International Journal of Engineering Trends and Technology (IJETT) – Volume 13 Number 6 – Jul 2014
Signal Transmission through Selection Combining
Diversity Technique in Multiple Input Multiple
Output Systems
Mr. Prashant Singh
Delhi,India
Abstract-Selection combining diversity technique of
combining two or more signals in such a manner that the
signal with the largest signal to noise ratio is selected first
and this kind of diversity technique is generally used to
eradicate long term fading. The Rayleigh fading model
has been discussed. The definition of multiple input
multiple output systems has also been discussed. The
method of signal combining through selection combining
diversity technique has also been studied.
Keywords: Rayleigh fading, Binary phase shift keying,
Additive white Gaussian noise channel, signal to noise
ratio.
autocorrelation function of the Rayleigh fading channel is
periodic and the envelope decays slowly after the initial zero
crossing.[5][6]
The received signal at the receiver from the transmitter while
passing through a fading channel can be expressed as
y(t) = A ∑
INTRODUCTION
Diversity technique is generally used to eradicate the effects
of fading and intersymbol interference. It is a process of
combining two or more signals in such a manner that the
effects of interference and fading are reduced and the signal
clarity improves. The diversity technique used in this paper
is the selection combining technique and the signal
transmission through multiple input multiple output systems
and using selection combining diversity technique has been
discussed.
II.
MATHEMATICAL
FADING
MODEL
OF
RAYLEIGH
(i))
Here, a(i) is the attenuation of the ith multipath component
and (i) is the phase shift of the ith multipath component.
These are random variables. The above equation can also be
expressed as[3]
y (t) = A (
I.
( ) cos(2 ft +
(
) cos (2 ft ) -
(t)
sin (2 ft ) )
Here, ( ) and ( ) are random processes[1].If the value
of N is large which means that a large number of scattered
waves are present, after applying the central limit theorem
we get ( ) and
( ) are zero mean Gaussian random
variables.[2]
The instantaneous signal to noise ratio per bit in a fading
channel is given by
= ((R)^2) ( ) [3]
Here, R is the Rayleigh distribution and is the signal to
noise ratio. is the signal power per bit while
is the
power spectral density of the noise signal.[2]
The probability of error for Binary phase shift keying when
Rayleigh fading[3][2] model is a sort of collection of a large
Rayleigh fading is employed is given as:
number of objects in the environment that can scatter or
deflect the signal much before it has arrived at the
P = 0.5 ( 1 – (avg ( )/(1+ avg ( ))) [3]
receiver.[4]The central limit theorem states that if the signal
scattering is more than the threshold level the impulse
MULTIPLE INPUT MULTIPLE OUTPUT SYSTEMS
response of the system can be modelled to be the Gaussian III.
process [2][1]and the parameters of the process are
MIMO systems are those in which there are multiple
independent of the distribution of the individual components.
antennas as input to the system and multiple antennas as
This process is zero mean as there is no dominant scattered
output to the system[4][5].The MIMO systems provide a
components[2] .The phase angle is evenly distributed
linearly increasing sgnal transmission capacity which
between 0 and 2π radians. The
increases with an increase in the number of antennas.This
increase does not require an increase in the bandwidth or
power to the system[3].MIMO systems exploit the fading
ISSN: 2231-5381
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Page 291
International Journal of Engineering Trends and Technology (IJETT) – Volume 13 Number 6 – Jul 2014
effects so as to increase the channel capacity[2].Spatial
diversity is used to increase the signal to noise ratio so that
the signal quality at the receiving end can improve. Other
diversity techniques like polarization, frequency and time
diversity [2]can also be used to improve the signal clarity. In
a MIMO system the data is transmitted in a large number of
parallel streams and each of these streams are transmitted
through the communication channel through distinct paths
and hence suffer different amounts of time delays and hence
are detected at the receiver at varying differences of times so
that some are able to survive the deep fading effects and
hence certain useful output can be obtained[2].The data
signals received at the output should not be correlated with
each other and this would increase the signal to noise ratio of
the signals received at the receiver as output to the MIMO
system[2].The output signals should be linearly independent
to each other.[2]
Instantaneous signal to noise ratio in branch i is given as
=(
) ( | ℎ |^2) [3]
ℎ is the channel gain that is a complex quantity.
E is the energy per symbol while
density of the white noise
is the power spectral
Probability density function of the signal to noise ratio in
branch i is given as
P(i)=
exp(- / ) [2]
is the average signal to noise ratio.
Average output signal to noise ratio is given as
=
∑
(1/ )[2]
Fig 1 MIMO System
IV.
SELECTION
TECHNIQUE
COMBINING
DIVERSITY
There are difficulties in the transmission of signals through
the multiple input multiple output systems such as signal
interference, path loss, shadowing etc[2].This is due to the
fact that the signals have to go through different paths from
the transmitter to the receiver and hence they suffer from
various disturbances[2].They suffer from different amounts
of attenuations and suffer from large scale or small scale
fading.[2]
So as to improve the signal quality we have to use the
diversity techniques[2].The selection combining diversity
technique involves the selection of the signal with the
highest signal to noise ratio.
Fig 2 Selection combining diversity technique
ISSN: 2231-5381
Fig 3 Signal to noise ratio vs time for selection combining technique
V.
IMPLEMENTATION AND RESULTS
Fig 4 Bit error rate vs signal to noise ratio for selection combining and
Rayleigh fading
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International Journal of Engineering Trends and Technology (IJETT) – Volume 13 Number 6 – Jul 2014
nRx=1 represents Rayleigh fading channel and nRx=2
represents Selection combining diversity technique.
VI.
CONCLUSION
The selection diversity combining technique is not as
efficient as the other diversity techniques like maximal ratio
combining and the equal gain combining techniques but it
reduces the fading effect to a certain extent. The type of
modulation used in my implementation is binary phase shift
keying technique and the fading used is the Rayleigh fading .
In selection combining diversity technique it is difficult to
measure the signal to noise ratio alone and a switching
technique has to be used.
REFERENCES
[1] Simon Haykin,”Communication Systems”,Wiley Publisher
[2] T Rappaport,”Wireless Communication:Principles and
practice”,Prentice Hall,Inc New Jersey,1996
[3] William Jakes,”Microwave Mobile Communications,IEEE Press 1974
[4] J D Parsons,”The Mobile Radio Propagation Channel”,John Wiley and
Sons Limited,2000
[5] J Proakis,”Digital Communications”,McGraw Hill,Inc New York,Third
edition ,1995
[6] J Proakis and M Salehi,”Contemporary Communication Systems using
MATLAB”,Brooks/Cole,2000
[7] J Preyton Z Peebles,”Probability,random variables and random signal
principles”,McGraw Hill,Inc 1993
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