Analysis of uplink and downlink capacities for two-tier cellular system

J.-S.Wu J.-K. Chung M.-1-.Sze

Indexing terms: CDMMTDMA strategies, Cellular architectures

Abstract: Combining macrocell and microcell in a two-tier cellular system is highly attractive because it provides a balance between maximising the number of users per unit area and minimising the network control associated with handoff. The authors examine the system capacity of a two-tier cellular architecture employing three TDMAi CDMA strategies. Both the uplink and downlink are evaluated via mathematical analysis. Results indicate that system performance degrades for either a larger macrocell or microcell and capacities are inadequate for users near the macrocell’s boundary. It also shows a huge discrepancy between the results obtained for the centre cell against those for the boundary cell.

1 Introduction

The DS-CDMA cellular system provides an effective approach of providing more capacity than AMPS to satisfy the increasing demand for mobile communica- tion service [l-51. On the other hand, microcells can provide more capacity than macrocells per unit area. Combining macrocell and microcell with a two-tier overlaying and underlaying cellular system is a highly promising alternative, because this provides a balance between maximising the number of users per unit area (which favours microcells) and minimising the network control associated with handoff (which favours macro- cells). However, the cochannel interference from micro- cell to macrocell and vice versa in a two-tier system is different from that in a homogeneous structure (i.e. consisting of only macrocells or only microcells). More- over, system performance also depends on the access methods such as TDMA or CDMA. Thus, examining the system performance for various TDMAiCDMA sharing strategies in a two-tier system is a worthwhile task.

I et a1 [6] addressed the capacity issue for a two-tier cellular architecture with respect to four different accessing approaches (via CDMA and TDMA). How- ever, they only considered the performance for the 0 IEE, 1997

IEE Proceedings online no. 19971648 Paper first received 8th July 1996 and in revised form 26th February 1997 The authors are with the Department of Electrical Engineering, National Central University, 32054 Chung-Li, Taiwan, Republic of China

center microcell in a dedicated macrocell and only for the uplink performance. In this article we extend 1’s results in two directions. First, we analyse the system performance for any microcell and macrocell in terms of interference and capacity. Secondly, downlink capac- ity for users located at the boundary among microcells and macrocells is discussed. The results show that the capacities of microcell are inadequate, particularly for users near the macrocell boundary because of the large amounts of cross-tier interference.

2 Network model and assumptions

A narrowband TDMA system is generally accepted as a standard for the second-generation cellular system, such as GSM and ADC. As an alternative to the digital system based on TDMA method, a CDMA cellular system proposed by Qualcomm has also become a standard as IS-95 [7] recently. In a two-tiered system, a performance study involving various CDMA/TDMA sharing strategy in macrocells and microcells is a worthwhile task. In this article we examine the follow- ing three systems: System I: CDMA in macrocells and TDMA in micro- cells System 11: TDMA in macrocells and CDMA in micro- cells System 111: CDMA in both macrocells and microcells In each system the same spectrum is used for both CDMA and TDMA. Hence, user capacities are limited by cross-tier interferences. Section 3 explores study of cochannel interference and capacity issues only for System I while a similar analytic technique can be applied for studying System I1 and System 111. Additional assumptions and conditions are described as follows.

Fig. 1 illustrates a two-tier cellular configuration where a macrocell is the union of many equal micro- cells. The macrocell’s size is also the same. Given a cell (macrocell or microcell), we immediately refer to the cells contiguous to it as ring-1 cells, those contiguous to the ring-1 cells as ring-2 cells, etc. Thus, a (n, i)th microcell relative to a macrocell base station is referred to as the ith microcell belonging to the nth ring, where i = 1, 2, ..., n. The (0, 0) microcell denotes the centre microcell in a macrocell.

We assume that a TDMA radio channel bandwidth of 30kHz with three time slots can have an equivalent channel bandwidth of lOkHz (i.e. Bch = 10kHz). The required carrier to interference power ratio ( C/qTDMA

405 IEE Proc.-Commun., Vol. 144, No. 6, December 1997

in both the uplink and downlink is 12dB [8]. Frequency reusing factors in the macrocellular and microcellular tiers are four.

I

Fig. 1 Two-tier structure

For a CDMA system, the bit rate per user is 9.6kbitls. The spread-spectrum bandwidth is Wss = 1.25MHz and the chip rate is 1.288MHz. The required Eb/NO for uplink and downlink are about 7 and 5dB, respectively, for a bit error rate less than 0,001. Since the processing gain is 21dB, the threshold values of (C/qCDMA are -14dB for uplink and -16dB for down- link, respectively.

For the microcell, the propagation model similar to [9] is adopted, where the lower bound model is selected in the worse case. Thus, Pr = PtLp where

25 loglo(d/r$) 40 log,, (d / r$ )

d 5 r$ = 4h\hm

d > r; L, = Lb + 20 + Lb = 12010g[X2/(87rh~hm)]I

P, and P, are received power and transmitted powcr, respectively; A is the wavelength, hb and h, are antenna heights of basestation and mobiles, respectively, d is the distance between base antenna and mobile antenna. Typical values being used are A = 0.33m (frequency = 900MHz), h, = ISm, and microcell hbu = 9m. Thus, break points for microcell are Tou = 164m, and Lh = 69.87dB. For the sake of convenience, we express the equation as follows:

where tl = 2833, and tz = 1.353, respectively.

[IO]. Thus the path loss is given by For the macrocell, we use the propagation model in

L, = max[A + B log d , 38.1 + 20 log d] where A = 88 - 13.82 log h, + C, and B = 49 - 6.55 log hb. If the antenna height of macrocell is 60m and the clutter correction factor C is -12dB for residential area, we find macrocell propagation model as

where t = 1.39 x IO'. In the uplink, we assume ideal power control for CDMA and TDMA tiers. That is, CDMA basestation receives the same power from CDMA users (denoted as Pc). Similarly, TDMA base station receives the same power from TDMA users (denoted as PT).

P, = Pt / ( t . (2)

406

3 Capacity analysis for uplink

In the following we derive the uplink capacity for Sys- tem I where macrocells use CDMA and microcells use TDMA. First, we evaluate the interference to a TDMA micr ocell .

3. I TDMA microcells We consider an arbitrary (n, i)th TDMA microcell in a CDMA macrocell and calculate the interference to this microcell which mainly consists of the interference due to six adjacent CDMA macrocells Ictl, interference due to CDMA users in the same macrocell Ict2, and cochan- ne1 interference due to TDMA users It, from other microcells.

/ microcell

macrocell BSj

Fi 2 Calculation of interference j?om adj,cent macrocells to a micro- ce 8. ICtI

3. I . I Calculation of I& To calculate the interfer- ence due to CDMA users from six adjacent CDMA macrocells, we denote the macrocell base station BAYj, j = 1 - 6, in the following analysis. Under the assump- tion of perfect power control the received power at the macrocell base station is the same for each mobile sta- tion (denoted as P,). According to Fig. 2, mobile emis- sion power is

where k = d(r2 + h f ) and hl = hbM - h,. The parame- ters k and r denote the path length and mobile-to- macrocell base ground distance, respectively. Thus, the power received by the (n, i)th microcell base station is

Pt = Pc(t ' k3 .735) ( 3 )

(4)

where I = d(x2 + h j ) , x2 = DJ" + r2 - 2D,r cos 9, and h2 hbu - h,. The parameter I is [he distance between

mobile antenna in macrocell and base station antenna of (n, i)th microcell, x is mobile-to-microcell base U aound distance and DI is the ground distance between the (n, i)th microcell base and the macrocell base BS, which is derived in the Appendix. We assume that N , mobiles are uniformly distributed in a circular macro- cell of radius r,, thereby making the density of mobiles to be p = Ndmd. Thus, the total interference from six adjacent CDMA macrocells calculated by performing numerical integration is

where Bch is the equivalent bandwidth of each channel in the TDMA system and Wss is the spread-spectrum bandwidth in the CDMA system.

IEE Proc.-Commun., Vol. 144, No. 6. Decemher 1997

3.1.2 Calculation of lct2: The interference Ict2 is due to CDMA users belonging to the dedicated macrocell where the microcell is embedded in, say SSO. Calculat- ing I,,, depends on the location of a CDMA user (it may be located in the microcell or macrocell) and the mobile's power. The mobile emission power is the same as shown in eqn. 3 and the power received by the (n, i)th microcell is

where 1 = d(x2 + h j ) is shown in Fig. 3 and x2 = Do2 + r2 - 2D0 - r cos 8. The parameter 1 is the distance between mobile antenna in macrocell and base station antenna of (n, i)th microcell, x is mobile-to-microcell base ground distance and Do is the ground distance between the (n, i)th microcell base and the macrocell base BS, which is derived in the Appendix. Thus,

(7 ) B c h

Ict2 = [2 irM P, , p . r drdd x - 1 wss where P, is denoted in eqn. 6. There is no closed-form expression for eqn. 7. Therefore I,,, must be calculated by numerical integration.

(n& microcell

macrocell BS,

Fig.3 microcell Ictz

Calculation of interference .from dedicated macrocell users to

3.1.3 Calculation of It< Assume that a perfect power control and the received power at the TDMA microcell base station is PT. To obtain the interference caused by other TDMA microcells we follow a similar analysis as Lee [2] and obtain

and

N,"

9(%)2 where N, is the number of TDMA users in each micro- cell and D is the cochannel distance. Thus

To maintain the quality of communication the uplink carrier-to-interference ratio must be greater than a

IEE ProcCommun., Vol. 144, No. 6, December 1997

threshold (C/qTDAM (e.g. 12dB for a TDMA system), so

PT ( L t l +I&) + Itt (:) T D M A = 12dB (9)

For the sake of convenience we introduce the coeffi- cient I,,,, to represent the sum of interference ICtl + Ict2 in terms of P, . N , . (Bch/Wss). That is I,,, = (Icfl + I c f 2 ) / [ P c . Nc . (Bch/ Wss)]. Consequently, substituting I,, into eqn. 9 by eqn. 8 gives

3.2 CDMA macrocells We consider the interference to a CDMA macrocell which consists of interference owing to CDMA users in macrocells I,,, and the interference from microcells Itc.

3.2. I ; For the first part, according to [6], the interfer- ence caused by CDMA macrocell users is given by I,, = (1.5 N, - 1)Pc.

(n& microcell \ macrocell BS,

Fig. 4 Cakulation % of I,,

3.2.2 ; To calculate I,, we consider 20 rings of micro- cells and the nth ring consists of 6n microcells. In this case a mobile's emission power in a microcell also depends on the microcell's breakpoint which is shown in Fig. 4. Thus

(11) PT . tl . k2.5 if 0 I: k 5 r;

P t = { PT . t z * k4 if r$ < k 5 ru where k = d(r2 + h?) and h2 = hbu - h,. The power received by macrocell basestation is

pt pr = t-13.735

Hence, P, consists of two parts, i.e.

and

where 1 = d(x2 + h:) is shown in Fig. 3 and x2 = Do2 + r2 - 2D0 . r cos 8. The parameter 1 is the distance

407

between mobile antenna in (n, i)th microcell and base station antenna of macrocell, x is mobile-to-macrocell base ground distance and Do is the ground distance between the (n, i)th microcell base and the macrocell base BSo which is derived in the Appendix. Thus, the interference caused by the ( E , i)th TDMA microcell is

I(,,,) = 2 1 f P T 1 . p - r drdd+ 2 J JPTp . p . r circid 0 0 0 r g

(12) where p = Nt/nr? is the mobiles' density in a TDMA microcell. From this discussion, the interference caused by the closest 20 rings of microcells is

n,i

i = l , . . . ,n To maintain the quality of communication, the required average bit energy-to-noise density ratio must be greater than a threshold, (Eb/IV)cDMA. Thus

where R is the data rate for a CDMA user and we assume that frequency reusing factor in a TDMA system is four. For the sake of convenience we introduce the coefficient Itcl to represent the interference I,,, in terms of PT . ATt. That is Icf = Itc/(PT . Nt). We let I,, = I , , . (PT . N J . Combining eqns. 10 and 13 and eliminating PT yields the relation of uplink capacity in terms of macrocell users and microcell users as follows:

1.5R

<IC($) - R

C D M A wss

4 Capacity analysis for downlink

The downlink capacity for a microcell or a macrocell becomes worse if multiple microcells or macrocells are neighbouring. The downlink power received by mobiles near a cell boundary is generally the weakest. The mobiles located at the cell boundary suffer the interfer- ence from adjacent microcells and macrocells and the dedicated microcell or macrocell. The following analy- sis considers the downlink capacity for mobiles near the boundary for microcells and macrocells.

4. I TDMA microcells For a microcell's mobile at the cell boundary, the inter- ference is mainly from adjacent first ring 6 TDMA microcell base stations It,, and neighbouring 12 macro- cell base stations I,,. Thus, we obtain

PT Itt = 6- t z - D4

408

and

I,t = PC NC [3rG3,3.735 + 3(2rM)-3.735

B c h x - 1 + 6 ( 2 . 6 3 r ~ ) - ~ . ~ ~ ~ ] x ~

wss t

For a microcell, the downlink (C/l) must be greater than a threshold of (C/oTDMA to satisfy the quality of service. Thus

PT. r;4/t2 Ict + Itt = 12dB (15)

Substituting Ict and I,, into eqn. 15 yields

3.387NcPc ($) rG3 7357-,& (9),,,, PT 2 r 1

4.2 CDMA macrocells If a macrocell user is located at the cell boundary, interference is suffered mainly from the 12 closest mac- rocell base stations (including its dedicated macrocell BS) IC,, and the 12 closest microcell base stations IfC. Thus we obtain

+ 3 N ~ ( 2 r ~ ) - ~ . ~ ~ ~ + 6 N c ( 2 . 6 3 r ~ ) - ~ . ~ ~ ~ ] 1

= (3.387Nc - l)Pc-rG4 t and

1 t 2

Itc = 3.312NtPT--rL4

For a macrocell, the downlink (C/I) must be greater than a threshold of (C/qCDMA to satisfy the quality of service, i.e.

PC7"u3.735t-1 tP1(3.387Nc - ~ ) P , r h ~ . ~ ~ ~ + 3.312 x4NtP~t , l r ,~

' ('),DMA

= -16dB (17) By combining eqns. 16 and 17, the relation of downlink capacity can be obtained in terms of macrocell users and microcell users as follows:

IEE Pro,.-Commun., Vol. 144, No. 6, December 1997

5 Numerical results

We discuss the relation between microcell capacity and macrocell capacity with respect to the microcell’s loca- tion and size. In addition to uplink performance, downlink performance is also considered for macrocell or microcell users at the boundary. By assuming that the macrocell’s radius is 6000 m, the microcell’s radius is ru = 6000 mi(2n + 1) if n rings of microcells are fully deployed in a macrocell.

Table 1: Uplink cochannel interference for system I

(0,O) (1,l) (22) (3,3) (4,4) (5,5)

5 rings of microcells

Ictl, 3.020 3.271 4.191 6.475 1.226 2.938 I c ~ 1.183 4.080 5.303 2.468 7.425 1.754 /t6 = 6.276 x 10-5

4 rings of microcells

lctl, 3.020 3.404 4.964 9.699 2.672 Icu 1.183 8.453 1.132 5.312 1.607 I, = 6.663 x

3 rings of microcells

Icq, 3.020 3.689 7.032 2.322 Ice, 1.183 2.151 2.955 1.402 /td = 7.214 x

/,ti = /ctl, . Pc . Nc. (Bc,/Wss) I C 0 = Icn. . Pc Nc . (Bc,/Wss)

Table 1 reveals the interference to (n, i)th microcell for system I (microcells use TDMA and macrocells use CDMA) where Ictlt, and Ict2r denote the interference coefficients caused by ring-1 macrocells users and its dedicated macrocell users, respectively, and I,, denotes the interference coefficient to a dedicated macrocell caused by 20 rings of nearby TDMA microcells users. As indicated in this Table, Ict2‘ is greater than Zctll for any microcell, a microcell located far from the base sta- tion of its dedicated macrocell suffers more interference from its dedicated macrocell users and from adjacent macrocell users, and if a microcell’s radius is increased (i.e. the number of microcells in a ring is decreased) a dedicated CDMA macrocell base station suffers more interference from TDMA microcell users because their emission power becomes stronger.

3E

3c

2E 2? % - = 2(

._ a 1:

- 0 0

E

1c

C

C

I

0 2 4 6 8 10 12 14 16 18

capacities with j b e rings of microcells macrocell users

Fig. 5 - ( 5 , 5 ) * (4, 4) ++ (3, 3) ~- (2 , 2)

( I , 1) xx (0, 0)

IEE Proc.-Commun., Vol. 144, No. 6, December 1997

Fig. 5 shows the permissible capacity region for five rings of microcells in a dedicated macrocell in terms of macrocell users and microcell users that system I can accommodate. Owing to the effect of cochannel inter- ference, microcell capacity is decreased if the number of macrocell users increases and vice versa. Besides, micro- cell’s capacity degrades if it is close to a macrocell’s boundary.

Fig. 6 shows that the permissible capacity region of central microcell with respect to its size (i.e. three, four or five rings of microcells in a dedicated macrocell). The smaller the microcell implies the more users it can accommodate. Alternatively, macrocell capacity is increased with a decrease in the microcell’s radius if the number of microcell users is fixed. The reason is that the macrocell base station suffers less interference from microcells if the latter’s radius and emission power become smaller.

Fig. 7 displays similar characteristics for the (n, n)th microcell. Because the microcell is near the macrocell’s boundary, its capacity will degrade particularly if a microcell’s area becomes larger due to cross-tier inter- ference.

35

35

3c

25 L J 20 - - 0

g 15 E ._

i o

5

0

macrocell users Fig. 6 , Capacities in (0, 0) th microcell - 5-ring microcells W# 4-ring microcells ++ 3-ring microcells

2 4 6 8 10 12 14 16 ’

macrocell users Fig.7 - 5-ring microcells W 4-ring microcells ++ 3-ring microcells

Capacities in (n, n)th microcell (n = 3, 4, 5)

Fig. 8 shows the capacity region for systems I and I1 (macrocells use TDMA and microcells use CDMA method), and system I11 (macrocells and microcells use CDMA method). Although eqn. 14 shows the capacity relation for system I, the analysis can be easily

409

extended for systems I1 and 111. According to Fig. 8, systems I and I1 exhibit similar characteristics while system 111 performs the best. The system capacity degrades for microcells near the macrocell boundary shown in Fig. 9.

macrocell users Performance comparison of three systems for (0, 0) th microcell Fig. 8

- system I - - system I1

svstem 111

30 25 I

ob! 5 10 15 20 25 30 3!

I

macrocell users Performance comparison of three systems for (5, 5)th microcell Fig.9

- system I - ~ system I1

system I11

macrocell users Downlink capacities of three s ~ ~ t s t e m s Fig. 10

- system I - - system II W system I11

Fig. 10 shows the downlink capacity region for users located at the macrocell’s boundary for three systems. Again it shows that system I11 performs the best.

From this discussion, we infer that the uplink capacity for (0, 0)th microcell (i.e. centre microcell) is

410

better than that of (n, n)th microcell by roughly lo4 times owing to smaller interference from macrocells if the microcell size is the same. This finding also suggests that 1’s results [6] overestimated the capacity per cell too much if only considering the centre microcell’s performance.

6 Conclusion

We have examined the capacity of a two-tier overlay- inglunderlaying cellular system in this paper. We extended the previous result not only for off-centre microcells but also for downlink via mathematical analysis.

Analytic results indicated that the capacities are poor, particularly for users near the macrocell’s bound- ary because of large amounts of cross-tier interference. We compared the performance results for the three sys- tems. According to these results, the system in which both macrocells and microcells use CDMA accessing method exhibits the optimum performance in the uplink and in the downlink.

The results demonstrate that cochannel interference between microcells and macrocells is much stronger and is difficult to perform power control which is conventionally used in a homogeneous environment. We thus conjecture that a preferable option to assigning different R F channels to different tiers to avoid a power control problem and excessive interference.

7 References

1 GILHOUSEN, K.S., JACOBS, I.M., PADOVANI, R., VITERBI, A.J., WEAVER, L.A., and WHEATLEY, C.E.: ‘On the capacity of a cellular CDMA systems’, IEEE Trans. Veh. Technol., 1991, 40, pp. 303-312

2 LEE, W.C.Y.: ‘Overview of cellular CDMA’, IEEE Trans. Veh. Technol., 1991, 40, pp. 291-302

3 JUNG, P., BAIER, P.W., and STEIL, A.: ‘Advantages of CDMA and spread spectrum techniques over FDMA and TDMA in cellular mobile radio application’, IEEE Trans. Veh. Technol.,

4 KIM, K.: ‘CDMA cellular engineering issues’, IEEE Trans. Veh. Technol., 1993, 42, (3), pp, 345-349

5 BAIER, A., and FIEBIG, U.-C.: ‘Design study for a CDMA- based third-generation mobile radio system’, IEEE J. SeZ. Areas Commun., 1994, 12, pp. 733-743 I, C.L.: ‘A microcellimacrocell cellular architecture for low- and high-mobility wireless users’, IEEE J. Sel. Areas Commun., 1993,

7 ‘CDMA network engineering handbook’. Qualcomm, March 1991

8 RAITH, K., and UDDENFELTD, J.: ‘Capacity of digital cellu- lar TDMA systems’, IEEE Trans. Veh. TechnoZ., 1991, 40, (2), pp. 32S331

9 MILSTEIN, L.B.: ‘On the feasibility of a CDMA overlay for per- sonal communications networks’. IEEE J. Sel. Areas Commun..

1993,42, pp. 357-364

6

11, (6) , pp. 885-891

1992, 10, (4), pp. 655-668 10 PAHLAVAN, K., and LEVESQUE, A.H.: ‘Wireless information

networks‘ (Wiiley, 1995)

8 (n, i)th microcell base station and adjacent macrocell base station D,

Fig. 11 reveals a (n, i)th microcell in a dedicated mac- rocell with base station BS, and we wish to find the distance between the centre of (n, i)th microcell and an adjacent macrocell base station BSI. First, the distance between the (n, i)th microcell and BSo, d , , , , , is given

dTU,,,, = 2.7-,. d G a = 1 , 2 , . . . , n (19) where r, is the radius of a microcell, and the distance between two adjacent macrocell base station is 2 . R,.

Appendix: Calculation of distance between

i , !

by [41 i

,

IEE Proc -Commun , Vol 144, No 6, December 1997

Hence, if we can determine the angle a, D1, can be obtained. From Fig. 11, the angle 8 is obtained by

and the angle p is determined by the following expres- sion

n (21)

The relation between angle d, and angle p is @ = p ~ 30". Thus, we obtain a = d, - 8 = p - 30" - 8. Since the angle between the vectors BS,,BS' and BSo,BSj+l, j = 1, ..., 5, is 60°, the angle 8 between the vectors BSo,BSj and SS,, (n,i) can be determined as follows:

rj = a + ( j - 1) x 60' j = 1 , 2 ,

Finally, the distance between (n, i)th microcell base sta- tion and the base station of an adjacent macrocell can be obtained as

Dj = d(2~L)~ + d2 Tu,7z , z - 2(2&) . dru,n,i * COSTj

j = 1 , 2 , . . . , 6

i.... BSO ,,__. 1 2 '....'

(23) Fig.11 base

Calculation of distance between microcell base and macrocell

IEE Proc-Commun., Vol. 144, No. 6, December 1997 41 1