Potential Throughput Improvement of FD MIMO in Practical Systems

Transcription

1 2014 UKSim-AMSS 8th European Modelling Symposium Potential Throughput Improvement of FD MIMO in Practical Systems Fangze Tu, Yuan Zhu, Hongwen Yang Mobile and Communications Group, Intel Corporation Beijing University of Posts and Telecommunications Abstract Installing large number of antennas at the transmitter or/and the receiver can increase the channel capacity significantly in theory, however, practical implementations need to consider different system aspects, e.g. compatibility with existing beamforming scheme and reference signal overhead, in order to realize the system level throughput gain in practice. In this paper, we first use an idealized full dimensional multiple input multiple output (FD-MIMO) system to quantize the potential system throughput gain of FD-MIMO systems. We then introduce the reference signal overhead limitation by virtualizing large number of antennas to a limited number of antenna ports. The simulation result shows that through proper antenna virtualization the system throughput gain of one idealized FD-MIMO system can be achieved within reference signal overhead limitation. Keywords FD-MIMO; antenna virtualization; I. INTRODUCTION Beamforming technology is incorporated into LTE standards since Rel.8, and it is proven to be a practical technology to increase the received strength of the signal-of-interest and reduce the inter/intra-cell interference, hence improve the overall system capacity [1]. However, in conventional system the antennas are typically equipped in one dimension array with few antennas. In order to meet the demanding of ever growing data usage, advanced MIMO technologies are highly desired for future LTE-A system. Recently, full dimensional multiple input multiple output (FD-MIMO) has been discussed in the academy and industry [2]. FD-MIMO can leverage the significantly increased freedom offered by the advanced antenna arrays with large number of antenna elements which can be adjusted individually [3]. When one planar antenna array is used, the transmitter can adjust the beam direction in elevation dimension in addition to azimuth dimension to concentrate the energy to the user of interests while minimizing the interference leakage to co-scheduled users in the same cell or users in the neighboring cells. In a traditional closed loop beamforming technology, the transmitter uses the beamforming matrix, which is designed by the receiver, to match the property of the channel matrix. When the number of transmit antenna increases, the dimension of the channel matrix also increases. The straightforward method to fully explore the increased freedom of the channel matrix is to enable the receiver to measure the full dimensional channel matrix and design the beamforming matrix correspondingly. However, this is often intractable in practical systems due to the prohibitive reference signal overhead when the number of transmit antennas are large. In order to design a closed loop FD-MIMO system with limited reference signal overhead, one feasible method is to design the large beamforming matrix as a product of two much smaller matrices. The left matrix virtualizes large amount of antennas to a limited number of antenna ports for channel state information (CSI) measurement and the right matrix further virtualizes the reduced dimension virtual channel matrix to one or more layers for data transmission. The transmission of left virtualization matrix is similar to channel state information reference signal (CSI-RS) transmission which was introduced to LTE Rel.10. One design option is to use block diagonal matrix for the left matrix to realize one electrical downtilt and existing LTE codebooks for the right matrix to beam-form in azimuth dimension [4]. Although this design option is simple for implementation, we believe other non-block diagonal structure, if well designed, will further improve the system performance. In [5], subspace tracking was proposed as a different way to design the two precoding matrices. In subspace tracking scheme, the left channel virtualization matrix is initialized and further trained over time while the right matrix is quantized using a codebook. By using multiple iterations, the left matrix would approach the subspace which covers the major directions of the intended users. In this paper, we first define the FD-MIMO baseline system which uses fixed block diagonal matrix as the left matrix. In order to quantize the performance upper bound of FD-MIMO systems, we then define one ideal system in which the full channel matrix is ideally known by the transmitter. We derive the performance upper bound based on the ideal system by using the principle eigen-beam of the full channel matrix. We then define a FD-MIMO system based on ideal subspace. In the ideal subspace system, we assume the channel covariance matrix is known by the transmitter. And the enb calculates ideal subspace by using the principal eigen-beams from the average channel covariance matrix of all active users and uses it to construct the left channel virtualization matrix. Compared with the ideal system which we use to derive the performance upper bound, the major difference in the ideal subspace system is that we introduced the limitation of number of reference /14 $ IEEE DOI /EMS

2 signal ports. In order to focus on the design of the left matrix, we use ideal sounding to feedback the right matrix. Thus the effective channel matrix for both the baseline and the ideal subspace systems are known to the transmitter. The main motivation to introduce the ideal subspace system is to verify whether the performance upper bound can be achieved in practical systems when there is limitation on number of reference signal ports. The remainder of this paper is organized as follows. Section II introduces the system model. Section III briefly reviews the 3D MIMO channel model designed by 3GPP. Section IV defines the baseline, ideal and ideal subspace system using the system model in Section II. Section V provides the simulation results using LTE-A simulation methodology. Finally, conclusions are presented in section VI. Notation: We use ( ) H to denote Hermitian transpose operation, to denote the matrix norm, det( ) to denote the determinant of a matrix, CN (0, 1) to denote zero-mean and unit-variance circulary-symmetric complex-gaussian random variable, N t to denote number of transmit antennas, N c to denote the number of transmit antenna ports, N p to denote the number of transmission layer, N r to denote the number of receive antennas, N v to denote the number of antennas in vertical domain of one planar array, N a to denote the number of antennas in azimuth domain of one planar array, h user to denote the user height in meters, n fl to denote the number of floor of user stands, N fl to denote the number of floor of one building, λ to denote the wave length, d v to denote the spacing between two consecutive vertical antenna elements, K to denote dimensional reduction factor as described in (6). II. SYSTEM MODEL We consider one generalized MIMO system. The enb is equipped with N t antennas and each user is equipped with N r receiver antennas. enb transmits N p layer data symbols. The system model is given by: y = ρhpx + n (1) where y is N r 1 receive signal, ρ is per data symbol signal to noise ratio (SNR), H is N r N t channel, P is N t N p precoding matrix, x is N p 1 transmit data symbol vector, n is N r 1 additive white Gaussian noise (AWGN), whose entries are independently and identically distributed i.i.d. CN (0, 1). In FD-MIMO systems, N t is usually much larger than that of the conventional MIMO systems. For example, one planar antenna array may have 40 antenna elements. For single user transmission, the channel capacity is: where I Nr C = log 2 det(i Nr + ρ N t HH H ) (2) is N r N r identity matrix. III. 3D MIMO CHANNEL In MIMO communication, the system performance is highly related to the propagation channel. Therefore, the channel modelling is vital to MIMO related studies. Although radio electromagnetic wave is 3D in nature, the elevation angles are absent for simplicity in 2D SCM [6]. In order to study FD-MIMO systems, the elevation dimension is added to the propagation model. 3D channel model was first presented in the WINNER2 project [7] and 3GPP further studied the 3D channel model in TR [8]. Other than introducing elevation angles, user distribution is also not always on the ground in 3D MIMO channel model. The user distribution on the vertical dimension can better model the traffic in the real world. The indoor user distribution in elevation domain is modelled as (3), assuming indoor users are evenly distributed in low rise buildings in the elevation dimension: h user = 3(n fl 1) (3) where n fl is uniformly distributed from 1 to N fl, N fl is uniformly distributed from 4 to 8. The main difference between the azimuth and elevation dimension in 3D-MIMO channel is that the angle spread of the elevation dimension is much narrower than in the azimuth dimension due to lack of scatters. Other than the angle spread, the distribution of the line-of-sight angle is also much narrower in the elevation dimension than azimuth dimension due to the low building height considered in the model. IV. FD-MIMO BEAMFORMING SCHEMES This section discusses the FD-MIMO beamforming schemes including the baseline, ideal system and ideal subspace system. We first present a general FD-MIMO beamforming scheme in the subsection A. Then we give the baseline and ideal FD-MIMO beamforming scheme in subsection B. At last, the ideal subspace beamforming scheme is given in subsection C. A. General FD-MIMO Beamfoming Scheme In conventional LTE-A system, one reference signal is transmitted for one antenna port in order to enable the user to measure the CSI of that antenna port. If we use one reference signal for one antenna in FD-MIMO systems, the overall reference signal overhead can be prohibitive. Thus one feasible way is to virtualize the total number of N t antennas to a limited number of N c antenna ports and user measures CSI from N c antenna ports. This can be represented as: y = HP c P d + n = ĤP d + n (4) where P c is N t N c matrix and P H c P c is identity matrix, P d is N c N p matrix, and Ĥ = HP c is the effective 421

3 channel matrix with dimension of N r N c. While P c can be cell-specific, P d is usually user-specific. Other symbols have same meanings as in (1). After the antenna to antenna port mapping, the channel capacity is: C = logdet(i Nr + ρ N c ĤĤH ) = logdet(i Nr + ρ N c HP c (HP c ) H ) system performance is 102 degree. Thus P c can be written as equation (7): P c = W(θ) W(θ) (7) logdet(i Nr + ρ N t HH H ) Virtualizing the large number of antennas to a limited number of antenna ports will affect the channel capacity to some extent. If the P c is not well designed to match the channel property, the channel capacity will be highly reduced no matter how P d is designed. In a practical system, it means that the formed beamforming directions cannot cover all the users of interests. Otherwise, the system capacity can be mostly achieved. If we define dimensional reduction factor as equation (6), K antennas are mapped to one antenna port on average. (5) K = N t N c (6) If we assume that P c is cell-specific, reference signal overhead can be reduced to the maximum. The ideal system can then be viewed as a special case of the ideal subspace system with K equals to one. It is then of interests how large K can practically be if the users are realistically distributed in three-dimensional space for a given number of N t transmit antennas. In practical network, it is often observed that the traffic distribution over geographical area has strong correlation, because the traffic can come from the same building or even the same floor and still served by one macro cell. Thus it is not uncommon that several users share similar eigen-beam directions. This physical phenomenon can be explored to reduce reference signal overhead and simplify the overall system design. B. Baseline and Ideal Beamforming Schemes In this section, we define the baseline and ideal systems of FD-MIMO. In the baseline FD-MIMO system, we design P c as block-diagonal matrix which realized one single electrical downtilt using DFT vector. Each column of N v antenna elements are mapped to one port to realize one electrical downtilt, so the dimensional reduction factor K equals N v in the baseline system. We assume that all cells apply the same electrical downtilt. We choose the downtilt to minimize interference to the neighbor cells from 90 degrees zenith angle which points to horizon. When number of antenna elements is 10 and DFT vectors are used to virtualize each column of vertical antenna elements, the best cell common downtilt to maximize the overall where W(θ) = [w 1 (θ), w 2 (θ),..., w Nv (θ)] T, w m (θ) = 1 Nv e j 2π λ dv(m 1)cos(θ), m = (1, 2,..., N v ). We use this system to derive the baseline performance of FD-MIMO. In the ideal system, which is used to derive the performance upper bound, the precoding matrix P of each user is derived from the single value decomposition of each user s uplink sounding channel matrix H s. H sh Hs H s = U(s) (s)v(s)h (8) where V(s) = [v(s),, v Ntx (s)],and v i (s)(1 i N tx ) is the i th eigen beam of user s with size N t 1, (s) is N t N t diagonal matrix of eigenvalues. enb would use v 1 (s) as the optimal rank one precoder for user s. Note that in ideal system, each antenna is mapped to one antenna port, therefore the dimensional reduction factor K equals to one. C. Ideal Subspace Beamforming Scheme As described in subsection IV.A, the precoding matrix P can be represented by the product of P c and P d in order to save reference signal overhead and simplify the system design. In this subsection, we propose a beamforming method based on ideal subspace for FD-MIMO, assuming the channel covariance matrix is ideally known by the transmitter. The proposed beamforming method is described as follows, Step 1: enb estimates each user s UL channel H s from UL sounding; Step 2: enb calculates the average channel covariance matrix R ave : R ave = 1 S H sh Hs (9) S s=1 where S denotes total number of users in one cell. Step 3: enb constructs the matrix P c which is formed by the N c largest principal eigen beams from the average channel covariance matrix R ave. R ave = U V H (10) where is N t N t diagonal matrix of eigenvalues λ 1, λ 2, λ 3... λ Nt, V = [v 1, v 2, v Nt ] and v i (s)(1 i N tx ) is the i th eigen beam of user s with size N t 1. Suppose that λ 1 λ 2 λ 3 λ Nc λ Nt, P c can be designed as: P c = [v 1, v 2, v Nc ] (11) 422

4 We assume the ideal effective channel HP c is known to the transmitter thus the performance of the idealized subspace system is solely dependent on the design of P c. This avoids introducing quantization errors to the design of P d and simplifies the comparison of the systems in this paper. The eigenvalues tend to be equal, if the spatial property of users channel matrices H s is of little correlation. In order to maintain the overall system performance, we still need to do the beamforming in the full dimensional space as the ideal beamforming scheme. But in real networks, the spatial properties of users of the same cell, especially the vertical component of the channel, can be correlated. The spatially correlated eigen beams are enhanced more than those isolated eigen beams. This could result in unbalanced eigenvalues of the average channel covariance matrix. Compared with the 3D beamforming which employs block diagonal matrix for P c, the subspace based design of P c employs a nonblock diagonal structure. Note that, P c can create narrow 3D beams and point those beams to all the active users within one enb s coverage. V. SIMULATION RESULTS In this section, we compare the performances of the baseline, ideal system and the ideal subspace system performance in LTE-A system. The system level simulation is operated using the 3GPP LTE-A evaluation methodologies, and the 3D channel model in TR [8].The main simulation parameters are given in Table I. We compare the system performance using a greedy multi-user MIMO scheduler. The scheduler keeps pairing more users until the proportional fairness metrics for one sub-band does not increase. The Table II [9] shows the performance of the baseline and ideal system performance of FD-MIMO. The potential system throughput gain in FD-MIMO system is significant for both 3D-UMa and 3D-UMi environments. Note that the potential performance gain is relatively higher in 3D-UMi than 3D-UMa due to that the distribution of the vertical lineof-sight angle is larger in 3D-UMi environments. Then we discuss how the dimensional reduction factor K and system design affect the overall performance of FD-MIMO. Figures 1 and 2 illustrate the FD-MIMO performance of the baseline, ideal and ideal subspace system in 3D-UMa and 3D-UMi scenarios respectively. The 40 ports case means that enb has N t = 40 antenna ports to transmit thus there is no dimensional reduction, which is the ideal system performance of FD-MIMO as mentioned in subsection IV.B. The baseline system, as mentioned in Section IV.B, maps N v = 10 antennas to one antenna port, thus the dimensional reduction factor K equals 10. When number of antenna ports equals 4 or 8, it is for ideal subspace system as mentioned in Section IV.C. It can be seen that when the number of antenna ports equals to 8 and the dimensional reduction factor K is 5, the ideal Parameters Scenarios enb antenna configuration user antenna configurations Channel acknowledge at enb Duplex Network sync TABLE I SIMULATION PARAMETERS Values 3D-UMa,3D-UMi N v = 10, N a = 4, X-pol(+/45),0.5λ H/V 2R x X-pol(0/+90) Ideal sounding feedback FDD Synchronized user per cell 10 user speed user dropping user antenna pattern Traffic model Scheduler Receiver Hybrid ARQ 3 kmph three dimensional Isotropic antenna gain pattern Full-buffer PF Ideal channel estimation Ideal interference modeling MMSE-IRC receiver Maximum 4 transmissions TABLE II BASELINE AND UPPER BOUND PERFORMANCE OF FD-MIMO Cell-edge(bps/Hz) Cell Avg(bps/Hz) 3D-UMa Baseline 0.045(100%) 1.84(100%) 3D-UMa Ideal 0.062(139%) 2.75(149%) 3D-UMi Baseline 0.039(100%) 1.75(100%) 3D-UMa Ideal 0.082(158%) 3.92(224%) subspace system performance approaches the ideal system performance. If the dimensional reduction factor is too large in one cell such as K equals 10 and the number of antenna ports is 4, the overall system performance is jeopardized due to that some UEs may fall out of the subspace. Thus we observe that the number of virtualization antenna ports N c should approach the number of active users in one cell while overall performance as approaches that of the ideal system. Also it is possible to achieve the performance of ideal systems with limited number of antenna ports. VI. CONCLUSION In this paper, we have discussed different beamforming method in the FD-MIMO system. A proposed beamforming method based on ideal subspace is presented to analyze the design of antenna port virtualization matrix and the overall system performance. From the simulation results, we observed that if FD-MIMO system is properly implemented, the ideal system performance can be achieved with limited number of reference signal antenna ports. REFERENCES [1] Q. Li, G. Li, W. Lee, M. il Lee, D. Mazzarese, B. Clerckx, & Z. Li, MIMO techniques in WiMAX and LTE: a feature overview, IEEE Communications Magazine, vol. 48, no. 5, pp , May

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