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Performance of a L-branch predetection EGC receiver over independent Hoyt fading channels for M-ary coherent and noncoherent modulations using PDF-based approach

TL;DR: In this article, the performance of a L-branch predetection equal gain combining receiver has been analyzed in independent Hoyt fading channels with arbitrary fading parameters applying classical probability density function (PDF) based approach.
Abstract: Performance of a L-branch predetection equal gain combining receiver has been analyzed in independent Hoyt fading channels with arbitrary fading parameters applying classical probability density function (PDF) based approach. An approximate but highly accurate PDF of the sum of independent Hoyt random variables has been used for the analysis. Simple and easy to evaluate expressions for the outage probability and amount of fading have been obtained. An expression for average symbol error rate, in the form of an infinite series with a single integral with finite limits has been obtained which is applicable for a number of M-ary coherent and noncoherent modulations. Numerically evaluated results have been compared with the published results to verify the correctness of the derived expressions.

Summary (2 min read)

I. INTRODUCTION

  • Performance of a predetection equal gain combining (EGC) diversity receiver in fading channels is known to be close to the performance of the optimum maximal ratio combining (MRC) receiver, with relatively less implementation complexity [1] .
  • Recently, with an aim to generalize and obtain a better fit for the experimental data, several new fading distributions such as the κ-µ, η-κ and η-µ have been proposed [7] - [9] .
  • Interestingly, in [7] an approximate but highly accurate PDF of the sum of independent Hoyt random variables (RVs) has been presented using moment based estimators.
  • This useful result can be readily applied to analyze the performance of a L-branch predetection EGC receiver in independent Hoyt fading channels using PDF-based approach.
  • In Section IV, the numerical evaluation steps have been discussed.

II. CHANNEL AND RECEIVER

  • The channel has been assumed to be slow, frequency nonselective, with Hoyt fading statistics.
  • Assuming spatial diversity fading signals are available, a predetection EGC receiver with the structure as shown in Fig. 1 has been used for receiving the signals.
  • The L-branch predetection EGC combiner cophases the received signals and produces at its output the algebraic sum of these cophased signals.
  • The detector following the combiner is suitable for the detection of the signal, corresponding to the modulation scheme employed at the transmitter.
  • The authors in a recent publication have presented this PDF which can be given as [10] EQUATION Using (5) it is now convenient to analyze different performance measures of a predetection EGC receiver in independent Hoyt fading channels using the PDF-based approach.

C. Average Symbol Error Rate

  • For a given modulation scheme, the ASER of any receiver can be obtained by averaging the conditional SER P(ε|γ) over the PDF of the receiver output SNR p γ (γ).
  • For a number of M-ary modulation schemes these parameter values have been listed in Table I .
  • The indefinite integral involved can be analytically solved using the identity [11, (3.381.4) ].
  • The above expression (12) for the ASER of a predetection EGC receiver in Hoyt fading channels is useful for the following two major reasons:.
  • Using the available software packages such as MATLAB and MATHEMATICA etc. this evaluation can be performed easily for a required degree of accuracy.

1) M-ary Phase Shift Keying Modulation: Substituting the parameters for MPSK modulation from Table I into (12), the ASER expression can be expressed as

  • 2) M-ary Differential Phase Shift Keying Modulation: Substituting the parameters for MDPSK modulation from Table I into (12), the corresponding ASER expression can be given as EQUATION ) where f (θ) is defined in Table I .
  • NUMERICAL EVALUATION Analytical expressions for P out (7) , AF (8) and ASER (13)-( 16) have been numerically evaluated.

V. RESULTS AND DISCUSSION

  • From the curves shown, it can be inferred that the severity of fading increases with increase in the fading parameter b and decreases with increase in L. ASER versus SNR E s /N 0 per branch has been plotted for MPSK and MDPSK modulations in Figs.
  • It is important to observe the low SNR region of these plots where the curves are either crossing each other or overlapping.
  • This gives an option to choose a less complex modulation scheme and/or less number of branches when receivers are likely to operate in low SNR environments.
  • The plotted results have been compared with the matching cases in [5, Figs. 4(a) and 4(b)] and found to be matching closely.
  • The observations from these plots can be explained in the manner similar to that presented for equal branch SNR case.

VI. CONCLUSION

  • The authors have analyzed the performance of a Lbranch predetection EGC diversity receiver in independent Hoyt fading channels, with non-identical and arbitrary fading parameters, applying the PDF based approach.
  • Using an approximate but highly accurate expression for the PDF of the sum of independent Hoyt RVs, expressions for the outage probability, amount of fading and ASER have been obtained.
  • The ASER expression is in the form of an infinite series with a single integral having finite limits and is applicable for a number of coherent and noncoherent modulation schemes.
  • For the purpose of illustration, simplified expressions for the MPSK and MDPSK modulations have also been given.
  • Numerically evaluated results have been plotted and compared with the particular cases of the published results to check the correctness of the obtained analytical expressions.

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Performance of a L-Branch Predetection EGC
Receiver over Independent Hoyt Fading Channels
for M-ary Coherent and Noncoherent Modulations
using PDF-Based Approach
Akash Baid
IIT Guwahati, India
Email: akash@iitg.ernet.in
Pratik Kotkar
IIT Guwahati, India
Email: pratik@iitg.ernet.in
P. R. Sahu
Department of ECE
IIT Guwahati, India
Email: prs@iitg.ernet.in
Abstract—Performance of a L-branch predetection equal gain
combining receiver has been analyzed in independent Hoyt fading
channels with arbitrary fading parameters applying classical
probability density function (PDF) based approach. An approx-
imate but highly accurate PDF of the sum of independent Hoyt
random variables has been used for the analysis. Simple and
easy to evaluate expressions for the outage probability and
amount of fading have been obtained. An expression for average
symbol error rate, in the form of an infinite series with a
single integral with finite limits has been obtained which is
applicable for a number of M-ary coherent and noncoherent
modulations. Numerically evaluated results have been compared
with the published results to verify the correctness of the derived
expressions.
Index Terms- Diversity, Hoyt fading, equal gain combining,
average symbol error rate, PDF.
I. INTRODUCTION
Performance of a predetection equal gain combining (EGC)
diversity receiver in fading channels is known to be close to the
performance of the optimum maximal ratio combining (MRC)
receiver, with relatively less implementation complexity [1].
The performance analysis of a L-branch predetection EGC
receiver is not easy compared to MRC. The reason is due to the
age old problem of obtaining the probability density function
(PDF) of the sum of L fading envelopes, which is not known in
closed-form for L 3 [2]. This void eliminates the possibility
of applying the direct and simple PDF-based approach [1]
to the performance analysis of a predetection EGC receiver
beyond L = 2. Over the years, in an effort to obtain the per-
formance for L 3, the researchers have developed a number
of alternative approaches such as characteristic function (CF),
Parseval’s theorem method, Pad´e approximation etc. [2]-[6].
Recently, with an aim to generalize and obtain a better fit
for the experimental data, several new fading distributions
such as the κ-µ, η-κ and η-µ have been proposed [7]-[9].
Interestingly, in [7] an approximate but highly accurate PDF
of the sum of independent Hoyt random variables (RVs) has
been presented using moment based estimators. This useful
result can be readily applied to analyze the performance of
a L-branch predetection EGC receiver in independent Hoyt
fading channels using PDF-based approach.
In this paper, we analyze the performance of a L-branch
predetection EGC receiver in independent Hoyt fading chan-
nels with arbitrary fading parameters. Analytical expressions
for the outage probability and amount of fading (AF) and
average symbol error rate (ASER) for M-ary, coherent and
non-coherent modulation schemes have been obtained.
The paper is organized as follows. In Section II, we
introduce the channel and the receiver system model. The
performance analysis has been presented in Section III. In
Section IV, the numerical evaluation steps have been discussed.
Results and discussion have been presented in Section V.
Finally, we conclude the paper in Section VI.
II. CHANNEL AND RECEIVER
The channel has been assumed to be slow, frequency non-
selective, with Hoyt fading statistics. The complex low-pass
equivalent of the signal received at the l
th
input branch (1
l L) over one symbol duration T
s
can be expressed as
r
l
(t) = α
l
e
jφ
l
s(t) + n
l
(t), 0 t T
s
, (1)
where s(t) is the transmitted symbol with energy E
s
and
n
l
(t) is the additive white Gaussian noise (AWGN) with two
sided power spectral density 2N
0
. The RV φ
l
represents the
instantaneous phase of the signal received at the l
th
branch
and the RV α
l
is the fading amplitude assumed to be Hoyt
distributed whose PDF can be given by [2]
f (α
l
) =
2α
l
l
q
1 b
2
l
exp
α
2
l
l
1 b
2
l
!
×I
0
b
2
l
α
2
l
l
(1 b
2
l
)
, α
l
0,1 b
l
1, (2)
where
l
= E
α
2
l
, b
l
is the fading severity parameter and I
ν
(·)
is the νth-order modified Bessel function of the first kind.
Assuming spatial diversity fading signals are available, a
predetection EGC receiver with the structure as shown in

1
2
L
Output
Detector
O/P Bits
EGC
Predetection
γ
1
γ
2
γ
L
γ
o
Fig. 1. Predetection EGC receiver
Fig. 1 has been used for receiving the signals. The receiver
consists of an L-branch predetection EGC combiner followed
by a detector. The L-branch predetection EGC combiner
cophases the received signals and produces at its output
the algebraic sum of these cophased signals. The detector
following the combiner is suitable for the detection of the
signal, corresponding to the modulation scheme employed at
the transmitter.
The received instantaneous SNR at the l
th
input branch of
the EGC combiner can be given by γ
l
=
E
s
N
0
α
2
l
, whose average
value is
¯
γ
l
=
E
s
N
0
E
α
2
l
=
E
s
N
0
l
. Assuming ideal cophasing of
L signals in the EGC combiner, the instantaneous output SNR
of the predetection EGC receiver can be given by [2]
γ
o
= (E
s
/LN
0
)(α
1
+ α
2
+ . .. + α
L
)
2
(3)
whose average value is
¯
γ
0
= (E
s
/LN
0
)E[α
2
], where α = α
1
+
α
2
+ . .. + α
L
. An useful expression for the PDF of α i.e.,
the sum of arbitrary number of independent Hoyt distributed
random variables has been presented in [7] using moment
based estimators which can be given as
p
α
(α) =
4
π
Γ(µ)
µ
µ+
1
2
hα
2
µ
H
µ
1
2
exp
2µhα
2
×I
µ
1
2
2µHα
2
, (4)
where = E
α
2
, h
4
=
2 + η
1
+ η
/4 and
H
4
=
η
1
η
/4. The parameters , η and µ in (4)
are required to be estimated for which the procedure is given
in the Appendix. From (3) and using the relation = E
α
2
the average output SNR can be obtained as
¯
γ
o
=
E
s
LN
0
.
An expression for the PDF of γ
o
i.e., p
γ
o
(γ
o
) can be obtained
from (4), recognizing the relation between α and γ
0
from
(3) (i.e., γ
o
=
E
s
LN
0
α
2
) and using standard formula for the
transformation of RVs. The authors in a recent publication
have presented this PDF which can be given as [10]
p
γ
o
(γ
o
) =
2
πh
µ
Γ(µ)
µ
¯
γ
o
µ+
1
2
γ
o
H
µ
1
2
e
2µh
¯
γ
o
γ
o
×I
µ
1
2
2µH
¯
γ
o
γ
o
. (5)
Using (5) it is now convenient to analyze different performance
measures of a predetection EGC receiver in independent Hoyt
fading channels using the PDF-based approach.
III. PERFORMANCE ANALYSIS
A. Outage Probability
The outage probability P
out
is a standard performance crite-
rion characteristic of diversity communication systems operat-
ing over fading channels [1]. It is defined as the probability that
γ
o
falls below a specified threshold value γ
t
. Mathematically,
P
out
=
γ
t
Z
0
p
γ
o
(γ
o
)dγ
o
. (6)
For the predetection EGC receiver in independent Hoyt fading
channels, P
out
can be obtained by substituting (5) into (6).
The integral in (6) can be solved by applying the identity [11,
(3.381.1)]]. After simplification the expression for P
out
can be
given by
P
out
=
2
12µ
π
h
µ
Γ(µ)
k=0
H
2h
2k
γ
f
2µ + 2k,
2µh
¯
γ
o
γ
t
k!Γ
µ + k +
1
2
, (7)
where γ
f
(·,·) is the incomplete gamma function [11].
B. Amount of Fading
The AF is the measure of the severity of the fading channel
often appropriate in the more general context of describing
the behavior of diversity systems with arbitrary, combining
techniques and channel statistics [1]. It is defined as the
ratio of the variance to the mean square value of the output
instantaneous SNR γ
o
. For predetection EGC receiver an
expression for AF can be given by using γ
o
from (3) as
AF =
var(γ
o
)
¯
γ
2
o
=
E
γ
2
o
¯
γ
2
o
1 =
E
α
4
2
1. (8)
Thus, AF can be obtained by evaluating E
α
4
from (19) for
k = 4 and then putting it in (8). Alternatively, it can also be
evaluated by obtaining E
α
4
directly from (4). The integration
involved can be solved using the identity [11, (3.381.4)]. The
final expression after simplification can be given as
AF =
µ +
1
2
µh
µ+2
3
F
1
µ + 1,µ +
3
2
,1; µ +
1
2
;
H
h
2
#
1,(9)
where
3
F
1
(·,·, ·; ·;·) is the hypergeometric function. The above
expression converges fast since the magnitude of its argument
H
h
< 1.
C. Average Symbol Error Rate
For a given modulation scheme, the ASER of any receiver
can be obtained by averaging the conditional SER P(ε|γ) over
the PDF of the receiver output SNR p
γ
(γ). It can be given by
[2]
P
e
=
Z
0
P(ε|γ) p
γ
(γ)dγ. (10)

TABLE I
PARAMETERS O F S E V E R A L M-A RY M O D U L ATION SCHEMES.
f (θ) = 1 cos(π/M)cos θ [2]
.
Modulation u
max
a
u
(θ) β(θ) η
u
MPSK 1
1
π
sin
2
(π/M)
sin
2
θ
π
π
M
MDPSK 1
sin(π/M)
π f (θ)
f (θ) π/2
MQAM 2
4
π
1
M
1
u
1.5
(M1) sin
2
θ
π/(2u)
MPAM 1
2
π
(1
1
M
)
3
(M
2
1)sin
2
θ
π/2
DEBPSK 2
2
π
(1)
u1
csc
2
θ π/(2u)
For an M-ary modulation scheme, P(ε|γ) can be expressed in
a unified manner as [2]
P(ε|γ) =
u
max
u=1
η
u
Z
0
a
u
(θ)e
γβ(θ)
dθ, (11)
where a
u
(θ), β(θ), η
u
and u
max
are parameters of the mod-
ulation scheme. For a number of M-ary modulation schemes
these parameter values have been listed in Table I.
A general expression for the ASER can be obtained by
substituting (5) and (11) into (10) and solving the integral
w.r.t γ
o
. The indefinite integral involved can be analytically
solved using the identity [11, (3.381.4)]. The final expression
can be given by
P
e
=
2µ
h
¯
γ
o
!
2µ
k=0
2µH
¯
γ
o
2k
(µ)
k
k!
×
u
max
u=1
η
u
Z
0
a
u
(θ)
2µh
¯
γ
o
+ β(θ)
2x
k
dθ, (12)
where x
k
4
= µ + k and (µ)
k
is the Pochhammer’s symbol [2].
The above expression (12) for the ASER of a predetection
EGC receiver in Hoyt fading channels is useful for the
following two major reasons:
1) It can be used for any digital modulation scheme for
which the parameters a
u
(θ), β(θ), η
u
and u
max
are
known.
2) It is applicable for L-independent fading branches with
arbitrary fading parameters b
l
,l = 1,2. .., L.
The above expression contains a single integral with finite lim-
its. Using the available software packages such as MATLAB
and MATHEMATICA etc. this evaluation can be performed
easily for a required degree of accuracy. It is also interesting to
note that for some particular cases, discussed below, the above
single definite integral can be analytically solved resulting in
simple algebraic expressions.
Below we present some particular cases of the modulation
schemes for which the above general expression (12) can be
simplified further.
1) M-ary Phase Shift Keying Modulation: Substituting the
parameters for MPSK modulation from Table I into (12), the
ASER expression can be expressed as
P
e,MPSK
=
1
π
2µ
h
¯
γ
o
!
2µ
k=0
2µH
¯
γ
o
2k
(µ)
k
k!
×
π
(
1
1
M
)
Z
0
dθ
2µh
¯
γ
o
+
sin
π
M
sin θ
2
2x
k
. (13)
For the case of M = 2, i.e. for BPSK modulation, (13) can be
solved using the identities [11, (3.211), (8.384.1)] which after
further simplification can be given by
P
e,BPSK
=
1
2Γ(µ)
µ
h
¯
γ
o
!
2µ
k=0
Γ
2x
k
+
1
2
k!x
k
Γ
x
k
+
1
2
×
2
F
1
2x
k
,2x
k
+
1
2
;2x
k
+ 1;
2µh
¯
γ
o
,(14)
where
2
F
1
(·,·; ·; ·) is the Gaussian hypergeometric function
[11].
2) M-ary Differential Phase Shift Keying Modulation:
Substituting the parameters for MDPSK modulation from
Table I into (12), the corresponding ASER expression can be
given as
P
e,MDPSK
=
2µ
h
¯
γ
o
!
2µ
k=0
(µ)
k
k!
π/2
Z
0
dθ
f (θ)
h
2µh
¯
γ
o
+ f (θ)
i
2x
k
,
(15)
where f (θ) is defined in Table I.
For the case of M = 2, i.e. for binary DPSK modulation,
(15) can be solved using the identities [11, (3.211),(8.384.1)]
and the resulting simplified expression can be given by
P
e,DPSK
=
2µ
h
¯
γ
o
2µh
!
2µ
k=0
2µH
¯
γ
o
2µh
2k
(µ)
k
k!
(16)
IV. NUMERICAL EVALUATION
Analytical expressions for P
out
(7), AF (8) and ASER (13)-
(16) have been numerically evaluated. For the purpose of
simplification of evaluation, without loss of generality, we have
assumed
l
|
L
l=1
= 1. This enables us to express
¯
γ
l
= E
s
/N
0
which is convenient for all evaluations. The value of fading
parameter has been assumed to be identical for all branches
i.e. b
1
= b
2
= ... = b
L
= b. The outage probability P
out
has
been evaluated as a function of the ratio
¯
γ
1
/γ
t
by expressing
¯
γ
o
/γ
t
= (
¯
γ
1
/γ
t
)(/L) in (7). The value of for any L can be
obtained by evaluating (19) for k = 2. For unequal branch SNR
case, an exponentially decaying power delay profile given by
l
=
1
e
δ(l1)
,0 δ 1, has been assumed [1]. Evaluation
of each expression requires the values of H and h which can
be obtained by first obtaining the values of η and µ from (17)-
(20) in the Appendix and then substituting them into (4). In
the evaluation of the expressions involving infinite series, 20

{
L = 6
L = 3
L = 2
¯
γ
1
/γ
t
(dB)
Outage Probability
-10 -5 5 10 20150
0.8
0.4
b =
10
6
10
5
10
4
10
3
10
2
10
1
10
0
Fig. 2. Outage probability P
out
vs.
¯
γ
1
/γ
t
for different L and b.
terms have been found to be sufficient for an accuracy at least
up to 7th place of decimal digit.
V. RESULTS AND DISCUSSION
In Fig. 2 P
out
versus
¯
γ
1
/γ
t
has been plotted for different
values of L and b. It can be observed from this figure that P
out
decreases from a maximum value of unity to very small values
with increase in the ratio
¯
γ
1
/γ
t
. This implies that the outage,
for a fixed
¯
γ
1
, varies directly with γ
t
, which is intuitively
satisfying. It can also be observed that for a fixed γ
t
, P
out
reduces with increase in L. It is due to the reason that including
more number of branches improves
¯
γ
o
resulting in less outage.
Further, it can be noted that for a given L, P
out
varies directly
with b, as expected. The outage probability results obtained
here have been compared with the published results in [5,
Fig. 5, L = 2,3] and found to be matching closely. AF versus
channel parameter b has been plotted for different values of
L in Fig. 3. From the curves shown, it can be inferred that
the severity of fading increases with increase in the fading
parameter b and decreases with increase in L.
ASER versus SNR E
s
/N
0
per branch has been plotted for
MPSK and MDPSK modulations in Figs. 4 and 5, respectively.
Curves for ASER have been shown for L = 2,3 and 6, each
one for M = 2,4 and 8. The value of b has been taken to
be 0.5 in these plots. The common observation is that the
ASER decreases with increase in E
s
/N
0
and L whereas it
increases with increase in M, which is as expected. It is
important to observe the low SNR region of these plots where
the curves are either crossing each other or overlapping. This
indicates that in this region of SNR the ASER of the receiver
is almost independent of M and L. This gives an option to
choose a less complex modulation scheme and/or less number
of branches when receivers are likely to operate in low SNR
environments. The plotted results have been compared with
the matching cases in [5, Figs. 4(a) and 4(b)] and found to
be matching closely. This observation validates the accuracy
1.0
0.8
0.2
0.0
0.6
0.4
0 0.1 0.2 0.3 0.7 0.8 0.90.4 0.5 0.6
Amount of Fading
L = 2
L = 3
L = 5
L = 6
b
Fig. 3. Amount of fading vs. b for L = 2, 3, 5 and 6.
{
5 20 25 300
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
0
E
b
/N
0
(dB)
1510
L = 6
L = 3
L = 2
ASER
2
M =
8
4
Fig. 4. ASER vs. E
s
/N
0
for MPSK modulation for different L and M.
of our derivations. ASER versus E
s
/N
0
for unequal branch
SNRs and arbitrary fading parameters b
l
has been shown in
Fig. 6. For the purpose of illustration, curves have been shown
for L = 3 and 5 each one for δ = 0,0.5 and 1 for 4PSK
modulation. For each L, we have arbitrarily taken b
1
= 0.3 and
b
l
= b
1
+0.1, 2 l L. The observations from these plots can
be explained in the manner similar to that presented for equal
branch SNR case.
VI. CONCLUSION
In this paper, we have analyzed the performance of a L-
branch predetection EGC diversity receiver in independent
Hoyt fading channels, with non-identical and arbitrary fading
parameters, applying the PDF based approach. Using an
approximate but highly accurate expression for the PDF of
the sum of independent Hoyt RVs, expressions for the outage
probability, amount of fading and ASER have been obtained.
The ASER expression is in the form of an infinite series

{
ASER
5 20 30
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
L = 6
10 15 250
L = 3
L = 2
E
b
/N
0
(dB)
2
4
8
M =
Fig. 5. ASER vs. E
s
/N
0
for MDPSK modulation for different L and M.
with a single integral having finite limits and is applicable for
a number of coherent and noncoherent modulation schemes.
For the purpose of illustration, simplified expressions for the
MPSK and MDPSK modulations have also been given. For
binary modulation cases, these finite integral expressions have
been solved to the expressions containing elementary and
special mathematical functions. Numerically evaluated results
have been plotted and compared with the particular cases of
the published results to check the correctness of the obtained
analytical expressions.
APPENDIX
ESTIMATORS FOR HOYT RANDOM VARIABLES
The expressions to obtain parameters , η and µ are
reproduced below from [7]:
η
1,2
=
2c
p
3 2c ±
9 8c
2c +
p
3 2c ±
9 8c
, (17)
µ
1,2
=
2
E[α
4
]
2
1 + η
2
1,2
(1 + η
1,2
)
2
, (18)
where = E
α
2
and c
4
=
E
[
α
6
]
3
3E
[
α
4
]
2
+2
2
E
[
α
4
]
2
1
!
2
. From (17) and
(18) two pairs of η and µ are possible i.e. (η
i
,µ
i
),i = 1,2.
The appropriate pair is the one for which the deviation
|E[α] E[α]
i
|,i = 1, 2 is the smallest.
The formula to obtain the moments of α is given as below:
E
h
α
k
i
=
k
k
1
=0
k
1
k
2
=0
.. .
k
L2
k
L1
=0
k
k
1
k
1
k
2
.. .
k
L2
k
L1
×E
h
α
kk
1
1
i
E
h
α
k
1
k
2
2
i
.. . E
h
α
k
L1
L
i
(19)
0
0.5
1
ASER
{
L = 5
( b
l
|
5
l=1
= {0.3, 0.4, 0.5, 0.6,0.7})
L = 3
( b
l
|
3
l=1
= {0.3, 0.4, 0.5})
E
s
/N
0
(dB)
δ =
4PSK
10
6
10
5
10
4
10
3
10
2
10
1
10
0
0 5 10 15 20 25 30
Fig. 6. ASER vs. E
s
/N
0
for unequal branch SNRs for 4PSK modulation.
The k
th
moment of Hoyt summand α
l
is given by
E
h
α
k
l
i
=
1 b
2
l
1+k
2
Γ
1 +
k
2
k/2
l
2
F
1
1 +
k
4
,
1
2
+
k
4
;1; b
2
l
. (20)
REFERENCES
[1] M. K. Simon, and M. S. Alouini, Digital Communication over Fading
Channels, 2nd Ed., John Wiley & Sons, Inc., 2005.
[2] A. Annamalai, C. Tellambura, and Vijay K. Bhargava, “Equal Gain
Diversity Receiver Performance in Wireless Channels, IEEE Trans. on
Commun., vol. 48, No. 10, pp.1732-1745, Oct. 2000.
[3] A. A. Abu-Dayya and N. C. Beaulieu, “Microdiversity on Rician fading
channels, IEEE Trans. on Commun., vol. 42, pp. 2258-2267, Jun. 1994.
[4] Q. T. Zhang, “Probability of Error for Equal-Gain Combiners Over
Rayleigh Channels: Some Closed-Form Solutions, IEEE Trans. on
Commun., vol. 45, No. 3, pp. 270-273, Mar. 1997.
[5] D. A. Zogas, G. K. Karagiannidis and S. A. Kotsopoulos, “Equal gain
combining over Nakagami-n (Rice) and Nakagami-q (Hoyt) generalized
fading channels, IEEE Trans. on Wireless Commun., vol. 4, no. 2, pp.
374- 379, Mar. 2005.
[6] Cyril-Daniel Iskander and P. T. Mathiopoulos, “Exact performance
analysis of dual-branch equal-gain combining in Nakagami-m, Rician
and Hoyt fading, IEEE Trans. Veh. Technol, vol. 57, no. 2, pp. 921-
931, Mar. 2008.
[7] Jose C. Silveira Santos Filho and Michel Dacoud Yacoub, “Highly
accurate η µ approximation to the sum of M independent nonidentical
Hoyt variates,
IEEE Antennas and Wireless Propagation Lett.,
vol. 4,
pp. 436-438, 2005.
[8] M D Yacoub et al., “The Symmetrical η κ Distribution: A General
Fading Distribution, IEEE Trans. on Broad., vol. 51, no. 4, Dec. 2005.
[9] M. D. Yacoub, “The κ µ and η µ distribution, IEEE Antenna and
Propagation Mag., vol. 49, no. 1, pp. 68-81, Feb. 2007.
[10] A. Baid, H. Fadnavis and P. R. Sahu, “Performance of a predetection
EGC receiver in Hoyt fading channels for arbitrary number of branches,
IEEE Commun. Lett., vol. 12, no. 9, pp. 627-629, Sept. 2008.
[11] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and
Products, 5th ed., San Diego, CA: Academic, 1994.
Citations
More filters
Proceedings ArticleDOI
17 Mar 2011
TL;DR: In this paper, closed-form expressions for the channel capacity of an L-branch equal gain combining diversity receiver over Hoyt (Nakagami-q) fading channels are derived for adaptive transmission schemes.
Abstract: Closed-form expressions for the channel capacity of an L-branch equal gain combining diversity receiver over Hoyt (Nakagami-q) fading channels is derived for adaptive transmission schemes. To obtain capacity expressions, probability density function of the combiner out put signal-to-noise ratio (SNR) is used. The capacity expressions are given in terms of Yacoub's integral, a general solution for which is presented in the literature recently. Further, an expression is derived for optimal cutoff SNR for the optimal power and rate adaptation scheme. A study on the effects of fading parameters and diversity order on the channel capacity of the systems for different techniques have been presented.

4 citations

References
More filters
Book
01 Jan 1943
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform

27,354 citations


"Performance of a L-branch predetect..." refers background in this paper

  • ...where γ f ( ; ) is the incomplete gamma function [ 11 ]....

    [...]

01 Jan 1917
TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions
Abstract: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = −

11,190 citations


Additional excerpts

  • ...,(14) where 2F1 (·, ·; ·; ·) is the Gaussian hypergeometric function [11]....

    [...]

  • ...k!Γ ( μ+ k + (1)2 ) , (7) where γ f (·, ·) is the incomplete gamma function [11]....

    [...]

Book
01 Jan 2004
TL;DR: The book gives many numerical illustrations expressed in large collections of system performance curves, allowing the researchers or system designers to perform trade-off studies of the average bit error rate and symbol error rate.
Abstract: noncoherent communication systems, as well as a large variety of fading channel models typical of communication links often found in the real world, including single- and multichannel reception with a large variety of types. The book gives many numerical illustrations expressed in large collections of system performance curves, allowing the researchers or system designers to perform trade-off studies of the average bit error rate and symbol error rate. This book is a very good reference book for researchers and communication engineers and may also be a source for supplementary material of a graduate course on communication or signal processing. Nowadays, many new books attach a CD-ROM for more supplementary material. With the many numerical examples in this book, it appears that an attached CD-ROM would be ideal for this book. It would be even better to present the computer program in order to be interactive so that the readers can plug in their arbitrary parameters for the performance evaluation. —H. Hsu

6,469 citations

BookDOI
05 Nov 2004

2,299 citations


"Performance of a L-branch predetect..." refers background or methods in this paper

  • ...For unequal branch SNR case, an exponentially decaying power delay profile given by Ωl = Ω1e−δ(l−1),0 ≤ δ ≤ 1, has been assumed [1]....

    [...]

  • ...Amount of Fading The AF is the measure of the severity of the fading channel often appropriate in the more general context of describing the behavior of diversity systems with arbitrary, combining techniques and channel statistics [1]....

    [...]

  • ...This void eliminates the possibility of applying the direct and simple PDF-based approach [1] to the performance analysis of a predetection EGC receiver beyond L = 2....

    [...]

  • ...Outage Probability The outage probability Pout is a standard performance criterion characteristic of diversity communication systems operating over fading channels [1]....

    [...]

  • ...INTRODUCTION Performance of a predetection equal gain combining (EGC) diversity receiver in fading channels is known to be close to the performance of the optimum maximal ratio combining (MRC) receiver, with relatively less implementation complexity [1]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors proposed two general fading distributions, the kappa-mu distribution and the eta-mu distributions, for line-of-sight applications, for which fading models are proposed.
Abstract: This paper presents two general fading distributions, the kappa-mu distribution and the eta-mu distribution, for which fading models are proposed. These distributions are fully characterized in terms of measurable physical parameters. The kappa-mu distribution includes the Rice (Nakagami-n), the Nakagami-m, the Rayleigh, and the one-sided Gaussian distributions as special cases. The eta-mu distribution includes the Hoyt (Nakagami-q), the Nakagami-m, the Rayleigh, and the one-sided Gaussian distributions as special cases. Field measurement campaigns were used to validate these distributions. It was observed that their fit to experimental data outperformed that provided by the widely known fading distributions, such as the Rayleigh, Rice, and Nakagami-m. In particular, the kappa-mu distribution is better suited for line-of-sight applications, whereas the eta-mu distribution gives better results for non-line-of-sight applications.

728 citations

Frequently Asked Questions (1)
Q1. What are the contributions in "Performance of a l-branch predetection egc receiver over independent hoyt fading channels for m-ary coherent and noncoherent modulations using pdf-based approach" ?

In this paper, the performance of a L-branch predetection equal gain combining receiver has been analyzed in independent Hoyt fading channels with arbitrary fading parameters applying classical probability density function ( PDF ) based approach.