1. Performance Analysis of Multi User MIMO System with Block-Diagonalization Precoding Scheme
Yoon Hyun Kim and Jin Young Kim,
Kwanwoon University, Department of Electronics Convergence Engineering, Wolgye-Dong, Nowon-Gu, Seoul, Korea.
{yoonhyun,
Abstract. As the demand of high quality service in next generation wireless communication systems, a high performance of data transmission requires an increase of spectrum efficiency and an improvement of error performance in wireless communication systems. In this paper, we propose a multi-user multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with cyclic delay diversity and block diagonalization precoding method to improve system capacity with maintaining good error performance for n WLAN system. The results of mathlab simulation show the improvement of system capacity in n wireless indoor channel environment.
Keywords: Multi-user MIMO, Cyclic delay diversity, Coded OFDM, Block- diagonalization, n WLAN system
1 Introduction
Increasing demand of high performance in next generation wireless communication systems is enabled by the use of system that combines multi-user Multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) system. MIMO system provides multiple independent transmission channels, thus, under certain conditions, leading to a channel capacity that increases linearly with the number of antennas and improving system reliability in limited frequency resources [1- 3]. Also OFDM is an efficient technique for reducing the effect of inter-symbol interference (ISI) and inter-carrier interference (ICI) due to using multi-carrier modulation in frequency selective fading channel. This technology accomplishes the high data rates and improves the reliability in wireless communications [4].
Recently, we study multi-user MIMO system which improves the system capacity by using the pre-coding method such as dirty paper code (DPC) and block diagonalization (BD). DPC is an optimal scheme to achieve the system capacity of multi-user MIMO downlink channel. DPC is not proper in practical wireless communication systems because it needs data of other users and the perfect channel state information, it means that system complexity is very high. Block diagonalization is simply implemented due to low complexity than DPC. Block diagonalization is used to suppress co-channel interference which is happened by transmit of other users
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2. 2 Proposed System Model r H Td~n H Td HkTi 0, i z k . (2)
in same frequency and time. Block diagonalilazation, whose complexity is lower than DPC complexity, changes multi-user MIMO channel to multiple single-user MIMO channels [5-6].
In this paper, we propose multi-user MIMO OFDM system with cyclic delay diversity (CDD) scheme for n system. The n wireless local area network (WLAN) is one of the key techniques in the next generation wireless communication systems. And we use block diagonalization due to the co-channel interference cancellation and the low complexity. The proposed multi-user MIMO OFDM system improves the system capacity by using CDD scheme than multi-user MIMO OFDM system without CDD [7].
This paper is organized as follow: In Section 2, we introduce block diagonalization of multi-user MIMO OFDM system and WLAN channel model. Section 3, we explain the proposed scheme which uses CDD scheme. In Section 4, we compare the system performance between the multi-user MIMO OFDM system with CDD scheme and without CDD scheme according to different channel model. Finally, we conclude the proposed scheme in Section V.
2 Proposed System Model
In the multi-user downlink channel with K users and a single base station, the base station has NT antennas, and the ith user has ni,r antennas. The total number of
antennas at users is defined to be ¦ . The Liu 1 transmit vector of the ith K
N n
Ri 1i ,R
user is defined by di which is operated by IFFT. The Ntu Li pre-coding matrix of the
ith
user is defined by Ti which is lying on the null space of the channel matrix of other users. The ni,ru Nt channel matrix from the base station to the ith user is defined by Hi. The parameters of the channel matrix are independently identically distributed (i.i.d) and complex Gaussian probability variance (mean is 0, variance is 1). The Liu 1 received matrix of the ith user is defined by ri. The received matrix is defined as
r H Td~n
i i ¦ k k i
k 1
K , (1)
H Td
i i i ~ H T d n
¦ ~
i k ki
k 1,kzi
where the ni,ru 1 noise vector vi is independently identically distributed, mean of
element is 0, variance is 2
V and additive Gaussian white noise (AWGN).
The second factor of (1) means the co-channel interference which is transmitted for other users in same frequency and time. The block diagonalization is used to cancel co-channel interference. The condition of co-channel interference cancellation is given by
HkTi 0, i z k . (2)
Throughout this paper, it is assumed { }K 1
Hk k is perfectly known at the base
station in order to find the pre-coding matrices and the estimation of SNR. To find Ti,
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3. Vi is first ni,r right singular vectors. Vi and Vi1 computed in
the pre-coding matrices are lying on the null space of Hi which is the (K-1)ni,rx NT channel matrix excepted the channel matrix of the user i. Hi is defined as
H i = ª H T 1 T
- , (3)
where T indicates transposition.
The condition of co-channel interference cancellation, which is (2), is satisfied to fine the null space of Hi by using the singular value decomposition (SVD). The SVD operation of Hi is defined as *
Hi U =A i i ª ¬ Vi Vi º 1/4 ,
1 0 (4) where * means hermitian transpose. Ui is the (K-1)ni,r x (K-1)ni,r unitary matrix and left singular matrix. Ai is the (K-1)ni,rx(K-1)NT diagonal matrix. Vi1 is the first Ni right singular vectors, and Vi 0 is the last NT —Ni right singular vectors. 0 Viforms null space of Hi. Ni is rank of Hi. Let the number of columns of the pre-coding matrix Ti equal ni,r to reduce the complexity of detection and maximize the system capacity. It is needed that SVD of multiply Hi by Vi0 , and defined as
HiVi Ui[ Ai 0][ V i V i ] , (5)
1 0*
where 1
Vi is first ni,r right singular vectors.
The pre-coding matrix Ti of user i is computed by using 0
Vi and Vi1 computed in
(4) and (5), respectively. The precoding matrix is defined as
Ti =V i Vi . (6) Ti computed by (6) satisfies the condition of the co-channel interference cancellation. If we define the system channel matrix H and the pre-coding matrix T as
H =
[H H
1 2
T T ,
T =[T1 T2
(7)
[ V
1 " 1 2 2 .
Multiply H by T converts multi-user MIMO channel to multiple single-user MIMO channel. It is block diagonalization which is defined as
r0 7; 0 0 H2T2
º » » »
0 K K .
H T 1/4
(8) HT
The block diagonal pre-coded data of each user is summed and transmitted at the antennas of the base station. So the received signal vector is defined simplicity as
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4. ª ºrdn [rid «¬did «¬nK1/4 R = HTD + N , (9) .
Fig. 1. Multi-user MIMO OFDM system with CDD
R = HTD + N ,
ª ºrdn
1 r r
[rid «¬did «¬nK1/4
(9) .
The co-channel interference is canceled by block diagonalization. So each user receives the desired data which is canceled the data of other users.
1/ 2
[X] ={[Rtx ] ® [Rrx ]1 [Hiid ] , (10)
The block diagram for the conventional L -branch diversity receiver is shown in Fig. 1. In order to guarantee that the signals between each pair of receiver antennas fade independently, each receiver antenna is sufficiently separated in space. It¶s assumed that the search step size is Tc / 2 . All correlators are associated with the
same phase of the local dispreading code. And the outputs X l , l 0, 1,=L..., —1, of
the L correlators are combined into one decision variable V . This combining scheme is EGC. Then the decision variable V is compared to a threshold T in order to make a decision whether codes are aligned or not. The threshold value T is determined by using the cell averaging-constant false alarm rate (CA-CFAR) algorithm [8].
The search mode employs a serial search strategy. Whenever the decision variable V exceeds the threshold T , the system decides that the corresponding delay of the locally generated PN sequence is the correct one and enters into the verification mode. If V does not exceed T , the phase of a locally generated PN sequence is rejected. Then, another phase is chosen to update the decision variable and above operation is repeated. This conventional structure requires additional hardware units according to increasing diversity branches so that both the cost and complexity increase.
The proposed receiver employs delay diversity schemes which can increase diversity order with low cost and complexity. The received signal from one of the two
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5. antenna element is intentionally delayed by the amount of the predetermined value ' . In order to avoid overlapping with the intentionally delayed signals from the delay branches, ' should be larger than the maximum excess path delay for the meaningful multipath signals from the normal branches. In this receiver, half of L branches are for the normal branches and the remaining L / 2 branches are for the delay branches. The proposed DDR has L diversity branches. The signals of the normal and delay branches are input to the correlators in sequence. Then, the correlator outputs are combined into one decision variable V using EGC scheme. And then, V is compared with the threshold T in order to determine whether codes are aligned or not.
The proposed receiver does not require additional hardware units and space compared with the conventional diversity receiver, shown in Fig. 1. Therefore, for the proposed receiver, we can save cost and reduce complexity.
4 Simulation Results
We analyze the proposed scheme by a computation simulation. The simulation parameters are presented in table I. We simulate the error performance according to IEEE n indoor channel model. The computation simulation is performed under the base station and users know perfect channel state information. Each user use one antenna, the number of user is 2 and the number of base station¶s antennas is 2. If user uses multiple antennas, we can use joint demodulation processing to increase the BER performance, while this processing increases the system complexity.
The error performances of multi-user MIMO OFDM with CDD are depicted in Fig. 2. BER graphs shows the 3~4dB gain compared with multi-user MIMO OFDM system without CDD.
Fig. 2. BER performance of multi-user MIMO OFDM system with CDD (QPSK and Coding rate 1/2)
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6. 5 Conclusions Acknowledgments
Multi-user MIMO OFDM systems will be used to improve the spectrum efficiency which is very important because frequency resource is limited and wireless communication systems will be increased in next generation wireless communications. So, in this paper, we propose a multi-user MIMO OFDM system with CDD and block diagonalization precoding method to improve BER performance with wireless WLA) channel model C and D for n WLAN system. The results of mathlab simulation show the improvement of BER performance in n wireless indoor channel environment. So the proposed scheme of this paper can be applied to many systems in the advanced wireless communications such as biological data transmission and home network systems.
Acknowledgments
This work was, in part, supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No ), and in part, supported by the MKE (The Ministry of Knowledge Economy), Korea, under the ITRC (Information Technology Research Center) support program supervised by the NIPA (National IT Industry Promotion Agency)" (NIPA-2012-(C )).
References
M. Jankiraman, Space-Time Codes and MIMO Systems, Artech House Publishers, 2004.
D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005.
A. Goldsmith, S. A. Jafar, N. Jindal, and S. Vishwanath, "Capacity limits of MIMO channels," IEEE J. Select. Areas Commun., vol. 21, no. 5, June 2003, pp
L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for Broadband Multi-User Communications, WLANs and Broadcasting, John Wiley & Sons, 2003.
C. Windpassinger, R. F. H. Fischer, T. Vencel, and J. B. Huber, "Precoding in multi-antenna and multi-user communications," IEEE Trans. Wireless Commun., vol. 3, no. 4, July 2004, pp
Q. H. Spencer, C. B. Peel, A. L. Swindlehurst, and M. Haardt, "An introduction to the multi-user MIMO downlink," IEEE Commun. Mag., vol. 42, no. 10, Oct. 2004, pp
G. Bauch and J. Shamim Malik, "Parameter optimization, interleaving and multiple access in OFDM with cyclic delay diversity," IEEE Trans. Veh. Technol., vol. 1, pp. 505 — 509, May
A. M. Saleh and R.A. Valenzuela, "A statistical model for indoor multipath propagation," IEEE J. Select. Areas Commun., vol. 5, 1987, pp
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