IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 10, OCTOBER 2006
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Effect of Cell Shape on Design of CDMA Systems for Urban Microcells Seungwook Min, Hassan M. El-Sallabi, Member, IEEE, and Henry L. Bertoni, Fellow, IEEE
Abstract— Placing antennas of low power base stations below surrounding buildings, as in urban microcells, makes propagation characteristics strongly dependent on the building environment. As a result, propagation in these urban microcells is nonisotropic, so that the assumption of circular cells used in planning of conventional cellular systems is no longer valid. Assuming circular cells leads to a more conservative system design, implying more base stations. This work investigates the effect of cell shape, due to non-isotropic propagation, on the out-of-cell interference and Erlang capacity of CDMA system. Propagation is described by measurement derived models for low antennas in a rectangular urban street grid. The analysis is done for soft handoff protocols. Index Terms— Cell planning, cell shape, propagation model, system capacity.
I. I NTRODUCTION
D
UE to high demand of mobile services, urban mobile communication systems provide high capacity by shrinking cell size. One approach to shrinking cell size is to lower both the base station antennas and transmission power. In this case radio propagation is confined and strongly dependent on building size and locations. The capacity of code division multiple access (CDMA) systems has been shown to be strongly influenced by in-cell and out-of-cell interference, which in turn is dependent on the propagation characteristics of the environment [1] - [7]. It is well known that the up-link interference from the mobiles in other cells is the limiting factor of system capacity [5] - [7]. A primary issue for cell planning of the CDMA systems is therefore the minimization of up-link interference [5], taking into account the propagation characteristics of the environment. Most research on CDMA network planning has made use of an isotropic propagation model, in which the propagation characteristics are the same for any radial direction from the base station [2], [4] - [9]. Away from the high rise core of North American cities, the buildings are of nearly uniform height and organized by the rectangular street grid
Manuscript received July 6, 2004; revised September 7, 2005 and December 12, 2005; accepted March 4, 2006. The associate editor coordinating the review of this paper and approving it for publication was H. Yanikomeroglu. This work was supported by the New York State Office of Science, Technology and Academic Research (NYSTAR) funded Center for Advanced Technology in Telecommunications (CATT) of Polytechnic University. S. Min is with the Electronics and Telecommunications Research Institute (ETRI), 161 Gajeong-dong, Yuseong-gu, Daejeon 305-350, Korea (e-mail:
[email protected]). H. M. El-Sallabi is with Helsinki University of Technology, Otakaari 5 A, Espoo, FIN-02015 HUT, Finland (e-mail:
[email protected]). Henry L. Bertoni is with Polytechnic University, 6 MetroTech Center, Brooklyn, NY 11201 USA (e-mail:
[email protected]). Digital Object Identifier 10.1109/TWC.2006.04427
into rows. In this environment, measurements for low base station antennas have shown that the propagation is strongly dependent on the direction relative to the street grid [1], [10] [16]. In particular, the path loss is different to mobiles located on streets that are line of sight (LOS), lateral, and non-lineof-sight (NLOS) with respect to a base station. Modeling of radio wave propagation for the low antenna case as being isotropic, as in previous studies [5] - [8], is done at the expense of a standard deviation that is larger by 2 dB or more [14], [16]. A larger value of standard deviation in turn implies a larger out-of-cell interference, which results in a more conservative design employing more base stations for the same traffic. In contrast, using accurate propagation models to avoid systematic modeling errors when evaluating the out-ofcell interference leads to efficient cell planning having less infrastructure. To quantify the relation between prediction accuracy and system design, we consider non-isotropic models for two dimensional cell coverage in residential areas. In such scenarios, the propagation, in terms of cell shape, is strongly affected by the position of buildings with respect to the position of the base station and mobile terminal [13], [14]. If the cell shape is assumed to be defined by the equi-received power contour, then for an isotropic propagation, the equireceived power contours are circles. In this case the circles are approximated by perfect hexagons, which are used as a basic cell shape for tessellation. However, for low base station antennas in areas having regular street grids, the equi-received power contour shape is a diamond or squeezed hexagon [16] - [19]. Alternatively, the cell shape can be defined through the registration of mobiles, in which case cell shape will be strongly influenced by the base station deployment. We investigate how different base station deployments affect the cell shape defined through mobile registration, and examine its effect on the system capacity under conditions of full loading. For a fully loaded system, the in-cell interference on the uplink is ku S, where ku is the average number of mobiles per cell and S is the power received from an in-cell mobile under conditions of ideal power control. The out-of-cell interference is f ku S, where f is the ratio of the power received at the base station from out-of-cell mobiles to that from in cell mobiles. In this study we find the ratio f of the mean outof-cell to in-cell interference in microcellular systems using a measurement-based, non-isotropic path loss model. Distinct formulas are employed for propagation paths that are LOS, lateral and NLOS. We investigate the effect of the cell shape on the system capacity, assuming the system to be loaded by mobiles uniformly distributed along the streets. Efficient cell
c 2006 IEEE 1536-1276/06$20.00
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 10, OCTOBER 2006
Fig. 1. Propagation types to the registered and reference base stations and conceptual cell shape defined by M and N . TABLE I PARAMETERS A AND 10n FOR VARIOUS P ROPAGATION T YPES
Where hb is the base station antenna height and hbd is average building height in meters, Δh = hb − hbd and sgn (Δh) =
−1 1
Δh < 0 Δh ≥ 0
shapes that have high capacity are identified through lower values of the out-of-cell interference ratio f for soft handoff. Finally, since system capacity is the parameter of real interest, we examine the influence of cell shape on the capacity. II. PATH L OSS M ODELS AND U RBAN M ICROCELL S HAPE Microcells in a residential neighborhood built on flat terrain and organized along a rectangular street grid, as commonly found in North American cities, is depicted in Fig. 1. The dimensions 2D and 2d of the street grid are shown by the horizontal and the vertical distance, respectively. The buildings are assumed to occupy an area on each block that has dimensions Bh and Bν , as shown in Fig. 1. Measurements made in San Francisco and Oakland California indicated that the path loss to mobiles may be separated into distinct types depending on the location of the mobiles [13]. These path loss models have been used in [14], [15] for design of TDMA system for microcellular environment. The distinct propagation types are: LOS-near and LOS-far when the mobile is on the same street as the base station and within or beyond the break distance Rb ; Lateral Route (LR) when the mobile is on the two streets closest to the mobile that
are perpendicular to the LOS street; and NLOS for all the remaining streets as discussed in [13] - [15]. As indicated in Fig. 1, the mobile can have one propagation type to the registered base station and a different type of path to the reference base station. Assuming that mobiles X1 and X2 are registered to the central base station in Fig. 1, the propagation types for X1 are LOS (near-in) to the registered base station and non-line of sight (NLOS) to the reference base station in the lower left of Fig. 1. The propagation types for X2 are on lateral route (LR) to the registered base station and NLOS to the reference base station. For convenience, we define 16 classes depending on the type of path to the reference base station at which the interference is being computed and the type of path to the registered (controlling) base station. The formulas for mean path loss for the distinct propagation types all take the form PL (r) = A + 10n log10 r
(1)
where A is the received power at a distance r = 1 m, r in meters is the direct distance between the transmitter and the receiver, and n is a slope index. The values of A and n reported in [13] - [15] differ for each path type. They depend on the frequency fM in MHz, heights of the base station antenna hb in meters, height of building hbd in meters, as shown in Table 1 for Oakland, which is an environment of mixed building heights, and mobile antenna height hm = 1.6 m [14]. The LOS region is divided into near-in LOS and far-out ranges, separated by the breakpoint distance Rb = 4hb hm /λ. Also, Δh = hb −hbd is the base station antenna height relative to the buildings and sgn(Δh) = ±1 for Δh > 0 or Δh < 0. For the numerical examples in the paper we assume fM = 1800 MHz, 2d = 100 m, 2D = 200 m, hb = 8 m, hbd = 10 m and hm = 1.6 m, giving a break point distance of Rb = 307.2 m. We also assume street widths of 20 m so that buildings occupy a rectangular area whose dimensions are Bh = 180 m and Bν = 80 m. In using the results summarized in Table 1, we assume that all base stations are regularly located at mid block (see Fig. 1). Since the registration of a mobile to a base station is based on the path loss, the distance between base stations is significant, but the choice of a particular cell shape is not important. Thus the cells can be considered diamond cell shapes as outlined by the dashed line shown in Fig. 1 or the squeezed hexagons as outlined by the solid line. In order to keep track of the spacing between base stations, we think of the cells as being diamond shaped with dimensions M ×N , where M and N are the number of the horizontal building blocks and the vertical building blocks between neighboring base stations, as in Fig. 1. To investigate the effect of base station separation on the out-of-cell interference and the cell capacity, the diamond cell shape is changed by varying the horizontal distance unit M and the vertical distance unit N . For M N = 6, there are four kinds of cell shapes: M × N = 1 × 6; 2 × 3; 3 × 2; and 6 × 1, which are investigated in this work. For any shape, the cell area is determined by the area of the diamond 8M N Dd, where D and d are defined in Fig. 1.
MIN et al.: EFFECT OF CELL SHAPE ON DESIGN OF CDMA SYSTEMS FOR URBAN MICROCELLS
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The reference cell area So for soft handoff Nc = 2.
III. C ALCULATIONS OF O UT- OF -C ELL I NTERFERENCE Shadow fading has a strong influence on the out of cell interference via different mechanisms. For example, shadow fading can influence the base station to which a mobile is registered for the purposes of power control. For any mobile location, let Mk be the mean path loss to the k th base station, as given by (1), and let ξk be the shadow fading, which is assumed to be a Gaussian random variable in dB with standard deviation σ (taken to be 8 dB in the simulations). Under the soft handoff protocol, a mobile can simultaneously be connected to Nc base stations that are participating in soft handoff according to the least path loss. In order to simplify the simulations, we identify those base stations that can participate in soft handoff on the basis of the mean path loss Mk only, without shadow fading. In this way the participating base stations are predetermined by the mobile locations before the simulations are run. However as part of the simulation power control of the mobile is exercised by the base station with the least path loss Mk + ξk including shadow fading ξk . Shadow fading also influences the out of cell interference through power control by the base station to which the mobile is registered. Power control compensates for shadow fading to the registered base station, which can raise or lower the interference to any other reference base station used for computing f , unless the shadow fading to the reference base station is fully correlated with the fading to the controlling base station. In this study we make the usual assumption that the shadow fading from a mobile to any two base stations is partially correlated with normalized covariance (correlation coefficient) C, as discussed in [7], and use the value C = 1/2 that is commonly employed [7]. Multipath fading, which is partially mitigated by the signal bandwidth through the use of a Rake receiver and partly by coding with interleaving [6]. The mobiles contribute out-of-cell interference to all other base stations, including the non-controlling base stations participating in soft handoff. As a result, the out-of-cell interference is independent of whether or not the signal levels satisfy other conditions that may be required for the mobile to be in soft handoff, as discussed in Section III B. below. In
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what follows, we consider systems that allow Nc = 2, 3 base stations to participate in soft handoff. The identification of the base stations participating in soft handoff can be seen from Fig. 2 for the case of Nc = 2. Similar results, not shown, are obtained for Nc = 3. In Fig. 2 the locations for which the mean path loss to the reference base station is minimum are indicated by the crosses +, while the locations for which this path loss is second smallest are indicated by ×. The collection of locations for which the mean path loss is least to a particular base station is referred to as its cell. When calculating the out-of-cell interference at the reference cell, we consider two kinds of interference. One is the interference coming from the mobiles that are located inside the area So designated by the cross hatch, but controlled by the base station of an adjacent cell. The other is the interference from mobiles located outside So and power controlled by other base stations. Those are designated by ISo and ISo , respectively. A. Two Base Stations in Soft Handoff (Nc = 2) Defining the average path loss Mk to a mobile from the k th base station as in (1) the path loss and interference signal can be represented by PL = Mk + ξk or in linear scale PL (rk ) = 10
(Ak +ξk ) /10 nk rk
(2)
The interference at another base station is then (ξk +Ao )/10 nm 10 rm I (ro , rm ) = S rono 10(ξm +Am )/10 rnm = 10(ξo +ξm )/10 10(Ao −Am )/10 m S (3) rono where S is the power received from a single mobile at the controlling base station under ideal power control conditions. Mobiles located inside the reference cell area So shown in Fig. 2, as defined by the mean path loss Mk , can cause out-of-cell interference when the path loss Mo +ξo to the reference cell is larger than minimum path loss Mk +ξk to the neighboring cell that can participate in soft handoff. In this case the interference to the reference cell is E [I (rk , ro ) ; Mo + ξo > Mk + ξk ] κdA (x, y) ISo = So
(4) When (2) is used and the integration is converted to a sum over the simulation area Δxi Δyi , then rnk ISo = 10(Ao −Ak )/10 kno S ro (xi ,yi )∈So 10(ξo −ξk )/10 ; E (5) κΔxi Δyj Mo + ξo > Mk + ξk Here κ is user density (=users in a cell/area of cell), and E [·] is the conditional expectation for the average value of shadow loss term under the condition that the mobile is power controlled by the adjacent cell, i.e. that Mo + ξo > Mk + ξk , or equivalently that ξk − ξo < Mo − Mk . Since ξk and ξo are partially correlated Gaussian random variables with zero mean and standard deviation σ, then the random variable ζ defined by ζ = (ξk − ξo ) /b
(6)
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 10, OCTOBER 2006
√ with b = 1 − C √will be Gaussian with zero mean and standard deviation 2σ. The conditional expectation, after some mathematical manipulation, is then E 10(ξo −ξk )/10 ; ξk − ξo < Mo − Mk (Mo −Mk )/b
=
e −∞
2
bβζ
2
e−ζ /4σ √ dζ 4πσ
√ Mk − Mo =e Q 2bβσ + √ (7) 2bσ where β = (ln 10) /10. In (7) u 2 1 e−v /2 dv (8) Q (u) = √ 2π −∞ is closely related to the complementary error function. From (5) and (7), the out-of-cell interference from the mobiles located inside So is then represented by nk b2 (βσ)2 (Ao −Ak )/10 rk S ISo = e 10 rono (xi ,yj )∈So √ Mk − Mo 2bβσ + √ (9) Q κΔxi Δyj 2bβσ Additional interference comes from mobiles outside of So that are in soft handoff between the base station k and the base station m, and are therefore not power controlled by the reference base station. We assume that the mean path loss to base station k is less than that to base station m. The out-ofcell interference ISo from mobiles located outside reference cell has a component Ik representing the case when the path loss including shadow fading to base station k is less than that to the base station m or Mk + ξk < Mm + ξm , so that the mobile is under the control of the base station k. The other interference Im represents the case when the path loss to the base station m is less than path loss to base station k, or Mm + ξm < Mk + ξk . The net interference to the reference base station from the mobiles in soft handoff to base stations k and m is then Ik + Im = b2 (βσ)2
E
E
(xi ,yj )∈(Sk ∪Sm )
I (rk , r0 ) ; Mk + ξk < Mm + ξm +
κΔxi Δyj
(xi ,yj )∈(Sk ∪Sm )
I (rm , r0 ) ; Mk + ξk < Mm + ξm
κΔxi Δyj
(10)
where the first terms represent the interference from the mobiles which are under the power control of the base station k and the second terms come from the mobiles under the control of base station m. The conditional expectation in (10) can be obtained by the procedure used to get (7). We find that nk (Ao −Ak )/10 rk b2 (βσ)2 S 10 Ik = e rono (xi ,yj )∈(Sk ∪Sm ) bβσ Mk − Mm (11) Q √ + √ κΔxi Δyj 2 2bσ
2
Im = eb
(βσ)2
(xi ,yj )∈(Sk ∪Sm )
n (Ao −Am )/10 r m m S 10 rono
bβσ Mm − Mk Q √ + √ κΔxi Δyj 2 2bσ
(12)
From (9), (11) and (12), the ratio f of total mean out-of-cell interference to in-cell interference for Nc = 2 is
ISo + k=0 (Ik + Im ) m=0 (13) f= Sku B. The Number of Base Stations in Soft Handoff Nc ≥ 3 Generalizing the foregoing analysis for Nc = 2, we find the out-of-cell interference for the soft handoff in the case of Nc ≥ 3. Mobiles located in So can by definition be controlled by the reference base station, or by one of the neighboring base stations. Mobiles located outside So can only be controlled by the neighboring base station, but not by the reference base station. Let the subscript o designate the reference base station and k designate the controlling base station. Then a mobile located inside So will be controlled by a neighboring base station when Mk + ξk < Mo + ξo and when Mk + ξk is the minimum among all of the neighboring base stations that can participate in soft handoff to a mobile in So , that is c −1 Mk + ξk < M inN j=1 (Mj + ξj ). j=k
The interference from mobiles inside So can be expressed as [8] c −1 nk N (Ao −Ak )/10 rk S 10 ISo = rono (xi ,yi )∈So k=1 ⎡ ⎤ Nc −1 nj 10(ξo −ξk )/10 ; M inj=1 rj 10(Aj −ξj )/10 ⎦ κΔxi Δyj E⎣ = rknk 10(Ak +ξk )/10 no (Ao +ξo )/10 < ro 10 (14) The expectation term in (14) may be evaluated as shown below ⎤ ⎡ Nc −1 nj rj 10(Aj +ξj )/10 10(ξo −ξk )/10 ; M inj=1 ⎦ E [·] = E ⎣ = rknk 10(Ak +ξk )/10 no (Ao +ξo )/10 < ro 10 (ξo −ξk )(ln 10)/10 ; ξo + Mo > ξk + Mk e =E c −1 = M inN j=1 (ξj + Mj ) ⎡ ∞ − ξ −bβσ2 2 /2σ2 ⎤ e (k ∞ ) √ dξ k ⎢ −∞ ⎥ 2πσ ξk +(Mk −Mo )/b ⎥ ⎢ 2 ⎢ ⎥ − ξ −bβσ2 ) /2σ2 2 2 ⎢ Nc −1 ⎥ e ( o√ = eb (βσ) ⎢ dξ ⎥ o j=1 2πσ ⎢ ⎥ j=k ⎢ ⎥ 2 /2σ2 ∞ −ξj ⎣ ⎦ e√ dξj 2πσ 2
= eb
∞
(βσ)2
−∞ N c −1 j=1 j=k
ξk +(Mk −Mj )/b
2 e−z /2 √ Q z+ 2π
Q z+
Mk −Mj
bσ
Mk −Mo
bσ
+ 2bβσ
+ 2bβσ dz
(15)
MIN et al.: EFFECT OF CELL SHAPE ON DESIGN OF CDMA SYSTEMS FOR URBAN MICROCELLS
From (14) and (15), the interference from the reference is ⎡ N
n c −1
r k 10(Ao −Ak )/10 rkono S ⎢ ⎢ (xi ,yi )∈So k=1 ⎢ ∞ −z2 /2 Mk −Mo ⎢ e√ 2 2 ⎢ Q z + + 2bβσ bσ ISo = eb (βσ) ⎢ −∞ 2π ⎢ Nc −1 ⎢ j=1 ⎢ j=k ⎣ Mk −Mj Q z + bσ + 2bβσ dzκΔxi Δyj
cell
C. Soft Handoff Area
⎤
A mobile can be connected to two or three base stations if the differences between the strongest pilot signal and the pilot signals from the other base stations are less than a predetermined threshold. In other words, soft handoff occurs where the differences in path loss to the registered base station and to the other base stations is less than the predetermined value, typically 10 dB, for a time interval that is longer than some threshold. We neglect the time threshold in the simulation described here, the probability of soft handoff depends only on the difference of mean path loss and the soft handoff margin Msoft , and the soft handoff area can be determined probabilistically. For Nc = 2, let M1 and M2 be the smallest and the second smallest mean path losses. Then the probability for soft handoff is equivalent to the probability that the difference between the minimum path loss and the second small path loss to the base stations is less than the soft handoff threshold Msoft ,
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
(16) Mobiles located outside of So can also cause the out-ofcell interference to the reference base station. Again let the subscript o designate distances and path loss to the reference base station, and k designate the controlling base station. The contribution to the out-of-cell interference from mobiles outside of So can be expressed as follows ISo = ⎡ E⎣
10
N c −1
10(Ao −Ak )/10
(xi ,yi )∈So k=1 ; rknk 10Ak −ξk /10 nj < rj 10(Aj +ξj )/10 ,
(ξo −ξk )/10
for all j = k, j > 0
rknk S rono
⎤ ⎦ κΔxi Δyj
(17)
In (17), the conditional expectation is the average value of shadow loss term when the path loss to base station k is the minimum among the path losses to Nc base stations. The conditional expectation can be evaluated as shown below: ⎡
⎤ 10(ξk −ξo )/10 ; rknk 10(Ak +ξk )/10 n ⎦ E [·] = E ⎣ < rj j 10(Aj +ξj )/10 , for all j = k, j > 0 (ξk −ξ0 )/10 ; ξk + Mk > ξj + Mj =E e ⎡ ∞ ⎤ e−(ξk −bβσ2 )2 /2σ2 Nc √ dξk j=1 ⎥ 2 2 ⎢ 2πσ j=k ⎦ = eb (βσ) ⎣ −∞ ∞ −ξ 2 /2σ2 e √j dξj ξk +(Mk −Mj )/b 2πσ ∞ −z2 /2 N c −1 Mk −Mj e b2 (βσ)2 √ + 2bβσ dz Q z+ =e bσ 2πσ j=1 −∞
j=k
(18) From (17) and (18), the interference from outside of the reference cells is ⎡ ⎤ ∞ Nc
⎢ ⎥ (xi ,yj )∈So k=1 −∞ ⎢ ⎥ nk ⎥ b2 (βσ)2 ⎢ −z 2 /2 N c ISo = e (Ao −Ak )/10 rk ⎢ e√ S ⎥ j=1 10 ⎢ ⎥ rono 2π ⎣ ⎦ k j= Mk −Mj Q z + bσ + bβσ dzκdA (19) From (14) and (19), the ratio of out-of-cell interference to in-cell interference for Nc ≥ 3 is f=
ISo + ISo Sku
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(20)
Pr ob (soft handoff ) = |M1 + ξ1 − (M2 + ξ2 )| P < Msof t ξ2 − ξ1 =P · > −Msof t − (M2 − M1 ) ξ2 − ξ1 P (21) < Msof t − (M2 − M1 ) Here, ξ1 and ξ2 are partially correlated so that ξ2 − ξ1 can be replaced by the correlation coefficient C and the random variable ζ defined by (6). Thus the probability of being in soft handoff is −Msof t − (M2 − M1 ) Pr ob (soft handoff ) = P ζ > b Msof t − (M2 − M1 ) ·P ζ < b −Msof t − (M2 − M1 ) √ = 1−Q · 2σb Msof t − (M2 − M1 ) √ (22) Q 2σb where Q(.) is defined in (8). Fig. 3 is a plot of (22), showing that the soft handoff probability depends on the soft handoff threshold Msoft and the difference of the mean path loss. If the soft handoff threshold is made larger, the handoff probability increases, while if the difference of the mean path loss increases, the soft handoff probability decreases. The probability of being in soft handoff increases near the cell boundaries. In order to illustrate the area where it is most likely to occur for different placements M , N of the base stations, we have marked in Fig. 4 the regions with + where the soft handoff probability is greater than 50% for Msoft = 10 dB. It is seen from Fig. 4 that the M = 1, N = 6 base station placement has the largest soft handoff area, while the M × N = 3 × 2 placement has the least for various cell shapes with M N = 6.
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Probability in Soft Handoff for Soft Handoff Margin 1
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Fig. 3. Probability of soft handoff versus the difference between mean path loss between the strongest and second strongest pilot signals.
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TABLE II O UT- OF -C ELL I NTERFERENCE R ATIO f FOR D IFFERENT C ELL S IZE AND
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IV. S IMULATION R ESULTS Monte Carlo simulations have been carried out by accounting for mobiles in up to the tenth tier of cells about the reference cell. It was found that mobiles in tiers outside the first two give little contribution to f . The simulations reported below account for the interference power from mobiles located in the first three tiers. However, to account for power control under soft handoff, base stations located in the fourth tier were also taken into account. Other parameters in the simulations are as discussed previously. A. The Effect of the Cell Shape on f Here we investigate if there exists an optimal cell shape for different cell areas 2dDM N and how the cell shape and area effects f . Using (3), (15-22), the mean interference ratio is numerically calculated for cells of size up to M ×N = 10×10 for soft handoff. The results of the calculations are listed in Table 2. The minima of f lie in a band that is approximately given by M ≤ N ≤ M + 2 and for larger values of M by M + 1 ≤ N ≤ M + 2. Since we have assumed that D = 2d in the simulations, the hexagons in Fig. 1 for minimum outof-cell interference are squeezed in the vertical direction by approximately the factor d/D = 1/2. We define the cell shape factor to identify the same cell shape for all cell sizes. In a regular hexagon, the length of an
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(d) M xN = 6x1 Fig. 4.
Soft handoff area for M N = 6 when Nc = 2.
edge is equal to the distance from the center to a vertex. Hence in drawing hexagons in Fig. 1, we have taken the vertical sides to be equal in length to the vertical distance from the center to the vertex above it. As a result, the vertical distance is 2/3 of the distance 2N d. With this assignment, the cell shape factor (CSF) is defined by √ MD 2 MD √ = 3 CSF = (23) (2/3) N d Nd 3 √ The factor 2/ 3 is included so that for a regular hexagon CSF = 1. The cell shape factor CSF is representative of the shape, independent of cell size. For example if D = 100m √ and d = 50m, the cell shape factor is 2 3 for all the M = N cell shapes {1 × 1, 2 × 2, 3 × 3 · · ·}. In order to investigate the relation between the cell shape and the out-of-cell interference ratio f , the out-of-cell interference in Table 2 has been plotted as discrete points in Fig. 5 versus CSF obtained for various
MIN et al.: EFFECT OF CELL SHAPE ON DESIGN OF CDMA SYSTEMS FOR URBAN MICROCELLS
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Fig. 5. The relation between the cell shape factor and the out-of-cell interference ratio f under soft handoff for Nc = 2.
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Fig. 6. Comparison of the best cell shape between the simulation result and the cell shape factor estimation.
TABLE III Erlang C APACITY FOR C ELL S IZE AND S HAPE U NDER S OFT H ANDOFF (Nc = 2)
make use of the expression for the Erlang capacity per cell λ/μ derived in [8] for a fully loaded system. This formula incorporates the interference ratio through the factor (1 + f ) in the expression λ/μ =
values of M , N . As can be seen in Fig. 5, the out-of-cell interference ratio f depends on the cell shape factor. There exists the optimum cell shape where the out-of-cell interference ratio f has a minimum value. Taking the optimum shape factor to be 3, for a given horizontal distance M the value of N giving the lowest f can be obtained. The comparison is shown in Fig. 6, where it is seen that N is M or M + 1 for both approaches, except for N = 1 where the LOS path dominates the cell shape. Consequently, the out-of-cell interference depends on the cell shape factor but is almost independent of the product N M , which is proportional to cell area, except for the LOS dominant cell deployment with N = 1. For N = 1, the out-of-cell interference is independent of both the cell shape factor and cell coverage. It is seen from Fig. 5 that the soft handoff protocols with Nc = 2 do not effect the choice of cell shape. Although the simulations have assumed that D = 2d, it is expected that for other block dimensions the interference ratio f will still be minimum when M √≈ N , so that the optimum cell shape factor will be CSF ≈ 3D/d. B. Offered Traffic and Cell Capacity Out-of-cell interference is of importance not for its own sake, but because of its effect on system capacity. In order to study the relationship between cell shape and capacity we
(W/R) (1 − η) F (B, ν) (Eb /Io )median (1 + f ) γ
(24)
where, W/R is the ratio of total bandwidth to bit rate of each user, η is the ratio of background noise to acceptable maximum noise plus interference, Eb /Io is the ratio of bit energy to interference noise and γ is voice activity factor. The function F (B, ν) is defined by 2 F (B, ν) = exp − (βν) /2 1 + (B/2) exp 3 (Bν)2 /2 2 (25) 1 − 1 + 4 exp −3 (Bν) /2 /B where, β = (ln10)/10, ν is the standard deviation of powercontrolled signal due to imperfect power control and 2 (Eb /Io )median Q−1 (Pblock ) B= (26) (W/R) (1 − η) Here Q−1 (·) is the inverse of the function defined in (8), which gives the blocking probability Pblock . For calculations presented here we assume that the bandwidth W = 1.25 MHz, bit rate R = 9600 bps, ratio of noise to noise plus interference η = 0.1, (Eb /Io )median = 100.7 corresponding to 7 dB, and the voice activity factor γ= 0.4 [8]. Also, the standard deviation of power control is ν = 100.25 corresponding to 2.5 dB, and Pblock = 0.01 [8]. Table 3 shows the cell capacity for different cell sizes and shapes. The cell capacity is inversely proportional to the outof-cell interference so that it also depends on the cell shape or the cell shape factor, but is not sensitive to the cell area. It is seen from Table 3 that the maximum capacity for soft handoff with Nc = 2 and large cell sizes is about 16 Erlang/cell.
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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 10, OCTOBER 2006
TABLE IV
TABLE V
T RAFFIC I NTENSITY, C ELL S IZES AND B EST C ELL S HAPES
C OMPARISON B ETWEEN N ON -I SOTROPIC AND I SOTROPIC * M ODELS
*case for ρ = 0.1 does not refer to microcell conditions
This value determines the cell size or M N product necessary to support a given traffic intensity ρ Erlang/km, as listed in Table 4. The best cell shape can then be found from Table 3 by locating the minimum out-of-cell interference for the given M N product. Similar simulations for Nc = 3 indicate a maximum capacity for all large cell sizes of 17 Erlang/cell Comparison of the system capacity obtained using the nonisotropic propagation model of Table 1 to that obtained using a simpler isotropic model must recognize that fitting a single range dependence of the form (1) to the measurement derived model in Table 1 results in error having zero mean and a standard deviation σM of 5 - 6 dB [14], [16]. The deviation between the isotropic and non-isotropic models is strongly influence by LOS conditions on the street of the base station, so that the distribution of the deviations is not symmetric and does not follow a Gaussian distribution. Nonetheless, the deviation of the actual local mean path loss, including shadow fading, from the isotropic model will have a standard deviation that is a couple of dB greater than that of the nonisotropic model. Table 5 gives a comparison of the interference ratio f and system capacities predicted using the isotropic model with a standard deviation of 10 dB for cells in the shape of regular hexagons and the non-isotropic model with a standard deviation of 8 dB and cells having the squeezed hexagon cell shape. For the capacity comparison, the regular hexagons were taken to have the same area as that of the M × N = 3 × 3 squeezed hexagons. It is seen from Table 5 that the use of a non-isotropic model leads to a lower value of the out-of-cell interference ratio f , and to a higher system capacity. Improvement decreases with the number of base stations participating in soft handoff. V. C ONCLUSIONS The effect of cell shape on the out-of-cell interference ratio and capacity analysis of CDMA system for microcellular environment has been investigated. The study is based on measurement-based non-isotropic path loss model. Analysis of out-of-cell interference for soft handoff has been carried out. The out-of-cell interference ratio f is found to depend on the cell shape, but to be nearly independent of the size of the cell coverage, except for LOS dominant cell deployment. Based on this analysis, an optimum cell shape factor of about 3 is found to identify the cell shapes having the lowest value of f . The out-of-cell interference is inversely related to cell capacity, so that selecting cell shapes with low values f leads to greater cell capacity. As compared to the non-isotropic propagation model, isotropic propagation models will have systematic prediction errors that raise the standard deviation of predictions, as compared to measurements. Thus using isotropic propagation models to design symmetric cells with
*for n = 4 and ρ = 10 dB, from [7]
unity shape factor will lead systems having higher values of f , lower cell capacity, and require more base stations for the same offered traffic. While soft handoff reduces this effect, simulations show that 23% more base stations are needed for Nc = 3. R EFERENCES [1] H.-S. Cho, M. Y. Chung, S. H. Kang, and D. K. Sung, “Performance analysis of cross- and cigar-shaped urban microcells considering user mobility characteristics,” IEEE Trans. Veh. Technol., vol. 49, no. 1, pp. 105-116, Jan. 2000. [2] C. S. Kang, H.-S. Cho, and D. K. Sung, “Capacity analysis of spectrally overlaid macro/microcellular CDMA systems supporting multiple types of traffic,” IEEE Trans. Veh. Technol., vol. 52, no. 2, pp. 333-345, Mar. 2003. [3] B. T. Ahmed, M. C. Ramon, and L. H. Ariet, “Capacity and interference statistics of highways W-CDMA cigar-shaped microcells (uplink analysis),” IEEE Commun. Lett., vol. 6, no. 5, pp. 172-174, May 2002. [4] D. H. Kim, D. D. Lee, H. J. Kim, and K. C. Whang, “Capacity analysis of macro/microcellular CDMA with power ratio control and tilted antenna,” IEEE Trans. Veh. Technol., vol. 49, no. 1, pp. 34-42, Jan. 2000. [5] K. S. Gilhousen, et al., “On the capacity of a cellular CDMA systems,” IEEE Trans. Veh. Technol., vol. 40, no. 2, pp. 303-312, May 1991. [6] A. J. Viterbi, CDMA Principles of Spread Spectrum Communication. Boston, MA: Addison Wesley, 1995. [7] A. J. Viterbi, et al., “Soft handoff extends CDMA coverage and increases reverse link capacity,” IEEE J. Select. Areas Commun., vol. 12, no. 8, pp. 1281-1288, Oct. 1994. [8] A. M. Viterbi and A. J. Viterbi, “Erlang capacity of a power controlled CDMA system,” IEEE J. Select. Areas Commun., vol. 11, no. 6, pp. 892-899, Aug. 1993. [9] M. Chopra, K. Rohani, and J. R. Reed, “Analysis of CDMA range extension due to soft handoff,” 45th IEEE VTC, July 1995, pp. 917921. [10] D. Har, H. L. Bertoni, and S. Kim, “Effect of propagation modeling on LOS microcellular system design,” IJWIN, vol. 4, no. 2, pp. 113-123, Apr. 1997. [11] H. H. Xia, H. L. Bertoni, L. R. Maciel, A. L. Stewart, and R. Rowe, “Radio propagation characteristics for LOS microcellular mobile and personal communications,” IEEE Trans. Antennas Propagat., vol. 41, no. 10, pp. 1439-1447, Oct. 1993. [12] H. L. Bertoni, W. Honcharenko, L. R. Maciel, and H. H. Xia, “UHF propagation prediction for wireless personal communications,” in Proc. IEEE, vol. 82, 1994, pp. 1333-1359, Sep. 1994. [13] D. Har, H. H. Xia, and H. L. Bertoni, “Path-loss prediction model for microcells,” IEEE Trans. Veh. Technol., vol. 48, no. 5, pp. 1453-1462, Sep. 1999. [14] D. Har, “Effect of Propagation Modeling on Microcellular System Design.” Ph.D. diss., Polytechnic University, NY, May 1997. [15] D. Har and H. L. Bertoni, “Effect of anisotropic propagation modeling on microcellular system design,” IEEE Trans. Veh. Technol., vol. 49, no. 3, pp. 1303-1313, May 2000. [16] S. Min, L. Piazzi, and H. L. Bertoni, “The importance of path loss models for CDMA base station deployment,” in Proc. Korea-U.S. Science & Technology Symposium, Apr. 1998, pp. 456-460. [17] M. V. Clark, et al., “Reuse efficiency in urban microcellular networks,” IEEE Trans. Veh. Technol., vol. 46, no. 2, pp. 303-312, May 1997. [18] F. Niu and H. L. Bertoni, “Path loss and cell coverage of urban microcells in high-rise building environments,” IEEE Globecom, Nov./Dec. 1993, pp. 266-270.
MIN et al.: EFFECT OF CELL SHAPE ON DESIGN OF CDMA SYSTEMS FOR URBAN MICROCELLS
[19] L. R. Maciel and H. L. Bertoni, “Cell shape for microcellular systems in residential and commercial environments,” IEEE Trans. Veh. Technol., vol. 43, no. 2, pp. 270-278, May 1994. Seungwook Min received the B.S. degree from Seoul National University, M.S. degree from Korea Advanced Institute of Science and Technology, Korea, in 1987 and 1990, respectively, and Ph. D degree in electrical engineering from Polytechnic University, NY, USA, in 1999. From 1999 to 2002, he was employed by Samsung Electronics, as a principal engineer where he had developed WCDMA modem chipset. He is now developing the next generation WLAN chipset in ETRI, Daejeon, Korea. His current research interests include modem design, propagation modeling and system capacity analysis. Hassan M. El-Sallabi (S’99-M’03) received his B.Sc. (with honors) and M.Sc. degrees in Electrical Engineering from the Garyounis University (GU), Libya and received his licentiate and D.Sc. (with distinction) degrees from Helsinki University of Technology (TKK), Finland. He worked as telecommunication engineer in a general electric company, Benghazi Libya, where he held several positions. He also worked as an assistant lecturer at the Faculty of Engineering at GU, Libya. He held positions as a senior research engineer and a project manager in Radio Laboratory at TKK, Finland from September 2003-Septmber 2005. Dr. El-Sallabi also served as a Task Leader in WINNER European Commission project from January 2004 till the end of September 2005. Since October 2005, he has been a postdoctoral researcher in Information Systems Laboratory, Stanford University. His research interests include physical and stochastic channel modelling for wireless communications, diffraction theory, wireless system designs, time reversal communications and multi-antenna techniques. He has published more than 45 journal and conference papers, contributed to the organization of various international conferences as a member of the Technical Program Committee and as a session chairman, and served as a reviewer for many international journals.
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Henry L. Bertoni (M’67-SM’79-F’87) received the B.S. degree in Electrical Engineering from Northwestern University, Evanston, IL. in 1960, as well as the M.S. degree in Electrical Engineering in 1962, and the Ph.D. degree in Electrophysics in 1967, both from the Polytechnic Institute of Brooklyn (now Polytechnic University). After graduation he joined the faculty of the Polytechnic, serving as Head of the ECE Department (1990-95, 2001-04), and as Vice Provost of Graduate Studies (1995-96). His research has dealt with theoretical aspects of wave phenomena in electromagnetics, ultrasonics, acoustics and optics. He has authored or co-authored over 85 journal papers and 9 book chapters on these topics as well as the book Radio Propagation for Modern Wireless Systems, Prentice Hall PTR, 2000. Four journal articles have received best paper awards. During 1982-83 he spent sabbatical leave doing research on the acoustic microscope at University College London as a Guest Research Fellow of the Royal Society. His more recent research in electromagnetics has deal with the theoretical prediction of UHF propagation characteristics in urban environments. He and his students were the first to explain the mechanisms underlying characteristics observed for propagation of the Cellular Mobile Radio signals. This work has been incorporated into design tools for PCS cellular systems, and has earned him the 2003 James R. Evans Avant Garde Award for Contributions to Standard Propagation Models for the Wireless Telecommunications Industry of the IEEE Vehicular Technology Society. Currently he is exploring how the multipath propagation characteristics can be used for locating mobile terminals. Dr. Bertoni is a Life Fellow of the IEEE. He was the first Chairman of the Technical Committee on Personal Communications of the IEEE Communications Society, and was IEEE representative to, and chairman of the Hoover Medal Board of Award. He has served on the ADCOM of the IEEE Ultrasonics, Ferroelectric and Frequency Control Society, and is a member of the International Scientific Radio Union and the Radio Club of America. From 1998-2001 he was a Distinguished Lecturer of the IEEE Antennas and Propagation Society.
