Capacity of a wideband multirate CDMA system with multiservice in the presence of fading and power-control error

L. Wang, A.H. Aghvami and W.G. Chambers

Abstract: The interference-modelling capacity analysis method developed by Gilhousen et al. is modified to make it appropriate for investigating the capacity of a variable spreading gain (VSG) DS-CDMA system with multiservice in the presence of fading (both shadow fading and multipath fading) and power-control error. With this analytical model. the uplink capacity estimate of an integrated voice and long constraint delay data (LCD) services system is obtained. The capacity estimate is the maximum number of concnrrent voice users and LCD users that the system can support while their required QoS are met. Further studies are made of the effats of power allocation, power-control error and receiver diversity on system capacity.

1 Introduction

Current second generation mobile systems such its GSM and IS-95 are primarily designed to support voice service. Due to the large market demand, multimedia communica- tion including voice, data and video will be one of the most important new applications in third generation mobile systems (TGMS) such as UMTS (Universal Mobile Telecommunication System) [2]. CDMA for mobile and personal communication has attracted much attention in recent years because of its numerous advantages over other systems in wireless communication, i.e. high-spectrum efficiency, simple co-ordination in both time and frequency domains, higher security etc. In Europe, a third-generation standard for mobile communication, UMTS, has been proposed based on a wideband CDMA (W-CDMA) air interface. Currently, 3GPP (3rd Generation Partnership Project) is producing specifications for UTRA (UMTS terrestrial radio access) W-CDMA. It is believed that W- CDMA will play a dominant role in future mobile communications.

Much research has been done on the capacity of CDMA systems. In [I], a framework based on interference analysis was developed by Gilhousen ef d. to estimate cellular CDMA system capacity. Further investigations [3-51 were made on the effects of power-control error on cellular CDMA capacity. More recent work [6, 7] offers more accurate analysis for specific power control schemes. However, all the above work was mainly concerned with conventional voice-only CDMA systems. To support multiservice over CDMA systems, two main techniques, namely MC-CDMA (multicode CDMA) and VSG CDMA, have been proposed [S, 91. In [IO] and [I l l , multicode cellular systems supporting multiservice are studied. Recent results on a comparison study of these

Q IEE. 2003 IEE Proeeditigs online no. 20030143 doi:l0.1049/ip-com:20030144 P a p r fin1 wived 14th March ZWI and in revised form 2Rfh March 2002 Thhe il~tlmrs ace uitli the Centrc for Telecoinmunicaliuns Research. King's Collqe London. University of London. Strand. London WCZR ZLS. UK

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two techniques show that by completely eliminating self-interference a better performance can he achieved with MC-CDMA, but this requires a high level of complexity in the transceiver [12]. Besides, except for extremely high bit- rate (2Mbit/s) transmission in UMTS systems [2], VSG CDMA is adopted as the principal transmission scheme to support multiservice with multiple transmission rate requirements.

In this paper, a general analytical model is presented to estimate the uplink system capacity of a VSG CDMA cellular system that supports multiple services with different QoS requirements (bit error rate, outage probability, and transmission rate), in the presence of imperfect power control, and o f both shadow fading and multipath fading. A system capacity boundary is found as the maximum number of users of a particular class that can be supported in each sector, with the number of users per sector in each of the other classes specified, and with the QoS requirements of all the users satisfied. The system capacity is derived based on the interfercnce analysis method [I]. An integrated voice/LCD (long constraint delay) wideband CDMA cellular system is numerically evaluated with this model. In this evaluation, the two- dimensional system capacity estimate is obtained and the effects of introducing LCD on the voice capacity are examined, by considering three factors: received power level assignment due to service integration, receiver diversity designed to mitigate the multipath interference, and power- control error which is common to all CDMA wireless networks.

2 System description

We consider a CDMA system consisting of equal-size hexagonal cells. The base stations are located at the centres of all cells and employ directional antennas dividing a cell into three sectors perfectly. The total uplink bandwidth is confined to W Hz. The frequency reuse factor is 1. M classes of services are supported in this system. The users in each service class are uniformly distributed over the whole area and have the same transmission rate. Then with Ni (ie{l, ..., M } ) as the number of users of class i in each

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sector, the density of users in class i is pi = 2Ni/v'3. ( n e hexagonal cell radius has been normalised to unity.) ,411 the users' signals are spread over the whole bandwidth with a constant chip rate R,. Since, in the proposed system, each user uses just one spreading code to transmit its informa- tion, variable spreading gains are applied to different classes of service to meet their different transmission rate require- ments. The user activity is modelled as a binomial distribution. With this model, the activity random variable 4; of class i users is given as:

(1) 1 withprohabilityof a; 0 otherwise

The propagation model between transmitters and receivers assumes a path loss law with a path loss factor 4 [I]. In addition, shadow fading is modelled as a log-normal distribution 105/", where is a Gaussian random variable with standard deviation U , ~ , = X ~ B and zero mean [I]. Muhipath fading is assumed to follow a Raylei&h distribu- tion. A log-normal random variable IOxi1" is adopted to model the variation of the received signal power level [3] due to imperfections of the control loop. Here X is a normal random variable with zero mean and standard deviation ui,dB.

In ths paper, the outage probability, which is defined as prob(BEK > threshold). is introduced as a performance measure. Since the BER is directly related to Eb/N,, at the receiving point, the outage probability can be written as

P = prob(Eb/No<y)

where y is the desired E,JN, value to maintain BER helow the threshold.

In a system with Mclasses of services, each service has its own outage probability and BER requirement. The QoS constraints on the capacity become:

9 = P ~ O ~ ( ( $ ) ~ < Y ~ ) 5Pr.1 ...

(2)

where P, is the outage probability and P,,i is the outage probability threshold of the users in class i.

3 Performance analysis

3.7 formulation of the problem We assume that each cell site deploys a maximal ratio combiner (RAKE receiver). Then with L resolvable paths, the received signal power for a user in its home site [13], is

L

E. = Y? (3) /=I

where vi is the ith path signal strength. Then with the assumptions that multipath fading follows

a Kayleigh distribution and power-control error has a log- normal distribution, the probability density function for ?. is given as

.-pi- (In x - In S)- ')& 2 p u j

where S is the desired signal power and B= (In lO)/lO

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(4)

According to [13], the above joint Rayleigh-log-noimal distribution can he well approximated as an equivalent log- normal distribution as

where

Pi =In (G) are computed as in the Appendix.

Let 2. = S Z where x is a Gaussian random variable with mean value p and variance d.

If the total interference is modelled as additive white Gaussian noise, the outage probability for user c in the ith class with a transmission rate R , received signal power ii,< and processing gain G;= RJR; becomes

with dj = iGi/yi. Here we consider users' transmissions over the uplink as asynchronous, so that with a rectangular chip pulse the coefficient 3/2 is used [12]. Here lo,,;,c is the intracell interference, l,,,,t,i,c is the intercell interference suffered by user c, and tr is the background noise. Because of other users' activity, the outage probability of user c can be written as follows:

(7) where

B;(kj, Nj) = ( ; ) (a"' ' ( 1 - E,)'"~-~'

To calculate the outage probability from (7), the distribu- tions of three random variables

h # > i , C 4 Lu,, 4 c Ai., 4 c

->-and + need to be determined.

3.2 Modelling the sum of intracell interference and background noise The first two random variables needed in (7) can he expanded as

where (x j ;n - xi ,c) is a Gaussian random variable with zero mean and variance (o;.+&.

IEE Proc-Cooimun.. Vol. /SO, No I . Fchninr). 2003

Thus (8) becomes a sum of independent log- noiinal random variables. Such a sum has been well studied in [14, 151. Both studies suggest using another equivalent log-normal random variable to approximate the sum. So here we set up another log-normal random variable

where ZL,< is a Gaussian random variable. Since the power- control errors of all the users in the same class are i.i.d. random variables, corresponding to {xil: ..., p,;}, we use (8) to derive a set of i.i.d. random vanables {Z , , ,..., Z,,bri} with mean I I L ; and variance G:;. They are given as [I41

mn =In U , - 2 a n d . i U2 =ln($+ 1) (9) 2

and Uzj and D:, are given according to (7) as

and

3.3 Modelling intercell interference As for thc intercell interference, consider an out-cell user q of class j located at a distsnce d,,, from the reference cell site and d,, from its home cell sitc; the interference to the class i user c in the reference cell produced by this out-cell user, when it is active, becomes

where (z,,~ - x ; , ~ ) is a Gaussian random variable with zero mean and variance (U:,+ 6;) and (&-t,,) is also a Paussian random variable with zero mean and variance 2u;.

With the uniform user distribution. the total interference generated by users in the,fih class not in the reference cell in this sector area is

x @ ( t o - ~ ~ ~ d ~ l d " ~ x j , ~ l ~ i . ~ ) P , d where in is the cell-site index, for which we take di = mind: for further evaluation according to [I], and

n j n

otherwise

Following the procedure similar to that in [I] shows that the mean value i q ; and variance of ($/?.;) which represent

IEE Proc-Come,ri., VoL 150, No. i. Fi.Druory 2Ml3

the interference from out-the-cell users of class j are given as

mlt = .WJ)E(l/;.,)

where

and

g (2)- - - exp 1 2 ~ . ;;I

with G,! = Jfl2.; + $ and

Then finally. we get the outage probability of class f users as

P, = /w3,(mr)N(mb)d=7, U (15)

where

and N(mI) is a Gaussian density function with mean and variance given by

and inz; and uZi are computed as (9). Equation (15) can be numerically evaluated [ 161.

4 Numerical results

Our numerical study focuses on the uplink of a two-class DS-CDMA system consisting of 19 equal-size cells (up to two tiers). The iiumerical parameters are set as shown in Table 1. In particular, to comply with the UMTS specifica-

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Table 1: System parameters - Total bandwidth

Voice information rate

Voice transmission rate

Voice activity factor

Voice EdN, requirement

Voice spreading factor

LCD information rate

LCD transmission rate

LCD EdN, LCD spreading factor

0

5 MH2

8 kbitis

32 kbiVs

318 3.3dE

128

64 kbitk

256 kbitis

2.4dE

16

OdB

tions, the bandwidth is set as 5MHz [2]. Two primary classes of service (M= 2) are considered here: an 8 khit/s voice service (class I), and a 64 kbit/s long constraint delay service (LCD, class 2) . With the same channel coding and rate-match algorithm as in [17], the transmission rates for the two services become 32 kbit/s and 256 khit/s. Following the simulation results reported in [17], we chose 3.3dB as the required &IN, for voice with a BER threshold of IO-3 and 2.4dB for the LCD service with a BER threshold of

es are set as 1%. To assess the system capacity boundary through computing the outage probability with (15)> the receiving power levels have to be initially specified for every service class at first. Without loss of any generality, class 1 (voice) simal power (denoted as SI) is set as 1; moreover, we assume the same powerxontrol scheme is applied for both LCD and voice services. which means that the power-control errors for both services are the same. The system capacity boundary is evaluated as the maximum number of voice users per sector ( N I ) in each sector that can he supported, as a function of 'the number of LCD users per sector (N2) in the system.

Figs. lu and Ib show the number of voice users as a function of the ratio S2/S, with two LCD users. In both figures, the voice capacity increases at first with increasing S2/S,. but after reaching a peak, starts turning down. Thus there is an optimum value of &/SI at which the voice capacity is maximised with a given number of LCD users, as shown in Fig. 2. With &/SI below this optimum value, the number of voice users is reduced to stop the LCD users losing their QoS, while above this value the number of voice users is reduced because of excessive interference from LCD users.

Figs. 2a and U give system capacity boundaries with optimum power levels allocated to LCD users. Both of them show that there is a linear relationship between the capacity of LCD users and that of voice users. Fig. 2u gves the system capacity boundaries with different numbers L of resolvable paths. As L increases, a larger number of voice users and LCD users can be accommodated since the received signal fluctuates less. The improvement on the system capacity boundary becomes lcss significant as L increases. It is interesting to note that the voice capacity loss rate (the reduction in the number of voice users needed to accommodate one more LCD user in the system) is almost a constant value of 20 for any value of L. Decreasing the power-control error also reduces the fluctuations in the received signal and so the system capacity increases as shown in Fig. 26. However, the voice capacity loss rate increases from 20 with I dB (L=4 and L= 6) of power- control error (PE) to about 25 with 2 dB (L = 4 and L = 6)

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Both services' outage probab

1 2 3 4 5 6 7 8

40 1

1 2 3 4 5 6 7 8

s, is1 b

Fig. 1 ullorariori (I With viirious power-control errors (PE) and with L = 4 h With different numbers L of resolvable paths in a Rake system and with a powercontrol error of LOdB

Voice cupaciry us u function if rlie rurion oJ power

I+ L=3 I t L=4 -A- L=5

+%+ L.7 X L=6

1 2 3 4 5 number of LCD users

a

80

+ L=4 PE= Id0 + L=4 PE= 1.568 + L=4 PE=2dB - - L.6 P E = Id6

- .O - L=6 PE= 1.5dB - L=6 PE= 2dE

0 E

20

1 2 3 4 5 6 number of LCD users

b

Fig. 2 Capuciry boundaries n With a powercontrol error of 1.5dB h With L = 4 and L=6

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of power-control error, which indicates that, when integrat- ing LCD services into the system, an accurate power- control scheme not only improves the overall system capacity but also reduces the effect of introducing LCD senice on voice capacity. In Fig. 26. the capacity bound- aries with L=6 and P E = I S d B and with L = 4 and PE= 1 dB are very close, and so are those with L = 6 and PE=2dB and L=4, PE= 1.5dB. This observation leads to altemative physical-layer design choices where the network designer can opt for a receiver structure with some compromise between the power-control mechanism and receiver diversity, while supporting a specified system capacity.

5 Conclusion

In this paper_ we have presented an analytical model to estimate the system capacity boundaries for a cellular VSG CDMA system with multiservice by computing the system outage probability based on interference modelling. In this analytical model, slow fading due to shadowing, fast fading due to multipath transmission, and powercontrol error were taken into account. The capacity estimate of an integrated LCD/voice service wideband ( 5 MHz) system was obtained. This study has shown the effects of introducing LCD service on voice capacity while taking into consideration power allocation, receiver diversity and powercontrol errors. The results would be useful for future call admission control and media access control studies.

6 Acknowledgment

The project is supported by EPSRC under grant GR/ N64236/01.

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References

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8 Appendix

The mean value of (4) is expressed as

id) dy (In x - In SI*

x exp(- 28205

Integrating over y , we obtain cc

I ex.(- (Inx - Ins)- '). = /%&E 0 28'4

Then by substituting In x - In S

80, z =

we obtain

Similarly the mean square value is found to be

E ( $ ) = L ( L + I ) exp(2 In s + 2 j 2 4 ) The mean value and mean square value of the log-normal distribution in (5) are given as

and

~ ( x ' ) = e x p ( 2 ~ + 2.:) To match the first two moments we need

Lexp S + L =exp ( ( and

L(L + I ) exp(2 In s + 2f124) = exp(2 In s + 2 4 ) Solving these equations, we obtain

In [ I I]? the Kolmogorov-Smymov test carried out to verify this approximation shows that as the number of resolvable paths increases, the approximation becomes better. The approximation is very accurate with three or more resolvable paths (a situation typical for a wideband channel of 5 MHz bandwidth).

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