CDMA Soft Blocking

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Soft-Blocking Based Resource Dimensioning for CDMA Systems

Joe Huang

Flarion Technologies Inc., USA

[email protected]

135 Route 202/206 South, Bedminster, NJ, USA

Tel: 908-997-2022 Fax:908-947-7090

ChingYao Huang and Chie Ming Chou

Wireless Information and Technologies Lab

Electronics and Engineering Department

National Chiao Tung University, Taiwan

[email protected]

1001 Ta Hsueh Rd., HsinChu, Taiwan

Tel: 886-3-5712121 ext: 54175 Fax:886-3-5714361

Keywords: Outage Probability, Soft blocking, Dimensioning, Capacity, Noise rise, Erlang

Abstract

In this paper, a new resource-dimensioning concept based on both the allowable noise rise and traffic

statistics is presented. The soft blocking probability based on the outage probability and the assumption of

the Poisson arrival and exponential services time are first derived. To have a consistent view on the traffic

engineering (dimensioning), the relationship between outage probability, soft blocking probability and hard

blocking probability is discussed. Results indicate that in a CDMA system, resource dimensioning based

only on the outage probability and Erlang-B model is not sufficient to ensure the objective of achieving a

blocking probability target. Two soft-blocking based dimensioning methods, combining the consideration

of both the noise rise and traffic statistics, are proposed for resource dimensioning of 3G CDMA systems.

I. INTRODUCTION

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It is well known that, unlike a TDMA (time division multiple access) or FDMA (frequency division

multiple access) mobile cellular system, the number of channels (capacity) available to mobile users in a

CDMA system is not fixed. Therefore the concept of Erlang capacity in CDMA is proposed based on the

limit on the noise rise (i.e., total interference density to thermal noise ratio) [1-3]. In other words, the

capacity in a CDMA system is limit by the allowable noise rise rather than a fixed number as used in the

TDMA or FDMA systems. Also, different from the channelized systems (like TDMA or FDMA systems),

the concept of soft blocking is used. As defined in [1,4], the reverse-link blocking in a CDMA system

occurs when interference level, due primarily to other user activities, reaches a predetermined level above

the background noise level. This type of blocking is called soft blocking, as opposed to the hard

blocking performed in FDMA or TDMA systems. However, although the term soft blocking is used,

there is really no blocking performed during the derivation of the blocking probability in [1]. That is, all

incoming users are allowed into the system to facilitate the calculation of the noise rise. Later on, the

authors use outage probability in [5] instead to more properly name this phenomenon. In this paper, we

calculate the soft blocking probability of a CDMA system as a function of the outage probability with an

overload control in action. We assume that blocking is performed if the acceptance of an incoming user will

cause the noise rise of the system to exceed the desired threshold level. This quality-based soft blocking and

the traditional traffic statistics will be considered in the new resource dimensioning designs.

The paper is organized as follows: In Section II, outage probability and soft blocking probability are

considered based on the noise rise and a generic overload control to ensure connection quality. New

resource dimensioning concepts are discussed in Section III. Conclusions are included in Section IV.

II. OUTAGE PROBABILITY AND SOFT BLOCKING

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Given there are k users in an isolated sector, applying the Central Limit Theorem, the reverse link

conditional outage probability can be written as

=>=

)(

)()1()|)1((

ZVar

ZEQkZPOk

(1)

whereZis the total received power-to-interference ratio from all users and background noise

i

k

i

iW

RZ

=

=1

(2)

))(exp(}{)( 221 += mkE

W

RZE (3)

]}{)exp(}{)[)(2exp()()( 22222 EEmkWRZVar += (4)

To include the effect of other-cells interference, using a fixed other-sectors-to-serving-sector interference

ratio,f, the equation (3) and (4) can be rewritten as

))(exp(}{)1()( 221 ++= mkEf

W

RZE (5)

]}{)exp(}{)[)(2exp()1()()( 22222 EEmkfW

RZVar ++= (6)

where W is the CDMA bandwidth per carrier; R is the data rate; 0/IEb= is the received bit energy to

interference ratio, which is assumed to be lognormally distributed with mean mdB and standard deviation

dB; represents voice activity; 00 /IN= is the thermal noise to maximum total acceptable interference

density ratio (or the inverse of the maximum acceptable noise rise) and 10/)10(ln= (to match with field

experimental results [1])

If the traffic assumes Poisson arrival (with arrival rate ) and exponentially distributed service time (mean

service time 1/), the probability that there are kusers in the system if no blocking is performed is

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/

!

)/( = ek

pk

k (7)

Therefore, the outage probability, considering only the noise rise, of the system is simply

=

=0k

kkout OpP (8)

If we assume the incoming user will be blocked only if the addition of this user will cause the noise rise of

the system to exceed the desired level at the time of arrival, the blocking probability of the system given

that there are already kusers in the system is Ok+1, and the arrival rate into the system is reduced to (1 - Ok+1)

due the action of blocking. The Markov chain for such a generic overload-controlled CDMA system is

shown in Figure 1.

0

2

(1-O1)1

(1-O2)2

(1-Ok)kk-1

k

Figure 1, Markov chain for CDMA Soft Blocking

It is straightforward to show that the stationary distribution associated with this Markov chain is

= =

=

=

0 0

0

)1(!

)/(

)1(!

)/(

~

l

l

j

j

l

k

i

i

k

k

Ol

Ok

p

(9)

Moreover, the soft blocking probability of the considered CDMA system becomes

=+=

01

~

k

kkSB OpP (10)

Here the soft blocking is derived based on the control of the connection quality measured by the noise rise.

Using Equation (4) and Equation (5), it is easy to show that

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=

=0

~)1(k

kSB pkP

(11)

This is basically the manifestation of Littles theorem [7]. That is, the average number of users in the

system is equal to the effective average arrival rate times the average service time (i.e., average Erlang

usage).

Note that even in an overload-controlled soft blocking system, the outage probability is not zero. The

reason is that, even at the time of admission, the system can accommodate an incoming user without

overloading the system; the system can still run into outage after the user enters the system because of the

voice activity and power control error fluctuation. The corresponding outage probability incorporating the

effects of overload control can be expressed as

=

=0

~~

k

kkout OpP (12)

In Fig. 2, we plot the soft blocking probability (solid line), outage probability without soft blocking (dashed

line) and outage probability with soft blocking (dash-dot line) as a function of the offered voice traffic load

using the following parameter values for a cdma2000 system: W = 1.2288 MHz, R=9.6 kHz, m = 4 dB

(assuming pilot-assisted coherent detection), = 2.5dB, = 0.3 (corresponding to 5.23 dB noise rise),

E{}=0.5 (including reverse link pilot overhead), E{2}=0.39 and f = 0.55. It can be seen that the outage

probability of the system is reduced in the presence of soft blocking. Moreover, when the outage

probability is low, the soft blocking probability is approximately the same as the outage probability. The

two curves intersect between 1% and 2%. As the offered load increases, the soft blocking probability

becomes significantly less than the outage probability. One can also observe that the when soft blocking is

invoked, the remaining system outage probability is always less than the soft blocking probability (since

Ok+1 > Okfor all k).

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15 20 25 30 35 40 45 5010

-3

10-2

10-1

100

Total Erlang Loading

Outage/SoftBlockingProbability(%

)

outage probability w/o soft blocking

outage probability with soft block ing

soft blocking probability

Figure 2

It is interesting to note that, mathematically speaking, hard blocking (the total number of channels available

for service is fixed assumed to be N) can be said to be a special case of soft blocking if we define the

conditional outage probability of a hard blocking system as

(13))(1 kNUO hk =

HereU[N - k] represents a unit step function, i.e., U[N - k] = 1 if kN, and U[N - k] = 0 if k


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The overall blocking probability of a CDMA system with N channel elements and generic overload control

based on noise rise is

=+=

01

~

k

sh

kksh

B OpP (15)

It is apparent that the blocking probability PB calculated from is always higher than that calculated

from either O

sh

kO

k(PSB) or (Erlang-B model) for any given Erlang load. This provides a constraint on how

outage probability and Erlang-B table can be applied to CDMA planning to determine the required number

of CEs.

h

kO

III. RESOURCE DIMENSIONING

The significance of soft blocking in resource (i.e., channel element or CE) dimensioning will be discussed

in this section. Observed the conventional Erlang-B formula

=

=k

i

i

k

ik

kB

0 !!

),(

(16)

= , k is channel elements (combined (12) (13) we can get the same formula), we can find system

blocking depends only on the channel elements and traffic load( ). But CDMA systems are interference

limited systems and its system blocking should have relation with interference (soft blocking). So

conventional practice in resource dimensioning based on the outage probability and Erlang-B model is not

sufficient to ensure user connection quality and/or the objective of achieving a blocking probability target.

Take an example: if we design a CDMA system based on 6% outage probability (Pout (8)), the capacity of

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the system can be seen from Fig. 2 to be around 27 Erlang. When we take traffic statistics into consideration

(assuming CEs=34), for the same loading, the system blocking (PSB) is 4% from Fig. 3.

15 20 25 30 35 40 45 5010

-3

10-2

10-1

100

Total Erlang Loading

Blocking

Probability(%)

overall blocking probability (N=34)

hard blocking probability (N=34)

soft blocking probability

Figure 3

Now we want the system to have 4% blocking probability and 27.5 Erlang, we check Erlang-B table to

determine the required number of CEs (before considering the handoff overhead). The result be

uncorrected, because the minimum blocking probability of the CDMA system at this operating point (due

to generic overload control) is 5% (as can be seen from Fig. 4), no matter how many channel elements we

put in. Therefore, we either need to lower the capacity to achieve the blocking probability target or increase

the blocking probability target to accommodate the capacity. In Fig. 3, it is seen that the overall blocking

probability is just 5% and is higher than either the hard or soft blocking probability. So using overall

blocking probability with Erlang-B table can make resource dimensioning more accurately.

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A more accurate approach talked above is to determine the required the number of CEs directly based on

Equation (15) for the target overall blocking probability and the desired Erlang capacity. In Fig. 4, we plot

the required number of CEs as a function of the offered Erlang load for overall blocking probabilities of

4% , 5% and 6%, respectively (to be more accurate, the required number of CEs presented in the curve

should be rounded up when it is not an integer).

10 15 20 25 30 35 40 45 5020

25

30

35

40

45

50

Offered Erlang Load

RequiredNumberofCEs

2% overall blocking

4% overall blocking

6% overall blocking

2% hard blocking

4% hard blocking

6% hard blocking

Figure 4

For reference purposes, we also plot the hard blocking probabilities (i.e., Erlang-B model) as a function of

offered Erlang load. It can be seen that for a target blocking probability, and when the offered load is

relatively low, the required number of CEs increases with the offered load, and the overall blocking

probability curve pretty much coincides with the hard blocking probability curve. However, unlike the hard

blocking curve, when the offered load continues to increase, the required number of CEs in a CDMA

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system reaches a critical point beyond which the blocking probability target is unreachable, due to the kick-

in of the overload control. That is, the Erlang capacity (corresponding to a blocking probability target) of a

CDMA system is upper-bounded by the Erlang capacity determined by the soft blocking probability, no

matter how many channel elements are available.

CONCLUSIONS

In the conventional wisdom, the CDMA soft capacity is calculated based on the allowable noise rise.

Elrang-B is then used to have a proper dimensioning on the required resources (e.g., the required number of

channel elements). We have shown that such an approach is not sufficient to guarantee the expected

blocking probability. To achieve better resource dimensioning, the effects of soft blocking should be taken

into account. Two approaches have been proposed in this paper: 1) The Erlang capacity of a CDMA system

is first determined based on the soft blocking probability. The required number of CEs can then be

determined via Erlang-B table, and 2) we can more accurately determine the required the number of CEs for

the target overall blocking probability and the desired Erlang capacity directly based on the overall blocking

probability (including soft blocking and hard blocking). The soft-blocking based dimensioning methods,

combining the consideration of both the noise rise and traffic statistics, are proposed for resource

dimensioning of 3G CDMA systems.

REFERNCES

[1]. Viterbi, A. M. and Viterbi, A. J., Erlang Capacity of a Power Controlled CDMA System, IEEE

Journal on Selected Areas in Communications, August 1993, 11, (6), pp. 892-900

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[2]. Koo, I., Ahn, J., Lee, J, and Kim. K., Analysis of Erlang Capacity for the Multimedia DS-CDMA

Systems, IEICE TRANS. FUNDAMENTALS, VOL.E82-A, NO.5 MAY 1999

[3] Insoo KOO, Jeongrok Yang and Kiseon KIM, Analysis of Erlang Capacity for the Multimedia DS-

CDMA Systems with the Limited Number of Channel Elements, IEICE Trans. on Communication,

Vol.E84-B, No.12, December 2000

[4]. Padovani, R., Reverse Link Performance of IS-95 Based Cellular Systems, IEEE Personal

Communications, 3rdquarter, 1994, pp. 28-34

[5]. Viterbi, A.J., CDMA: Principles of Spread Spectrum Communications (Addison-Wesley, 1995)

[6]. Bertsekas, D. and Gallager R., Data Networks (Prentice Hall, 1992)

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