# A Novel 3D Beamforming Scheme for LTE-Advanced System

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2 ports can be written as: H (k) m = m,1,1 m,1,2 m,2,1 h(k) m,s,1 h(k) m,s,2 m,1,t h(k) m,s,t (2) where h(k) m,s,t = V i=1 ŵ s,i (3) m,s,t is the channel coefficient from the sth antenna port of the mth sector to the tth antenna port of the kth UE (we assume that each antenna port of UE has only one antenna element) ŵ s,i is the weight of the ith antenna element on the sth antenna port which affects the antenna pattern in the vertical direction Notice that in traditional passive antenna, these weights ŵ s,i are fixed, ie, they cannot be adjusted (k) h according to channel state information is the channel coefficient from the ith antenna element on the sth antenna port of the mth BS to the tth antenna port of the kth UE Fig 1 Each site is sectorized into three sectors and the arrows shows the main beam direction of each sector 1, 2 and 3 are the orders of three sectors of the cell Fig 2 Two dimensional array antenna model defined in 3GPP TR Since each antenna port contains V vertical antenna elements, the channel coefficient H (k) m composed of S antenna III THREE DIMENSIONAL BEAMFORMING ALGORITHM A Overview of Conventional Beamforming Algorithms Beamforming is a signal processing technique which applies the beamforming weights to adjust the phase and the amplitude of signals to form the beam pattern toward the desired direction The beamforming weights are applied on each antenna elements as shown in Fig 2 w s,i represents the beamforming weight of the ith element on the sth antenna port There are some methods to design beamforming weights such as eigenstruct method and null steering method [3] [4] Eigenstruct method is to consider the eigenvector with maximum eigenvalue as the beamforming weights to concentrate power to the desired direction On the other hand, null steering method is to find the steering vector which can null the interference from other sectors The concept of eigenstruct method is shown below At first we defined our channel model as (2), and we rearrange all channel coefficients in each column to form a channel vector, ie, H s =[ h s,1, h s,2,, h s,t ] T represents channel coefficient vector of sth port Therefore, we can rewrite (2) as: H = [ ] H1 H2 HS (4) To apply Eigenstruct beamforming method, we perform sigular value decomposition (SVD) on channel matrix H to find the eigenvector After performing SVD, the channel matrix H can be expressed as: H = U Σ V H (5) where U is a T T unitary matrix, Σ is a T S rectangular diagonal matrix, and V H (the conjugate transpose of V) is a S S unitary matrix T is the number of receiver antenna and S is the number of transmit antenna Then We

3 take the first right singular vector V 1 (the first column of matrix V) as our beamforming weights Thus in (1), w m (k) =V 1 Since the singular vectors of V are mutually orthogonal, ie, V 1 (V s ) H = 0, s 1 The transmit signal power can be concentrated on the largest singular value of matrix Σ Thus the UE received signal strength can be maximized However, conventional beamforming methods only consider two dimensional (2D) channel model Fig 3 shows the beam pattern comparison between 2D beamforming and 3D beamforming Fig 4 Compared with 3D beamforming case (right side), UE 1 will surfer from more leakage of power in fixed θ etilt case (left side) Fig 3 The comparision of beam pattern in 2D beamforming case and in 3D beamforming case We can observe in Fig 3 that the fixed vertical beam pattern in 2D beamforming will cause the decrease of SINR performance of UE 1 and UE 3 Therefore, 3D beamforming has been proposed to improve the performance of beamforming For tradtional passive antenna systems, the BS is configured with a fixed electrical downtilt angle θ etilt However, fixed θ etilt cannot satisfy all UEs with different elevation angles Furthemore, in nowadays, UEs may sometimes be served in the same building but in different floors With AAS, 3D beamforming weights can be designed to replace the beamforming weights of the fixed electrical downtilt angle, so that we can improve the performance of the scenarios as shown in Fig 4 We introduce two methods to find the beamforming weights for UEs in 3D channel model B 3D Beamforming Algorithm based on Direction of Arrival Since direction of arrival (DOA) information is much easier to estimate than full channel state information, DOA-based beamforming has been wildly discussed [5] The concept of DOA-based beamforming is that BS estimates the reference signals of the desired UE to find the DOA information of UE and utilize DOA information to design the corresponding beamforming weights The DOA based beamforming weights are the steering vectors contained DOA information and are defined as: w = 1 N 1 exp( j 2π λ (2 1)d cos( φ DOA )) exp( j 2π λ (N 1)d cos( φ DOA )) where N is the number of BS antennas, d is the BS antenna elements spacing and φ DOA is the estimation DOA of the UE The performance of received signals can be improved because steering vectors which contain DOA information will form beam pattern to the desired direction φ DOA In 3D channel model, the zenith angles between BS and UEs are different so that we need to estimate one more dimension of DOA to form beam pattern more precisely There are some methods [6] to estimate two dimensional DOA, ie, the estimated zenith angles θ DOA and the estimated azimuth φ DOA Due to the increase of DOA dimension, the beamforming weights should also be two dimensions We define horizontal beamforming weights as w H and vertical beamforming weights as w V The vertical beamforming weights are formed in the same way as (6) except that φ DOA is replaced by estimated zenith angle θ DOA and N is replaced by the number of vertical antenna elements N V And the horizontal beamforming weights are designed as : w H = 1 NH (6) 1 exp(j 2π λ (2 1)d sin( θ DOA ) sin( φ DOA )) exp(j 2π λ (N H 1)d sin( θ DOA ) sin( φ DOA )) where N H is the number of horizontal antenna elements and θ DOA is the estimated zenith degree Noticed that the horizontal beamforming weights take both azimuth and zenith DOA information into account After we obtain both w H and w V, we replace the fixed downtilt beamforming weights ŵ s,i in (3) with DOA based vertical beamforming weights w V, and DOA based horizontal beamforming weights w H is substituted for the precoding vector w (k) m in (1) With these (7)

4 two beamforming vectors w H and w V, we can still achieve beamforming gain in the case of 3D channel model C Proposed 3D Beamforming Algorithm based on Eigen structure method For conventional passive antenna system, the weight ŵ s,i in (3) cannot be adjusted dynamically With AAS, we now can adjust the weight according to each UE s condition In our proposed 3D beamforming algorithm, we replace fixed downtilt weight ŵ by vertical beamforming weights w v to dynamically adjust beam pattern according to every user s height and then also apply horizontatal beamforming to form beam more precisely The procedure of our proposed beamforming algorithm is as follows : Step 1: To obtain vertical beamforming weights of the sth port w V,s, we rearrange all antenna element channel coefficient into antenna port channel matrix P(k) m,s (8) and then replace H in (4) with P (k) m,s weights w V,s (P (k) m,s) H = (P (k) m,s) H w V,s = = 1,m,s,1 1,m,s,2 to find vertical beamforming 2,m,s,1 V,m,s,1 1,m,s,T V,m,s,T Step 2: We regard the vertical beamforming weights w V,s as dynamic eletrical downtilt angle of the antenna port Therefore, we combine the antenna element channel coefficient (k) of the sth antenna port into h m,s,t which represents the sth antenna port channel coefficient from the mth BS to the tth port of the kth UE, and the combination can be written as: 1,m,s,1 2,m,s,1 V,m,s,1 w V,s,1 1,m,s,2 w V,s,2 1,m,s,T w V,s,V V,m,s,T m,s,1 m,s,2 m,s,t (9) Step 3: After applying vertical beamfotrming, we have to obtain horizontal beamforming weights We rearrange the (k) channel coefficients h m,s,t which is obtained from previous steps to get the channel coefficient vector of sth port H(k) m,s = [ (k) (k) m,s,1, h m,s,2,, h m,s,t ] and then we rearrange all channel (k) vectors H m,s from all ports of BS into the complete channel matrix H (k) m (10) Then we can perform SVD on H (k) m to get the horizontal beamforming weights w H in the same way as the eigenstruct beamforming method introduced in section IIIA) (8) H (k) m = H (k) m,1 H (k) m,2 H (k) m,s T = m,1,1 m,1,2 m,1,t m,2,1 h(k) m,s,1 m,2,2 IV SIMULATION RESULTS h(k) m,s,2 m,2,t h(k) m,s,t (10) In this section, we show the performance of different beamforming algorithms in terms of post receiver signals to interference and noise ratio (SINR) The detailed system simulation parameters are defined in 3GPP TR as shown in Table 1 We assume that the sites can perfectly estimate the channel state information and DOA information of all UEs TABLE I SIMULATION CONFIGURATION PARAMETERS Parameters Values Environment 3D-UMa[8] Cellular layout 19 sites(57 sectors) Inter-site distance(isd) 500 m / 1732 m Carrier frequency 2 GHz Number of PDSCH RBs 50 Bandwidth 10MHz Channel model defined in 3GPP TR Shadowing std 7dB TX antenna port 4 TX elevation elements 4 / 10 per antenna port RX antenna port 2 RX elevation elements 1 per antenna port Antenna configuration cross-polarized Antenna spacing 05λ Maximum antenna gain 8 dbi BS TX power 46 dbm BS height 25 m UE height 3(n-1)+15, n U(1,N fl ),in meters where N fl U(4,8) UE distribution Uniform in cell UE number 10 UEs per sector UE speed 3 km/h Downtilt angle 12 (500 m) / 35 (1732 m) There are 19 hexagonal sites which is sectorized into 3 sectors with 10 UEs uniformly distributed in each sector and UEs choose which sectors to attach by geographical distance based wrapping Fig 5 shows the SINR result of ISD 500 (m) case with different number of vertical elements We compare the performance of 3 different beamforming algorithms, ie, 3D dynamic beamforming designed by Yan Li [7] (Li BF), DOA-based beamforming algorithms (DOA BF) and the proposed algorithm introduced in section II (proposed- BF) with no beamforming case (no BF) As can be seen in Fig 5, the SINR performance of our proposed beamforming is much better than DOA BF and Li BF We also show the simulation result of diffetent antenna models in Fig 6 where the vertical elements of a port are 10 instead of 4 Our propose beamforming algorithm also outperforms other beamforming

5 algorithms in 10 elements case The numerical result of ISD 500 (m) case is shown in Table 2 The average SINR improve more in 10 element case This is because more vertical antenna elements will make beam pattern more precise Fig 7 CDF of post receiver SINR of ISD 1732 (m) case with 4 antenna Fig 5 CDF of post receiver SINR of ISD 500 (m) case with 4 antenna Fig 8 CDF of post receiver SINR of ISD 1732 (m) case with 10 antenna TABLE III SIMULATION RESULT OF SINR IN THE SCENARIO OF ISD 1732(M) Fig 6 CDF of post receiver SINR of ISD 500 (m) case with 10 antenna TABLE II SIMULATION RESULT OF SINR IN THE SCENARIO OF ISD 500(M) no BF Li BF[7] 4 element(mean) db db 4 element (cell edge) db db 10 element(mean) db db 10 element(cell edge) db db DOA BF proposed BF 4 element(mean) db db 4 element (cell edge) db db 10 element(mean) db db 10 element(cell edge) db db Fig 7, Fig 8, and Table 3 show the performance of ISD 1732 (m) case Compared with ISD 500 (m) case, the SINR performance obtain less gain This is because when the radius become larger, the downtilt angle configuration become less no BF Li BF[7] 4 element(mean) db db 4 element (cell edge) db db 10 element(mean) db db 10 element(cell edge) db db DOA BF proposed BF 4 element(mean) db db 4 element (cell edge) db db 10 element(mean) db db 10 element(cell edge) db db apparent In spite of this, our proposed algorithm still obtain obvious gain in these two scenarios V CONCLUSION In this paper, we introduce a new 3D beamforming algorithm for 3D urban macro scenario in LTE-A network With our proposed beamforming algorithm, we form the beam pattern not only in azimuth angle but also in zenith angle so that the performance in 3D urban macro scenario can be improved Simulation results show that our proposed algorithm

6 obtain 20 db gain in mean SINR and 25 db gain in cell edge SINR in ISD 500 (m) case and nearly 14 db gain in mean SINR and 15 db gain in cell edge SINR in ISD 1732 (m) case We also show that increasing the number of vertical antenna elements can enhance the beamforming gain REFERENCES [1] Salo, Jari, et al MATLAB implementation of the 3GPP spatial channel model (3GPP TR 25996), on-line, 2005 Jan [2] Godara, Lal Chand Application of antenna arrays to mobile communications II Beam-forming and direction-of-arrival considerations, Proceedings of the IEEE, vol8, no8, , 1997 [3] Paulraj, Arogyaswami, and Thomas Kailath Eigenstructure methods for direction of arrival estimation in the presence of unknown noise fields, IEEE Transactions on Acoustics, Speech and Signal Processing, vol 34, no 1, 13-20, 1986 [4] Mouhamadou, Moctar, Patrick Vaudon, and Mohammed Rammal Smart antenna array patterns synthesis: Null steering and multi-user beamforming by phase control, Progress In Electromagnetics Research,vol 60, , 2006 [5] Krishnaveni, V, and T Kesavamurthy Beamforming for Direction-of- Arrival (DOA) Estimation-A Survey, International Journal of Computer Applications vol 61, no 11, 4-11, 2013 [6] Shahbazpanahi, Shahram, et al Robust adaptive beamforming for general-rank signal models, IEEE Transactions on Signal Processing, vol 51, no 9, , 2003 [7] Li, Yan, et al Dynamic Beamforming for Three-Dimensional MIMO Technique in LTE-Advanced Networks, International Journal of Antennas and Propagation, 2013 [8] 3GPP TR V200 3rd Generation Partnership Project,Technical Specification Group Radio Access Network,Study on 3D channel model for LTE (Release 12) [9] 3GPP TR V1210 Technical Specification Group Radio Access Network, Study of Radio Frequency (RF) and Electromagnetic Compatibility (EMC) requirements for Active Antenna Array System (AAS) base station (Release 12)

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