J.N. Dike, S.I Orakwue and  Edward O. F

Department of Electrical and Electronic Engineering, University of Port Harcourt, Nigeria




A major problem affecting the capacity of Wideband Code Division Multiple Access (WCDMA) is interference. This work focuses on reducing co-channel interference problem by the application of adaptive sectorisation in non-uniform traffic. It considers an  isolated areas of congested traffic called Hot Spots (HS). It is envisaged that the traffic density inside a HS is many more times that outside the HS. A more even traffic distribution among sectors is attempted by re-adjustment of sector boundaries using  finite antenna beam switching. System capacity is estimated on the basis of tolerable interference in a sector taking into account intrasector and intersector interference in a multicell environment. Perfect power control in the uplink is assumed. Path losses and shadowing losses is considered. It is  shown that a significant improvement in system capacity could be obtained with adaptive sectorisation.


Keywords: Interference, WCDMA, sectorisation, antenna beam




WCDMA is the radio interface for the present day third generation cellular mobile communication systems. The capacity of a WCDMA cellular system is determined by the amount of interference it can tolerate Giuliano, . Mazzenga and Vatalaro ( 2001). This interference is in  two forms. The interference arising from other traffic in the same cell and the interference arriving from traffic in near-by cells. If the traffic could be redistributed among cells so as to minimize the overall interference in a given cell more traffic can be accepted in that cell. In a sectorised cell, the redistribution of traffic could be achieved by adaptive sectorisation.


This paper looks at the capacity of a WCDMA system where the user distribution consists of high density pockets called Hot Spots (HS). A HS is formed by the gathering of many users in a small area. In this study, the user densities (within and outside the HS) are assumed to be uniform although the user density inside the HS is much higher than the user density outside the HS. The user density ratio in these two regions is taken as a parameter that reflects the traffic environment.


Use of adaptive sectorisation to minimize the total received and transmitted power by all users  has been studied in Saraydar and  Yener (1999). Adaptive sector control using Butler matrix fed circular array is given in Mahmoudi, et al. (1999) and the impact of sectorisation on WCDMA network is discussed in Wacker,  et al.(1999). These works have  assumed ideal antenna characteristics and thus the non-interference between sectors. Giuliano et al. (2001) have considered the use of adaptive sectorisation in WCDMA systems to enhance capacity in a HS environment. Their study is based on the rotation of sectors to share the hot spots among the adjacent sectors.


The approach used in this investigation to improve cell capacity is to employ adaptive sectorisation. The sector coverage in a cell can be controlled by the use of antenna structures that allow finite beam switching. Finite width beams are combined to cover an area of a cell that is divided into three sectors. Sectors could be adjusted in such a way that a given sector covers a HS either fully or partially. The finite antenna beam switching provides a simple and robust technique for sector boundary adjustment.


System model

For this paper, the system model considers only the first tier of co-channel interfering cells, which means that there are six co-channel interfering (adjacent) cells. Therefore, the geometry of the interference model can be represented as shown in Figure 1. The interference from second and third tiers to the home cell is extremely small Chung and  Wen(1998), and thus is ignored. In Figure 1 home cell A consists of sector A1 , A2 , and A3   of which A1   is the home sector where the HS is located. A2 and A3  are adjacent sectors, and B1, B2 , B3 , C1, C2 , and C3  are near-by sectors from which the home sector may receive interference.


It is assumed that the users in each sector, including those in home sector, are uniformly distributed. However, the traffic density in the HS region (Figure 1) is several times higher than that outside the HS. In this investigation the mobility characteristics of users are ignored. Cells are assumed to be hexagonal in shape and identical in size.


Propagation model


The signal propagation in the mobile channel (when fast fading is ignored) is generally modeled as a product of three components, one inversely proportional to a power of the distance representing the path loss, the second a random variable with lognormal distribution representing the shadowing losses, and the third representing the directional antenna gain Viterbi et. al(1994) and Gilhousen et al.(1991). The shadowing represents slow variations in signal strength even for mobile users. On the other hand, fast fading, which is largely due to multipath propagation, can be assumed to have no effect in the average signal power level Viterbi et. al(1994). Hence, for a user at a distance r from a Base Station (BS) at an angle θ as in Figure 1, the total propagation path loss is a function of r, ζ , and A(θ ), given by

PL(r,ζ ,θ ) = r n · 10ζ/10  · A(θ ),                                                                                (1)

where A(θ ) is the antenna gain in the direction of mobile station (MS), and n is the propagation path loss  exponent which typically has a value of 4. ζ  is a random variable with normal distribution, (10ζ/10  represents the log-normal shadowing process). Due to shadowing the local mean of signal power fluctuates around the area mean with log-normal distribution, and the standard deviation σ  of this distribution generally varies between 6 dB and 12 dB and has






Figure 1. Geometry of the system model for interference evaluation.

A  typical value of 8 dB. In order for a BS to be the most favorable to a MS the PL(r,ζ ,θ ) with respect to that BS must be smaller than the PL(r,ζ ,θ ) with respect to all other BSs Chatovich and Jabbari (1994).


Adaptive antenna array factor

In applications such as cellular mobile systems, where adaptive sectorisation is required, there is a need for the down link beam to scan in different directions in the azimuth and two of the most common scanning techniques used are the mechanical scanning and the electronic scanning. In case of mechanical scanning, the array can be rotated mechanically through 360 to give all-round coverage and can be adopted when the rotating structure is not too large. In other cases electronic scanning is preferred. The main beam of an antenna array consisting of several equally spaced elements points in a direction θs  to the array normal when the phase difference between adjacent elements is given by Connor (1989).


β = k · d · sin θs ,                                                                                                      (2)

where k  = 2π /λ (λ is the free space wave length) and d is the spacing between adjacent elements. Thus, by varying the phase difference β the beam can be steered through various directions. However, it is to be noted that for an element spacing of about

half wavelength,beam steering is restricted to about ±60 to avoid grating lobes.

Since the Array Factor of a linear array of N elements is given by

N 1

AF ) =       exp [j · n(k · d · sin θ + β)],                                                                   (3)





Figure 2. (a) Antenna element radiation pattern (RFS). (b) Array factor (superimposed for θs  = 45 , 15, –15 and (–45). (c) Resultant pattern (superimposed for θs  = (45, 15, –15 , and –45 ).






















































When element spacing is λ/2, substituting (2) into (3), we have,

N 1

AF(θ ) =       exp [j · n · π · (sin θ + sin θs )],                                                               (4)


where 0   θ 360  and θs   = [45 , 15 , 15,  45 ]. If A(θ ) represents the radiation pattern of a single element of the array, the resultant Antenna Pattern AP ) is found by pattern multiplication (i.e., as the product of A ) and AF ))


AP ) = A(θ ) · AF ) .                                                                                                 (5) By  varying  the  element  spacing  d  and/or  the  phase  difference  β  between  element excitations, the array factor and the resultant array pattern can be varied.

Figure 2(a) shows the radiation pattern of a single element of the antenna array . Figure 2(b) shows the antenna array patterns corresponding to main beam directions 45, 15 ,15 and 45. Figure 2(c) gives the resultant antenna pattern obtained by pattern multiplication. Each element of the antenna array is a λ/2 dipole and the array spacing and the phase of feed current are controlled to obtain the desired radiation pattern. It can be seen that the main beam can be steered to cover a desired part of a sector.


Adaptive sector control

We consider a BS antenna structure that consists of twelve fixed 30  beams per cell. The narrow  beams are combined to obtain 3 composite beams, which would substitute for the beams provided by the normal 120 directional antenna. Next, keeping the number of sectors fixed at 3 per cell, we may adaptively change the sector size by combining an appropriate number of narrow beams (Figure 1). Obviously, each sector acts like a cell with it is own pilot signal and the softer handover is responsible for switching the users from one sector to another.


The adaptive sectorisation allows sector beamwidths to be approximately 30, 60, 90, 120, 150, 180, or 210 degrees. Switched beams can adjust the sector size to include either fully or partially an area of high user density, that is, Hot Spot (HS). By using adaptive beam switching the traffic can be shifted from heavily loaded HS sectors to sectors that are underutilized.












System capacity evaluation

Sectorised cell capacity



In this analysis we assume that perfect power control is in place in the uplink. This mean that the signal strength S received by a sector BS due to the presence of a MS in the sector is the same for every MS in the sector, and is true for all sectors. Then the received Signal-to- Interference Ratio (SIR) at a sector BS can be expressed as,







=     Iintra + Iinter  +



η,                                                                                (6

where Iintra  is the interference occurring within the sector, Iinter  is the interference arriving from neighbouring sectors, and η is the background thermal noise. If Ni    is the number of users in the sector,

Iintra=(Ni1)S.                                                                                                                                                                                                                                                                                                                                                                                                                           (7)

To evaluate Iinter  consider a MS situated in the nearby sector B1  (Figure 1). The inter-cell interference by mobile station (MS) located outside the home cell is influence by the position (distance and angular orientation) of the MS. As shown above, in fig. 1 the distance r from its respective controlling base station, BS, and ro from the home cell base station, BSo depicts the geometry of this situation. The inter-cell interference on the reverse link (with perfect power control) can be expressed as




            =                                                           (8)

Where n is propagation loss exponent, r is the distance of the MS from its own base station, BS1, ro is the distance of the MS from the home cell base station, BS­ to and  are random variables representing the log-normal shadowing process in neighbor cell and home cell respectively.

The total interference power received at the home cell base station, BS0 due to users in the interfering cell can be found as

Iinter =2                                              (9)

The SIR of reverse link can be found by substituting equation 7 and 9 into 6










Table 4.2  Simulation Parameter


Data rate, Rb                                                                9.6kbps

Chip rate, W                                                                1.2288Mcps

Required Eb/No                                                                       7.4db

Standar deviation of shadow fadind, d                                    8dB

Cell radius, R                                                               1km

Reverse link SIRth                                                       -13.6dB

Number of sector N                                                     3


System access

When an MS chooses to access a certain sectors BS, the sectors BS will check whether the prevailing SIR is greater than the minimum (threshold) value required. If the SIR is less than the threshold the MS is blocked. This threshold value, SIRth, is a function of Eb /N0  and the system Processing Gain (PG) and is given by SIRth[dB] = Eb /N0 [dB] PG (dB). The Eb /N0  required in a WCDMA system is about 7.4 dB if the bit-error rate is not to exceed 10 Chung et al. 1998.

The SIRth based algorithm for call admission is a distributed mechanism Chung et al. 1998.  It can be used by each sectors BS to determine whether or not a sector admits a call. If SIR >  SIRth  the call request is accepted. Otherwise, the call request is rejected. Therefore, the call blocking probability is given by,


Pb  = Pr{SIR SIRth} .                                                                                          (13)


System simulation

The number of users the system can support is evaluated using a computer simulation according to (13). The simulation is based on the system parameters shown in Table 1.

The HS is in the home sector A1   (Figure 1) (which therefore is also called the Hot Spot Sector (HSS)) and the HSS can vary from 30  to 120  in steps of 30. In this investigation we consider a case where Hot Spot Area (HSA) is completely inside the HSS . In both cases it is assumed that the HSA is confined to a strip of dimension L × W where W is the arc width of the HS and L is its radial length. The cell radii in all scenarios are normalized to unity and the conventional hexagonal cell pattern is assumed. Perfect power control is also assumed so that the received power at the sectors BS from all mobiles within the sector is the same. A uniformly distributed mobile population is generated with random locations within the home and the six nearby sectors. This is done by generating two sets of random numbers that assign an angular position and a radial distance to each mobile. The radial position is the distance of the MS from the home BS. The individual path losses (coupled with the shadowing effect) are calculated for each MS in order to evaluate the SIR at the sector BS.


The system capacity is evaluated in terms of possible number of users in each sector when at most 1% new call blocking is experienced in any of the sectors. The cell capacity is the sum of three sector capacities.


The simulation starts with empty system (no users any where) and proceeds by adding users progressively, one user at a time, positioning each user at a randomly selected location in each sector and in HS region. Every time a user is added (any where in the system) the SIR at the BSs of all sectors are evaluated to see that with the added user the system blocking probability does not exceed the stipulated value. When the blocking probability exceeds the stipulated value the simulation terminates and the number of users in each sector and the sector causing the simulation termination are noted


Case of per fec t antenna

The case of a perfect antenna serves as a reference to examine the system under ideal conditions and to compare it with the practical case. The sector coverage in this case (with perfect antenna) is assumed to be uniform over the entire sector and there is no spillover of main lobe or occurrence of side lobes in the radiation pattern.

Where  W = 20

Figure 3 shows the results for the case of perfect antenna for a blocking probability of 1%,

in the overall system. As mentioned earlier, in Figure 1, A1   is the HSS, A2   and A3   are the adjacent sectors, and B1 , B2 , B3, C1, C2, C3   are the nearby sectors. In the absence of HSs there is uniform traffic in every cell (HS to non-HS user density ratio is 1) and the system offers a traffic capacity of 34 users/sector. This is taken as the reference. The results (Figure 3) indicate that when all sectors are of the same size (i.e., A1   = 120 ), the possible number of users in hot spot sector A1  increases with increasing user density in HS while the possible number of users in adjacent (A2   or A3 ) and nearby (B1 , C1,.. .) sectors decreases with increasing user density in HS. Simulation shows that in this situation blocking always occurs first in A1 . This is in contrast to the situation when A1   is 60 or 30. In these cases blocking first occurs in the adjacent sectors (A2   or A3 ) and then moves to A1   as the HS to non-HS user density ratio reaches 5 and 10, respectively. The system capacity (per cell) can be obtained at a give HS to non-HS  user density ratio by summing up the number of users in each sector. Figure 5 illustrates this situation and shows the cell capacity as a function of HS to non-HS user density ratio. It can be seen that there is an overall capacity improvement which starts at a user density ratio of about 5, and reaches a maximum value of about 37% of the nominal capacity at a user density ratio of about 15.


Figure 3.  Sector capacity versus hot-spot to non-hot spot user density ratio (Case 1, W  = 20 ) (case of perfect antenna).



It shows that the overall capacity improvement in this case starts to occur at a user density ratio of about 2 and it reaches about 60% of the nominal capacity at a user density ratio of about 12.




In this investigation we reviewed the basic concepts underlying cellular wireless communication systems in order to bring the issue of capacity in WCDMA cellular systems to the forefront. In particular, we considered the case of capacity improvement in cellular  WCDMA systems when non-uniform user distributions (hot spots) are involved in the coverage area.


The system capacity was estimated in terms of the number of users the cell (or sector) could accommodate while providing an acceptable quality of service. The quality of service is measured in terms of the system blocking probability which in turn reflects the acceptable signal-to-interference ratio. In order to calculate the interference arising in the system we considered a sectorised multi-cell model, with a hot spot located in the home sector, and the rest of the mobile population evenly distributed in the neighbor sectors. In calculating interference at sector BSs, both intra and inter sector interference were taken into account. The random locations of the mobile users in home and neighbor sectors and the normal radio signal propagation environment, including path-loss and slow fading (shadowing) were considered.


Studied was the possibility of using adaptive sectorisation as a means of reducing interference in sectors where it appears crucial in a bid to increase the overall capacity of the system. It was  found  achievable. It was also found that the adaptive sectorisation could be easily implemented using finite antenna beam switching, and for that purpose practical array antennas could be employed. The capacity improvement obtainable with adaptive sectorisation (in the presence of hot spots) is a function of user density in the