A Novel 3D Beamforming Scheme for LTE ... - Semantic Scholar
A Novel 3D Beamforming Scheme for LTE-Advanced System Yu-Shin Cheng1∗ , Chih-Hsuan Chen2 Wireless Communications Lab., Chunghwa Telecom Co., Ltd. No. 99, Dianyan Rd., Yangmei City, Taoyuan County 32601, Taiwan E-mail:
1∗
[email protected], 2 [email protected]
Abstract—Beamforming is a well-known signal processing technique to increase the received signal strength to a chosen direction. Recently, the three dimensional (3D) beamforming technique has gained a growing interest due to its potential to enable various strategies like user specific elevation beamforming and vertical sectorization. Compared with conventional horizontal beamforming, 3D beamforming exploits the channel’s degrees of freedom in the elevation direction with the active antenna system (AAS). Currently, 3GPP is on the study phase of this advanced MIMO technique and is working on the 3D channel model specification. In this paper, we propose a new 3D beamforming algorithm which combines conventional horizontal beamforming and elevation beamforming. Simulations are used to evaluate our proposed beamforming algorithm in urban macro environment with different inter-site distance (ISD). Index Terms—LTE-Advanced, Beamforming, 3D channel
I. I NTRODUCTION Multi-input multi-output (MIMO) is one of the most important technologies in wireless communication. Long-Term Evolution (LTE) specified by 3GPP adopts this technology to improve spectrum efficiency and throughput. LTE has defined several transmission modes (TM) for different MIMO transmission schemes. For example, TM 3 is open-loop codebookbased precoding scheme, and TM 4 is closed-loop codebookbased precoding scheme. Both of these transmission modes use PMI to choose precoding weights from codebook to apply on antenna elements. Because of the limitation of codebook size, beam pattern generated by limited precoding weights cannot be adjusted precisely to optimize the performance. Thanks to the non-codebook-based precoding scheme introduced in LTEAdvanced, the precoding weights could form more accurate beam pattern direct to the destination. This non-codebookbased precoding technology is also known as beamforming, and the precoding weights are also called beamforming weights. There are some methods to find beamforming weights [2], such as eigenstructure method which needs full channel state information to set the eigenvector of signal subspace as beamforming weights, and null-steering beamforming which needs only direction of arrival (DOA) to design beamforming weights. Since beamforming weights depend on channel state information, the channel model plays an important role in the design of beamforming weights, i.e., an accurate channel model aids the design of precise beamforming weights. Due to the appearance of more and more high rise buildings, mobile users are sometimes located at the same horizontal angle but different elevation angles. Tranditional channel models such as 3GPP spatial channel model (SCM) in [1] only describe chanCopyright IEICE - Asia-Pacific Network Operation and Management Symposium (APNOMS) 2014
nel in 2D (only horizontal angle). Recently, 3GPP introduces a new 3D channel model in TR 36.873 [8] for LTE-Advanced system. However, conventional beamforming algorithm can only be used on the 2D channel model. A new 3D beamforming algorithm which considers both elevation angle and horizontal angle has been proposed. The new 3D beamforming algorithm uses active antenna system (AAS) technology to adjust not only antenna weights of horizontal antenna ports but each antenna elements in the vertical direction. In this way, the channel’s elevation degree of freedom can be exploited. The transmit power can be more concentrated on the target UEs and the interferences to other cells can be reduced. In this paper, we propose a new 3D beamforming algorithm which jointly considers the antenna elements in horizontal and vertical directions. The performance of our proposed algorithm is verified in different scenarios. The rest of the paper is organized as follows. In section 2, we describe the system model of our simulation environment. Details of the 3D beamforming algorithm are shown in section 3. Section 4 shows the simulation results of the proposed algorithm in different scenarios and the comparision with conventional 2D beamforming. Section 5 is the conclusion. II. S YSTEM MODEL There are N sites in the cellular network. Each site is sectorized into three sectors, and each sector contains K users. The total number of sectors in the network is M(=3N). The cellular network model is depicted in Fig. 1. For the kth UE served by mth sector, the received signals can be written as :
(k) (k) (k) ym = H(k) m w m xm +
M X
K X
(i) (i) (k) H(k) (1) n w n xn + n m
n=1,n6=m i=1 (i)
where xn ∈ CS×1 is the transmit signals of the nth sector (i) to the ith UE, wn is the precoding vector of the nth sector to the ith UE. Notice that the second term of (1) is the (k ) interference from other cells and nm ∈ CS×1 is the additive white Gaussian noise. In this paper, the precoding vector will (k) be designed as beamforming weights. Hm ∈ CT×S is the channel matrix from the mth sector to the kth user , S is the number of antenna ports on BS and T is the number of antenna ports on UE. The 2D antenna array model shown in Fig. 2 is defined in 3GPP TR 37.840 [9].
ports can be written as: (k) ˜ h m,1,1 ˜(k) hm,1,2 H(k) m = .. . (k) ˜ hm,1,T ˜(k) = where h m,s,t
V X
˜(k) h m,2,1 .. . ··· ···
˜(k) h m,S,1
˜(k) h m,S,2 .. . (k) ˜ · · · hm,S,T
··· ··· .. .
(k)
w ˆ s,i · hi,m,s,t
(2)
(3)
i=1
˜(k) is the channel coefficient from the sth antenna port of h m,s,t 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). w ˆ 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 w ˆ s,i are fixed, i.e., they cannot be adjusted ˜(k) according to channel state information. h i,m,s,t 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.
III. T HREE D IMENSIONAL B EAMFORMING A LGORITHM 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. ws,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, i.e., ˜ s,1 , h ˜ s,2 , ..., h ˜ s,T ]T represents channel coefficient vector ˜ s =[h H of sth port. Therefore, we can rewrite (2) as: ˜1 H ˜2 · · · H ˜S H= H (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:
Fig. 2. Two dimensional array antenna model defined in 3GPP TR 37.840.
H = U · Σ · VH
Since each antenna port contains V vertical antenna ele(k) ments, the channel coefficient Hm composed of S antenna
(5)
where U is a T ×T unitary matrix, Σ is a T ×S rectangular diagonal matrix, and VH (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
take the first right singular vector V1 (the first column of (k) matrix V) as our beamforming weights. Thus in (1), wm =V1 . Since the singular vectors of V are mutually orthogonal, i.e., V1 · (Vs )H = 0, ∀s 6= 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 θetilt case (left side).
defined as: 1 w= √ N
1 (2 − 1)d · cos(φ˜DOA )) exp(−j 2π λ .. . 2π exp(−j (N − 1)d · cos(φ˜DOA ))
(6)
λ
B. 3D Beamforming Algorithm based on Direction of Arrival
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, i.e., 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 wH and vertical beamforming weights as wV . 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 NV . And the horizontal beamforming weights are designed as : 1 2π (2 − 1)d · sin( θ˜DOA ) · sin(φ˜DOA )) exp(j 1 λ wH = √ .. NH . 2π exp(j (NH − 1)d · sin(θ˜DOA ) · sin(φ˜DOA ))
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
where NH 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 wH and wV , we replace the fixed downtilt beamforming weights w ˆs,i in (3) with DOA based vertical beamforming weights wV , and DOA based horizontal beamforming weights wH is (k) substituted for the precoding vector wm in (1). With these
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 θetilt . However, fixed θetilt 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.
λ
(7)
two beamforming vectors wH and wV , we can still achieve beamforming gain in the case of 3D channel model.
˜ (k) H m,1 ˜ (k) H m,2 .. . (k) ˜ Hm,S
T
˜ (k) h m,1,1
˜ (k) h m,2,1
··· .. . .. .
˜ (k) h m,S,1
˜ (k) ˜ (k) ˜ (k) C. Proposed 3D Beamforming Algorithm based on Eigen (k) h h h m,2,2 m,S,2 = m,1,2 H = (10) m structure method .. .. .. . . . For conventional passive antenna system, the weight w ˆs,i ˜ (k) ˜ (k) ˜ (k) h h · · · h m,1,T m,2,T m,S,T in (3) cannot be adjusted dynamically. With AAS, we now IV. S IMULATION R ESULTS can adjust the weight according to each UE’s condition. In our proposed 3D beamforming algorithm, we replace fixed In this section, we show the performance of different downtilt weight w ˆ by vertical beamforming weights wv to dy- beamforming algorithms in terms of post receiver signals namically adjust beam pattern according to every user’s height to interference and noise ratio (SINR). The detailed system and then also apply horizontatal beamforming to form beam simulation parameters are defined in 3GPP TR 36.873 as more precisely. The procedure of our proposed beamforming shown in Table 1. We assume that the sites can perfectly algorithm is as follows : estimate the channel state information and DOA information Step. 1: To obtain vertical beamforming weights of the sth of all UEs. port wV,s , we rearrange all antenna element channel coefficient (k) (k) TABLE I hi,m,s,t into antenna port channel matrix Pm,s (8) and then S IMULATION CONFIGURATION PARAMETERS (k) replace H in (4) with Pm,s to find vertical beamforming Parameters Values weights wV,s . Environment 3D-UMa[8] (k) (k) (k) Cellular layout 19 sites(57 sectors) h1,m,s,1 h2,m,s,1 · · · hV,m,s,1 Inter-site distance(ISD) 500 m / 1732 m . . (k) .. .. Carrier frequency 2 GHz · · · h (k) H (8) Number of PDSCH RBs (Pm,s ) = 1,m,s,2 50 .. .. .. . . ··· . Bandwidth 10MHz (k) (k) Channel model defined in 3GPP TR 36.873 h1,m,s,T ··· · · · hV,m,s,T Step. 2: We regard the vertical beamforming weights wV,s as dynamic eletrical downtilt angle of the antenna port. Therefore, (k) we combine the antenna element channel coefficient hi,m,s,t ˜(k) which represents the sth of the sth antenna port into h m,s,t antenna port channel coefficient from the mth BS to the tth port of the kth UE, and the combination can be written as: (k) (k) (k) h1,m,s,1 h2,m,s,1 · · · hV,m,s,1 w V,s,1 .. .. wV,s,2 (k) . ··· . h (k) (Pm,s )H · wV,s = 1,m,s,2 .. .. .. .. . . . . ··· w (k) (k) V,s,V h ··· · · · hV,m,s,T (k) 1,m,s,T ˜ h m,s,1 ˜ (k) hm,s,2 = (9) .. . ˜ (k) h m,s,T
Step. 3: After applying vertical beamfotrming, we have to obtain horizontal beamforming weights. We rearrange the ˜(k) which is obtained from previous channel coefficients h m,s,t (k) ˜ m,s steps to get the channel coefficient vector of sth port H (k) (k) (k) ˜ ˜ ˜ = [h m,s,1 ,hm,s,2 ,...,hm,s,T ] and then we rearrange all channel (k ) ˜ m,s from all ports of BS into the complete channel vectors H (k) (k) matrix Hm (10). Then we can perform SVD on Hm to get the horizontal beamforming weights wH in the same way as the eigenstruct beamforming method introduced in section III.A)
Shadowing std TX antenna port TX elevation elements RX antenna port RX elevation elements Antenna configuration Antenna spacing Maximum antenna gain BS TX power BS height UE height
UE distribution UE number UE speed Downtilt angle
7dB 4 4 / 10 per antenna port 2 1 per antenna port cross-polarized 0.5λ 8 dBi 46 dBm 25 m 3(n-1)+1.5, n∼U(1,Nfl ),in meters where Nfl ∼U(4,8) Uniform in cell 10 UEs per sector 3 km/h 12◦ (500 m) / 3.5◦ (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, i.e., 3D dynamic beamforming designed by Yan Li [7] (Li BF), DOA-based beamforming algorithms (DOA BF) and the proposed algorithm introduced in section II (proposedBF) 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
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 elements per port
Fig. 5. CDF of post receiver SINR of ISD 500 (m) case with 4 antenna elements per port
Fig. 8. CDF of post receiver SINR of ISD 1732 (m) case with 10 antenna elements per port TABLE III S IMULATION 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 elements per port
TABLE II S IMULATION RESULT OF SINR IN THE SCENARIO OF ISD 500( M )
4 element(mean) 4 element (cell edge) 10 element(mean) 10 element(cell edge) 4 element(mean) 4 element (cell edge) 10 element(mean) 10 element(cell edge)
no BF 2.8317 dB -5.6637 dB 6.0435 dB -4.0020 dB DOA BF 6.9036 dB -3.7003 dB 16.2070 dB -0.2175 dB
Li BF[7] 3.8182 dB -4.5049 dB 10.8825 dB -2.5722 dB proposed BF 17.0083 dB 9.2625 dB 26.6644 dB 21.8808 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
4 element(mean) 4 element (cell edge) 10 element(mean) 10 element(cell edge) 4 element(mean) 4 element (cell edge) 10 element(mean) 10 element(cell edge)
no BF 2.7673 dB -4.7611 dB 3.3459 dB -4.2878 dB DOA BF 6.4643 dB -3.9186 dB 6.6245 dB -3.7566 dB
Li BF[7] 3.4576 dB -4.4544 dB 4.2521 dB -4.2346 dB proposed BF 16.9272 dB 8.3580 dB 19.9923 dB 7.2770 dB
apparent. In spite of this, our proposed algorithm still obtain obvious gain in these two scenarios. V. C ONCLUSION 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
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. R EFERENCES [1] Salo, Jari, et al. ‘‘MATLAB implementation of the 3GPP spatial channel model (3GPP TR 25.996), ” 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, vol.8, no.8, 1195-1245, 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, 95-106, 2006. [5] Krishnaveni, V., and T. Kesavamurthy. ‘‘Beamforming for Direction-ofArrival (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, 2257-2269, 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 36.873 V2.0.0 ‘‘3rd Generation Partnership Project,Technical Specification Group Radio Access Network,Study on 3D channel model for LTE (Release 12)” [9] 3GPP TR 37.840 V12.1.0 ‘‘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)”
1∗
[email protected], 2 [email protected]
Abstract—Beamforming is a well-known signal processing technique to increase the received signal strength to a chosen direction. Recently, the three dimensional (3D) beamforming technique has gained a growing interest due to its potential to enable various strategies like user specific elevation beamforming and vertical sectorization. Compared with conventional horizontal beamforming, 3D beamforming exploits the channel’s degrees of freedom in the elevation direction with the active antenna system (AAS). Currently, 3GPP is on the study phase of this advanced MIMO technique and is working on the 3D channel model specification. In this paper, we propose a new 3D beamforming algorithm which combines conventional horizontal beamforming and elevation beamforming. Simulations are used to evaluate our proposed beamforming algorithm in urban macro environment with different inter-site distance (ISD). Index Terms—LTE-Advanced, Beamforming, 3D channel
I. I NTRODUCTION Multi-input multi-output (MIMO) is one of the most important technologies in wireless communication. Long-Term Evolution (LTE) specified by 3GPP adopts this technology to improve spectrum efficiency and throughput. LTE has defined several transmission modes (TM) for different MIMO transmission schemes. For example, TM 3 is open-loop codebookbased precoding scheme, and TM 4 is closed-loop codebookbased precoding scheme. Both of these transmission modes use PMI to choose precoding weights from codebook to apply on antenna elements. Because of the limitation of codebook size, beam pattern generated by limited precoding weights cannot be adjusted precisely to optimize the performance. Thanks to the non-codebook-based precoding scheme introduced in LTEAdvanced, the precoding weights could form more accurate beam pattern direct to the destination. This non-codebookbased precoding technology is also known as beamforming, and the precoding weights are also called beamforming weights. There are some methods to find beamforming weights [2], such as eigenstructure method which needs full channel state information to set the eigenvector of signal subspace as beamforming weights, and null-steering beamforming which needs only direction of arrival (DOA) to design beamforming weights. Since beamforming weights depend on channel state information, the channel model plays an important role in the design of beamforming weights, i.e., an accurate channel model aids the design of precise beamforming weights. Due to the appearance of more and more high rise buildings, mobile users are sometimes located at the same horizontal angle but different elevation angles. Tranditional channel models such as 3GPP spatial channel model (SCM) in [1] only describe chanCopyright IEICE - Asia-Pacific Network Operation and Management Symposium (APNOMS) 2014
nel in 2D (only horizontal angle). Recently, 3GPP introduces a new 3D channel model in TR 36.873 [8] for LTE-Advanced system. However, conventional beamforming algorithm can only be used on the 2D channel model. A new 3D beamforming algorithm which considers both elevation angle and horizontal angle has been proposed. The new 3D beamforming algorithm uses active antenna system (AAS) technology to adjust not only antenna weights of horizontal antenna ports but each antenna elements in the vertical direction. In this way, the channel’s elevation degree of freedom can be exploited. The transmit power can be more concentrated on the target UEs and the interferences to other cells can be reduced. In this paper, we propose a new 3D beamforming algorithm which jointly considers the antenna elements in horizontal and vertical directions. The performance of our proposed algorithm is verified in different scenarios. The rest of the paper is organized as follows. In section 2, we describe the system model of our simulation environment. Details of the 3D beamforming algorithm are shown in section 3. Section 4 shows the simulation results of the proposed algorithm in different scenarios and the comparision with conventional 2D beamforming. Section 5 is the conclusion. II. S YSTEM MODEL There are N sites in the cellular network. Each site is sectorized into three sectors, and each sector contains K users. The total number of sectors in the network is M(=3N). The cellular network model is depicted in Fig. 1. For the kth UE served by mth sector, the received signals can be written as :
(k) (k) (k) ym = H(k) m w m xm +
M X
K X
(i) (i) (k) H(k) (1) n w n xn + n m
n=1,n6=m i=1 (i)
where xn ∈ CS×1 is the transmit signals of the nth sector (i) to the ith UE, wn is the precoding vector of the nth sector to the ith UE. Notice that the second term of (1) is the (k ) interference from other cells and nm ∈ CS×1 is the additive white Gaussian noise. In this paper, the precoding vector will (k) be designed as beamforming weights. Hm ∈ CT×S is the channel matrix from the mth sector to the kth user , S is the number of antenna ports on BS and T is the number of antenna ports on UE. The 2D antenna array model shown in Fig. 2 is defined in 3GPP TR 37.840 [9].
ports can be written as: (k) ˜ h m,1,1 ˜(k) hm,1,2 H(k) m = .. . (k) ˜ hm,1,T ˜(k) = where h m,s,t
V X
˜(k) h m,2,1 .. . ··· ···
˜(k) h m,S,1
˜(k) h m,S,2 .. . (k) ˜ · · · hm,S,T
··· ··· .. .
(k)
w ˆ s,i · hi,m,s,t
(2)
(3)
i=1
˜(k) is the channel coefficient from the sth antenna port of h m,s,t 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). w ˆ 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 w ˆ s,i are fixed, i.e., they cannot be adjusted ˜(k) according to channel state information. h i,m,s,t 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.
III. T HREE D IMENSIONAL B EAMFORMING A LGORITHM 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. ws,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, i.e., ˜ s,1 , h ˜ s,2 , ..., h ˜ s,T ]T represents channel coefficient vector ˜ s =[h H of sth port. Therefore, we can rewrite (2) as: ˜1 H ˜2 · · · H ˜S H= H (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:
Fig. 2. Two dimensional array antenna model defined in 3GPP TR 37.840.
H = U · Σ · VH
Since each antenna port contains V vertical antenna ele(k) ments, the channel coefficient Hm composed of S antenna
(5)
where U is a T ×T unitary matrix, Σ is a T ×S rectangular diagonal matrix, and VH (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
take the first right singular vector V1 (the first column of (k) matrix V) as our beamforming weights. Thus in (1), wm =V1 . Since the singular vectors of V are mutually orthogonal, i.e., V1 · (Vs )H = 0, ∀s 6= 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 θetilt case (left side).
defined as: 1 w= √ N
1 (2 − 1)d · cos(φ˜DOA )) exp(−j 2π λ .. . 2π exp(−j (N − 1)d · cos(φ˜DOA ))
(6)
λ
B. 3D Beamforming Algorithm based on Direction of Arrival
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, i.e., 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 wH and vertical beamforming weights as wV . 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 NV . And the horizontal beamforming weights are designed as : 1 2π (2 − 1)d · sin( θ˜DOA ) · sin(φ˜DOA )) exp(j 1 λ wH = √ .. NH . 2π exp(j (NH − 1)d · sin(θ˜DOA ) · sin(φ˜DOA ))
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
where NH 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 wH and wV , we replace the fixed downtilt beamforming weights w ˆs,i in (3) with DOA based vertical beamforming weights wV , and DOA based horizontal beamforming weights wH is (k) substituted for the precoding vector wm in (1). With these
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 θetilt . However, fixed θetilt 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.
λ
(7)
two beamforming vectors wH and wV , we can still achieve beamforming gain in the case of 3D channel model.
˜ (k) H m,1 ˜ (k) H m,2 .. . (k) ˜ Hm,S
T
˜ (k) h m,1,1
˜ (k) h m,2,1
··· .. . .. .
˜ (k) h m,S,1
˜ (k) ˜ (k) ˜ (k) C. Proposed 3D Beamforming Algorithm based on Eigen (k) h h h m,2,2 m,S,2 = m,1,2 H = (10) m structure method .. .. .. . . . For conventional passive antenna system, the weight w ˆs,i ˜ (k) ˜ (k) ˜ (k) h h · · · h m,1,T m,2,T m,S,T in (3) cannot be adjusted dynamically. With AAS, we now IV. S IMULATION R ESULTS can adjust the weight according to each UE’s condition. In our proposed 3D beamforming algorithm, we replace fixed In this section, we show the performance of different downtilt weight w ˆ by vertical beamforming weights wv to dy- beamforming algorithms in terms of post receiver signals namically adjust beam pattern according to every user’s height to interference and noise ratio (SINR). The detailed system and then also apply horizontatal beamforming to form beam simulation parameters are defined in 3GPP TR 36.873 as more precisely. The procedure of our proposed beamforming shown in Table 1. We assume that the sites can perfectly algorithm is as follows : estimate the channel state information and DOA information Step. 1: To obtain vertical beamforming weights of the sth of all UEs. port wV,s , we rearrange all antenna element channel coefficient (k) (k) TABLE I hi,m,s,t into antenna port channel matrix Pm,s (8) and then S IMULATION CONFIGURATION PARAMETERS (k) replace H in (4) with Pm,s to find vertical beamforming Parameters Values weights wV,s . Environment 3D-UMa[8] (k) (k) (k) Cellular layout 19 sites(57 sectors) h1,m,s,1 h2,m,s,1 · · · hV,m,s,1 Inter-site distance(ISD) 500 m / 1732 m . . (k) .. .. Carrier frequency 2 GHz · · · h (k) H (8) Number of PDSCH RBs (Pm,s ) = 1,m,s,2 50 .. .. .. . . ··· . Bandwidth 10MHz (k) (k) Channel model defined in 3GPP TR 36.873 h1,m,s,T ··· · · · hV,m,s,T Step. 2: We regard the vertical beamforming weights wV,s as dynamic eletrical downtilt angle of the antenna port. Therefore, (k) we combine the antenna element channel coefficient hi,m,s,t ˜(k) which represents the sth of the sth antenna port into h m,s,t antenna port channel coefficient from the mth BS to the tth port of the kth UE, and the combination can be written as: (k) (k) (k) h1,m,s,1 h2,m,s,1 · · · hV,m,s,1 w V,s,1 .. .. wV,s,2 (k) . ··· . h (k) (Pm,s )H · wV,s = 1,m,s,2 .. .. .. .. . . . . ··· w (k) (k) V,s,V h ··· · · · hV,m,s,T (k) 1,m,s,T ˜ h m,s,1 ˜ (k) hm,s,2 = (9) .. . ˜ (k) h m,s,T
Step. 3: After applying vertical beamfotrming, we have to obtain horizontal beamforming weights. We rearrange the ˜(k) which is obtained from previous channel coefficients h m,s,t (k) ˜ m,s steps to get the channel coefficient vector of sth port H (k) (k) (k) ˜ ˜ ˜ = [h m,s,1 ,hm,s,2 ,...,hm,s,T ] and then we rearrange all channel (k ) ˜ m,s from all ports of BS into the complete channel vectors H (k) (k) matrix Hm (10). Then we can perform SVD on Hm to get the horizontal beamforming weights wH in the same way as the eigenstruct beamforming method introduced in section III.A)
Shadowing std TX antenna port TX elevation elements RX antenna port RX elevation elements Antenna configuration Antenna spacing Maximum antenna gain BS TX power BS height UE height
UE distribution UE number UE speed Downtilt angle
7dB 4 4 / 10 per antenna port 2 1 per antenna port cross-polarized 0.5λ 8 dBi 46 dBm 25 m 3(n-1)+1.5, n∼U(1,Nfl ),in meters where Nfl ∼U(4,8) Uniform in cell 10 UEs per sector 3 km/h 12◦ (500 m) / 3.5◦ (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, i.e., 3D dynamic beamforming designed by Yan Li [7] (Li BF), DOA-based beamforming algorithms (DOA BF) and the proposed algorithm introduced in section II (proposedBF) 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
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 elements per port
Fig. 5. CDF of post receiver SINR of ISD 500 (m) case with 4 antenna elements per port
Fig. 8. CDF of post receiver SINR of ISD 1732 (m) case with 10 antenna elements per port TABLE III S IMULATION 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 elements per port
TABLE II S IMULATION RESULT OF SINR IN THE SCENARIO OF ISD 500( M )
4 element(mean) 4 element (cell edge) 10 element(mean) 10 element(cell edge) 4 element(mean) 4 element (cell edge) 10 element(mean) 10 element(cell edge)
no BF 2.8317 dB -5.6637 dB 6.0435 dB -4.0020 dB DOA BF 6.9036 dB -3.7003 dB 16.2070 dB -0.2175 dB
Li BF[7] 3.8182 dB -4.5049 dB 10.8825 dB -2.5722 dB proposed BF 17.0083 dB 9.2625 dB 26.6644 dB 21.8808 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
4 element(mean) 4 element (cell edge) 10 element(mean) 10 element(cell edge) 4 element(mean) 4 element (cell edge) 10 element(mean) 10 element(cell edge)
no BF 2.7673 dB -4.7611 dB 3.3459 dB -4.2878 dB DOA BF 6.4643 dB -3.9186 dB 6.6245 dB -3.7566 dB
Li BF[7] 3.4576 dB -4.4544 dB 4.2521 dB -4.2346 dB proposed BF 16.9272 dB 8.3580 dB 19.9923 dB 7.2770 dB
apparent. In spite of this, our proposed algorithm still obtain obvious gain in these two scenarios. V. C ONCLUSION 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
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. R EFERENCES [1] Salo, Jari, et al. ‘‘MATLAB implementation of the 3GPP spatial channel model (3GPP TR 25.996), ” 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, vol.8, no.8, 1195-1245, 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, 95-106, 2006. [5] Krishnaveni, V., and T. Kesavamurthy. ‘‘Beamforming for Direction-ofArrival (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, 2257-2269, 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 36.873 V2.0.0 ‘‘3rd Generation Partnership Project,Technical Specification Group Radio Access Network,Study on 3D channel model for LTE (Release 12)” [9] 3GPP TR 37.840 V12.1.0 ‘‘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)”
