Separate Horizontal & Vertical Codebook Based 3D MIMO Beamforming Scheme in LTE-A Networks Yuan Yuan, Ying Wang, Weidong Zhang, Fei Peng Wireless Technology Innovation Institute, Key Laboratory of Universal Wireless Communication, Ministry of Education Beijing University of Posts and Telecommunications, Beijing 100876, P.R. China Email:
[email protected]
Abstract—Traditional two-dimensional (2D) multi-input multioutput (MIMO) beamforming technologies can only adjust the beamformers in the horizontal dimension according to horizontal channel information. However, due to the three-dimensional (3D) character of the real channel, 2D MIMO beamforming technologies can not achieve the optimal system throughput. In this paper, a 3D MIMO beamforming scheme is proposed, which takes into account vertical beamforming. In the proposed scheme, we first design a codebook for Vertical dimension based on 3D MIMO channel model; then a 3D MIMO beamforming scheme is proposed combining the proposed vertical beamforming codebook and legacy horizontal dimension beamforming codebook. Through simulation, we evaluate the proposed 3D MIMO beamforming scheme and compare it with former 2D beamforming technology. Owing to the additional spatial degrees of freedom in vertical dimension, our 3D MIMO beamforming scheme can effectively improve the overall system performance.
I. I NTRODUCTION wireless communication systems are expected to provide high data rates and a better quality of wireless signals satisfying demanding multimedia services such as video and teleconferencing. The so-called MIMO (multi-input multi-output) systems, in which multiple antennas are used at both transmitter and receiver, have been proposed to achieve these rates due to an improvement in spectrum efficiency [1]. Traditional MIMO systems are based on 2D MIMO spatial channel models in the sense that the double directivities of each path/subpath are expressed only in the XY-plane. Recently, 3D MIMO has attracted substantial research attention as an important technique to improve vertical coverage and overall system capacity [2] [3], in which the propagating waves are assumed to arrive not only from the azimuth plane but also the elevation plane. The 3D MIMO channel model is presented in [4] [5]. However, existing 2D MIMO beamforming technologies can only be made according to horizontal dimension channel information [6] [7] [8]. But in fact the real channel is 3D characterized, so the 2D MIMO beamforming technologies cannot achieve the optimal system throughput without considering vertical dimension channel information. In order to evaluate the potential for 3D MIMO system, it is of practical interest and importance to investigate 3D MIMO beamforming schemes, which takes into account vertical dimension channel information in 3D space. However, there is few papers discuss about it until now.
F
UTURE
In this paper, we propose a 3D MIMO beamforming scheme. First, a DFT-based beamforming codebook is designed for Vertical dimension, which is similar to the legacy 2D MIMO DFT-based codebook design. Further, we decide codebook size according to the elevation angle distribution in the vertical direction and simulation results. Then the 3D MIMO beamforming scheme is proposed, in which 3D MIMO channel are decomposed into a couple of 2D MIMO channel for consideration. Although it is a suboptimal spatial pattern, legacy codebook design criterion and feedback mechanism defined in Long Term Evolution Advanced (LTE-A) Release 10/11 can be reused. In this case, a couple of PMI (HorizontalPMI and Vertical-PMI) needs to be feedback to measure a 3D channel model. We make 3D MIMO beamforming by combining horizontal and vertical dimension beamforming according to the PMIs. Finally, performances of our proposed 3D MIMO beamforming scheme and traditional 2D MIMO beamforming are compared, and the results are analysed. The rest of this paper is organized as follows. Section II presents the 3D MIMO channel model. Section III describes the DFT-based beamforming codebook design for Vertical dimension and presents the 3D MIMO beamforming schemes. Section IV makes comparison of average cell spectral efficiency with different vertical beamforming codebook size N and decide the optimum codebook size. Simulation results of proposed 3D MIMO beamforming scheme are also presented and compared with traditional 2D MIMO beamforming scheme in this section. Finally, conclusions are drawn in Section V. II. S YSTEM M ODEL This section presents a 2D MIMO spatial channel model (SCM) in [9] and the 3D MIMO channel model, respectively. A. 2D Simplified SCM Model A simplified sketch of the SCM model is given in Fig.1. It does not consider the elevation spectrum; therefore, it is defined for the 2D case. The SCM considers N clusters of scatters and each simulation, or drop, varies the cluster statistics and array orientations. A cluster corresponds to a separate path and within the path, there are M unresolvable subpaths ( M equals 20 for SCM). For an S element linear BS array and a U element linear MS array, the 2D channel coefficients for one of N multipath components are given by a U -by-S matrix of complex
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hu,s,n (t) =
⎛ M Pn σSF ⎜ ⎜ ⎜ M m=1 ⎝
h3D u,s,n (t)
=
Pn σSF M
(v)
χBS (θn,m,AoD ) (h) χBS (θn,m,AoD )
T
√
(v,v)
exp(jΦn,m ) √ (h,v) rn2 exp(jΦn,m )
(v,h)
rn1 exp(jΦn,m ) (h,h) exp(jΦn,m )
(v)
χM S (θn,m,AoA ) (h) χM S (θn,m,AoA )
× exp(j2πλ0 −1 ds sin(θn,m,AoD )) × exp(j2πλ0 −1 du sin(θn,m,AoA )) × exp(j2πvn,m t)
⎤ ⎞ ⎛ T ⎡ (v,v) (v,h) −1 (v) exp jΦ k exp jΦ n,m n,m n,m F (φ , θ ) BS,s n,m n,m ⎜ ⎦ ⎟ ⎣ (h) ⎜ ⎟ (h,v) (h,h) −1 FBS,s (φn,m , θn,m ) ⎜ ⎟ kn,m exp jΦn,m exp jΦn,m ⎜ ⎟ M ⎜ ⎟ ⎜ ⎟ ⎜ ⎟. (v) FM S,u (ϕn,m , Ψn,m ) ⎜ ⎟ m=1 ⎜ × ⎟ (h) ⎜ ⎟ FM S,u (ϕn,m , Ψn,m ) ⎜ ⎟ ⎝ ⎠ −1 ¯ −1 ¯ × exp j2πλ0 r¯s Φn,m × exp j2πλ0 r¯u Ψn,m × exp (j2πvn,m t)
⎞ ⎟ ⎟ ⎟. ⎠ (1)
(2)
amplitudes. We denote the 2D channel matrix for the nth multipath component (n = 1, · · · , N ) as H2D n (t). The (u, s)th component (u = 1, · · · , U ; s = 1, · · · , S) of H2D n (t) denoted (t), can be written as (1), with the 2D superscript as h2D u,s,n indicating wave propagation in two dimensions, θn,m,AoD and θn,m,AoA denote the azimuth angle of departure (AAoD) and elevation angle of departure (EAoD) for the mth subpath of the nth path in 2D MIMO channel model, respectively.
Fig. 2.
Fig. 1.
Simplified SCM model for 2-D case
[9]
B. 3D SCM Model In 3D channel modeling, the departure and arrival angles have to be modeled using not only the azimuth angle in XYplane, but also the elevation angle with respect to the Z axis [2], [10], [11]. A spherical coordinate system for 3D channel model is shown in Fig.2. In this case, the 2D channel modeling expressed in (1) can be straightforwardly extended to the 3D case, as shown in (2). (v) (h) Where FBS,s (φn,m , θn,m ) and FBS,s (φn,m , θn,m ) are complex field patterns of the sth transmit antenna at BS for V polarization and H polarization,respectively; the symbols φn,m and θn,m denote the azimuth angle of departure (AAoD) and elevation angle of departure (EAoD) for the mth subpath of the nth path, respectively; r¯s = [xs , ys , zs ] is the vector denoting the position of the sth transmit antenna at BS in
(v)
Spherical coordinate system for 3-D model
[2]
(h)
3D space; FM S,u (ϕn,m , Ψn,m ) and FM S,u (ϕn,m , Ψn,m ) are complex field patterns of the uth receive antenna at UE for V polarization and H polarization,respectively; the symbols ϕn,m and Ψn,m denote the azimuth angle of arrival (AAoA) and elevation angle of arrival (EAoA) for the mth subpath of the nth path, respectively; r¯u is the vector denoting the position of ¯ n,m and Ψ ¯ n,m the uth transmit antenna at UE in 3D space; Φ are the unit vectors denoting the 3D direction of departure wave and arrival wave for the mth subpath of the nth path, respectively; vn,m denote the doppler frequency shift, which is obtained by the azimuth angle of arrival Ψn,m , the elevation angle of arrival ϕn,m and the angle of the MS velocity vector θv . III. 3D MIMO B EAMFORMING S CHEME A 3D MIMO beamforming scheme is proposed in this section. First, a DFT-based beamforming codebook is designed for Vertical dimension beamforming; then 3D MIMO
beamforming is made by combining horizontal dimension beamforming and Vertical dimension beamforming in some way. A. Vertical Beamforming Codebook Design To measure a 3D channel model accurately, we need to feedback a couple of 2D PMIs for horizontal dimension and vertical dimension. Existing codebook is designed for 2D MIMO horizontal dimension, so a codebook must be designed for vertical dimension beamforming. Independent codebook designs for horizontal and vertical dimensions can be supported by a dimension flag indicated in the CSI-RS configuration signaling. The DFT-based beamforming weight-vector codebook is considered as an effective design for spatially correlated channels. The LTE standard favours the Discrete Fourier Transform (DFT) based codebook proposed in [12] [13] for its simplicity, whose beamforming weight-vector codewords are actually permuted columns of a DFT matrix. Therefore we propose to adopt the DFT-based beamforming codebook for vertical dimension codebook design as well. The DFT-based codebook is constructed as follows, which is defined in [14]: g , Pg (m, n) = √1M exp j 2π Mm n+ G
The comparision of horizontal and vertical codebook in 3D MIMO channel is presented in Table I. TABLE I HORIZONTAL/VERTICAL CODEBOOK COMPARISION Horizontal Codebook
Vertical Codebook
Codebook
DFT-based codebook
DFT-based codebook
Spread Angles
0◦
0◦ − 180◦
Codebook Size N
N = 16
N =8
Feedback overhead
4 bits
3 bits
−
360◦
B. 3D MIMO Beamforming Scheme
A 3D MIMO beamforming scheme is proposed, in which 3D MIMO channel are decomposed into a couple of 2D MIMO channels for consideration. Although it is a suboptimal spatial pattern, legacy codebook design criterion and feedback mechanism defined in LTE-A Release 10/11 can be reused. Step 1:Independent horizontal and vertical 2D MIMO CSI measurements are made to feedback a couple of PMIs to measure a 3D channel model. The independent 2D MIMO horizontal channel matrix for the nth multipath component (n = 1, · · · , N ) is defined 2D m = 0, 1, · · · M − 1; n = 0, 1, · · · M − 1; g = 0, 1, · · · G − 1. as Hn (t) in section II. The (u, s)th component (s = 2D (3) 1, · · · , S; u = 1, · · · , U ) of H2D n (t) is given by hu,s,n (t), where Pg (m, n) is the gth DFT precoding matrix, every which is presented in formula (1). The horizontal 2D PMI can be selected from legacy codecolumn of a DFT matrix corresponds to the beamforming weight-vector of antenna, M denotes the number of transmit book according to the 2D horizontal channel coefficient matrix antennas and G denotes the number of DFT precoding matrix, given above and feedback to BS. Similar to formula (1), we can denote the independent 2D which decide the codebook size N . For the codebook with G precoding matrix and M vector in each matrix, the codebook MIMO vertical channel matrix for the nth multipath comsize will be G × M , e.g. when the number of transmit antennas ponent (n = 1, · · · , N ) as HVn (t). The (u, s)th component (u = 1, · · · , U ; s = 1, · · · , S) of HVn (t) is given by M =4, G=2, then the codebook size N = 2 × 4 = 8. As mentioned above, in a DFT-based beamforming codehVu,s,n (t) T book, every column of a DFT matrix corresponds to the beam (v) M χ (ϕ ) n,m,AoD forming weight-vector of antenna. When the channels are high σSF BS = PnM (h) spatially correlated, every column codebook can corresponds χBS (ϕn,m,AoD ) m=1 to an beamformed angle. The larger the codebook, the more √ (v,v) (v,h) and finer corresponding angles. However, we need to feedback exp(jΦn,m ) rn1 exp(jΦn,m ) × √ more bits with lager codebook which leads more system (h,v) (h,h) rn2 exp(jΦn,m ) exp(jΦn,m ) overhead. Hence we should make the best selection of the codebook size N for vertical dimension considering tradeoff (v) χ (ϕ ) n,m,AoA between beamforming accuracy and feedback overhead. MS × (h) In fact, different from horizontal dimension, angles spread in χM S (ϕn,m,AoA ) vertical dimension is much smaller. More specifically, in UMi Scenario, users spread over 0◦ − 360◦ in horizontal dimension × exp(jkds sin(ϕn,m,AoD )) × exp(jkdu sin(ϕn,m,AoA )) but only 0◦ − 180◦ in vertical dimension. With the change of cell radius and antenna height, the range in vertical dimension × exp(j2πvn,m t). (4) may even be less. For this reason, there is no need to feedback the same bits for vertical dimension as horizontal dimension. ϕn,m,AoD and ϕn,m,AoA denote the elevation angle of deparSimulation results with different codebook size N will be ture (EAoD) and elevationh angle of arrival (EAoA). given in Section IV, which decides the optimum codebook The vertical 2D PMI can also be selected from the codebook size N for vertical dimension should be equal to 8 in UMi which is proposed in this paper according to the 2D vertical scenario. channel coefficient matrix given above and feedback to BS.
Step 2:Using the independent horizontal and vertical 2D MIMO PMIs reported from MS, 3D MIMO beamforming is made by combining two independent precoding matrices represented by the horizontal & vertical PMI. In this paper, we assume that the base station is equipped with 4 transmit antennas and the MT with 4 receive antennas, hence we can transmit four data streams at most. In a horizontal 2D MIMO system, we assume that transmitter only transmits two streams, which are mapped to four antennas through a 4 × 2 horizontal precoding matrix. The input-output relationship can be expressed as: 4×2 2×1 +n y4×1 = H4×4 2D W2D x x 1 4×4 4×2 = H2D W2D + n, x2
H4×4 2D
(5) 4×2 W2D
is the 2D MIMO channel matrix and is where the horizontal MIMO precoding matrix. Whereas in 3D MIMO system, owing to the additional spatial degrees of freedom in Vertical dimension, we can transmit more data streams which can be mapped to antennas by Vertical precoding matrix as well. Then we can assume that transmitter can transmit four streams in a 3D MIMO system, two more streams than in horizontal 2D MIMO system. Using the proposed 3D MIMO precoding matrix which is composited of horizontal precoding matrix and vertical precoding matrix, the input-output relationship can be expressed as 4×2 WV4×2 x4×1 + n y4×1 = H4×4 3D WH ⎤ ⎡ x1 4×2 ⎢ x2 ⎥ ⎥ WV4×2 ⎢ = H4×4 3D WH ⎣ x3 ⎦ + n x4 x1 x3 4×4 4×2 4×2 = H3D WH + WH + n, x2 x4 (6)
TABLE II SIMULATION PARAMETERS Parameters
Assumption
Network layout
19 sites, 3 sectors per site
Traffic Model
Full Buffer
ISD
500m
Load
10 UE per sector
Carrier frequency
2.0GHz
Bandwidth
10MHz
Channel model
ITU, Umi, 2D and 3D channel
UE speed
3 km/h
Antenna configuration
Tx: Nt = 4, ULA with 0.5λ spaced
Scheduler
Proportional Fair
UE Receiver
MMSE
Rx: Nr = 4
Fig. 3.
Average cell spectral efficiency for different vertical codebook size
Fig. 4.
CDF curves of spectral efficiency for 3D/2D beamforming schemes
where H4×4 3D is the 3D MIMO channel matrix which we de4×2 is the horizontal MIMO precoding scribed in section II. WH 4×2 matrix and WV is the vertical MIMO precoding matrix. IV. S IMULATION R ESULTS This section presents simulation results with different vertical beamforming codebook size to decide optimum codebook size of vertical beamforming codebook and evaluates the performance of the proposed 3D MIMO beamforming scheme presented in Section III. The system performance is evaluated by means of systemlevel simulations using 3GPP LTE-Advanced evaluation methodologies [15]. We mainly consider the typical deployment scenarios UMi. Table II gives the main system level simulation parameter configuration. Fig.3 make comparision of cell throughout with different vertical beamformer codebook size. We can see that the codebook size N increases from 4 to 8, the performance is improved, however, when larger codebook size 16 is used, The performance is similar to the performance with codebook size
8. Therefore, the codebook size 8 should be the best selection for vertical beamformer codebook with considering tradeoff between performance and feedback overhead. Fig.4 compares the performance of our 3D MIMO beam-
V. C ONCLUSION In this work, we have investigated the 3D MIMO beamforming problem. A DFT-based beamforming codebook is designed for vertical dimension and vertical codebook size is decided according to the elevation angle distribution in the vertical direction and simulation results. In particular, a 3D MIMO beamforming scheme is proposed to improve the overall system capacity. By considering the additional spatial degrees of freedom in Vertical dimension, we can transmit more data streams at BS. Numerical results showed that our proposed 3D MIMO beamforming scheme can reasonably improve the overall system capacity performance compared with conventional 2D MIMO beamforming. ACKNOWLEDGEMENT Fig. 5.
Cell-average spectral efficiency for 3D/2D beamforming schemes
This research is supported by National Key Project (2013ZX03003009), National Nature Science Foundation of China (NSF61121001), PCSIRT (No.IRT1049) R EFERENCES
Fig. 6.
Cell-edge spectral efficiency for 3D/2D beamforming schemes
forming scheme and traditional 2D MIMO codebook-based beamforming. We can see that the gain achieved by our 3D MIMO beamforming scheme can be as large as 3-4dB compared with traditional 2D MIMO beamforming. This confirms the effectiveness of the 3D MIMO beamforming scheme. This is because our 3D MIMO beamforming scheme can distinguish data streams in both horizontal dimension and vertical dimension, but traditional 2D MIMO beamforming can only distinguish data streams in horizontal dimension. So we can transmit more data streams by using proposed 3D MIMO beamforming scheme without introducing severe interference. Therefore our 3D MIMO beamforming scheme has a better performance than traditional 2D MIMO beamforming. Fig.5 and Fig.6 shows the cell-average spectral efficiency and cell-edge spectral efficiency of our 3D MIMO beamforming scheme and traditional 2D MIMO beamforming scheme in UMi scenario. We can observe that, 2D MIMO can already meet all the ITU requirement, but the proposed 3D MIMO beamforming scheme further improves the performance. The performance gain can be 13%.
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