When beamforming is employed in the uplink without feedback channel, the beam pattern for the downlink can be generated using the weight used for uplink beamforming. However, this scheme may result in significantly performance degradation in the frequency division duplex (FDD) because of carrier frequency offset between the uplink and downlink. In this paper we propose a novel downlink beamforming algorithm based on least square method with some constraint points which have same gain in the up/downlink beam pattern. From the constraint points, we generate downlink weight and also propose how to choose the constraint points in order to satisfy the desired signal-to-interference power ratio. Simulation results show that the proposed method can sufficiently reduce the interference from other space division multiple access (SDMA) signals, providing interference-free spatial channel

Hwang, Sung-Soo

Lee, Ki-Yong

SNU Open Repository and Archive

2003 年度 第 16 回 信號處理合同學術大會論文集 第 16 卷 1 號  - 568 -   A novel downlink beamforming scheme  for FDD/SDMA systems  Ki-Yong Lee *, Sung-Soo Hwang **  and Yong-Hwan Lee ***School of Electrical Engineering and INMC, Seoul National University Kwanak P. O. Box 34, Seoul 151-744, Korea  * hijack20@fruit.snu.ac.kr, ** taoist@fruit.snu.ac.kr, *** ylee@snu.ac.kr Abstract: When beamforming is employed in the uplink without feedback channel, the beam pattern for the downlink can be generated using the weight used for uplink beamforming. However, this scheme may result in significantly performance degradation in the frequency division duplex (FDD) because of carrier frequency offset between the uplink and downlink. In this paper we propose a novel downlink beamforming algorithm based on least square method with some constraint points which have same gain in the up/downlink beam pattern. From the constraint points, we generate downlink weight and also propose how to choose the constraint points in order to satisfy the desired signal-to-interference power ratio. Simulation results show that the proposed method can sufficiently reduce the interference from other space division multiple access (SDMA) signals, providing interference-free spatial channel.  Keywords: FDD, SDMA, downlink beamforming  Ⅰ. Introduction   In recent, the use of SDMA systems has been proposed as an efficient way to improve the spectral efficiency to meet the capacity demand in mobile communication systems [1]. The SDMA system can support multiple users with the same radio channel in the same cell. In particular, it is often required for the downlink to provide higher transmission rates than the uplink.   Downlink beamforming is a powerful method for increasing the downlink capacity by providing the channel reuse in the same cell. In the time division duplex (TDD) system, it can be assumed that both the uplink and downlink have similar channel condition. As a result, it can be possible to use the same beam pattern for the uplink and downlink. In the frequency division duplex (FDD) system, since carrier frequency of the uplink and downlink is different, the beam pattern of the uplink and downlink should be differently determined [5-7]. If the beamforming weight used for the uplink is directly applied to the downlink, the location of the main lobe and nulls can be shifted, inducing interference to other users. When high-level modulation is employed, it can cause significant performance degradation  To solve this problem, several methods have been proposed. Although the use of a feedback channel can be considered [2], it requires a large overhead. Direction of arrival (DOA) can be computed using [3], but it may require large implementation. The null can be broaden to be robust to variation of the carrier frequency [4]. However, this approach may be effective only when the system uses many antennas. Carrier frequency calibration approach [5,6] maintains same main lobe position, and Null constraint (NC) [7] maintains the same null positions in up/downlink beam patterns. But the former don’t maintain nulls for other users while desired user maintains same main lobe regardless of carrier frequency difference, the latter also increases the complexity that is searching for all null positions.   In this paper, we provide a practical method for downlink beamforming in the FDD/SDMA systems. The beamforming weights for the downlink is generated that for the uplink. The proposed scheme is based on least square method with some constraint points which have same gain in the up/downlink beam pattern. And we also propose constraint points selecting method that guarantees signal-to-interference ration (SIR) of desired user.    This paper is organized as follows. System model is presented in Section 2. In Section 3, the proposed downlink beamforming algorithm is derived. Section 4 verifies the performance using simulation. Finally, Section 5 summaries conclusions.  II. System model   We consider a multi-input single-output (MISO) channel for each user, i.e., the base station has an N  antenna array and each mobile has a single antenna. Let  denote the an i  ,1 ,i L≤ ≤h( )N 1×  spatial channel from the base station to the mobile , where i L  is the number of mobiles [9]. We assume that the base station simultaneously communicates with L  mobiles with downlink beamforming.  The transmitted signal can be represented as   ( ),1Ld i iis t==∑x w  (1) where  is the downlink weight vector of the 1 2, , , ,[   ... ]NTd i d i d i d iw w w=wthi − mobile, ( )is t  is the transmitted data symbol of the thi − mobile and the superscript  denotes the transpose of a vector. The received signal for Tthi −  mobile can be represented as   ( ) ( ) ( )* *, , ,  1LH Hi i d i i j d j i ij ir t s t s t n i L≠= + + ≤∑w h w h ≤  (2) where  denotes zero-mean additive white Gaussian noise in2003 年度 第 16 回 信號處理合同學術大會論文集 第 16 卷 1 號   - 569 - ( ) 1* H Hd−=w A AA Bwwith variance 2σ , and the superscripts * and  denote the conjugate and conjugate transpose of a vector, respectively. The first term on the right side of (2) is the desired signal and the second term is the interference to  mobile. Thus, SIR of the  mobile can be represented as Hthi −thi −*u  (11) To reduce the computational complexity, we can  equal to KN . Then we have   (12) * 1d u−=w A Bw* 2,2,,  1Hd i ii LHd j ij ii Lγ≠=∑w hw h≤ ≤  (3) And the downlink beam pattern is represented by   ( )Hdown d dG θ= w a  (4) As an example, Fig 1 depicts downlink beam pattern according to constraint points of the derived downlink weight equation (12) when 4N = , 3L =  located at  and the carrier frequency of the uplink and downlink is 1  and , respectively. We consider two sets of constraint points,  and .  ο ο ο[50 ,10 ,- 20 ]990.5MHz2175MHzο ο ο ο[52 ,30 ,12 ,- 25 ] ο ο ο ο[60 ,20 ,- 20 ,- 60 ]where ( )d θa  is the downlink steering vector given by  ( )( )j sin j 1 sin[1 .... ]dd d2 2 NTd e eπ θ π θλ λθ× −=a d  (5) and dλ  is the downlink carrier wavelength and  is the space between the elements. Similarly, the uplink beam pattern is represented by d ( )Hus u uG θ= w a  (6) -100 -80 -60 -40 -20 0 20 40 60 80 100-60-50-40-30-20-100degreeGain (dB)uplinkproper constraint pointsimproper constraint points where ( )u θa  is the uplink steering vector   ( )( )j sin j 1 sin[1 .... ]ud d2 2 NTu e eπ θ π θλ λθ× −=a u  (7) Fig 1.  Beam pattern (according to constraint point) and uλ  is uplink carrier wavelength.   III. Proposed scheme   We consider the minimization of beam pattern difference between the uplink and downlink for all θ , while duplex array approach [8] is minimizing the steering vector difference of up/downlink and steering vector-modifying approach [10] transforms uplink steering vector into downlink steering vector. For easy of realization, we consider only  constraint points K ( ) ( ),   =1,2,...,u i d iG G iθ θ= K  (8)  As it can be seen in Fig 1, it is necessary to properly choose the constraint points to obtain the desired performance. Thus, we propose the proper constraint points selecting method following as: As Fig 2, (a) First of all, we estimate the 3dB beam width of each users. (b) And then we choose nulls that are included the estimated 3dB beam width. (c) The chosen nulls decide to constraint points, iθ . (d) The other points, which subtract number of users from , may be chosen uniformly. Here, the selected Kiθ  has a main role in guaranteeing same gain at iθ  location of up/downlink  or -100 -80 -60 -40 -20 0 20 40 60 80 100-70-60-50-40-30-20-100degreeGain (dB)3dB BWO O   ( ) ( ), =1,2,...,H Hu u i d d i   iθ θ=w a w a K  (9) This condition can be represented in a matrix form,   (10) * *d u=Aw Bwwhere ( )( )( )j sin j sinj sin j sinj sin j sin1  .... 1  .... ....1  .... 1 12 2K K2 2 N -12 2 N -12 2 N -1e ee ee eπ θ π θλ λπ θ π θλ λπ θ π θλ λ×××⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎦⎣Ad dd dd dd dd dd d12****....Nddddwww⎡ ⎤⎢ ⎥⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦w,  Fig 2. Constraint points selecting method  ( )( )( )1 12 2j sin j sinj sin j sinj sin j sin1   .... 1   .... ....1   .... K K2 2 N -12 2 N -12 2 N -1e ee ee eπ θ π θλ λπ θ π θλ λπ θ π θλ λ×××⎡ ⎤⎥⎥⎥⎥⎥⎢⎢ ⎥⎢= ⎢⎢ ⎥⎢ ⎥⎢⎢⎣ ⎦Bu uu uu ud dd dd d12****....Nuuuuwww⎡ ⎤⎢ ⎥⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦w,     We summarize the proposed downlink algorithm following as:  1) Choose the nulls that is included the 3dB beam width of each user’s main beam  2) Choose the other points uniformly  3) Insert the selected constraint points to equation (12),  and generate  dw 4) Compute gain ratio, A   where K N≥ . Thus, the optimum weight is determined by 2003 年度 第 16 回 信號處理合同學術大會論文集 第 16 卷 1 號   - 570 - If ( )( )interfencedown idown iGAGθδθ=∑ ≥ , go to step 5.   null positions are not also generated any interference, the proposed beamforming can provide the SDMA channel.  Fig 4 show the BER performance of the conventional and proposed beamforming for each user, located in 20ο− ,10ο , 50ο  when antenna elements is four, modulation use QAM. The proposed downlink beamforming outperforms conventional beamforming. Especially, in the case of user , we see the error floor at BER 64311 10−× , because user  is effected severe interference by distortion of beam pattern.  3Otherwise go to step 2. where A  is signal to interference gain ratio in iθ  location and δ  is a threshold of acceptability at base station.   5) Choose  dw Ⅳ. Numerical Results 12 14 16 18 20 22 24 26 28 301E-51E-41E-30.010.1ConventionalProposedDownlink beamforming => Antenna element : 4, 3 user,   Computer simulations are carried to verify the performance of proposed algorithm. The simulation parameters are shown in Table 1. The number of accommodated users is three. The DOA of each user is 20ο− , 10ο and 50ο . The average power of each user is equal. We assume MISO channel that the base station has four, five, and six transmitting antenna elements, while the number of receiving antenna element at mobile is one. The antenna element spacing is uλ /2 where uλ  is wavelength corresponding to an uplink carrier frequency. The modulation uses QAM. 6464QAMBERSNR per symbol No interfence user1(conventional) user1(Proposed) user2(conventional) user2(Proposed) user3(conventional) user3(Proposed)  Table 1.  Simulation parameters Access scheme SDMA DOA of user 1, power 20ο− , dB 0DOA of user 2, power 10ο , dB 0DOA of user 3, power 50ο , dB 0Modulation level 64 QAM Number of antenna  elements(at BS) 4,5,6  Uplink : Downlink Carrier freq 1990.5MHz : 2175MHz  Noise Gaussian Fig 4.  BER performance at the mobile (according to each user)   Fig 5 shows the BER performance of user 1 when the degree of freedom increases, that is, the number of antenna elements is four, five, and six ( )4,5,6N = , respectively. It also shows the same performance regardless of the number of antenna elements  12 14 16 18 20 22 24 26 28 301E-51E-41E-30.010.1ConventionalProposedDownlink beamforming => Antenna element : 4, 5, 6 , 64QAM, -20 userBERSNR per symbol  Fig 3. shows the downlink beam pattern of user 1 located at 20ο− . We denote True(uplink), conventional, and proposed using conventional and proposed method. Here, the conventional method uses uplink weights for downlink directly while the proposed method uses the beamforming algorithm proposed in this paper. In the beam pattern using conventional method, the interference of user 3 is increased more than about dB because the nulls are shifted from direction of original interference. Thus conventional beamforming can’t provide the SDMA channel that is required high SIR. With proposed method, it is not generated any interference. And as the other  25 No interference element : 4, Conventional element : 4, Proposed element : 5, Conventional element : 5, Proposed element : 6, Conventional element : 6, Proposed  Fig 5.  BER performance at the mobile       (according to antenna elements)  -100 -80 -60 -40 -20 0 20 40 60 80 100-60-50-40-30-20-100degreeGain (dB)TrueConventionalProposed Ⅴ. Conclusion  In this paper, we propose a novel downlink beamforming algorithm without performance degradation in FDD/SDMA system. The proposed method is based on putting the constraint points in up/downlink. From the constraint points, we generate the downlink weight equation also propose how to choose the Fig 3.  The proposed downlink beam pattern 2003 年度 第 16 回 信號處理合同學術大會論文集 第 16 卷 1 號   - 571 -constraint points satisfying quality of requirement to get a proper SDMA channel. The proposed method is simple and inexpensive method, which don’t need feed back information. And the results of computer simulations show that the performance of the proposed algorithm outperforms the conventional case regardless of each users and the number of antenna elements.  References  [1] Chryssomallis, M, “Smart antennas,” IEEE antenna and propagation magazine, vol. 42, pp. 129-136, June 2000 [2] D. Gerlach, A. Paulraj, “Adaptive transmitting antenna arrays with feedback,” IEEE signal processing letters, vol. 1, pp. 150-152, Oct. 1994 [3] Guanghan Xu and Hui Lui, “An effective transmission beamforming scheme for frequency-division-duplex digital wireless communication systems,” ICASSP 1995, vol. 3, pp. 1729-1732, May. 1995 [4] Er. M.H, “ Technique for antenna array pattern synthesis with controlled broad nulls,” IEE Proceeding H, vol. 135, pp. 375-380, Dec. 1988 [5] H. Taoka, S. Tanaka, T. Ihara, and M. Sawahashi, “Adatptive antenna array transmit diversity in FDD forward link for W-CDMA and broadband packet wireless access,” IEEE  wireless communications, vol. 9, pp. 34-41, Apr. 2002 [6]Ying-Chang Liang, and F. Chin, “FDD DS-CDMA downlink beamforming by modifying uplink Beamforming Weights,” VTC 2000, vol. 1, pp. 170-174, Sept. 2000 [7]Ying-Chang Liang, and F. Chin, “Two suboptimal algorithms for downlink beamforming in FDD DS-CDMA mobile radio,” IEEE journal on selected area in communications, vol. 19, pp. 1264-1275, July. 2001 [8] Gregory G. Raleigh, Suhas N. Diggavi, V.K Jones and A. Paulraj, “A Blind adaptive transmit antenna algorithm for wireless communication,” ICC1995, vol.3, pp. 1494-149 9, June. 1995 [9] Martin Schubert and Holger Boche, “ Solvability of Coupled Downlink Beamforming Problems,”  GLOBECOM 2001, vol. 1, pp. 614-618, Nov. 2001 [10] Angeliki Alexou, Ran Hong Yan, “Downlink capacity enhancement by employing SDMA in GSM,”  Sensor array and multichannel signal processing workshop. 2000,  pp. 413-417, March. 2000 [11]Gene H., Matrix Computations, The Johns Hopkins University Press, 1989     

A novel downlink beamforming scheme for FDD/SDMA systems

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A novel downlink beamforming scheme for FDD/SDMA systems

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