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Intercell Interference Reduction by the Use of Chebyshev Circular. Antenna Arrays with Beam Steering. Karim Kabalan, Ali El-Hajj, Ali Chehab, Elias Yaacoub.
24th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2007) March 13-15, 2007 Faculty of Engineering, Ain shams Univ., Egypt

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Intercell Interference Reduction by the Use of Chebyshev Circular Antenna Arrays with Beam Steering Karim Kabalan, Ali El-Hajj, Ali Chehab, Elias Yaacoub Electrical and Computer Engineering Department American University of Beirut, P.O.Box 11-0236 Riad El-Solh / Beirut 1107 2020 LEBANON [email protected]

Abstract: - Advanced antenna arrays at the base stations are one of the key techniques to reduce interference in WCDMA cellular systems. This paper presents the use of the beam steering method with circular arrays along with Chebyshev current distributions in order to reduce the value of the ratio of intercell interference to received intracell power in WCDMA cellular systems. The intercell to intracell interference ratio of the beam steering case with the proposed arrays is compared to that of the conventional omnidirectional case. The obtained results demonstrate a notable superiority of the proposed antenna arrays. Key-Words: - Circular antenna arrays, beamforming, intercell interference, WCDMA.

1 Introduction The number of subscribers in 3G WCDMA cellular networks is expected to grow significantly in the coming years. However, the number of served users is downlink limited in many scenarios due to increased interference [1]. Advanced antenna technologies are one of the key techniques used to reduce interference [2], [3]. Furthermore, adaptive beamforming increases cell coverage and user capacity through antenna gain and interference rejection [4]. In the literature, there are many contributions to investigate the performance gains by using adaptive antenna arrays at WCDMA base stations (e.g. see [5], [6], [7], [8], [9], [10]). In [11], the antenna patterns were assumed unaltered (beam broadening, grating lobes…) when the beam is steered from its main direction. In this paper, to overcome this problem, the transformation presented in Section 3 allows obtaining a pattern with 360 degrees symmetry in the azimuth plane. 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. This paper proposes the use of the beam steering method with circular arrays along with Chebyshev current distributions in order to reduce the value of the ratio of intercell interference to received intracell power in WCDMA cellular systems. Section 2 presents the definition of the ratio of intercell interference to received intracell power. Section 3 describes the circular antenna arrays used and their characteristics. Section 4 contains a general description of the simulation model and presents the obtained results. Finally, conclusions are drawn in Section 5.

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24th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2007) March 13-15, 2007 Faculty of Engineering, Ain shams Univ., Egypt

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2 Intercell to Intracell Interference Ratio The ratio F of intercell interference to received intracell power is defined in [12] as: J

Fk ,l =



Ptot , j g k , j

i =1, j ≠ l

Ptot ,l g k ,l

(1)

In (1), l is the mobile (MS) of interest, served by base station (BS) k, Ptot is the total base station transmit power, J is the number of cell sectors in the network, and gk,j is expressed as:

g k , j = K ( d kj ) ξ kj Gkj −n

(2)

In (2), the following notation is used: - J is the number of cell sectors in the network. - K is the path gain. - n is the pathloss exponent. - dkj is the distance from BS k to MS j. - Gkj is antenna gain from BS k in the direction of MS j. - ξkj is the lognormal shadowing from BS k to MS j. ξkj in dB is a zero-mean Gaussian random variable with variance σ2. It can be expressed as: ξ kj (dB ) = aξ BS ,kj + bξ MS , j (3) In (3), a2+b2=1. The means E(ξkj)=E(ξBS,kj)=E(ξMS,j)=0 and the variances Var(ξkj)=Var(ξBS,kj)=Var(ξMS,j)= σ2. The first term ξBS,kj is independent from one BS to another and corresponds to the path from the given BS to the MS. The second term ξMS,j is common to all BSs and corresponds to the surroundings of the MS. σ is the standard deviation for shadowing. A logical assumption is that a2=b2=1/2. In [10], the downlink capacity is studied when adaptive antennas are employed where the average 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 [13]. Therefore to avoid this assumption and to keep the system model general, [11] extends the capacity calculation method presented in [14] for omnidirectional network structures (1 sector per cell with base station installed at the cell center and equipped with an omnidirectional antenna). In the following sections, we will compare the values of F when beam steering is used with the proposed circular arrays to the case of omnidirectional antennas.

3 Beamforming with Circular Antenna Arrays 3.1

Circular Array to Linear Array Transformation

In [15], a method that transforms a circular array to a virtual linear array was used to synthesize a DolphChebyshev pattern with circular arrays, leading to a pattern with a constant side lobe level, similarly to the case of linear arrays. The approach of [15] was applied in [16] to generate Bessel patterns with circular arrays. This transformation needs a large number of elements on the circular array. In [16], this transformation was also applied on the stacked circles forming cylindrical arrays to enhance the directivity in the direction of the desired elevation angle. The transformation is defined as: av(θ, φ) = JFa(θ, φ)

(4)

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24th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2007) March 13-15, 2007 Faculty of Engineering, Ain shams Univ., Egypt 1 ω − h ω −2 h ... ω − ( N −1) h    : : ... :  : 1 ω −1 ω −2 ... ω − ( N −1)  (5) With Where:  1  F= 1 ... 1  1 1 N  ω 2 ... ω ( N −1)  1 ω1   : : ... :  : 1 ω h ω 2 h ... ω ( N −1) h    and N the number of elements of the circular array.

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ω = e j 2π / N

J = diag{( j m N J m ( kr sin θ 0 )) −1}

(6)

With k the wave number, θ0 the direction of maximum radiation, and m = − h,..., 0,..., h . In (6), Jm is the Bessel function of the first kind of order m and “r” is the radius of the circular array.

[a(θ , ϕ )]i = e

jkr sin θ cos(φ −

2π ( i −1) ) N

(7)

In (7):

i ∈{1, 2,..., N } a: array response vector of the circular array av: array response vector of the virtual linear array The number of elements of the virtual linear array is defined as: Nv = 2h + 1 and h is chosen such that:

  | J (kr sin θ 0 ) | N −1 max h || h ≤ and h− 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 [15] to get a Dolph-Chebyshev pattern, and in [16] to get a Bessel pattern. av_desired(θ,φ) = Cav_uniform (θ, φ) = CJFa(θ, φ) (10) Equation (10) is represented by Fig. 1 [15]. Fig. 1 represents a pre-processing procedure that transforms the array element space to a mode space, called also spatial harmonics [15]. The result is a virtual array in which the spatial response has a form similar to that of a linear array.

a1 a2 aN

av-h

c-h

JF

av+h c+h

Fig. 1: Modal transformation for uniform circular arrays.

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24th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2007) March 13-15, 2007 Faculty of Engineering, Ain shams Univ., Egypt

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3.2 Arrays Used in the Simulations In the simulations of Section 4, for the beam steering case, Base Stations are assumed to be equipped by identical circular arrays with kr = 10 and N = 33 elements. To obtain the Chebyshev pattern using the transformation of Section 3.1, we consider ε = 0.001 and θ0 = 90 degrees, then we find the highest value of h that satisfies (9). The circular to linear array transformation is applied to the circular arrays to get virtual linear arrays with 20 dB side lobe level (sll) and Chebyshev current distributions, i.e. the weight vector C corresponds to the Chebyshev excitation coefficients of a linear array with Nv elements. The performance of these circular arrays with beam steering is compared to the conventional case where cells are equipped with identical omnidirectional array antennas. The directivity and the number of elements of the omnidirectional arrays don’t influence the value of F in (1), since the value of the antenna gain G is the same in all directions for omnidirectional arrays. Consequently, it will be simplified in the calculations. We defined the antenna arrays without specifying their constitutive antenna element. Hence, they are considered to be formed of isotropic elements. The microstrip patch designed in [17] for 3G cellular systems can, for example, be used as the constituent element of the antenna arrays. However, in [17], the mutual coupling between patches is not studied in the case of circular arrays with high number of elements. But in [18], the Matrix Pencil (MP) method is used to almost eliminate mutual coupling for any type of elements in an antenna array. It was shown in [18] that direction of arrival estimation using CDMA/MP is fast, accurate, and effective in multipath fading situations. Since MP is beyond the scope of this paper, we will assume that mutual coupling, element imperfections, and excitation inaccuracies, lead to patterns close to the one of Fig. 2, and consequently we work with the array factors independently of the actual constituent elements.

Fig. 2: Normalized array factor in the azimuth plane of the circular antenna arrays used in the simulation.

4 Simulation Results and Discussion The adopted simulation model is based on a symmetric network of equivalently equipped BSs, i.e. all the BSs either have omnidirectional antennas or 3 sectors each equipped with the proposed circular antenna arrays. The simulated network consists of 7 hexagonal cells (21 sectors). In the simulation model, the link between a MS and a BS consists of pathloss and shadowing whereas fast fading is assumed to be averaged out by perfect power control, diversity, and channel coding. Fig. 3 represents the simulated network and shows the sector of interest.

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24th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2007) March 13-15, 2007 Faculty of Engineering, Ain shams Univ., Egypt

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Fig. 3: Cell Numbering and Reference Sector. Finally, it is important to mention that the MSs are assumed to be uniformly distributed over the entire network. The BSs are assumed to transmit at their maximum power. This assumption leads to the simplification of the power term in Equation (1). We consider K = - 50 dB and σ = 8 dB. The pathloss exponent n is varied from 2 to 5 in increments of 0.5, i.e. in the interval of practical values appearing in empirical measurements [19]. The average of 10000 independent iterations is taken. In each iteration, the following steps are executed: - A user is created in a random location. - The distance and the angle from the mobile to each base station are computed. - The antenna gains Gkj from each base station in the direction of the mobile are determined from the antenna patterns (these gains are equal in the omnidirectional case). - The lognormal shadowing samples ξkj are generated randomly. - From the above steps, the terms gk,j in (2) can be computed. - Then, Fkl in (1) is computed for this user. Finally, the average value of F is computed. Note that the mobile users were assumed to be only in the azimuth plane. The results are shown in Table 1.

n 2 2.5 3 3.5 4 4.5 5

Omnidirectional Proposed Circular Arrays 3.277 0.10604 2.2621 0.063742 1.5956 0.054304 1.1569 0.038335 0.89106 0.030023 0.71268 0.022983 0.59134 0.019671

Table 1: Simulation Results of Favg. These results are plotted in Fig. 4. Obviously, the average value of F for the beam steering method with the proposed circular arrays is more than an order of magnitude less than the conventional omnidirectional case. These results indicate less intercell interference compared to the received intracell power. The proposed circular array has a lower F, because it has a narrow beam and 20 dB sidelobes, ensuring good interference rejection. The superiority of the steered beam adaptive antenna scheme is evident. The novelty in this paper is the combination of beam steering with the transformation used in [15] to reduce intercell interference. We notice from Fig. 4 that F decreases when n increases. This result is expected, since the larger n, the more the power is attenuated, and the less it can interfere with users in neighboring cells.

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24th NATIONAL RADIO SCIENCE CONFERENCE (NRSC 2007) March 13-15, 2007 Faculty of Engineering, Ain shams Univ., Egypt

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Fig. 4: Favg as a function of the pathloss exponent n.

5 Conclusion An implementation of advanced antenna strategies in WCDMA/UMTS has been presented. Beam steering was combined with a transformation that converts a circular array to a virtual linear array and yields a Chebyshev pattern in the azimuth plane. The proposed advanced antennas, when compared to the omnidirectional case, led to a considerable decrease of the ratio of intercell interference to intracell power.

References: [1] H. Holma and A. Toskala, WCDMA for UMTS, Wiley, 2000. [2] J. S. Blogh and L. Hanzo, Third Generation Systems and IntelligentWireless Networking: Smart Antennas and Adaptive Modulation, John Wiley and Sons, 2002. [3] T. Baumgartner, Smart Antenna Strategies for the UMTS FDD Downlink, PhD Thesis, Technische Universitaet Wien, August 2003. [4] J. Litva, T. Lo, Digital Beamforming in Wireless Communications, Artech House, 1996. [5] A. F. Naguib, A. Paulraj, and T. Kailath, ”Capacity Improvement with Base-Station Antenna Arrays in Cellular CDMA”, IEEE Transactions on Vehicular Technology, Vol. 43, No. 3, August 1994. [6] F. Chin, Y. Zhou, Y. C. Liang, and C. C. Ko, ”Downlink Capacity of Multi-Rate DS-CDMA with Antenna Array and SIR Based Power Control in Multi-Cell Environment”, IEEE Vehicular Technology Conference(VTC), September 2000. [7] B. Goeransson, B. Hagerman, S. Petersson, and J. Sorelius, ”Advanced Antenna Systems for WCDMA: Link and System Level Results”, IEEE PIMRC 2000, London, September 2000. [8] M. Ericson, A. Osseiran, J. Barta, B. Goeransson, and B. Hagerman, ”Capacity Study for Fixed Multi Beam Antenna Systems in a Mixed Service WCDMA System”, IEEE PIMRC 2001, San Diego, October 2001. [9] M. Itani, M. Dillinger, Z. Dawy, and J. Luo, ”Switched Multi-Beam Investigations for the Forward Link of WCDMA”, IEEE 3G wireless 2001, San Francisco, May 2001. [10] J. Barta, S. Petersson, and B. Hagerman, ”Downlink Capacity and Coverage Trade-Offs in WCDMA with Advanced Antenna Systems”, IEEE Vehicular Technology Conference (VTC), May 2002. [11] E. Yaacoub, R. El Kaissi and Z. Dawy, ”Chebyshev Antenna Arrays for WCDMA Downlink Capacity Enhancement”, IEEE PIMRC 2005, Berlin, September 2005. [12] K. Hiltunen and R. De Bernardi, ”WCDMA Downlink Capacity Estimation”, IEEE Vehicular Technology Conference (VTC), Tokyo, May 2000.

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[13] Z. Dawy, S. Jaranakaran, and S. Sharafeddine, ”Intercell Interference Margin for CDMA Uplink Radio Network Planning”, IEEE PIMRC 2004, Barcelona, September 2004. [14] W. U. Pistelli and R. Verdone, ”Power Allocation Strategies for the Downlink in a W-CDMA System with Soft and Softer Handover: The Impact on Capacity”, IEEE PIMRC 2002, Lisbon, September 2002. [15] B. K. Lau and Y. H. Leung, “A Dolph-Chebyshev Approach to the Synthesis of Array Patterns for Uniform Circular Arrays”, IEEE International Symposium on Circuits and Systems, Geneva, Switzerland, May 28-31, 2000. [16] E. Yaacoub, Pattern Synthesis with Cylindrical Arrays, Master Thesis, American University of Beirut, September 2005. [17] A. Kuchar, Aperture-Coupled Microstrip Patch Antenna Array, Master Thesis, Technische Universitaet Wien, March 1996. [18] T. Sarkar, M. Wicks, M. Salazar-Palma, R. Bonneau, Smart Antennas, John Wiley & Sons, 2003. [19] A. Goldsmith, Wireless Communications, Cambridge University Press, 2005.

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