Performance evaluation of channel inversion precoding for downlink multi-user MIMO system

The Journal of China Universities of Posts and Telecommunications October 2009, 16(5): 20–24 www.sciencedirect.com/science/journal/10058885

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Performance evaluation of channel inversion precoding for downlink multi-user MIMO system CHEN Zhi-yong ( ), WANG Wen-bo, PENG Mu-gen, LI Ren Wireless Signal Processing and Network Laboratory, Key Laboratory of Universal Wireless Communication, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract

In downlink multi-user multi-input multi-output (MU-MIMO) system, not every user (user equipment (UE)) can calculate accurately signal to interference and noise ratio (SINR) without prior knowledge of the other users’ precoding vector. To solve this problem, this article proposes a channel inversion precoding scheme by using the lower bound of SINR and zero-forcing (ZF) algorithm. However, the SINR mismatch between lower bound SINR and actual SINR causes the inaccurateness of adaptive modulation and coding (AMC). As a result, it causes degradation in performance. Simulation results show that channel inversion precoding provides lower throughput than that of single user multi-input multi-output (SU-MIMO) at high signal-to-noise ratio (SNR) (>14 dB), due to the SINR mismatch, although the sum-rate of channel inversion precoding is higher than that of SU-MIMO at full SNR regime. Keywords MU-MIMO, channel inversion precoding, CQI feedback, AMC, lower bound SINR, zero-forcing

1

Introduction 

MU-MIMO system is considered as one of the most promising technologies in improving system performance for next generation wireless communication. It has been attracting much more attention in recent years owing to its strength in multi-user diversity and spatial diversity [1–2]. By using the precoding technique, the downlink MU-MIMO system can provide more cell throughput than SU-MIMO through exploiting accurate channel state information (CSI) at the transmitter [2–3]. In addition, the technology of AMC is applied to the downlink MU-MIMO system to improve throughput. With the AMC technique, the modulation and coding scheme (MCS) is changed according to the CSI adaptively. Thus, obtaining channel information at the base station (BS) is crucial for MU-MIMO precoding scheme. In previous works, several precoding schemes have been developed to approach the sum capacity but are generally complex to implement, when full CSI is known at the BS. In Refs. [4–6], ZF precoding is used to mitigate the multi-user Received date: 08-12-2008 Corresponding author: CHEN Zhi-yong, E-mail: [email protected] DOI: 10.1016/S1005-8885(08)60263-0

interference (MUI). In Ref. [7], a method is proposed that uses a per-user successive minimum mean squared (MMSE) precoding. These methods have been demonstrated to perform well. However, they require full CSI of all UEs to be utilized at the BS, which is unrealistic in practice. Several other precoding methods have been studied in the Refs. [8–13], considering limited CSI. These researches take a step further and actually quantize the CSI at the UE before feeding it back to the BS. Using an exhaustive codebook (CB), the BS has to learn the CSI through channel quality indicator (CQI) and the index of precoding matrix sent by each UE. However, a limitation of limited CSI is that not every UE is able to obtain prior knowledge of other UEs’ CSI. Consequently, each UE needs to estimate the CQI without prior knowledge of other user’s precoding vectors. In Refs. [8–13], all authors consider the lower bound of SINR as CQI, which results in a CQI mismatch between the feedback CQI and the actual transmit CQI. Hence, the feedback CQI is not good enough to support AMC and user selection scheme, which causes significant performance loss. However, these studies did not consider the CQI mismatch and AMC technique, and the results imply that maintaining an unreasonable sum-rate performance without performance loss.

Issue 5

CHEN Zhi-yong, et al. / Performance evaluation of channel inversion precoding for…

Hence, AMC should be considered when evaluating the performance. In this article, the authors describe the channel inversion precoding which uses lower bound SINR and ZF. Each UE calculates a lower bound SINR and treats it as CQI. Then, after obtaining the precoding matrix, the BS uses ZF algorithm to adjust CQI in others to reduce CQI mismatch. They also compare the performance in terms of sum-rate and throughput, where the throughput is calculated by using AMC. The main contributions of this article are as follows: 1) The authors design a completely feasible downlink MU-MIMO beamforming scheme based on channel inversion which is identified to cover the CQI calculation, codebook quantization, CQI adjusting, user selecting scheduling and link adaptation.

Fig. 1

¦HW x jS

i

j

j

 ni

H iWi xi  ¦ H iW j x j  ni N   

jS noise signal j zi  

(1)

interference

where H i represents the N r u N t channel matrix from the BS to the ith UE. Wi is the precoding vector of the ith UE and xi is the data symbol of the ith UE. ni represents the noise vector of the ith UE at the receiver, whose element is zero mean Gaussian random variables with variance V 2 . It is assumed that the data symbol xi has statistical power E ª xi º 1 . ¬ ¼ Then, the precoding matrix W is described as follows: 2

W

ª¬W1T W2T ... WMT º¼

T

2) To further reduce the mismatch between estimated CQI and actual CQI, the authors propose that the BS adjusts the feedback CQI. According to each UE’s beamforming vector, the BS generates the beamforming matrix based on ZF algorithm and adjusts the CQI by using the beamforming matrix.

2 Downlink MU-MIMO system model The MU-MIMO downlink system model is described in Fig. 1. It is assumed that the BS has Nt transmitting antennas and K users, each with Nr receiving antennas. It is also assumed that service will be provided to M users selected from K users ( KıN tıM ıN r ) . Denote that S is the set

of selected users, and M denotes S cardinality.

MU-MIMO downlink system

According to Fig. 1, the received signal vector of the ith UE (i  S ) can be expressed as: yi

21

(2)

Let Gi denote the receive filter matrix of the ith UE. Then the actual SINR of the ith UE is given by:

* iactual

Gi H iWi

2

Gi V 2  ¦ Gi H iW j 2

2

(3)

jS j zi

Here, note that Eq. (3) is difficult to obtain because the ith UE does not have prior knowledge of the other users’ precoding vectors W j . Therefore, this article develops a feasible MU-MIMO channel inversion precoding scheme to cover CQI (SINR) calculation, codebook quantization, user selection and link adaptation to improve the performance. The main scheme of this precoding is as follows: 1) According to the singular value decomposition (SVD), each UE quantizes its channel information with a given codebook based on the minimum Euclidean distance criterion.

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Then UE estimates the lower bound SINR without the knowledge of other UE’s precoding vectors [10–11]. 2) Because there is SINR mismatch between the feedback CQI and the actual CQI, the BS needs to adjust the feedback CQI by using the precoding matrix. Thus, the adjusted CQI approximates to the actual CQI. 3) Based on the greedy algorithm, the BS selects UEs with the highest ideal sum-rate, and decides the precoding matrix. According to the adjusted CQI, MCS is optimized for each UE to maximize sum-rate and calculate the practical throughput.

3 Channel inversion precoding scheme

where U i is the unitary matrix, thus U iH

U i Di ª¬Vi1 Vi 0 º¼ where U i is a Hi

diag

^

Oi ,1

Oi ,2 ...

unitary

`

matrix,

and

Di

Oi , r , (Oi ,1 ! Oi ,2 ! ... ! Oi , r ! 0) is the i

Ct . Therefore, for the ith UE is

*

ı

U iH H i cos 2 T i

V  2

2 2 H U i H i sin

Ti

* ilow

(7)

Here, based on this observation, there is an SINR mismatch between actual SINR and lower bound SINR. The first element of the * ilow is considered as the CQI and the ith UE feedbacks

(8)

ZF precoding and SINR adjusting (at the side of BS)

After each UE sends CQI and the index of codebook t to the BS, the BS selects all possible S * sets as S  S * . The BS combines Vˆ as follows: i

(4) N r u ri

1 H i

2

actual i

3.2

H

1.

Ti , the lower bound of SINR can be calculated as [8–13]

3.1

of H i . Then one can obtain its SVD for any matrix H

V

Let us define cosTi

it to the BS. Ki * ilow (1)

Based on the estimated channel, each UE is able to perfectly estimate its channel matrix. Let ri denote the rank

2

In Refs. [9–14], a method for SINR estimation is introduced, where the UE considers the lower bound SINR as actual SINR.

In this section, the authors design a channel inversion precoding scheme from the UE side to the BS side. Approximate SINR for CQI feedback (at the side of UE)

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i

non-zero eigenvalue values of H i H iH . Vi1 holds the first right singular vector, and Vi 0 holds the last N t  ri right

Wˆ p

ªVˆpH VˆpH ... VˆpH º ; p  S * (9) i 1 M ¼ ¬ i where pi shows that the ith UE belongs to p subset. Given a p subset, the zero forcing precoding matrix can be calculated as W p Wˆ Hp (Wˆ pWˆ Hp ) 1

(10)

singular vectors. Vi1 contains the highest information of H i

For the ith UE, the actual transmit precoding given by the BS is the ith column of W p , denoted as W p ,i . It is obvious

than Vi 0 due to the maximum Oi ,1 . Thus, the ith UE selects

that W p ,i is different from Vˆi due to the ZF algorithm.

1 i

V

as precoding vector.

According to the minimum Euclidean distance criterion, the ith UE (i  S ) quantizes Vi1 and chooses a quantization vector Vˆi as: Vˆi

Ct ; t

arg max

q 1,2,..., Q

V

1 H i

Cq

(5)

where C q is the qth code word corresponding to the qth column of the codebook C , and Q is the size of this codebook. Each UE shares knowledge of its codebook with the BS, and sends the index of selected code word (CW) to the BS. When the channel matrix H i is known to the ith UE, U iH can be considered as receiver weight Gi . The actual SINR of the ith UE can be rewritten as:

* iactual

U iH H iWi jS j zi

2

K

eff p ,i

3.3

K p ,i

2

W p ,i VˆpHi W p ,i

(11)

User selecting scheduler (at the side of BS)

The base station (BS) regards Wˆ p as effective channel, and according to Eq. (11), the sum-rate of p subset is given by Rp

M

¦ log (1  K 2

eff p ,i

)

(12)

i 1

2

V 2  ¦ U iH H iW j

Hence, the feedback CQI is adjusted by the BS to reduce the SINR mismatch. BS calculates the effective SINR of the ith UE at p subset based on Eq. (10) as

(6)

To obtain the sum-rate, the BS needs to select S from S * set according to R S max* R p p S

(13)

Issue 5

CHEN Zhi-yong, et al. / Performance evaluation of channel inversion precoding for…

In general, solving Eq. (13) requires a full force search over all subset S * of 1,2,…,M UEs. The computation complexity for this search is K ! > M !( K  M )!@ , which is unacceptably high for a large number of K users. Therefore, the authors use the greedy algorithm for user selecting scheduling. The specific steps are presented as follows: S Initialization: let S0 m ‡ , < m {1,2,!, K } and R 0 0 For i=1 to M

arg max R Si1 *{k } o Si k < \ Si 1

R Si1 *{si }ıR Si1 Si Si 1 * {si }

If Else

S

Si 1

End End

3.4

AMC (at the side of BS)

With AMC, the modulation and code rate are adaptively changed according to the channel state information, for increasing the system throughput and spectrum efficiency of wireless communication system like LTE and WIMAX. If the channel (as K eff ) of the selected UE is relatively strong, a transmission scheme with higher spectrum efficiency may be selected by AMC. The throughput can be calculated as ȉ (1  f (K Seff ))W[ ½° (14) ¾ s.t f (K Seff )İD °¿ where W denotes the channel coding rate, [ denotes the modulation order, D is the target PER of the system and f (˜) denotes the function that converts the CQI information into PER information for each MCS [14]. Based on the target PER, the BS selects the MCS that yields the largest throughput while remaining within the PER target bound. It is noteworthy that the predicted throughput in Eq. (14) is just used to select MCS for the selected users and after the selected users detect the received signal, the actual throughput is collected to evaluate the system performance.

4

Table 1 Simulation parameters Channel model UE speed Antenna configuration OFDM structure Subframe duration Receiver detection Feed back interval CQI delay Total user number Scheduling method AMC Target PER Data channel coding

ITU Pedestrian B 6tap Tx correlation=0; Rx correlation=0 3 km/h 2 u 2 case 1 024/600, 7 OFDM/subframe 0.5 ms MMSE 5 ms 0.5 ms 20 Max C/I 25 MCS 0.1 Convolution Turbo coding

The LLS considers an MU-MIMO system with 2 transmitting antennas at the BS and in total 20 users at the receiver, and each user has 2 antennas. Therefore, the BS just allocates 2 UEs at a chunk. The single SU-MIMO case based on SVD precoding is also simulated for a comparison with the MU-MIMO. In the SU-MIMO case, only one UE is scheduled over the same time-frequency resource block, in which all the data streams from the BS are assigned to one UE at one chunk. Fig. 2 shows the performances of channel inversion precoding and SU-MIMO with different SNR in different cases. In this simulation, the authors set Q 6 bit for channel inversion precoding, while for SU-MIMO, Q 4 bit. The sum-rate of the channel inversion precoding is higher than the SU-MIMO with the same case at all SNR range, since the channel inversion precoding for the MU-MIMO has multi-user diversity gain (MUDG). However, the practical throughput should be considered. By comparing AMC throughputs, as displayed in Fig. 2, the channel inversion precoding is just better than the SU-MIMO at low SNR (<14 dB), while the SU-MIMO is better at high SNR. This is because the channel inversion precoding uses lower bound SINR when estimating the SINR at the UE side, and there is a great

Simulation results

The link level simulator (LLS) uses the 3GPP LTE system modulations and parameters shown in Table 1. The multiple FEC code word (MCW) is used in each transmission. 25 MCS are adopted including QPSK, 16QAM and 64QAM with the code rate 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5 and 7/8, respectively. The DFT codebook is used in the LLS.

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Fig. 2 Throughput vs. SNR plots for channel inversion precoding and SU-MIMO

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The Journal of China Universities of Posts and Telecommunications

gap between the lower bound SINR and the actual SINR at high SNR. As a result, the inaccurate MCS will degrade the performance. By comparing the sum-rate in channel inversion precoding case with AMC throughput, it is found that the AMC throughput is 2 dB–10 dB lower than the sum-rate. For the region of high SNR, this is caused by the limited number of MCS, while for the region of at low SNR it results from inaccurately estimated SINR. Fig. 3 displays the performance of channel inversion precoding with different amount of users at different SNR. The channel inversion precoding has more throughputs than that of the SU-MIMO case when SNR is low. When SNR is high, the SU-MIMO has a higher throughput over the channel inversion precoding case when there are few users in the system (user number < 7).

Fig. 3 Throughput vs. user number plots for channel inversion precoding

5

Conclusions

This article studies channel inversion precoding with limited feedback for MIMO systems and investigates the performance with CQI estimations, codebook quantization, CQI adjusting, user selecting scheduling and link adaptation. To reduce the impact of mismatch between estimated CQI and actual CQI on link adaptation, the article proposes that the BS adjusts the feedback CQI by using ZF algorithm. In the simulations, the 3GPP LTE system is used to evaluate the performance of channel inversion precoding. The results demonstrate that channel inversion precoding has higher sum-rate than SU-MIMO at all SNR, while it has lower throughput than SU-MIMO at high SNR. Additionally, when there are few users in the system, the AMC throughput

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of channel inversion precoding is lower than SU-MIMO at high SNR. Hence, it is concluded that channel inversion precoding using lower bound SINR can be used in practical system at low SNR, but cannot be used at high SNR. Acknowledgements This work was supported by the National Natural Science Foundation of China (60602058), the Hi-Tech Research and Development Program of China (2006AA01Z257).

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(Editor: WANG Xu-ying)