factor of a low-rate user with a
 l ,i
source rate of Ri when it is transmitted at a line
transmission rate of Rl;
 i original activity factor of the ith source type.
If the rate of a traffic type is equal to the line
transmission rate, then  l ,i =  i .
m1
ni
m2
   l ,i , j E bi    ( k i' , j   'l ,i , j ) E bi'
Eb1 normalizes both side of (12.). Suppose that
Ri
Rl
 l ,i   i 
ni
i 1 j 1
The system transmits data at the line transmission
rate Rl. Both side of (11.) are divided by Rl, then
186
ni
E (e sui )  E ni  E  l ,i , j (e
s l , i , j
m1
Where    ri  i  i
)
j 1
i 1
(21.a)
R
 exp[  i  i i (e s  1)]
Rl
E (e sui )  Eni
ni
E
j 1
k i , j   l , i , j
 exp[  i i ( k 
(e
m
Ri
R '  kRl
  ri '  i'  i' ( k  i
).
Rl i 1
Rl
2
The Chernoff bound of the outage probability is
s ( k i , j   l , i , j )

 
 K
Pout  exp K  ln( )  1 


K
  


)
(21..b)
Ri  kRl s
)(e  1)]
Rl
(23.)
Numerical results and analysis
Therefore, ui and ui’ are the Poisson distributed
variables with parameters (  i  i
(  i'  i' ( k 
Ri'  kRl
) ), respectively.
Rl
Ri
)
Rl
and
Suppose that
different traffic types are independent, x is also a
Poisson distributed variable with parameter
m1
r 
i
i 1
i
Ri
R'  kRl
  ri ' i'  i' ( k  i
).
Rl i 1
Rl
m2
i
The outage
probability can be described as
Pout  Pr ( x  K )  e 


k   K 
( ) k
k!
Based on the theory and method mentioned
above, we give the numerical results of the impact
of the line transmission rate choice on the
upstream
channel’s
capacity
in
the
S-CDMA-HFC system with integrated traffic.
The parameters of three traffic types are shown in
Table 1.
Fig. 3 shows that the impact of the line
transmission rate choice on the outage probability
of the upstream channel of the S-CDMA-HFC
system with different low-rate traffic types, where
η=0.25. Curves group 1, 2 and 3 in the figure
(22.)
Voice
Data 1
Date 2
Data 3
Video
Source Rate（Kbps）
9.6
8.0
16.0
32.0
76.8
Information Rate（Kbps）
8.0
7.2
14.4
28.8
64.0
13
12
Activity Factor
3/8
[7]
1
Modulation （QPSK）
QOS（dB）
127
7
9
QOS variance
11
2.5
Table 1: The parameters of different traffic types
st
nd
indicate voice, 1 data and 2 data respectively.
Fig. 3 shows that the outage probability of the
upstream channel to transmitting one of the
low-rate traffic types is different if the line
transmission rate is distinct. The higher the line
transmission rate, the larger the upstream
channel’s capacity. Moreover, the higher the line
transmission rate, the larger the frequency
resource expense.
Comparing three curves
groups, we can make out that the impact of the
line transmission rate choice on the multiple
low-rate traffic types with different source rates is
distinct. It relates to the source rates and activity
factors of the traffic types.
Fig. 4 shows that the impact of the line
transmission rate choice on the outage probability
of the upstream channel of the S-CDMA-HFC
system with different high-rate traffic types,
whereη=0.25. Curves group 1 and 2 indicate
3rd data and video respectively. Fig. 4 shows
that the outage probability of the upstream
channel to transmitting one of the high-rate traffic
types is different if the line transmission rate is
distinct. The higher the line transmission rate,
the larger the upstream channel’s capacity.
Moreover, the higher the line transmission rate,
the larger the frequency resource expense.
Comparing two curves groups, we can make out
187
that the impact of the line transmission rate choice
on the multiple high-rate traffic types with
different source rates is distinct. It relates to the
Po ut 0
(LOG)
-1
source rates of the traffic types. The higher the
source rate, the smaller the impact.
(1)
(3)
(2)
-2
Chernoff Bound
-3
Gaussian Approximation
Line T rans. Rate=16Kbps
-4
Line T rans. Rate=24Kbps
-5
Line T rans. Rate=32Kbps
-6
0
100
200
300
400
500
ρi
Fig. 3: Impact of the line transmission rate on the low-rate traffic types
Po ut 0
(LOG)
-1
(1)
-2
(2)
Chernoff Bound
-3
Gaussian Approximation
Line T rans. Rate=16Kbps
-4
Line T rans. Rate=24Kbps
-5
Line T rans. Rate=32Kbps
-6
0
5
10
15
20
25
30
ρ
i
Fig. 4: Impact of the line transmission rate on the high-rate traffic types
Po ut 0
(LOG)
-1
(1)
(2)
-2
(3)
Chernoff Bound
(4)
-3
Gaussian Approximation
Line T rans. Rate=16Kbps
-4
Line T rans. Rate=24Kbps
-5
Line T rans. Rate=32Kbps
-6
0
10
20
30
40
50
60
ρi
Fig. 5: Impact of the line transmission rate on the integrated traffic types
Fig. 5 shows that the impact of the line
transmission rate choice on the outage probability
of the upstream channel of the S-CDMA-HFC
system with multiple integrated traffic, where η
=0.25. Curves group 1, 2, 3 and 4 the traffic
type integrated voice and 2nd data, the traffic type
integrated voice and video, the traffic type
integrated 2nd data and video, the traffic type
integrated voice, 2nd data and video respectively.
Here, we assume that  i of the different traffic
188
types is same. It is shown in this figure that the
outage probability of the upstream channel to
transmitting one of the integrated traffic types is
different if the line transmission rate is distinct.
The higher the line transmission rate, the larger
the upstream channel’s capacity. Moreover, the
higher the line transmission rate, the larger the
frequency resource expense. Comparing four
curves groups, we can see that the impact of the
line transmission rate choice on the multiple
integrated traffic types is different. If a high –rate
traffic type is integrated, the corresponding
outage probability will be increased sharply, and
the impact of the line transmission rate on the
capacity will be weakened.
Conclusions
In the S-CDMA-HFC system with integrated
traffic, multiple traffic types have different source
rates. To simplify the system design, we choice
a line transmission rate for transmitting the
integrated traffic types. In this paper, the model
of the S-CDMA-HFC system with integrated
traffic is introduced. The impact of the line
transmission rate choice on the upstream
channel’s capacity is analyzed. By means of the
numerical results, we obtain the following
conclusions:
① . If the line transmission rate choice is
different, the outage probability of the upstream
channel to transmitting one of the types is
distinct. The higher the line transmission rate,
the larger the upstream channel’s capacity.
Moreover, the higher the line transmission rate,
the larger the frequency resource expense.
② . The impact of the line transmission rate
choice on the low-rate traffic types is different.
It relates to the source rates and activity factors
of the traffic types.
③ . The impact of the line transmission rate
choice on the high-rate traffic types is different.
It relates to the source rates of the traffic types.
④ . The impact of the line transmission rate
choice on the multiple integrated traffic types is
different. If the high –rate traffic type is
integrated, the corresponding outage probability
will be increased sharply, and the impact of the
line transmission rate on the capacity will be
weakened.
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