Codebook Design for LTE-A Downlink System

Codebook Design for LTE-A Downlink System Lu Wu, Jinhui Chen, Hongwei Yang and Di Lu Research & Innovation Center, Alcatel-Lucent Shanghai Bell, Shanghai, China Email: {lu.wu, jinhui.chen, hongwei.yang, di.a.lv}@alcatel-sbell.com.cn Abstract—Multiple-input multiple-output (MIMO) has been adopted by long term evolution (LTE) and its updated version LTE-Advanced (LTE-A) to increase the spectrum efficiency. However, the benefits of multi-user (MU) MIMO highly rely on the accurate channel knowledge at the transmitter. So proper codebook design is a key problem for LTE-A FDD downlink system. In this paper, a codebook design with phase adjustment in the precoder targeting wideband channel properties is proposed. The average cell spectrum efficiency and cell-edge user spectrum efficiency of the proposed scheme are evaluated through system level simulation and compared to the discrete Fourier transform (DFT) based feedback scheme. The results show that the proposed codebooks significantly improve feedback efficiency and system performance for co-polarized linear antenna array.

I. I NTRODUCTION Multiple-input multiple-output (MIMO) spatial multiplexing is recognized to be capable of dramatically increasing the spectrum efficiency of wireless communication [1] and has been adopted by the 3rd Generation Partnership Project (3GPP) long term evolution (LTE) and its updated version LTE-Advanced (LTE-A) as one of the key techniques. High data rates (326 Mbps for LTE [2], 1 Gbps for LTE-A [3][4]) and high spectrum efficiency are some of the requirements for these standards. These ambitious targets can be achieved only by the usage of advanced MIMO techniques. It is well known that multi-user (MU) MIMO is very sensitive to the accuracy of channel knowledge at the transmitter. Contrary to single user (SU) MIMO, limited feedback in MU-MIMO limits the gain of spatial multiplexing due to the quantization error. In other words, as signal-to-noise ratio (SNR) increases, MU-MIMO becomes interference limited due to the intra-cell interference induced by the quantization error. In a frequency division duplex (FDD) system, the transmitter gets the channel state information (CSI) via quantization and limited feedback from each user. In recent 3GPP meetings, it has been agreed that the feedback framework allows the report of two matrices selected from two separate codebooks [5]. One matrix targets wideband and/or long-term channel properties, and the other matrix targets frequency-selective and/or short-term channel properties. Hence, the design for the two codebooks is a main problem. In practice, co-polarized linear antenna array is a typical configuration in LTE-A systems. There should be a proper codebook design corresponding to this antenna array. In LTE-A discussions, many feedback proposals have been presented to quantize the two matrices. Among these schemes, discrete Fourier transform (DFT) based feedback [6] is a smart design and receives the most concern,

which selects a cluster of beams first, then performs beam selection and co-phasing between two antenna subgroups. But this codebook design does not perform well in co-polarized linear antenna array since it does not fully match the channel characteristic of this antenna configuration due to the limited co-phasing. In this paper, we indicate that precoder should have the form of DFT vector for closely-spaced co-polarized linear antenna array due to the high spatial correlation. Then an enhanced DFT based codebook is proposed herein with phase adjustment added in the precoder targeting wideband CSI. By use of this phase adjustment, the channel characteristic of copolarized arry can be fully utilized as much as possible without increasing codebook size. Hence, compared to DFT based feedback [6], CSI feedback efficiency and system performance with the proposed codebook can be improved significantly for co-polarized antennas. As to cross-polarized linear antenna array, since the feedback granuality is the same, the proposed codebook can still perform well as DFT based feedback, which is also demonstrated by system level simulations. The remainder of this paper is organized as follows. Section II introduces the downlink system model. Section III firstly describes DFT based feedback, then derives the proposed codebook. System level simulation results are presented in Section IV. Finally, Section V provides some concluding remarks. Notation: (·)T is transpose, nmodN denotes the modulus function, and diag(a1 , a2 , · · · , aN ) represents a diagonal matrix with a1 , a2 , · · · , aN being the main diagonal elements. II. T HE D OWNLINK S YSTEM M ODEL In 3GPP LTE-A, MIMO and orthogonal frequency division multiplexing (OFDM) are employed for downlink system. Suppose that each base station (BS) has Nt transmit antennas and each user is equipped with Nr receive antennas. At BS, the transmitted signal for subcarrier k can be expressed as x(k) = F(k)s(k)

(1) T

where s(k) = [s1 (k), s2 (k), · · · , sR (k)] is a R × 1 vector containing the encoded MIMO complex data symbols at subcarrier k, R is the rank of the transmission, and F(k) is a Nt × R complex precoding matrix. Codebook based precoding is employed for LTE-A FDD system. Each user selects the codeword in the predefined codebook to represent the CSI from the served BS, and sends the preferred codeword index to the BS. There are some criterias to select codeword, such as maximum capacity

and chordal distance. Then BS retrieves the downlink CSI according to the codeword index fed back from user, and performs proportional fairness scheduling by greedy search based on maximum weighted sum capacity. If SU mode is scheduled, the precoding matrix F(k) is set as the codeword fed back by the corresponding user. Otherwise, if MU mode is scheduled, F(k) is usually calculated by zero-forcing (ZF) method based on the downlink CSI of each scheduled user. III. C ODEBOOK D ESIGN How to design the codebook effectively quantizing the CSI is a very important question for FDD downlink system. In recent 3GPP meetings, it has been agreed that the CSI feedback framework allows the report of two matrices selected from two separate codebooks. One matrix targets wideband and/or long-term channel properties, and the other matrix targets frequency-selective and/or short-term channel properties. Hence, the two codebooks need to be designed properly. A. DFT Based Feedback In recent LTE-A meetings, a two-stage codebook design is agreed in [6]. The recommended codeword W for a subband is W = W1 W2 (2) where W is a Nt × R matrix, the outer matrix W1 ∈ C1 is a Nt × Nb matrix representing the wideband CSI, and the inner matrix W2 ∈ C2 is a Nb × R matrix. This structure is well-suited for efficiently supporting common antenna setups such as closely spaced cross-polarized or co-polarized linear array. To see how correlations properties are exploited, first consider the common case of an array of closely spaced cross-polarized antennas. The antennas can then be divided into two separate subgroups depending on the polarization direction of the antenna. The correlation is high among the channels within an antenna subgroup while channels from different antenna subgroups fade in an independent manner, and to some extent with reduced cross-talk due to the use of orthogonal polarizations. Such an antenna setup thus creates quite pronounced channel properties, which are well-matched to a block diagonal structure of W1 , i.e., [ ] X 0 W1 = (3) 0 X where X targets a co-polarized antenna subgroup. Since the correlation is high within the antenna subgroup, it makes sense to use a grid of beam codebook implemented from DFT based precoder vectors. Thus, X is composed by Nb Nt × 1 adjacent DFT vectors. The inner matrix W2 selects one beam in W1 and adjusts the relative phase shift between polarizations. For rank 1, W2 could be formed as [ ] 1 Y W2 = √ (4) 2 aY In the equation above, a represents co-phasing, and Y ∈ {e0 , e1 , · · · , eNb −1 }

(5)

where ek denotes a Nb × 1 elementary vector with all zeros except for the (k + 1)-th element with value 1. For rank 2, [ ] 1 Y1 Y2 W2 = √ (6) 2 bY1 −bY2 where b represents co-phasing, and Y1 , Y2 are selected from the elementary vectors. With proper selection of a and b, the design in equations (3)-(6) can also be made to suit the closely spaced co-polarized linear array. Assume that the whole band is divided into M subbands. The sizes of C1 and C2 are denoted by N1 and N2 bits respectively. At first, user selects codeword W1 in codebook C1 on the whole band. Then on each subband, user selects codeword W2 in codebook C2 to match the subband CSI. Hence, the overhead of DFT based feedback is N1 + M N2 bits. Based on the design described above, 8-Tx codebooks for DFT based feedback are concretely presented in [6] for copolarized and cross-polarized antennas. 128 beams are generated from the multiplication of W1 and W2 , in which only sixteen beams have the form of 8-Tx DFT vectors matching the spatial characteristic of co-polarized antenna setup. In W1 , X is composed of four adjacent overlapping beams. Each beam is one of 32 4-Tx DFT vectors. The use of adjacent overlapping beams is to reduce edge effect in frequencyselective precoding. Thus sixteen W1 codewords could be obtained as } { (15) (1) (0) C1 = W1 , W1 , · · · , W1 [ (k) ] X 0 (k) , k = 0, 1, · · · , 15 (7) W1 = 0 X(k) where

[ ] X(k) = b2kmod32 b(2k+1)mod32 · · · b(2k+3)mod32 [ ] 2πm 2πm∗2 2πm∗3 T bm = 1, ej 32 , ej 32 , ej 32 , m = 0, 1, · · · , 31. (8)

W2 codebook C2 is composed of column selection and QPSK co-phasing, and is expressed as follows: • Rank 1 {

[ ] [ ] 1 1 Y Y W2 ∈ C2 = √ ,√ , 2 [ Y ] 2 [jY ]} 1 1 Y Y √ ,√ 2 −Y 2 −jY Y = {e0 , e1 , e2 , e3 } •

Rank 2

{

(9)

[ ] 1 Y1 Y2 W2 ∈ C2 = √ , 2 [ Y1 −Y2 ]} 1 Y1 Y2 √ 2 jY1 −jY2 (Y1 , Y2 ) ∈ {(e0 , e0 ), (e1 , e1 ), (e2 , e2 ), (e3 , e3 ), (e0 , e1 ), (e1 , e2 ), (e0 , e3 ), (e1 , e3 )} (10)

B. Proposed Codebook For closely-spaced co-polarized linear array, the dominated eigen-vector of the channel correlation matrix can be approximated by a DFT vector due to the high spatial correlation. So the rank-1 precoder W needs to be designed as DFT vectors specific to this antenna configuration. In the DFT based feedback described in Section III-A, the co-phasing in W2 is important for matching the phase shift between the two antenna subgroups. However, due to the limited selection of co-phasing, 8-Tx codebooks for DFT based feedback only provide sixteen DFT vectors from total 128 beams. If more DFT vectors are wanted, it needs more bits for co-phasing, which must increase the codebook size and the feedback overhead. In this section, an enhanced two-stage codebook is proposed to overcome this problem without increasing the overhead of DFT based feedback. Define the N × 1 DFT vector as [ ] 2πm(N −1) T 2πm m M fM,N = 1, ej M , · · · , ej , m = 0, 1, · · · , M − 1 (11) where M/N denotes the value of oversampling. It is obvious that the phase shift between two subgroups is fixed for the (m + 1)-th DFT vector, i.e., 2πm(N/2)/M . Basing on this observation, we indicate that for co-polarized antenna, there is no need to feed back any bit for co-phasing due to the fixed phase shift of each beam. In the following, we propose adding the fixed phase shift of each beam into W1 in equation (3) to construct DFT vectors. Furthermore, an unified codebook design is provided for both co-polarized and cross-polarized linear array. Define Z(k) as follows, which is comprised by Nb DFT vectors. [ ] k Nb k1 k2 Z(k) = fM,N , f , · · · , f (12) M,Nt /2 M,Nt /2 t /2 Define

( ) 2πkN (Nt /2) 2πk1 (Nt /2) 2πk2 (Nt /2) b M M M Λ(k) = diag ej , ej , · · · , ej

(13) Then we propose W1 as follows: ( (k) ) Z 0 (k) W1 = , k = 0, 1, · · · , N1 − 1 (14) 0 Z(k) Λ(k) With the diagonal matrix Λ(k) added, each corresponding columns in the first and second block diagonal matrix can construct Nt -Tx DFT vectors. Thus, for co-polarized antenna, only beam selection is needed in W2 , i.e., • Rank 1 [ ] 1 Y W2 = √ 2 Y Y = {e0 , e1 , · · · , eNb −1 } (15) •

Rank 2

[ ] 1 Y Y W2 = √ 2 Y −Y Y = {e0 , e1 , · · · , eNb −1 }

(16)

If an unified codebook is needed for both co-polarized and cross-polarized antenna, the codebook proposed above can be modified by just adding a co-phasing factor a in W2 , which targets the phase adjustment between two antenna subgroups for cross-polarized antenna. Then W2 is constructed as • Rank 1 [ ] 1 Y W2 = √ 2 aY •

Rank 2

Y = {e0 , e1 , · · · , eNb −1 }

(17)

[ ] 1 Y Y W2 = √ 2 aY −aY Y = {e0 , e1 , · · · , eNb −1 }

(18)

Next, as an example, the proposed 8-Tx codebook is presented in the following. { } (0) (1) (15) C1 = W1 , W1 , · · · , W1 [ (k) ] X 0 (k) W1 = , k = 0, 1, · · · , 15 (19) 0 X(k) Λ(k) where

[ ] X(k) = b2kmod32 b(2k+1)mod32 · · · b(2k+3)mod32 ([ 2π4 2π4 Λ(k) = diag ej 32 (2kmod32) , ej 32 ((2k+1)mod32) , ]) 2π4 2π4 ej 32 ((2k+2)mod32) , ej 32 ((2k+3)mod32) ] [ 2πm∗2 2πm∗3 T 2πm , m = 0, 1, · · · , 31. bm = 1, ej 32 , ej 32 , ej 32 (20)

And W2 codebook is written as • Rank 1 [ ] 1 Y W2 = √ 2 aY Y = {e0 , e1 , e2 , e3 } { {1}, co-polarized antenna a∈ {1, −1, j, −j}, unified codebook •

(21)

Rank 2

[ ] 1 Y Y √ W2 = 2 aY −aY Y = {e0 , e1 , e2 , e3 } { {1}, co-polarized antenna a∈ {1, −1, j, −j}, unified codebook

(22)

Obviously, compared to DFT based feedback in equations (7)-(10), the proposed codebooks presented above reduce payload size of 2M bits for co-polarized antenna. Besides, since the proposed codebooks provide the largest number of DFT vectors without increasing codebook size, the system performance can be further improved as the reduction of beam granularity. As to cross-polarized linear antenna array, although the proposed codebooks use different co-phasing to DFT based feedback, there is no big difference between their performance due to the same co-phasing granularity.

TABLE I S IMULATION PARAMETERS FOR LTE-A D OWNLINK

User antenna

Transmission scheme Scheduler

Feedback

Link adaptation HARQ Receiver type Control channel and reference signal overhead Simulation time

8 for 8Tx 8Tx: Co-polarized/Cross-polarized antennas with the spacing of half wave length, polarization angles of 90◦ /±45◦ 2Rx: half wave length spacing; co-polarized antennas with vertical polarization; cross-polarized antennas with polarization angles of 90◦ /0◦ ZF method, MU-MIMO, rank 1 per user Proportional fair and frequency selective scheduling, scheduling granularity of one subframe (1 ms) Wideband W1 , subband W2 and subband CQI: 5ms report periodicity, 6ms feedback delay Error: N(0,1dB) per PRB Synchronous HARQ, chase combining, max 4 retransmissions MMSE Fixed 0.3063 (As agreed in ITU evaluation) 800 subframes (1 ms/subframe)

0.9 0.8 0.7 0.6 CDF

Cell number Wrap-around model Duplex method and bandwidth Network synchronization Traffic model User number per sector Maximal number of co-scheduled users BS Antenna

3GPP case 1 3D, SCM-UMa, 8 degree angle spread 19 cells with 3 sectors per cell Yes FDD: 10MHz for downlink Synchronized Full buffer 10

0.5 0.4 0.3 0.2 0.1 0 0

Fig. 1.

DFT based codebook Proposed codebook 2000

4000

6000 8000 User Throughput (kbps)

10000

12000

14000

CDF of user throughput for 8Tx co-polarized antenna.

1 0.9 0.8 0.7 0.6 CDF

Deployment scenario

1

0.5 0.4 0.3

TABLE II S YSTEM L EVEL S IMULATION R ESULTS FOR 8T X C O - POLARIZED A NTENNA Codebook (N1 , N2 ) DFT based feedback Proposed codebook

Average SE (bps/Hz) 4.53 (100%) 4.97 (109.71%)

Edge SE (bps/Hz/user) 0.161 (100%) 0.171 (106.21%)

0.2 0.1 0 0

DFT based codebook Proposed codebook 1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

User Throughput (kbps)

Fig. 2.

CDF of user throughput for 8Tx cross-polarized antenna.

IV. S IMULATIONS This section shows the system level simulation with the presented codebooks for LTE-A FDD downlink system over 19 sites/57 pentagon-shaped cells. The main simulation parameters and modeling assumptions for LTE-A evaluation are summarized in Table I. The overall downlink bandwidth (10 MHz) is divided into 10 subbands, i.e., M = 10. We consider perfect channel knowledge at the user side and errorfree feedback transmission from each user. For MU-MIMO, lower bound of the post-detection signal to interference plus noise ratio (SINR) of each user is used as the channel quality indicator (CQI) [7]. After the MU-MIMO scheduling, BS adjusts the reported CQI according to the number of coscheduled users by multiplying a scaling factor, and equal transmit power is allocated to each data stream. Figure 1 and figure 2 show the cumulative distribution function (CDF) of user throughput for the proposed codebooks, which illustrates that the proposed codebooks help

increasing the system performance. Furthermore, Table II and III give the performance comparison in the form of spectrum efficiency (SE) between the proposed codebooks in equations (19)-(22) and DFT based codebooks [6]. It can be seen that with the same overhead, for co-polarized antenna, the proposed codebooks greatly outperform DFT based codebooks with about 10% gain on average cell SE, and 6% gain on celledge user SE. And for cross-polarized antenna, the proposed codebooks still show gain compared with DFT based codebook. Through system evaluations, it is demonstrated that the TABLE III S YSTEM L EVEL S IMULATION R ESULTS FOR 8T X C ROSS - POLARIZED A NTENNA Codebook (N1 , N2 ) DFT based feedback Proposed codebook

Average SE (bps/Hz) 3.64 (100%) 3.71 (101.92%)

Edge SE (bps/Hz/user) 0.114 (100%) 0.117 (102.63%)

proposed codebooks outperform DFT based codebook, while the overhead is not increased. V. C ONCLUSIONS In this paper, a codebook design is proposed by adjusting phase between polarizations in the precoder targeting wideband CSI. This design effectively matches the channel characteristics of co-polarized linear antenna array, since the largest number of DFT beams are constructed for this antenna configuration. System level simulation in a LTE-A system is performed to evaluate the performance of the proposed codebooks. The results show that compared to DFT based codebooks in [6], without increasing the feedback overhead, the proposed codebooks show significant gain on both average cell SE and cell-edge user SE for co-polarized antenna, while still outperform the latter for cross-polarized antenna. ACKNOWLEDGMENT This work is supported by National Science and Technology Major Projects under Grant 2009ZX03003-010 and 2011ZX03003-001-04. R EFERENCES [1] A. Paulraj, R. Nabar and D. Gore, Introduction to Space-Time Wireless Communications. Cambridge: Cambridge University Press, 2003. [2] Agilent Technologies, Agilent 3GPP Long Term Evolution: System Overview Developement and Test Challanges, May 2008. http://cp.literature.agilent.com/litweb/pdf/5989-8139EN.pdf. [3] E. Seidel, Progress on ”LTE-Advanced” - the new 4G standard, Jul. 2008. http://www.nomor.de/uploads. [4] 3GPP TR 36.913 v8.0.1, Requirements for further advancements for EUTRA (LTE-Advanced), Mar. 2009. [5] 3GPP, R1-101683, Way forward for Rel-10 Feedback framework, Ericsson, Huawei, Alcatel-Lucent, Alcatel-Lucent Shanghai Bell, LG Electronics, Marvell, Nokia, Nokia Siemens Networks, NTT DoCoMo, Panasonic, Philips, Qualcomm Inc., Research In Motion, Samsung, ST-Ericsson, Texas Instruments, ZTE. [6] 3GPP, R1-105011, Way forward on 8Tx codebook for Rel.10 DL MIMO, Alcatel-Lucent, Alcatel-Lucent Shanghai Bell, AT&T, CATT, CEWiT, CMCC, Ericsson, Kyocera, LG Electronics, LG-Ericsson, Marvell, Mitsubishi Electric, Motorola, NEC, Nokia, Nokia Siemens Networks, NTT DoCoMo, Panasonic, Qualcomm Inc., Samsung, Sharp, Sony Corporation, ST-Ericsson, Texas Instruments. [7] M. Trivellato, F. Boccardi, F. Tosato, User Selection Schemes for MIMO Broadcast Channels with Limited Feedback, in Proc. IEEE VTC2007Spring, Dublin, Ireland, Apr. 2007, pp. 2089-2093.