International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 2- April 2015
Hybrid Diversity Technique for Minimizing
Fading
B. Suresh Ram#, Dr. P. Siddaiah*, A. Kishore Reddy$
#Assoc. Professor, CMRCET, Hyderabad, *Dean, ANUCET, Guntur, $Asst. Professor, CMRCET, Hyderabad
Abstract:
In this Paper we propose a design which is the
combination of selection diversity and maximal ratio combining
techniques for minimization of fading. This system is analyzed
and compared with the other techniques by deriving the
expression for the Symbol Error Probability (SEP) of Hybrid
Selection-Maximal Ratio Combining wireless systems for
BFSKmin modulation scheme under multipath fading
environment. Independent Rayleigh fading diversity branch is
assumed for analysis with equal Signal-to-Noise Ratio averaged
over the fading channels. Virtual branch technique, which
transforms the ordered physical branches, which are dependent
into independent, and identically distributed virtual branches is
used, thereby permitting the derivation of exact SEP
expressions.
Keywords: Hybrid diversity, Symbol error probability,
diversity reception, virtual branch technique, rayleigh
fading channel
that “the expressions become extremely unwidely” for
L>3. The average signal-to-noise ratio (SNR) of hybrid
diversity system was derived in [2]; in [3], a virtual branch
technique is introduced to succinctly derive the mean as
well as the variance of the combiner output SNR of the
hybrid diversity system.
In this paper we extend [4] to derive symbol error
probability (SEP) for BFSKmin modulation with hybrid
system for any L and N under the assumption of
independent Rayleigh fading on each diversity branch with
equal SNR averaged over the fading. Selection combining
(SC) and MRC are shown to be special cases of our results.
Numerical results are illustrated for BFSKmin modulation
scheme and finally remarks and conclusions are presented.
I. INTRODUCTION
II. SYSTEM MODEL
Hybrid diversity is considered an effective
combining technique for achieving a good compromise
between system performs and complexity, by coherently
combining L largest signals form N available branches.
This scheme has been extensively studied when diversity
gain branch gains are independent, both ideally and non
ideally distributed, for general fading environments.
However, in practice, there often exist applications where
independent diversity branches are not available. For
example, in compact antenna systems, such as those
employed in handsets, the diversity branch fading are
correlated due to space limitations. Hybrid SelectionMaximal Ratio Combining is a diversity combing scheme
where L out of N diversity branches are selected and
combined using Maximal Ratio Combining (MRC). This
technique provides improved performance over L branch
MRC when additional diversity is available. Recently,
hybrid diversity has been considered as an efficient means
to combat multipath fading [1],[2],[3]. The bit error rate
(BER) performance of an hybrid diversity with L=2 and
L=3 out of N branches was analyzed and it was pointed out
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International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 2- April 2015




1
   ak ( ) 
d
1
k 1 0
n 1 
1  k ( ) 
n

K
III. SEP FOR COHERENT MODULATION WITH
HYBRID DIVERSITY TECHNIQUE
pe, S / MRC
Symbol error probability (SEP) for coherent modulation
with hybrid diversity technique for any L and N under the
assumption of independent rayleigh fading on each
diversity branch with equal SNR averaged over the fading
[5] is given by
pe, S / MRC
N
(3)
B. Limiting Case 2: MRC System
L


1
   ak ( ) 

k 1 0
1  k ( ) 


N


1
 
d
L
n  L 1 
1  k ( ) 
n

K
k
k
In MRC the received signals from all diversity branches are
weighted and combined to maximize the SNR at the combiner
output
[7].
The
N
N
i 1
i 1
output
SNR
of
MRC
is
 MRC    i     i .
(4)
(1)
MRC is a limiting case of hybrid diversity with L=N.
Where ak ( ) ,  , 
k
k
( )
are
the
parameters
particular to a specific modulation format and are
independent of the instantaneous. These parameters are
different for different coherent modulations
Substituting L=N into (1), the SEP with MRC is
pe, S / MRC
k
LIMITING CASES
SC is the simplest form of diversity combining whereby
the received signal from one of
N diversity branches is
selected
SNR
The
output
(5)
IV. SEP OF BFSKmin
A. Limiting Case1: SC System
[6].
N


1
   ak ( ) 
 d
k 1 0
1  k ( ) 
K
of
SC
The generalized expression for SEP for coherent
detection of BFSKmin modulation using hybrid diversity is
given
by
substituting
the
values,
is
ak ( ) 
 SC  max{ i }   (1).
1
2
1
k 
k ( )  (1  32 ) csc2 ( ) , K  1 ,


2
in (5)
(2)
The SEP expression for BFSKmin using hybrid diversity
Note that SC is limiting case of hybrid diversity
reduces to
with L=1. Substituting L=1 into (1), the SEP with SC
becomes
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International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 2- April 2015

Gain(dB)
L

1
1

2
 1  0.606sc ( ) 
0
2
Table.1 Diversity gain of hybrid diversity
technique
for various L with N=4 at 10-2
Pe, S / MRC  
Fig.2 shows the performance of BFSKmin of


N


1

d
L
n  L 1 
1  0.606 csc 2 ( ) 
n

(6)
hybrid technique for various N with L=2. Although the
incremental gain with which additional combined branch
becomes smaller as N increases, the gain is still significant
even with N=8. Furthermore, for L=2 at a 10-2 SEP, Hybrid
technique with N=8 requires about 6 dB lower SNR than 2branch MRC
V. RESULTS AND DISCUSSIONS
Fig.1 shows the performance of BFSKmin of hybrid
technique for various L with N=4. When L=1 the diversity
system becomes selection combining and when L=4, it
becomes maximal ratio combining. It is seen that most of
the gain of hybrid diversity is achieved for small L, e.g the
SEP for hybrid diversity is within 1 dB of MRC when
L=N/2.
Fig.2 Symbol Error Probability of BFSKmin with hybrid
diversity as a function of the average SNR per branch
for various N with L=2.
VI. CONCLISIONS
Fig.1 Symbol Error Probability of BFSKmin with hybrid
diversity technique as a function of the average SNR
per branch for various L with N=4.
Diversity
L=1
L=2
L=3
L=4
10.5
12.5
13.5
14
ISSN: 2231-5381
We designed a hybrid system which is the combination
of SC and MRC and its performance is evaluated using by
derived the SEP expression for coherent detection of
BFSKmin modulation in multipath-fading wireless
environments. A general expression was derived in terms
of the parameters of the specific modulation schemes. In
hybrid diversity, L out of N diversity branches are selected
using SC and combined using MRC. This technique
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International Journal of Engineering Trends and Technology (IJETT) – Volume 22 Number 2- April 2015
provides improved performance over L branch MRC when
additional diversity is available. We considered
independent Rayleigh fading on each diversity branch with
equal SNR’s, averaged over the fading. We analyzed this
system using a “virtual branch” technique which resulted
in a simple derivation of the SEP for arbitrary L and N
integral,” IEEETrans. Commun., vol. 46, no. 2, pp. 200210, Feb. 1998.
VII. REFERENCES
[1] Thomas Eng, Ning Kong, and Laurence B. Milstein,
“Comparison of diversity combining techniques for
Rayleigh-fading channels,” IEEE Trans. Commun., vol.
44, no. 9, pp. 1117–1129, Sept. 1996.
[2] Ning Kong and Laurence B. Milstein, “Combined
average SNR of a generalized diversity selection
combining scheme,” in Proc.IEEE Int. Conj. on Commun.,
June 1998, vol. 3, pp. 1556–1560, Atlanta, GA.
[3] Moe Z.win and jack H. winters, Analysis of hybrid
selection / maximal ratio combining in Rayleigh fading,”
in
proc.IEEE
Int.conf.
On
common,
June
1999,
vol.1, pp.6-10, Vancouver , Canada,
[4] A1bert Nikolaevich Shiryaev, Probafnlity, SpringerVerlag, New York, second edition, 1995. Richard Durrett,
Probability: Theory and Examples, Wadsworthand
Brooks/Cole Publishing Company, Pacific Grove,
California, first edition, 1991.
[5] Moe Z.win and jack H. winters, Analysis of hybrid
selection / maximal ratio combining in Rayleigh fading,”
IEEE Trans.commun., Vol.47, pp. 1773-1776, Dec.1999 .
[6] Peter J. Bickel and Kjell Doksum, Mathematical
Statistics: Basic Ideas and Selected Topics, Holden-Day,
Inc., Oakland, California,first edition, 1977.
[7] A. Annamalai, C. Tellambura, and Vijay K. Bhargava,
“A unified approach to performance evaluation of diversity
systems on fading channels,” “m Wireless Multimedia
Network Technologies, R. Ganesh and Z. Zvonar, Eds.
Kluwer Academic Publishers, 1999.
[8] John G. Proakis, Digital Communications, McGrawHill, Inc., New York,3rd edition, 1995
[9] Marvin K. Simon and Dariush Divsalar, “Some new
twists to problems involving the Gaussian probability
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