ROYAL INSTITUTE OF TECHNOLOGY KUNGL TEKNISKA HÖGSKOLAN. Department of Signals, Sensors & Systems Signal Processing S STOCKHOLM

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1 On Base Station Antenna Array Structures for Downlink Capacity Enhancement in Cellular Mobile Radio Per Zetterberg 9{{1 IR{S3{SB{9 ROYAL INSTITUTE OF TECHNOLOGY Department of Signals, Sensors & Systems Signal Processing S- STOCKHOLM KUNGL TEKNISKA HÖGSKOLAN Institutionen för Signaler, Sensorer & System Signalbehandling STOCKHOLM

2 On Base Station Antenna Array Structures for Downlink Capacity Enhancement in Cellular Mobile Radio Per Zetterberg Center for PersonKommunikation (CPK) Aalborg University, Denmark or Phone: (+5) Fax: (+5) August 11, 199 WHEN MAKING REFERENCES TO THE WORK HEREIN PLEASE REFER TO [], WHICH CONTAINS THE SAME INFORMATION. MORE INFORMATION ABOUT THE REFERENCE [] CAN BE OBTAINED FROM THE AUTHOR. Abstract This paper discusses some base station antenna array design options from a performance and algorithm viewpoint. In particular the paper contains a comparison of the downlink (base to mobile) performance of several antenna array topologies. We nd that the half a wavelength spaced linear array (covering 1 degrees) is a good alternative since it has high performance, and attractive properties for direction nding 1 Introduction There is an interest in the use of base station antenna arrays for increased capacity in mobile cellular networks, [3, 9, 11, 1, 1, 17, 19]. So far limited attention has been paid to the choice of antenna topology (spatial distribution of antenna elements), antenna element patterns and if the base should use the same or separate arrays for up and downlink. This paper discusses these issues from a performance and algorithm perspective. A comparison of the downlink signal to interference performance of some dierent topologies is also presented in the paper. The comparison assumes that optimal (with respect to the used performance criterion) transmit weighting vectors are selected. Optimization Per Zetterberg is a guest researcher at Aalborg University, Denmark until 31/-9. His home institute is Royal Institute of Technology, S- 1

3 of base station antenna array topology is also treated in [7]. However, while that paper optimizes topology to achieve uplink range extension, downlink capacity improvement is the objective here. Our results show that all the investigated topologies are able to reduce the amount of radiated interference by 5dB (in mean), compared to a conventional three sector site solution, assuming beam steering (without directed nulls), antenna elements per site, and a desired signal which is Gaussian distributed in azimuth angle with = 5 o. With frequency hopping or CDMA this translates roughly into a 5dB improvement in the downlink signal to interference ratio. We nd that the linear array (covering 1 degrees), the triangular and the circular has the highest performance. Among these three topologies we select the linear array because of the existence of ecient direction nding algorithms for this structure, see Section 5. Moreover, mutual coupling seems to be more tractable with this array structure. The paper is organized as follows: Section presents the basic modeling, problems and solutions of downlink beamforming in frequency division duplex (FDD) based cellular systems. If two arrays with the same topology but scaled to their respective wavelength are used for up and downlink, direction nding may be avoided. This was rst proposed in [11] and is explained in the framework of this paper in Section 3. The investigated topologies are introduced in Section. The performance results are presented in Section. Finally the conclusions are drawn in Section 7. Preliminaries In this section we will briey review a generic propagation model, and give the implications of that model for transmission with multiple antennas. We assume that there are a large number of rays connecting the base and the mobile. It is further assumed that the k:th ray has amplitude, A k, propagation delay k and is impinging from azimuth direction k at the base. Under these assumptions the multidimensional baseband impulse response between the single antenna at the mobile and the multiple antennas at the base, has the Fourier transform v RX (f) = X k A k exp(j(f + f RX ) k )a RX ( k ; f RX ); (1) in the uplink and v TX (f) = X k A k exp(j(f + f TX ) k )a TX ( k ; f TX ); () in the downlink, where f RX and f TX is the receive and transmit (center) frequencies respectively, and the functions a RX (; f) and a TX (; f) contain the relative phases and amplitudes of the antenna elements assuming a single ray from direction at frequency f. The maximum downlink performance is obtained only obtained if v TX (f) is known. However, in frequency division duplex systems, it is generally not possible to estimate v TX (f) from v RX (f) because of the large duplex distance f TX? f RX which causes decorrelation

4 between the up and downlink channels v TX (f) and v RX (f), [5]. When the mobile moves the time delays k of the scatterers will change since the distance between the mobile and the scatterers changes. The position and amplitudes of the eective scatterers will of course also change, but at a slower rate. Thus over a couple of wavelengths the following relationship may be considered valid k = k;? v cos( k )t=c; (3) where k; is the delay at time zero, v is the speed of the mobile, k is the angle between the speed vector of the mobile and the kth scatterer as seen from the mobile, t is time and c is the speed of light. This means that v(f) (both RX and TX) can be seen as a function of time where each term in the sum () is a cisoid (complex sinusoid). By estimating v RX (f) repeatedly (for instance in each timeslot) and forming the covariance matrix these vectors, an estimate of the following matrix is obtained R RX = Efv RX (f)v RX;H (f)g () = X k ja k j a RX (; f RX )a RX;H (; f RX ); (5) where the second equality follows if it is assumed that all Doppler frequencies f v cos( k )=c are distinct. Let us dene the corresponding matrix for the downlink R TX = Efv TX (f)v TX;H (f)g () = X k ja k j a TX (; f TX )a TX;H (; f TX ): (7) The idea is to use some kind of transformation to transform the estimate of R RX into an estimate of R TX. The matrix R TX may then be subsequently used in transmission algorithms as proposed in [, 11, 17, 19]. One way of doing the translation from R RX to R TX is to estimate a number of dominant angles of arrivals, k, and their corresponding amplitudes, A k, from R TX and subsequently use these estimates to approximate R TX. We will refer this approach as the direction nding (DF) approach. Another possibility is simply to use R RX as an estimate of R TX, [11]. We will refer to the latter method as the fading correlation reciprocity (FCR) method. 3 Receive and Transmit Arrays To obtain the full benet of base station antenna arrays in cellular networks it is necessary to use both spatially selective transmission and reception. Physically this may be realized by using separate receive and transmit arrays or by using the same array for both links. Using the same array requires an elaborate design of the antenna elements in order to obtain antenna elements with sucient bandwidth to cover both the receive and transmit band []. The structure of the receive and transmit array enter the framework above in the 3

5 antenna array response functions a RX (; f) and a TX (; f) respectively. The DF approach (see Section ) requires these functions to be known. If these functions are similar the FCR methods (see Section ) may be used. This case may arise if two arrays with identical topology but scaled to their respective wavelength are applied. A comparison of DF and FCR approaches has not been made so far. However, it may be anticipated that the fading reciprocity approach is more sensitive to gain and phase perturbations in the receive ampliers while the DF will be sensitive to the accuracy of the estimates of a RX (; f) and a TX (; f). Topologies The spatial distribution of the elements and their pattern determines the combined patterns that can be synthesized. Assuming that the nth element has antenna pattern p n (; f) and position x n ; y n with respect to a reference point (; ), the nth element of a(; f) will be given by a n (; f) = p n (; f) exp(jf y n sin()=c + jf x n cos()=c); () if mutual-coupling is neglected. The element patterns that will be considered are given by p n (; f) = < : cos () if j? n j < 9 o ; otherwise; (9) where is a shape parameter and n is the orientation of the element. The topologies that will be investigated in the following sections are the triangular array, the wing array, the linear array and the circular array. The details of the triangular and wing array are shown in Figure 1, while the remaining two topologies are easily derived from Figure and 1 respectively. The linear and the wing array typically covers a o to 1 o sector while the circular and triangular array covers 3 o. A natural question here is: what is the dierence between three linear arrays covering 1 degrees each and a triangular array? The dierence (as dened here) is that the triangular array uses all elements simultaneously in the downlink beamforming. while in the 3 1 o solution, one linear array is used at a time. In order to do downlink beamforming with the triangular array it is important that each linear side is physically close, typically not more than half a wavelength. In contrast, the uplink processing may very well combine all the elements even if the sub-arrays are widely spaced. 5 Direction Finding As mentioned in section, one way of obtaining R TX from R RX is to estimate a number of dominant directions k and their amplitudes in A k from R RX and subsequently use knowledge of a TX (; f) to estimate R TX. This can be done by using direction nding

6 o o o 1 o Figure 1: methods e.g [,, 1, 13, 15]. Direction nding methods can generally be divided into two classes: algorithms for arbitrary antenna congurations and algorithms only applicable to arrays with elements uniformally distributed on a straight line (ULA:s). For ULA:s a RX (; f) is given by a RX (; f) = p(; f)[1; exp(jf sin()=c); : : : ; exp(?j(m? 1)f sin()=c)] T ; () where is the inter element spacing, c is the speed of light, m is the number of antenna elements and p(x; f) is the element pattern. Equation (), assumes that there is no cross-coupling between the elements. With suciently many impedance loaded dummy elements on each end of the array () will hold even with cross-coupling. However, in that case the element patterns p(; f) will be distorted. However, that does not impair the translation from R RX from R TX, since the distortion can be modelled by the amplitudes A k. Thus there are two arguments for the linear array in the context of direction nding: the existence of more direction nding algorithms, and the possibility to handle cross-coupling with dummy-elements. The rst of these arguments is further strengthened by the fact that direction nding algorithms that requires linear arrays generally provides closed form solutions of multiple directions of arrivals and thus avoids searching multidimensional criterion functions e.g [, 1, 13]. Results In this section the performance of six antenna array solutions will be compared. All the solutions (except one) requires antenna elements to cover 3 degrees. However the 3 degrees are sectorized in dierent ways. The six solutions are: element linear array covering 1 degrees, element wing array covering 1 degrees, element linear array covering degrees, element triangular array covering 3 degrees, element circular array covering 3 degrees and element linear array covering degrees. 5

7 As a criterion to compare the dierent array topologies we use the quotient of the downlink power generated at the desired mobile, to the total power transmitted from the base. Thus we do not \null" co-channel users in other cells (there are no co-channel users in the same cell i.e no SDMA). The propagation between the mobile and the base is assumed to be built up by 11 rays with power following a Gaussian distribution in with mean at the mobile and standard deviation (the 11 rays are uniform distributed in the interval? 3; + 3 where is the direction of the mobile, and the total power is normalized as P N k=1 jaj k = 1). This model is realistic in environments where the base has a clear view of the coverage area. However, the mobile does not necessarily have to be in line of sight [1, 1]. If the base is transmitting with weighting vector w, it can be shown that the power (averaged over Doppler fading) received at the desired mobile is given by P d = w H R TX w; (11) where R TX is given by (7). The total emitted interference is given by where P i = w H Q TX w; (1) Q TX = Z o? o a TX (; f TX )a TX;H (; f TX )d: (13) We use P d =P i as our performance criterion. To make the comparison independent of estimation method e.g DF or FCR (see Section ), we use the optimal weighting vector with respect to to this criterion. It can be shown that the optimal vector w is given by the dominating generalized eigenvector of the matrix pair (R TX ; Q TX ) and the maximum value of P d =P i is the corresponding eigenvalue. In summary the following calculations are made to obtain the performance of certain topology, using a certain and : 1. Calculate a TX ( k ; f TX ) for k = (?3 + (k? 1)=1), k = 1; : : : ; 11.. Calculate R TX using (7) the previously calculated manifold vectors a TX ( k ; f TX ) and using ja k j = Q((?3 + (k? 1)=1)? :5)? Q((?3 + (k? 1)=1) + :5), where Q(x) is dened as Q(x) = R 1 ~x=x ()?:5 exp(?x =). 3. Calculate Q TX using (13) and a resolution of a degree.. Determine the maximum generalize eigenvalue of the matrix pair (R TX ; Q TX ). Figures 3,,9, 1, 15 and 1 shows the performance improvement over an ideal 1 degree antenna (the performance of this antenna can also be obtained according to the enumeration above) as a function of the angle of the desired user. The direction = is dened as the x-axis in Figures 3,,9, 1, 15 and 1 respectively. Symmetry yields that

8 the azimuth range shown in these gures are sucient. Figures 3,,9, 1, 15 and 1 also show the antenna pattern of some typical beams that the topologies in question are able to produce. In Figures,5,,11, 1 and 17 the mean performance gain EfP d=p ig (relative to the 1 sector antenna), under the assumption that the desired user is uniform distributed within the sector of coverage. Several antenna spacings and element directivities are plotted in each Figure. The element spacings and directivities that shown are the ones with the highest performance among in the sets = f:5; :; : : : ; 1:g and = f1; ; 3g. 7 Conclusions The results of previous section shows that the 3 degree solutions (the triangular and circular array) have a (mean) performance advantage of up to :db over the 1 degree linear array, :5dB over the wing array and 1dB over the degree linear array (using the best antenna spacings and element patterns in each case, and elements per site). Judging from these statistics we nd that the 1 degree linear array is an attractive solutions since it has almost the same performance as the triangular and circular array, but posses some advantages with respect to direction nding as was discussed in Section 5. However, the performance of 1 degree linear array degrades quite severely when the mobile moves towards = o, see Figure 3. We believe that this presents no real problem as the cell can be shaped (by shaping the broadcast channel accordingly) such that the radial distance between the base and the cell border is decreasing towards = o, and thereby reducing the probability of a mobile in that direction. This kind o cell shape is common already in current systems. Finally, the triangular and circular array are more dicult to mount since all elements has to physically close as was mentioned in Section, while the three linear arrays can be mounted several meters apart. The triangular and circular array also requires all branches to be calibrated together while with the 1 degree linear array solution, the receivers and transmitters can be calibrated in three groups of eight branches. In summary we nd three linear arrays covering 1 degrees to be the best solution among the investigated topologies, although the advantage over the other solutions is small. References [1] F Adachi, M.T Feeney, A.G Williamson, and J.D Parsons. \Crosscorrelation between the envelopes of 9Mhz signals received at a mobile radio base station site". IEE Proceedings,Pt. F, vol. 133, no.,, October 19. [] Y. Bresler and A. Mocovski. \Exact Maximum Likelihood Parameter Estimation of Superimposed Exponential Signals in Noise". IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 3, pp. 1{9, October 19. [3] U Forssen, J Karlsson, B Johannisson, M Almgren, F Lotse, and F Kronestedt. \Adaptive Antenna Arrays for GSM9/DCS". In Proceedings IEEE Vehicular Technology Conference, pp. 5{9,

9 [] D Gerlach and A Paulraj. \Base Station Transmitting Antenna Arrays for Multipath Environments". submitted to IEEE Transactions on Signal Processing, [5] S.S Jeng, H.P Lin, G Xu, and W.J Vogel. \Measurements of Spatial Signature of an Antenna Array". In IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, pp. 9{7, [] B Johannison. \Planar Antenna Array for Adaptive Beamforming". In Nordic Radio Symposium, pp. 177{, Saltsjobaden Sweden, April [7] J. Liang and A. Paulraj. \On Optimizing Base Station Antenna Array Topology for Coverage Extension in Cellular Radio Networks". In IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, pp. {7, September [] P. Mogensen, P. Zetterberg, H. Dam, P. Leth Espensen, S. Leth Larsen, and K. Olesen. \Algorithms and Antenna Array Recommendations". Technical Report A/AUC/A1/DR/P/1/xx-D.1., Tsunami(II), Contact pm@cpk.auc.dk or perz@s3.kth.se for a copy and information., September 199. [9] T Ohgane. \Spectral Eciency Evaluation of Adaptive Base Station for Land Mobile Cellular Systems". In Proceedings IEEE Vehicular Technology Conference, pp. 17{ 17, 199. [] B Ottersten, M Viberg, and T Kailath. \Analysis of Subspace Fitting and ML Techniques for Parameter Estimation from Sensor Array Data". IEEE Transactions on Signal Processing, vol., no. 3, pp. 59{, March 199. [11] G Raleigh, S.N. Diggavi, V..K Jones, and A Paulraj. \A Blind Adaptive Transmit Antenna Algorithm for Wireless Communication". In Proceedings IEEE International Conference on Communications, [1] R.Roy, A. Paulraj, and T.Kailath. \ESPRIT- A Subspace Rotation Approach to Estimation of Parameters of Cisoids in Noise". IEEE Transactions on Acoustics, Speech, and Signal Processing, no. 3, pp. 13, 19. [13] R.O Schmidt. \Multiple Emitter Location and Signal Parameter Estimation". In RADC Spectral Estimation Workshop, Griths AFB, NY, pp. 3{5, reprinted in IEEE Trans. Antennas Propagat., vol. AP{3, no. 3, pp. 1{9, Mar. 19., [1] S.C Swales, M.A Beach, D.J Edwards, and J.P McGeehan. \The Performance Enhancement of Multibeam Adaptive Base-Station Antennas for Cellular Land Mobile Radio Systems". IEEE Transactions on Vehicular Technology, vol. 39, pp. 5{7, February 199. [15] T Trump and B Ottersten. \Maximum Likelihood Estimation of Nomina direction of Arrival and Angular Spread Using an Array of Sensors". In Proceedings of COST 9 Adaptive Systems, Intelligent Approaches, Massively Parallel Computing and Emergent Techniques in Signal Processing and Communications, Vigo, Spain, January 1995.

10 [1] J.H Winters. \Optimum Combining in Digital Mobile Radio with Cochannel Interference". IEEE Transactions on Vehicular Technology, vol. 33, no. 3, pp. 1{155, August 19. [17] P Zetterberg. \A Comparison of two Systems for Down Link Communication with Antenna Arrays at the Base, Report Version". Technical Report IR-S3-SB-951, Signal Processing, Royal Institute of Technology, Sweden, Available by Netscape: Document URL: or by anonymous ftp to: ftp.e.kth.se directory /pub/signal/reports., Submitted to IEEE Transactions on Vehicular Technology. [1] P Zetterberg. \Mobile Communication with Base Station Antenna Arrays: Propagation Modeling and System Capacity". Technical Report IR-S3-SB-95, Available by Netscape: Document URL: or by anonymous ftp to: ftp.e.kth.se directory /pub/signal/reports., February Licentiate Thesis. [19] P Zetterberg and B Ottersten. \The Spectrum Eciency of a Basestation Antenna Array System for Spatially Selective Transmission". IEEE Transactions on Vehicular Technology, vol., no. 3, pp. 51{, August

11 Performance gain (db). Performance gain (db). Performance gain (db) Performance gain (db) element (1-degree) wing array element (1-degree) linear array 1 1 =.λ,ρ=3 =.7λ,ρ= =.5λ,ρ=1,,3 =.λ,ρ= =.λ,ρ= Angular spread in degrees (standard deviation) Figure : =.7λ,ρ=1 =.λ,ρ= Angular spread in degrees (standard deviation) Figure 5: 1 element linear array, =.5λ,ρ=1. degrees angular spread. 5 degrees angular spread. 1 element wing array, =.λ,ρ=3. degrees angular spread. 5 degrees angular spread. degrees angular spread. degrees angular spread. degrees angular spread. degrees angular spread Azimuth direction of desired mobile (degrees) Azimuth direction of desired mobile (degrees). Figure 3: Figure : Figure : Beampatterns of the element 1 degree linear array ( = :5, = 1). The inner circle represents the?db level. Figure 7: Beampattern of the element 1 degree wing array ( = :, = 3). The inner circle represents the?db level.

12 Performance gain (db). Performance gain (db). Performance gain (db) Performance gain (db) element triangular array 1 element (-degree) linear array 1 =.5λ,ρ=1,,3 =.λ,ρ=3 =.λ,ρ= =.7λ,ρ=1 =.λ,ρ= Angular spread in degrees (standard deviation) =.λ,ρ= Angular spread in degrees (standard deviation) Figure 11: Figure : element linear array, =.λ,ρ=3. 1 element triangular array, =.5λ,ρ=3. 1 degrees angular spread. degrees angular spread. 5 degrees angular spread. degrees angular spread. 5 degrees angular spread. degrees angular spread. degrees angular spread. degrees angular spread Azimuth direction of desired mobile (degrees) Azimuth direction of desired mobile (degrees). Figure 9: Figure 1: Figure : Beampatterns of the element degree linear array ( = :, = 3). The inner circle represents the?db level. Figure 13: Beampatterns of the element triangular array. The inner circle represents the?db level. 11

13 Performance gain (db). Performance gain (db). Performance gain (db) Performance gain (db) 1 element circular array 1 element (-degree) linear array =.λ,ρ=3 =.λ,ρ= =.5λ,ρ=1,,3 =.λ,ρ= =.λ,ρ=1 =.7λ,ρ=1 =.λ,ρ= Angular spread in degrees (standard deviation) 5 15 Angular spread in degrees (standard deviation) Figure 1: Figure 17: 1 element circular array, =.5λ,ρ=3. 1 element linear array, =.λ,ρ=3. degrees angular spread. degrees angular spread. 5 degrees angular spread. 5 degrees angular spread. degrees angular spread. degrees angular spread. degrees angular spread. degrees angular spread Azimuth direction of desired mobile (degrees) Azimuth direction of desired mobile (degrees). Figure 15: Figure 1: Figure 1: Beampatterns of the element circular array ( = :5, = 3). The inner circle represents the?db level. Figure 19: Beampatterns of the element degree linear array ( = :, = 3). The inner circle represents the?db level. 1