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.

1. International Journal of Electrical & Electronics Engineering 26 www.ijeee-apm.com
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, 2
shivkaran_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.
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
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].
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 MULTI-
USER 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
zxHxHxHy K
UL
K
ULUL
MAC
 ............2211
(1)
  z
x
x
HHH
K
UL
K
ULUL











 
1
21
...............

2. www.ijeee-apm.com International Journal of Electrical & Electronics Engineering 27











x
x
H
K
UL

1
(2)
Figure 2. Uplink channel model for MU-MIMO
The downlink model is shown in Figure 3. The received
signal is given by
zHy u
DL
uu
x  , where u=1, 2, 3……..K (3)
The overall system can be represented by following equations















y
y
y
K

2
1














H
H
H
DL
K
DL
DL

2
1
+














z
z
z
K

2
1
(4)
Figure 3. Downlink channel model for MU-MIMO
II. ANALYSIS OF DIRTY PAPER CODING
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 4. Communication system model using Dirty Paper
Coding
The received signal for such system is given by
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]
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 Cxu
~ , then the received signal is given as

3. International Journal of Electrical & Electronics Engineering 28 www.ijeee-apm.com


























































z
z
z
z
x
x
x
x
H
H
H
H
y
y
y
y
DL
DL
DL
DL
4
3
2
1
4
3
2
1
4
3
2
1
4
3
2
1
~
~
~
~
(9)
Here CH
DL
u
41
 is the channel gain between BS and uth
user. The Channel matrix H
DL
can be decomposed as





























q
q
q
q
llll
lll
ll
l
H
DL
u
4
3
2
1
44434241
333231
2221
11
0
00
000
(10)
Here qqqq 4321
,,, are orthonormal vectors. Let
 T
xxxxx 4321
 denotes a pre-coded signal
for  T
xxxxx ~~~~ 4321
~  . Transmitting xQ
H
, the
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












































z
z
z
z
Q
H
H
H
H
y
y
y
y
x
H
DL
DL
DL
DL
4
3
2
1
4
3
2
1
4
3
2
1












































z
z
z
z
x
x
x
x
llll
lll
ll
l
4
3
2
1
4
3
2
1
44434241
333231
2221
11
0
00
000
(11)
From the equation (11) the received signal for the first user is
given by
zxly 11111

(12)
The equation for interference free for first user is
xx ~11

(13)
By the same process equations for second, third and fourth
users are as follows
x
l
l
xx ~~ 1
22
21
22

(14)
x
l
l
x
l
l
xx 2
33
32
1
33
31
33
~ 
(15)
x
l
l
x
l
l
x
l
l
xx 3
44
43
2
44
42
1
44
41
44
~ 
(16)
The pre-coded signal by the equations (13), (14), (15) and
(16) can be expressed as









































x
x
x
x
x
x
x
x
~
~
~
~
~
~
~
4
3
2
1
4
3
2
1
1000
0100
0010
0001
(17)












































x
x
x
x
l
l
x
x
x
x
~
~
~
~
~
4
3
2
1
22
21
4
3
2
1
1000
0100
001
0001
(18)












































x
x
x
x
l
l
l
l
x
x
x
x
~
~
~ 4
3
2
1
33
32
33
31
4
3
2
1
1000
01
0010
0001
(19)














































x
x
x
x
l
l
l
l
l
l
x
x
x
x
~4
3
2
1
44
43
44
42
44
41
4
3
2
1
1
0100
0010
0001
(20)
By combining these four equations following pre-coded dirty
paper coding is achieved.

4. www.ijeee-apm.com International Journal of Electrical & Electronics Engineering 29
0 2 4 6 8 10 12 14 16 18 20
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Eb/No (dB)
BitErrorRate
Bit error rate versus Eb/No
Without DPC
With DPC


























































z
z
z
z
x
x
x
x
l
l
l
l
y
y
y
y
4
3
2
1
4
3
2
1
44
33
22
11
4
3
2
1
~
~
~
~
000
000
000
000
(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. SIMULATIONS AND DESIGN
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.
Table 1.Desisgn specifications for Dirty Paper Coding
NO. OF FRAMES 10
NO. OF PACKETS 250
NO. OF BASE STATION (BS)
ANTENNA
4
NO. OF MOBILE STATION(MS)
ANTENNA
4
NO. OF USERS 10,20,30
VI. RESULTS
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.
Figure 5. BER when number of users are 10
Figure 6. BER when number of user are 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
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
REFERENCES
[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.
0 2 4 6 8 10 12 14 16 18 20
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Eb/No (dB)
BitErrorRate
Bit error rate versus Eb/No
Without DPC
With DPC
0 2 4 6 8 10 12 14 16 18 20
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Eb/No (dB)
BitErrorRate
Bit error rate versus Eb/No
Without DPC
With DPC

5. International Journal of Electrical & Electronics Engineering 30 www.ijeee-apm.com
[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, 2nd
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, 2nd
ed, Wiley, New
York, 1997