International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013
Riciain Channel Capacity Comparison Between
(8X8) And (4x4) MIMO
Vivek Mankotia, Ankush Kansal
ME student THAPAR UNIVERSITY PATIALA INDIA , Assistant Professor, ECED THAPAR UNIVERSITY PATIALA INDIA
ABSTRACT The growth demand of Multimedia application
services and growth of contents of wireless application lead to
increasing interest to high speed communication. Multiple
input and multi output system are today considered as one of
most important research area of wireless communication. The
need of wireless multimedia application require need of higher
data rate. In this paper comparison of Rician channel capacity
has been used as measure for the efficiency of MIMO (8X8) and
(4x4) system. We have calculated the Rician channel capacity
with CSI or without CSI at transmitter with simulating
MATLAB.
Keywords
MIMO (Multi input Multi output), CSI(channel state
Information),MISO, SIM0
11. SYSTEM MODEL
We have [1] consider a MIMO system with
transmit array of
antenna and receive array of
antenna as shown in figure 1 . The transmitted
matrix is
× 1 column matrix X where
is ith
component which is transmitted from ith antenna.
If channel is unknown at the transmitter side we
⁄ . is given to
assume [2] that equal power
each transmitter antenna.
1. INTRODUCTION
MIMO system use array of multiple antennas
at both transmitter and receiver end. In the case of
MIMO system capacity increase and BER reduces.
Channel capacity is defined as the maximum rate
at which data can be transmitted with small error
probability. The capacity of MIMO channels is
calculate for the Rayleigh scenario. But in
practice, MIMO channels do not always follow
the Rayleigh fading condition. Actually, there is a
line-of-sight (LOS) path between the transmitter
and the receiver, and in such conditions, the
channel is represented by the Rician fading
model. Mathematically, the random channel
matrix in a MIMO Rician fading channel is a
complex Gaussian matrix with a nonzero mean
matrix, The Rayleigh fading model is a special
case of the Rician fading model by setting the
mean to zero.
ISSN: 2231-5381
T
R
A
N
S
M
I
T
T
E
R
R
E
C
E
I
V
E
R
CHANNEL
FIGURE 1 MIMO SYSTEM
Where
is the power across transmitter
irrespective number of antennas where
is
a ×
identity matrix. The transmitted signal
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013
bandwidth is so small that channel is assumed to
flat.
The channel matrix H is a
× complex
matrix. The component ℎ , of the matrix is the
fading coefficient from jth transmit antenna to ith
receive. If we suppose that channel matrix is
known at only receiver side not at transmitter side.
The channel matrix at receiver can be estimated by
training sequence. Noise at the receiver is another
column of size
× 1 , denoted by n. For a
deterministic channel as
∑
|ℎ , | =
, i = 1 , 2 ,3 …
DIFFRACTION
LOS
Transmitter
receiver
(1)
111. MIMO CHANNEL CAPACTY
For two random vector x and y the mutual
information is defined as
I(x,y) = H(y) – H(y|x)
(2)
Where H(y|x) the conditional entropy.
( ( | ))]
H( x/y) = -E[
Fig. 2
WAVE PROPAGATION
(3)
For a linear complex model
=
+
(4)
The mutual information is given as
I(y,x|H) =log det
+
(5)
The Shanon capacity is the maximum mutual
information between received vector and transmitted
vector
C(H)= det
+
(6)
When full transmitter CSI and receiver CSI are
available, the capacity of the MIMO system is
maximum.
SCATTERING
LOS (line of sight)
1V. RICIAN CHANNEL
There is line-of-sight (LOS) path between the
transmitter and the receiver, and in such
conditions, the channel is represented by the
Rician fading model. We can express H in matrix
notation as[9]
H=c
+
(7)
Where the specular [3] and scattered components
of H are denoted by superscripts, c>0, d >0 and
+
= 1.
is a matrix of unit entries. If there is no
correlation at the transmitter or at the receiver side
then the entries of
are independent usually
denoted by
.
REFLECTION
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013
•
If there is correlated fading then the
matrix can be modeled as [5],[6]
UNCORRELATED CHANNEL
100
90
=
∗
∗
(8)
Where
and
are the correlation matrix at
the transmitter and at the receiver side .
The correlation matrix R is defined[4]
≤
=
∗
>
(9)
H(correlated)[7][8]
•
•
•
∗H1+
=
∗
∗
80
70
capacity(bits /s /Hz)
•
•
Nt=Nr=8;k=0
Nt=Nr=8;k=5;
Nt=Nr=8; k=10
Nt=Nr=8;k=very large;
60
50
40
30
∗
20
(10)
10
0
v. RESULTS
0
5
10
15
SNR in dB
20
25
UNCORRELATES CHANNEL
Fig. 4 Rician chaneel capacity (8X8) when transmitter know the CSI.
45
Nt=Nr=4;k=0;
Nt=Nr=4;k=5;
Nt=Nr=4; k=10;
Nt=Nr=4;k=VERY LARGE;
40
TABLE 1
FOR MIMO(4X4) ( SNR IN db)
K
SNR=15
CAPACITY
0
24 bps/Hz
5
19 ‘’
10
17
SNR=25
CAPACITY
37 bps/Hz
30
28
SNR=30
CAPACITY
44 bps/H
37
35
20
TABLE 11
15
FOR MIMO(8X8) ( SNR IN db)
K
SNR=15
SNR=25
CAPACITY
CAPACITY
SNR=30
CAPACITY
0
5
10
92 bps/H
78
72
35
c a p a c it y (b it s / s / H z )
30
25
10
5
0
0
5
10
15
SNR in dB
20
25
30
Fig. 3 Rician chaneel capacity (4X4) when transmitter know the CSI
ISSN: 2231-5381
53 bps/Hz
40 ‘’
36
80 bps/Hz
65
60
In the case of mimo (8x8) capacity is more than as
compare to (4X4) MIMO system. When k=0 it acts as
rayleigh chaneel. When value of k is very very large it acts
as gaussian chaneel. As value of k increases the capacity
decreases.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013
FOR MIMO(4X4) ( SNR IN db)
K
SNR=15
CAPACITY
0
17 bps/Hz
5
12 ‘’
10
11
35
Nt=Nr=4;k=0;
Nt=Nr=4;k=5;
Nt=Nr=4; k=10;
Nt=Nr=4;k=VERY LARGE;
30
SNR=25
CAPACITY
28 bps/Hz
23
21
SNR=30
CAPACITY
35 bps/H
29
27
c a p a c it y (b it s / s / H z )
25
When transmitter has no idea of csi
20
TABLE IV
FOR MIMO(8X8) ( SNR IN db)
K
SNR=15
CAPACITY
0
32 bps/Hz
5
22 ‘’
10
19
15
10
SNR=25
CAPACITY
57 bps/Hz
42
28
SNR=30
CAPACITY
70 bps/H
54
49
5
0
0
5
10
15
SNR in dB
20
25
30
Fig. 5 Uncorrelated(4x4) rician chaneel capacity when transmitter has no
idea of CSI
In the case of mimo (8x8) capacity is more than as
compare to (4X4) MIMO system. When k=0 it acts as
rayleigh chaneel. When value of k is very very large it acts
as gaussian chaneel. When transmitter has no idea of CSI
equal power is given to each transmitter. As value of k
increases the capacity decreases.
In this case equal power is given to each
transmitter
35
UNCORRELATED CHANNEL
70
Nt=Nr=8;k=0
Nt=Nr=8;k=5;
Nt=Nr=8; k=10
Nt=Nr=8;k=very large;
60
Nt=Nr=4;rt=0.3 rr=0.5;k=0
Nt=Nr=4;rt=0.3 rr=0.5;k=5
Nt=Nr=4;rt=0.3 rr=0.5 k=10
Nt=Nr=4;rt=0.3 rr=0.5;k=1000
30
25
c a p a c it y (b it s /s / H z )
c ap ac ity (bit s / s /H z )
50
40
30
20
15
20
10
10
5
0
0
5
10
15
SNR in dB
20
25
30
Fig. 6 Uncorrelated(8x8) rician chaneel capacity when transmitter has no
idea of CSI
0
0
5
10
15
SNR in db
20
25
Fig. 7 Correlated Rician chaneel capacity(4x4) when transmitter know the CSI
TABLE 111
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International Journal of Engineering Trends and Technology (IJETT) – Volume 4 Issue 6 - June 2013
VI CONCLUSION
80
Nt=Nr=8;rt=0.3 rr=0.5;k=0
Nt=Nr=8;rt=0.3 rr=0.5;k=5
70
The effect of CSI is negligible at high SNR . For
low and values of SNR, CSI improves capacity for
Rician fading. For all values of SNR, as the value
of K increases, the Ergodic capacity decreases.
Rician channel capacity in case of (8X8) system is
more than (4x4)MIMO system.
Nt=Nr=8;rt=0.3 rr=0.5 k=10
Nt=Nr=8;rt=0.3 rr=.5;k=1000
capacity(bits/s/Hz)
60
50
40
30
20
V111 REFERENCES
10
0
0
5
10
15
SNR in db
20
25
30
[1]
Fig. 8 Correlated Rician chaneel capacity(4x4) when transmitter know the CSI
[2]
TABLE V
FOR MIMO(4X4) ( SNR IN db) rt=0.3 rr=o.5
K
SNR=15
SNR=25
CAPACITY
CAPACITY
0
19bps/Hz
29 bps/Hz
5
13 ‘’
21
10
12
19
[3]
SNR=30
CAPACITY
35 bps/H
26
24
[4]
[5]
TABLE VI
FOR MIMO(8X8) ( SNR IN db) rt=0.3 rr=o.5
K
SNR=15
SNR=25
CAPACITY
CAPACITY
0
38bps/Hz
59 bps/Hz
5
24 ‘’
42
10
20
38
[6]
SNR=30
CAPACITY
70 bps/H
54
48
. Correlation decrease the MIMO capacity.
[7]
[8]
[9]
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70
Nt=Nr=8;rt=0.3
Nt=Nr=8;rt=0.7
Nt=Nr=8;rt=0.3
Nt=Nr=8;rt=0.7
60
rr=0.3;k=0
rr=0.7;k=0
rr=0.3 k=5
rr=0.7;k=5
capacity(bits/s/Hz)
50
40
30
20
10
0
0
5
10
15
SNR in db
20
25
30
Fig. 9 Effect of correlation parameter on Rician chaneel chaneel capacity
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