Cylindrical Antenna Arrays for WCDMA Downlink Capacity Enhancement Elias Yaacoub, Karim Y. Kabalan, Ali El-Hajj, and Ali Chehab ECE Department, American University of Beirut P.O. Box: 11-0236 Beirut, Lebanon Email:
[email protected] Abstract— Advanced antenna arrays at the base stations are one of the key techniques to improve the downlink capacity of WCDMA cellular systems. Traditionally, linear and circular arrays are used to form the beams. In this paper, cylindrical antenna arrays with various types of input excitations are proposed, and the beam steering adaptive antenna technique is considered. The user capacity per cell among the linear, circular, and cylindrical arrays is presented and compared in a simulation environment supporting various types of adaptive antennas, soft/softer handover, and multiple services. A notable superiority of the proposed cylindrical antenna arrays was demonstrated by the simulation results. Index Terms— Adaptive antennas, antenna arrays, beamforming, cylindrical arrays, downlink capacity, WCDMA.
I. I NTRODUCTION The number of subscribers in 3G WCDMA cellular networks is growing significantly. However, asymmetric services that require very high data rates to the mobile stations, e.g. internet and video streaming, lead to the fact that the user capacity is mainly downlink limited [1]. One of the key techniques to increase downlink user capacity is the use of advanced antenna technologies at the base stations [2], [3]. Furthermore, adaptive beamforming increases cell coverage through antenna gain and interference rejection [4]. Performance gains of adaptive antenna arrays at WCDMA base stations are investigated in the literature through many contributions (e.g. see [5], [6], [7], [8], [9], [10]). All these references either assume uniform linear arrays (ULA), uniform circular arrays (UCA), or a set of beams without mentioning any specific arrays. In some cases, the antenna patterns are quantized into a set of levels to reduce the complexity of the simulation, e.g. two levels are used in [5] and [6] whereas three levels are used in [10]. Quantizing the antenna patterns into several levels reduces the accuracy of the results. Even when real antenna patterns are used [11], the patterns are assumed to be unaltered (beam broadening, grating lobes) when the beam is steered from its main direction. In this paper and in order to overcome this problem, a modified UCA to ULA transformation is used to obtain a pattern with 360 degrees symmetry in the azimuth plane. Hence, real patterns will be used and they will stay unaltered after steering the main beam. For beamforming, two methods are normally considered: fixed beam (FB) and steered beam (SB). Beam steering allows pointing the beam towards a specific user whereas fixed beam makes use of a specified number of fixed beams to cover a cell sector. In this work, we propose the use of the beam steering method with cylindrical arrays along with uniform, Chebyshev,
and Bessel current distributions for the downlink capacity enhancement of WCDMA cellular systems. In our analysis, we use the exact values of the antenna array factors without quantization, along with a generic semi-analytical expression derived in [11] for downlink capacity estimation with adaptive antennas, in order to compare the user capacity and the cell coverage of cylindrical arrays vs. ULA and UCA. We also take into account soft handover and multiple services. Section II presents the semi-analytical expression used in [11] to estimate the downlink capacity with adaptive antennas. Section III describes the various antenna arrays used and their characteristics. Section IV contains a general description of the simulation model and presents the obtained results. Finally, conclusions are drawn in Section V. II. D OWNLINK C APACITY E STIMATION Simple formulas for downlink capacity estimation have been derived in [12] and [13] for the 3-sector network structure (3 fixed sectors per cell). In [10], the downlink capacity is studied when adaptive antennas are employed where the ratio f of intercell to intracell interference is assumed to be the same as in [12], i.e. the case of 3-sector structure. However, the value of f highly depends on the number of sectors per cell and the used antenna patterns (side lobes and antenna gains), e.g. see [14]. Therefore to avoid this assumption and to keep the system model general, [11] extends the capacity calculation method presented in [15] for omnidirectional network structures (1 sector per cell with base station installed at the cell center and equipped with an omnidirectional antenna). In the next sections, the following notation is used: • Pmax is the maximum base station (BS) power per sector. • N0 is the noise power spectral density. • W is the chip rate. • K and n are the pathloss constant and pathloss exponent, respectively. • C is the maximum number of served users per sector. • Ns is the number of users belonging to service s. • Ns,sho is the number of users belonging to service s that are in soft handover (SHO). • ϕs,i is the fraction of power transmitted by the central BS (BS1 ) to mobile station (MS) i belonging to service s. • S is the number of services. • rji is the distance from BS j to MS i. • γ is the portion of downlink power allocated to traffic channels (1 − γ is reserved for broadcast channels). • λ is the orthogonality factor (λ = 0 indicates full orthogonality).
1-4244-0355-3/06/$20.00 (c) 2006 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2006 proceedings.
• •
• • • •
µs is the activity factor of users belonging to service s. W/Rs qs ≡ where [Eb /I0 ]th,s is the target signal [Eb /I0 ]th,s to interference ratio and Rs is the rate of service s, respectively. α(m) is the soft/softer handover gain due to m handover connections. m is the handover active set size. J is the number of cell sectors in the network. Gji is antenna gain from BS j in the direction of MS i. ξji is the lognormal shadowing from BS j to MS i. ξji in dB is a zero-mean Gaussian random variable with variance σ 2 . It can be expressed as: ξji (dB) = aξBS,ji + bξMS,i
where a2 + b2 = 1, (1)
E(ξji ) = E(ξBS,ji ) = E(ξMS,i ) = 0, and Var(ξji ) = Var(ξBS,ji ) = Var(ξMS,i ) = σ 2 . The first term ξBS,ji is independent from one BS to another and corresponds to the path from the given BS to the MS. The second term ξMS,i is common to all BSs and corresponds to the surroundings of the MS. We assume a2 = b2 = 1/2. Assuming a heavily loaded system where all BSs transmit at their maximum power (e.g. see [15]), the average received power by MS i from BS j can be expressed as:
Given the values of the necessary parameters including the users’ positions and shadowing samples, fixing the power level Pmax , and numerically reversing (8), the maximum capacity S C= Ns per cell sector can be calculated. s=1
III. B EAMFORMING WITH C YLINDRICAL A NTENNA A RRAYS A. Cylindrical Arrays The array factor of one circular array in the x-y plane is given by [16]:
(2)
The sum of the transmitted powers per sector should satisfy µs ϕs,i ≤ 1.
(3)
s=1 i=1
For a MS in soft/softer handover, we assume that the SIRs on each link are equal (e.g. see [12], [15]). The fraction of total BS power transmitted to MS i belonging to service s with m handover branches is given by: n J ξji Gji r1i N0 W (r1i )n + λ−1+ ξ G rji µs KPmax ξ1i G1i j=1 1i 1i ϕs,i = , m qs γ(λ + ) α(m) µs (4) where the index 1 is used to denote the central BS (BS1 ). Defining (Ns −Ns,sho )
mNs,sho (r1i )n (r1i )n G1i ξ1i G1i ξ1i i=1 + i=1 , qs m qs γ λ+ γ λ+ µs α(m) µs
Ps =
s=1
AFcircular (θ, φ) =
KPmax Gji . Pji = (rji )n Ns S
Substituting (4) in (3) with the expressions of (5), (6), and (7) and performing some manipulations, the total BS output power can be calculated as: S N0 W Ps K s=1 (8) Pmax = . S 1− Is
(5)
N
In (9), a is the radius, In and αn are the excitation coefficients’ magnitude and phase, N is the number of elements, φn = 2π(n − 1)/N is the angle in the x-y plane between the x-axis and the nth element, and k is the wave number. The array factor of a linear array on the z axis is given by [16]: AFlinear (θ) =
M
(Ns −Ns,sho )
Is =
i=1
γ λ+
qs µs
In (6), Ai = (λ − 1) +
µs
+
γ λ+
(10)
In (10), d is the inter-element spacing, bm are the excitation coefficients, M is the number of elements, and β = −kdcosθ0 , with θ0 the direction of maximum radiation. Cylindrical arrays were introduced in [17]. They are obtained by stacking circular arrays one above the other such that the elements form linear arrays in the vertical direction. It was shown in [17] that the array factor of a cylindrical array is equivalent to the multiplication of the array factor of a linear array on the z-axis by that of a circular array in the x-y plane. AF(θ, φ) = AFlinear (θ, φ).AFcircular (θ, φ) =⇒ AF(θ, φ) =
M
bm ejk(m−1)(kd cos(θ)+β) (11) jαn jka[sin θ cos(φ−φn )]
In e
e
n=1
mNs,sho
Ai
bm ejk(m−1)(kd cos(θ)+β)
m=1
× µs
(9)
n=1
m=1 N
and
In ej{ka[sin θ cos(φ−φn )]+αn }
Ai
i=1
m qs α(m) µs
n J Gji ξji r1i . G1i ξ1i rji j=1
,
B. UCA to ULA Transformation (6)
(7)
In [18], a method that transforms a UCA to a virtual ULA was used to synthesize a Dolph-Chebyshev pattern with circular arrays, leading to pattern with a constant side lobe level, similarly to the case of linear arrays. The approach of [18] was applied in [19] to generate Bessel patterns with circular arrays. Furthermore, it was applied on the stacked circles forming
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cylindrical arrays to enhance the directivity in the direction of the desired elevation angle. This transformation needs a large number of elements on the circular array. It is defined as: av (θ, φ) = JFa(θ, φ)
(12)
Where a is the array response vector of the circular array, and av is the array response vector of the virtual linear array. Moreover, 1 ω −h ω −2h · · · ω −(N −1)h .. .. .. .. . . . ··· . 1 ω −1 ω −2 · · · ω −(N −1) 1 . 1 1 1 1 1 (13) F= √ N 1 ω 1 2 (N −1) ω ··· ω . .. .. .. .. . . ··· . 1
ωh
ω 2h
···
ω (N −1)h
with ω = ej2π/N , N the number of elements of the circular array, and √ J = diag{j m N Jm (ka sin(θ0 ))−1 }; m = −h, ..., 0, ..., h (14) In (14), Jm is the Bessel function of the first kind of order m and a is the radius of the circular array. [a(θ, φ)]i = ejka[sin θ cos(φ−
2π(i−1) )] N
; i {1, 2, ..., N }
(15)
Fig. 1. Modal transformation for uniform circular arrays.
cylindrical arrays is compared to that of a 99 element circular array of the same radius with 20 dB sll Chebyshev excitations using the steered beam scheme, and to a 99 element uniform linear array of length equal to the diameter of the circular arrays. This linear array is used with the 3 sectors scheme. Hence, we are comparing antennas of the same dimensions and the same number of elements. The array factors of these antennas are shown in Fig. 2. In the following, the cases of the steered beam scheme using the cylindrical arrays with uniform, Chebyshev, and Bessel excitations of the transformed circular arrays are denoted by SB UCylA, SB CCylA, and SB BCylA, respectively. The case of the steered beam scheme using the transformed 99 element circular array is denoted by SB UCA, and the case of sectorized cells using the linear array will simply be referred to as the 3 sectors case.
The number of elements of the virtual linear array is defined as: (16) Nv = 2h + 1
(17)
(18)
Equation (18) is represented by Fig. 1 [18]. Fig. 1 represents a pre-processing procedure that transforms the array element space to a mode space, called also spatial harmonics [18]. The result is a virtual array in which the spatial response has a form similar to that of a linear array.
90 1
60 0.5 30
150
0.6 180
0
0.4 330
210
0.2
240
This approximation is valid only for N >> kr. Instead of obtaining the pattern of a uniform linear array from a circular array, we can multiply the array response vector of the virtual linear array by a weight vector C to get a desired pattern. This approach was applied in [18] to get a DolphChebyshev pattern, and in [19] to get a Bessel pattern. av desired (θ, φ) = av uniform (θ, φ) = CJFa(θ, φ)
120
|AF|
and h is chosen such that: |Jh−N (ka sin(θ0 ))| N −1 and > kr. In the simulation model, the geometrical location of the MSs determines whether they are considered in soft/softer handover, not their effective received SIR. This approach is used in [10] and [12], but not in [3] for example. The antenna elements were considered to be isotropic. Of course, in practice, other types of elements will be used, and the problem of mutual coupling between the array elements will have to be treated, as discussed in Section III. The problem of beam broadening due to steering is solved by the UCA to ULA transformation; however, sensitivity of smart antennas to beam pointing errors was not investigated. In the case of a pointing error, the maximum gain of the beam will not be pointing in the direction of the desired MS, leading to a lower SIR for this MS and to higher interference for other MSs. V. C ONCLUSIONS Advanced antenna strategies in WCDMA/UMTS using cylindrical antenna arrays were presented. A UCA to ULA transformation was used to provide 360 degrees symmetry for circular arrays, and their gain was increased by stacking them vertically, leading to a cylindrical structure. Cylindrical arrays with various current distributions were compared to linear and circular arrays with similar dimensions and number of elements. Besides the expected result of the steered beam method being superior to the traditional 3 sectors method, substantial increase in capacity was obtained with the proposed cylindrical arrays, which outperformed the linear and circular arrays due to their high gain, narrow beam and low sidelobes. R EFERENCES [1] H. Holma and A. Toskala, ”WCDMA for UMTS”, Wiley, 2000.
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