array (URA) and uniform cubic array (UCuA), with eight elements at both ends and fixed inter-element spacing. The

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1 Impact of Antenna Array Geometry on MIMO Channel Bigenvalues A.A. Abouda, H.M. El-Sallabi and S.G. Haggman Helsinki University of Technology P.O.Box 3000, FIN HUT, Finland {abouda, hsallabi, Abstract- Spatial correlation properties of MIMO channel highly depend on the propagation environment and the antenna array geometry. In this paper the impact of different antenna array geometries on MIMO channel eigenvalues is investigated in realistic microcellular propagation environment under different scenarios. Four different antenna array geometries are considered, namely, uniform linear array, uniform circular array, uniform rectangular array and uniform cubic array. All the considered geometries have same number of elements and fixed inter-element spacing. The uniform linear array geometry shows superiority to the other considered geometries. I. INTRODUCTION More services and higher data rates are the demands of wireless communication system end users. Contemporary technologies need to be developed to accommodate these demands, while maintaining robustness to wireless impairments. Multiple-input multiple-output (MIMO) techniques stand as a strong candidate to allow robustness against channel fading and interference as well as to enable high data rates [1]. MIMO systems in rich scattering environment can achieve performance, in terms of data and error rates, far in excess from that of conventional systems. However, high spatial correlation at either ends reduces the achievable performance significantly [2]. Spatial correlation properties depend on the propagation environment and antenna array geometry [2]. Previous works have focused on evaluating MIMO system performance under the assumption of uniform linear array at both ends. Despite the implementation advantages of other array geometries, they have not been extensively investigated. Recently, in [3] the impact of five antenna array geometries have been investigated using the clustered channel model [4] in indoor scenario. It is shown that in low spatial correlation environment the uniform linear array geometry outperforms the other array geometries. In [5] a compact MIMO antenna array is proposed by combining polarization diversity and space diversity into one arrangement consisting of a cube. It is shown that even for very small inter-element spacing considerable capacity is obtained due to polarization diversity. In this paper the impact of different antenna array geometries on MIMO channel properties is investigated in realistic propagation environment by analyzing the eigenvalues of the normalized channel correlation matrix. Four antenna array geometries are considered, namely, uniform linear array (ULA), uniform circular array (), uniform rectangular array (URA) and uniform cubic array (UCuA), with eight elements at both ends and fixed inter-element spacing. The investigation is carried out under different propagation types, line-of-sight (LOS) and non-line-of-sight (NLOS). The rest of this paper is organized as follows: in section li the channel model, which used for MIMO channel matrix computation is presented. Description of the propagation environment is give in section III. The antenna array geometries under study are described in section IV. The eigenvalues analysis method is presented in section V. The results and discussions are given in section VI. Section VII draws our conclusion. II. CHANNEL MODEL Spatial variant multi-ray propagation models for main street and perpendicular streets wave propagation in urban street grid are developed in [6] and [71, respectively. The propagation channel models are different from ray tracing models in a sense that there is no searching for coupling paths between base station (BS) and mobile station (MS) since all the ray characteristics, such as angle of arrival (AOA), angle of departure (AOD) and path length, are given in closed form expressions which results in significant reduction in computation time. Moreover, the propagation channel models take into account the environment physical parameters, such as electrical characteristics of wall and ground, street width and distances of BS and MS from walls. The models are developed based on electromagnetic theory rather than stochastic processes. In addition to that studying the impact of different antenna array geometries on MIMO channel properties based on field measurement is cost prohibited. Therefore, these propagation channel models are adopted for this study. The transfer function between jth transmit element and ith receive element is given by: gv,h(i, j) = gr (i,j) + 9VHR(ij) (1) where we grr V,H anda grdr gv,h are the total transfer functions due to the reflected-reflected (RR) rays group and reflecteddiffracted-reflected (RDR) rays group, respectively. The transfer function of the RR rays and the RDR rays are given in (2) and (3), (in the top of next page), respectively, where a ray k is represented by a set of five integers (im, S, n, a, g), m and n are the wall reflection orders in the main street and perpendicular streets, respectively, S = 1, /05/$ IEEE 568

2 RR( ) kn k rrk(,) 9V,SH (i I 4E n) (RVH(i,j))g(RH V,j))n(RH,V = k_=(m,s.rn,u,g) r i (2) YV,H RDR(f\-) ~t, - 4,rr k-(m,s,n,u.g,ck) 1 A A (jzk k, )) V.H (' j '))I (R n km k,v(i,j), kh kv (', t j (R H,V (i, j))md H,'1D1(i,j)D2(i,j)(Di (i, j) + D2 (i,j)) ( -j27r (D,(I,j)+D.,(i,j))) :e A (3) and u 1,2 = are for two sidewalls on the street for BS and MS, respectively, g = 0, 1 is for the ground reflection, A is the wavelength, r, is the rk path length, tn ]Zk Rkm ~~V,H' H,V and RH,V are the well-known Fresnel reflection coefficients for ground and wall reflections in main and perpendicular streets, respectively, with transmission in vertical, horizontal polarization, respectively, Dk is the diffraction coefficient at the vertical edge of the building corner, D1,2 is the distance from the BS and the MS to the diffraction point, respectively, C1,2,3,4 are four building corners. More details can be found in [6] and [7]. III. PROPAGATION ENVIRONMENT A street grid environment found in many cities is considered in this study. The geometry of the urban microcellular environment under study is depicted in Figure 1 where the grid pattern has 100 m x 50 m blocks of building and 25 m street widths for the main and perpendicular streets. The building street surface electrical parameters, relative permittivity 6r = 5 and conductivity a S/m. These are practical values = for city street concrete walls [8]. The environment multipath richness is function of the maximum reflection orders in main and perpendicular streets. Since one reflection order results in about 5 db loss, higher reflection orders than 7 result in very weak paths [9]. Therefore, the maximum reflection order is set to 7 in both main and perpendicular streets. The BS is mounted below the rooftops with antenna height 13 m at distances of 75 m from corner C, and 5 m from the wall, yo = 5 m. A MS with antenna height 1.8 m moves a distance of 100 m in differen routes, namely, A-B, C-D, E-F and G-H with x1 = 13 m and yq = 5 m. The considered traveling routes represent different propagation types. Traveling route A-B is a NLOS scenario where the channel matrix is expected to have Rayleigh distributed elements. The angular spread (AS) at both ends is high because of the high multipath richness of the propagation environment. The propagation mechanism that dominates the environment in this route changes with the MS location. At the beginning of the route there are strong LOS components due to the direct path and its ground reflected pair. These LOS components disappear after few samples when the MS moves inside the perpendicular street. After few samples from point A the environment will be dominated by the reflection mechanism. As the MS goes inside the perpendicular street the RR rays group will suffer from high attenuation due to multiple reflections and the diffraction mechanism will become more dominant. At the end of the route the RR rays group will vanish and only RDR rays group will be available. Most of the RDR rays group will be due to the signal diffracted from corner C3, (see Figure 1), which results in a scenario like LOS situation. The propagation scenario in traveling route E-F is a NLOS with high AS at both ends. Both RR rays group and RDR rays group are available in this route but the RR rays group will be less significant at the end of the route. Traveling route C-D is a pure LOS scenario with high AS at both ends and the channel matrix elements are expected to be Ricean distributed. Throughout the route the direct ray and its ground reflected pair and the two sidewalls reflected rays are the dominant propagation components. In traveling route G-H the separation distance between the BS and the MS is large, (325 m at point G), which results in a LOS scenario with low AS at both ends. In this case the channel matrix will be dominated by the direct path and its ground reflected pair. This is the worst case scenario for the MIMO system where less benefit can be obtained from the MIMO technique. C2) C3 x I BS c_-vl --D E GY -' yo C XII A B C4 Fig. 1. Urban street grid showing traveling routes under study. IV. CONSIDERED ANTENNA ARRAY GEOMETRIES The considered antenna array geometries are shown in Figure 2 where each geometry has eight omnidirectional elements with 0.5A inter-element spacing. These geometries represent three types of antenna arrays, one dimensional (ULA), two dimensional ( and URA) and three dimensional (UCuA). It is shown in [10] that the performance of the ULA geometry is highly dependent on the array orientation. However, the impact of antenna array orientation is beyond the scope of this F /05/$ IEEE 569

3 work. In this paper broadside array orientation is assumed for the BS antenna, (the ULA is transversal in the main street). In the MS side two array orientations are assumed, transversal in main street for routes C-D and G-H and transversal in perpendicular street for routes A-B and E-F ULA URA UCuA Fig. 2. Considered antenna array geometries. V. EIGENVALUES ANALYSIS There are different mechanisms contribute to the high performance achieved by MIMO systems. These mechanisms include spatial multiplexing, space diversity and power gain [11]. The contribution of each mechanism depends on the employed coding scheme, the propagation environment and the target average receive signal to noise ratio (SNR) [12]. Tradeoff between spatial multiplexing and diversity gain should be considered. In this work we assume spatial multiplexing scheme where different signals are transmitted from the different transmit elements in each time instant. Employing this scheme leads to maximize the spatial multiplexing gain and minimize the diversity gain [12]. The eigenvalue decomposition of the instantaneous channel correlation matrix is a useful tool for MIMO channel performance investigation [11]. The channel correlation matrix is defined as: R=HHH (4) where H is the narrowband normalized channel matrix and (.)H represents Hermitian transposition. Here we adopt the normalization technique that leads to constant average SNR over a distance of 7A in order to mitigate the effects of slow fading [13]. The total channel capacity is the result of the different MIMO mechanisms. When uniform power allocation strategy is employed the total channel capacity at average receive SNR p is given by [11]: N c=e log(l + Al N- (5) where Al is the jth eigenvalue, N is the total number of eigenvalues and Nt is number of transmit antenna elements. VI. RESULTS AND DISCUSSIONS In the following simulation results carrier frequency of 2 GHz and vertical polarization are assumed. The different antenna array geometries were deployed at both ends and the channel matrices were computed in each traveling route. Throughout the traveling routes, channel realizations were computed every 10 cm. A. Impact on total channel capacity The impact of the different antenna array geometries on the total channel capacity is shown in Figure 3 in terms of the cumulative distribution function (CDF) of the channel capacity at p = 20 db. The capacity of independent identical distributed (iid) Rayleigh fading channel is also shown as a reference. It is clear that the correlation at both ends highly affected by the antenna array geometry. The lowest spatial correlation is obtained by using the ULA geometry where the achievable median capacities are 33, 29, 36 and 21 b/s/hz, in traveling routes A-B, C-D, E-F and G-H, respectively. On the other hand using UCuA results in high spatial correlation and the achievable median capacities reduce to 16, 14, 16 and 11 b/s/hz, in the same traveling routes, respectively. Using the and the URA have similar impact on the correlation properties. It is evident that in the same propagation environment the mutual information have been highly affected due to the antenna array geometry. v Traveling route A-B iid I *eura UCuA '.,.../ : o Traveling route C-D F. Travelin3route E-F Travelin route g G-H CO d. 0.9 t e cn.... properie T 0.6. g-et more-... -h into... th 0.1 '.''...' ' ' Th eievle ditrbtin reveal 0 10 vluabl 20 30informatio Channel capacity [b/s/hz] Fig. 3. CDFs of the channel capacities in the studied traveling routes with different antenna array geometries. The eigenvalues distributions reveal valuable information about the channel properties. To get more insight into the performances of the different antenna array geometries the eigenvalues distributions in the considered traveling routes are studied. As a reference, the power gain distribution of single input single output (SISO) system, denoted as As, was calculated. The power gain distribution in the case of SISO system with Rayleigh distribution was also calculated and denoted as AR /05/$ IEEE 570

4 B. Eigenvalues distributions in LOS traveling routes Figures 4 and 5 show the impact of different antenna array geometries on the eigenvalues distributions in LOS traveling routes, C-D and G-H, respectively. It can be seen that in both routes the channel matrix has Ricean distributed elements since the distribution of As is steeper than that of AR. In terms of number of parallel channels, using the ULA results in four parallel channels with A1 >= As available 90% of the time in traveling route C-D. These parallel channels are capable of carrying high data rates to the receiver. In traveling route G-H the number of significant parallel channels reduces to two due to the low AS. The UCuA maintains only one significant channel in both routes since only one eigenvalue is larger than AS. Because the second eigenvalue in traveling route C-D is higher than that in traveling route G-H higher median capacity is obtained in traveling route C-D. The use of and URA geometries have similar impact on the eigenvalues distributions in both routes where the available significant channels in traveling routes C-D and G-H are two and one, respectively. Fig. 5. Eigenvalues distributions in traveling route G-H when different ULA 0 -t (,.T -0 v LM U RA UCuA -C / -1g.5--.1[ -2 g/ '; /i Eigenvalue [db] Fig. 4. Eigenvalues distributions in traveling route C-D when different C. Eigenvalues distributions in NLOS traveling routes The eigenvalues distributions in NLOS traveling routes, A- B and E-F, are shown in Figures 6 and 7, respectively. In these scenarios the channel matrix in both traveling routes has Rayleigh distributed elements since the distribution of As follows the distribution of AR closely. Using ULA, or URA in traveling route A-B results in four, three and three parallel channels available 90% of the time, respectively. When the UCuA is used only two significant parallel channels are available which reduces the achievable data rate significantly. Similar observations are made in traveling route E-F where there are four, three, three and two parallel channels available by using ULA,, URA and UCuA, respectively. Fig. 6. Eigenvalues distributions in traveling route A-B when different It can be noticed that the obtained results indicate that the performance of the different antenna array geometries depends on the number of array elements facing the direction of wave propagation and the distance between these elements. In the case of ULA geometry the number of elements facing the direction of wave propagation is eight with inter-element spacing 0.5A, while in the and the URA geometries the number of elements facing the direction of wave propagation are five, (half of the circle), and three, (one side of the rectangle), respectively, with real inter-element spacing < O.5A and 0.5A, respectively. For the UCuA geometry the interelement spacing is 0.5A with four elements facing the direction of wave propagation, (one side of the cube). The UCuA has two layers, upper layer and lower layer. The four elements in the upper layer and the four elements in the lower layer /05/$ IEEE 571

5 .. r /., : _, URA UCuA 0~~~~~~~~~~~~~~~~~~~ IEEE 7.ogs 16th International Symposium on Personal, Indoor and Mobile Radio Communications [7] H.M. El-Sallabi and P. Vainikainen,"Radio wave propagation in perpendicular streets of urban street grid for microcellular communications. Part I: Channel Modeling" Progress In Electromagnetic Research (PIER), vol. 40, pp , [8] T.A. Carl Johnk, Engineering Electromnagnietic Fields and Waves, John Wiley and Sons Inc., 1988, 637 p. Is [9] A.A Abouda, N.G. Tarhuni and H.M. El-Sallabi,"Model-based investigation on MIMO channel capacity in main street of urban microcells," 2 ig;..x. To appear in Proc. of IEEE Antennas and Propagation Syvnposilumn, o -10 o lo 2 Washington DC, USA, Jul. 3-8, [10] X. Li and Z. Nie,"Effect of array orientation on performance of MIMO wirelss channels," IEEE Antenna and Propagationi Letters, vol. 3, pp , [11] J.B. Andersen,"Array gain and capacity for known random channels with multiple element arrays at both ends", IEEE Jotrnal on Selected Areas in ComnJnlln., vol. 18, pp , [12] L. Zheng and D.N. Tse,"Diversity and multiplexing: A fundamental -1. -/ -10 L Eigenvalue [db] Fig. 7. Eigenvalues distributions in traveling route E-F when different antenna array geometries are used. tradeoff in multiple-antenna channels, " IEEE Tranis. Information Theomy, vol. 49, No. 5, pp , [13] K. Sulonen, P. Suvikunnas, L. Vuokko, J. Kivinen and P. Vainikainen,"Comparison of MIMO antenna configurations in picocell and microcell environments," IEEE Joatrnal on Selected Areas in commun., vol. 21, No. 5, pp , will have highly correlated signals because the radio wave propagation takes place in horizontal plane. This will reduce the number of effective antenna elements facing the wave propagation direction to about two. Therefore, distributing the antenna elements in three dimensions does not seem attractive in this propagation environment since the elevation spread is not significant. It should be noticed that in indoor propagation environment the three dimensional antenna array geometry could benefit from the ceiling and back reflected signals. VII. CONCLUSION We have shown that antenna array geometry has significant impact on the eigenvalues of MIMO channel. It is noticed that the performance of different antenna array geometries depends on the number of antenna elements facing the wave propagation direction. In outdoor microcellular environment under different propagation scenarios the ULA outperforms the other array geometries in terms of total channel capacity and number of significant parallel channels. REFERENCES [I] G.J. Foschini and M.J. Gans,"On limits of wireless communications in a fading environment when using multiple antennas," Wireless Personal Commun., vol. 6, no. 3, pp , [2] D.S. Shui, G.J. Foschini, M.J. Gans and J.M. Kahn,"Fading correlation and its effect on the capacity of multielement antenna systems," IEEE Trans. Commun., vol. 48, no. 3, pp , [3] A. Forenza and R.W. Heath Jr.,"lmpact of antenna geometry on MIMO commuincation in indoor clustred channels," in Proc. of IEEE Antennas and Propagation Sytnposium, vol. 2, pp , [4] A.A.M. Saleh and R.A. Valenzuela,"A statistical model for indoor multipath propagation," IEEE Journal on Selected Areas in Commotn., vol. 5, no. 2, pp , [5] J.B. Andersen and B.N. Getu,"The MIMO cube - a compact MIMO antenna," in Proc. of IEEE Wireless Personal Multimedia Comnmnun., vol. 1, pp , [6] H.M. El-Sallabi and P. Vainikainen,"Physical modeling of line-of-sight wideband propagation in a city street for microcellular communications," Journal of Electromagnetic Waves and Applications, vol. 14, pp , /05/$ IEEE 572