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IJEEE, Vol. 1, Issue 1 (Jan-Feb 2014)

e-ISSN: 1694-2310 | p-ISSN: 1694-2426

BER Performance of MU-MIMO System using Dirty Paper Coding Garima Saini1, Shivkaran Meghwal2 1,2

Electronics and Communication Engineering, National Institute of Technical Teachers, Training and Research, Chandigarh, India 1

garimasaini_18@rediffmail.com, 2shivkaran_sonel@yahoo.co.in

Abstract- In this paper Dirty Paper Coding for communication system is implemented. MIMO application that involves devices such as cell phones, pocket PCs require closely spaced antenna, which suffers from mutual coupling among antennas and high spatial correlation for signals. DPC is used for compensating the degradation due to correlation and mutual coupling. Simulation results show significant performance in terms of bit error rate (BER) by use of Dirty Paper Coding (DPC) for 4G communication.

base station must communicate with many users simultaneously. Therefore, the study of Multi-User MIMO (MU-MIMO) systems has emerged as an important research topic recently. The channel capacity of single user NR x NT MIMO systems is proportional to Nmin=min (NT, NR) [6]. In the Figure 1, shows multiple users are connected with station [7].

Index Terms- Dirty Paper Coding (DPC), Multi-User MIMO (MU-MIMO), Broad-Cast channels (BC), Multi-access channels (MAC), Correlation, Mutual coupling.

I. INTRODUCTION Wireless is an emerging field, which has been enormous growth in last several years. The huge uptake rate of mobile phone technology, wireless local area network (WLAN) and exponential growth of the internet have resulted in an increased demand for new methods of obtaining high capacity wireless network. The goal of 2G, 3G and 4G is to provide a wider range of services like as communications, video phones, and high speed internet access. To meet the requirements of emerging high bandwidth applications, wireless systems continue to strive for higher and higher data rates [1]. Large spectral efficiencies have been predicted for wireless system with multiple antennas when the channel exhibits rich scattering. It has been shown that MIMO systems have the potential for large information theoretic capacities. They provide several independent communications channels between transmitter and receiver. In an ideal multipath channel, the MIMO capacity is approximately N times the capacity of a single system, where N is the smaller size of the transmit or receive antenna elements. The channel capacity of MIMO system is found to be limited by correlation [2]. The spectral efficiency of 3G network is too low to support high data rate services at low cost. Since as soon as in MIMO 3G system the number of antenna elements will be increased, due to this capacity will reduced [3, 4]. As a consequence one of the main focuses of 4G is to significantly improve the spectral efficiency. This requirement of improvement in spectral efficiency makes use of Dirty Paper Coding [5]. For using application such as Wireless LAN, Cellular telephony, single International Journal of Electrical & Electronics Engineering

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Figure 1. A Multi-user MIMO system for K=4[7] Four users are connected into Figure 1. i.e. K=4. Three out of four users are selected and allocated communication resource such as time, frequency, and spatial stream. In multi-user K.NM antenna can communicate with a single BS antenna with NB antennas. So, (K.NM) x NB system are used for downlink and NB x (K.NM) MIMO system for uplink. II. MATHEMATICAL MODEL FOR MULTIUSER MIMO [7] A. Uplink Channel(Multiple access channel) In Figure 2. Uplink channel is mathematically modeled. We assume that Base stations (BS) and mobile station (MS) are equipped with NB and NM. The received signal is given by UL UL UL (1) y  H 1 x1  H 2 x2  ............ H K xK  z MAC

H

UL 1

H

UL 2

...............

H

UL K

 x1      z x   K

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H

UL

 x1       x   K

II. ANALYSIS OF DIRTY PAPER CODING (2) Dirty paper coding is a coding technique that pre-cancels known interference without power penalty. Only the transmitter needs to know this interference, but full channel state information is required everywhere to achieve the weighted sum rate Dirty Paper Coding. Dirty Paper Coding technique requires knowledge of the interference state in a non-causal manner [8]. The design of a DPC-based system should include a produce to feed side information to the transmitter. Interference free transmission can be realized by subtracting the potential interferences before transmission. The working of Dirty Paper Coding may be explained by the Figure 4.

Figure 2. Uplink channel model for MU-MIMO The downlink model is shown in Figure 3. The received signal is given by

y H u

DL u

x  zu , where u=1, 2, 3……..K

(3)

Figure 4. Communication system model using Dirty Paper Coding

The overall system can be represented by following equations The received signal for such system is given by

y  1  y2        y K 

H 1   DL H 2    +  DL  H K  DL

 z1     z2        z K 

(4)

S= Z+P+Q (5) Where, P is arbitrary interference known at transmitter, N is statistically independent Gaussian random variable. If known interference P is subtracted at receiver, it poses no problem. Similarly, known interference subtracts from transmitter, then transmitted signal Z'=Z-P (6) Now, the received signal is given by S'=Z'+P+Q

(7)

S'=Z-P+P+Q =Z+Q

(8)

IV. MATHEMATICAL EXPRESSION OF DIRTY PAPER CODING [7]

Figure 3. Downlink channel model for MU-MIMO

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Let consider the case of NB=4 (Number of Base station antennas), K = 4 (Number of Users) and NM,u =1 (Number of user at Mobile station) where u=1,2,3,4. If the uth user signal is given by u  C , then the received signal is given as

~ x

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x ~ x

 y   DL   ~     1   H 1DL   x 1   z1   y2  H 2   ~ x 2  z 2     DL   ~      y3   H 3   x 3   z 3     DL   ~ x    y4  H 4   4  z 4 Here

H

DL u

C

14

1

(9)

DL

l11  DL l H u  l 21  31 l 41

0   q1    0  q 2    0  q   3 l 44 q4

22

l l

32 42

33 43

1

2

3

2

31

3

2

3

(10)

H

4

l l l

22 32 42

0 0

l l

33 43

0   x1   z1      0   x2   z 2   0   x3   z3      l 44  x4  z 4

(11)

1

11

1

1

(12)

(15) 43

42

2

44

3

44

(16)

44

The pre-coded signal by the equations (13), (14), (15) and (16) can be expressed as

 x1  1 ~    x 2   0 ~ x  0  ~3   x 4  0

0 1 0 0

1  x1      0  x2    x   0  3   l 41  x4   l 44

0  ~ x 1 ~   0  x 2  0  ~ x 3  ~  1  x 4 

(17)

0 0 0    x1  1 0 0  ~  x 2 ~  0 1 0  x 3  ~ 0 0 1  x 4 

(18)

0 0 1 0

0 1  l 32

l

0   x1 0 0    x2   1 0  ~   x 3 ~  0 1  x 4  0

33

0 0 1

0 0

0

1

l l

42 44

 l 43

l

44

(19)

0  x1  0    x2  0    x3 1  ~    x 4 

(20)

By combining these four equations following pre-coded dirty paper coding is achieved.

The equation for interference free for first user is

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1

 x1   1    0  x2     x   l 31  ~3   l 33  x 4   0

From the equation (11) the received signal for the first user is given by

y l x  z

4

 x1   1    l 21  x2    ~   l 22 x 3 ~   0  x 4   0

DL y     z1   1   H 1DL     y2  H 2  H  z 2  x     DL  Q  z3  y3   H 3    DL      z 4   y  4  H 4 

0

32

1

41

effect of Q in equations (10) is eliminated through the channel by leaving the lower triangular matrix after transmission. The received signal is given as

l11   l 21 l  31 l 41

(14)

l l l x ~ x  x x  x l l l 4

4

T

1

3

33

4

3

1

l l x ~ x  x x l l

T

1

2

can be decomposed as

q , q , q , q are orthonormal vectors. Let signal x  x x x x  denotes a pre-coded x  ~ for ~ x ~ x ~ x ~ x  . Transmitting Q x , the Here

21

2

22

H

l l l

l x ~ x  ~ x l

is the channel gain between BS and uth

0 0

(13)

By the same process equations for second, third and fourth users are as follows

user. The Channel matrix

0

1

28

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0

l

22

0 0

0 0

l

33

0

0  ~ x 1   z1  ~    0   x 2  z 2    z3 0 ~ x 3     l 44  ~ x 4  z 4

Bit error rate versus Eb/No 0.4

0.3

(21)

It is concluded that Dirty Paper Coding is a scaled inverse matrix of the lower triangular matrix which is obtained from the channel gain matrix. V.

Without DPC With DPC

0.35

Bit Error Rate

y    1  l11  y2  0    y3   0   0  y4 

0.25 0.2 0.15 0.1 0.05

SIMULATIONS AND DESIGN

0

For simulations, matrix is taken with perfect channel state information at the receiver. QPSK modulation scheme is used for transmission. Equal power allocation is considered for all antennas at the transmitter. Ideal antenna length, λ/2 is taken for analysis [9]. Antenna arrays arrangement is side by side system. The following design specifications are taken.

NO. OF BASE STATION (BS) ANTENNA NO. OF MOBILE STATION(MS) ANTENNA NO. OF USERS

4 4 10,20,30

4

6

8

10 12 Eb/No (dB)

14

16

18

20

Bit error rate versus Eb/No 0.4 Without DPC With DPC

0.35 0.3

Bit Error Rate

250

2

Figure 6. BER when number of user are 20

Table 1.Desisgn specifications for Dirty Paper Coding NO. OF FRAMES 10 NO. OF PACKETS

0

0.25 0.2 0.15 0.1 0.05

VI. RESULTS

0

Bit error rate analysis is done for 4×4 matrix for with Dirty Paper Coding and without Dirty Paper Coding. The simulation is done between 0 to 20 dB. The number of iteration is 5000. Figure 5, 6 and 7 show the simulation results when numbers of users are 10, 20, and 30 at mobile station. Bit error rate versus Eb/No 0.45 Without DPC With DPC

0.4

0

2

4

6

8

10 12 Eb/No (dB)

14

16

18

20

Figure 7. BER when number of users are 30 Analysis shows that as the numbers of users increase, the performance of Dirty Paper Coding increases. It is observed that BER is reduced approximately 25% to 35% at 6 dB With Dirty Paper Coding. VII.

CONCLUSION

0.35

From the analysis it is concluded that system has better bit error performances when Dirty Paper Coding is used. Bit Error Rate is reduced when the numbers of users are increased

Bit Error Rate

0.3 0.25 0.2 0.15

REFERENCES

0.1 0.05 0

0

2

4

6

8

10 12 Eb/No (dB)

14

16

18

20

[1] Z.Tu and R.S. Blum, “ Multi-user diversity for a Dirty Paper approach,” IEEE Communication, Letter , Vol. 7, no. 8, pp. 370-372, 2003. [2] G.J.Foschini and M.J Gans, “On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas,” Wireless Personal Communications, Vol. 6, pp. 311-315, 1998.

Figure 5. BER when number of users are 10 www.ijeee-apm.com

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[3] P. N. Fletecher, M. Dean, and A. R. Nix, “Mutual coupling in multi element array antennas and its influence on MIMO channel capacity,” Electronics Letters, Vol. 39, no. 4, pp. 342-344, 2003. [4] R. Janaswamy, “Effect of element mutual coupling on the capacity of fixed length linear arrays,” Antennas and Wireless Propagation Letters,Vol. 1, no.8, pp.157-160, 2002. [5] Aditya kumar, Ajith Bhatt, Anil M .V., Prahlad T Kulkarni, “Dirty Paper Coding- A Novel Approach for Compact MIMO Systems,” IEEE Second International Conference on Communication System, Network and Application, pp. 86-89, 2010 [6] Foschini,G.J, “Layered space–time architecture for wireless communication in fading environment when using multi-element antennas,” Bell Labs Tech.J.,1(2), pp. 41-59,1996. [7] Yong Soo Cho, Jaekwon kim Won Young Yang, Chung-Gu Kang, MIMO-OFDM Wireless Communication with Matlab, 2 nd ed., Wiley Singapore, 2010. [8] U.Erez, S.Shami, and R.Zamir,“Capacity and lattice strategies for cancelling known interference,” in Proc. Int. Symp. of Information Theory Application , pp. 681-684, 2000, [9] C.A.Balanis, Antenna Theory: Analysis and Design, 2 nd ed, Wiley, New York, 1997

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