Int. J. Communications, Network and System Sciences, 2009, 7, 592-599
doi:10.4236/ijcns.2009.27066 Published Online October 2009 (http://www.SciRP.org/journal/ijcns/)
Performance Analysis of a Novel Dual-Frequency Multiple
Access Relay Transmission Scheme
Javier DEL SER1*, Babak H. KHALAJ2
1TECNALIA-TELECOM, 48170 Zamudio-Bizkaia, Spain.
2Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran.
Received June 26, 2009; revised July 31, 2009; accepted August 27, 2009
ABSTRACT
In this paper we present the performance analysis of a novel channel assignment scheme where two
non-cooperative independent users simultaneously communicate with their destination through a single relay
by using only two frequency channels. The analytic derivation of the probability of symbol error for two
main relay techniques will be provided, namely Amplify-and-Forward (AF) and Decode-and-Forward (DF).
As shown by the obtained results, our switched-frequency approach results in a model that can achieve full-
diversity by means of maximum-likelihood decoding at the receiver. Our results are especially important in
the DF case, since in traditional techniques (such as half-duplex two-time slot approaches) two sources si-
multaneously transmit on the same channel through the first time slot, which necessitates some sort of su-
perposition coding. However, since in our scheme both users transmit over orthogonal channels, such a cod-
ing scheme is not required. In addition, it is shown that the DF approach based on our novel channel assign-
ment scheme outperforms the AF scheme, especially in scenarios where the relay is closer to the receiver.
Keywords: Multiple Access Relay Channel, Frequency Switching, Non-Cooperative Networks, Maximum
Likelihood Decoding
1. Introduction
During the last years the use of relay nodes has attracted
a lot of attention in practical areas such as cellular net-
works, especially in scenarios where multiple antennas
cannot be installed in practice at any site. Deploying re-
lay nodes between sender(s) and receiver(s) provides
increased spatial diversity in the communication scenario
under consideration. The research community has shown
a great interest in this field: as to mention, for the single
user scenario with relay channels, capacity bounds are
computed for Detect-and-Forward (DF) based mecha-
nism in a Rayleigh fading environment [1,2]. The outage
capacity bounds for the case of a single user transmission
with relay in low signal-to-noise ratio regime is consid-
ered in [3], in which frequency division model for the
relay channel is assumed. The authors in [4] present the
performance limits of Amplify-and-Forward (AF) relay
channels for single user scenario, where a new transmis-
sion protocol is also proposed in order to achieve full
diversity. Recently, the use of practical coding schemes
at the relay has also been addressed in [5,6].
In this context, this paper will focus on the perform-
ance analysis of a non-cooperative two-source multiple
access relay channel (MARC) [7]. In the MARC channel,
two independent information sources transmit their data
to a common destination aided by a shared relay node,
which processes and combines the data from both
sources. The achievable rate region for the MARC
channel has been studied in [8] by employing a partial
detect-and-forward strategy at the relay. In multiuser
scenarios, cooperative ideas have also been proposed, so
that users could interact with each other in order to im-
prove each other’s performance in fading environments
[9–13]. In [14], the authors present an upper bound on
the diversity-multiplexing trade-off for the single user
relay channel. However, their proposed scheme does not
achieve full diversity for the whole block transmission
period, since samples in the second transmission slot are
not protected by relay re-transmissions. The authors also
extend their scheme to cooperative multiple access sce-
narios for the two user case in the absence of any addi-
tional relays. However, since such cooperative schemes
rely on an inter-user channel which consumes network

J. DEL SER ET AL. 593
resources and therefore limits their performance by the
condition of such a link [15], in this paper we will only
focus on non-cooperative multiple access channels.
Traditionally, the case of multiple users and a relay
has been addressed in a number of different ways. The
most straightforward approach is to extend single-relay
ideas to multiple users, in which each user uses a sepa-
rate frequency and diversity is achieved by utilizing two
time-slots. Such an approach is basically an extension of
the well-known delay diversity schemes [16,17] and [18],
which will naturally lead to a total of four orthogonal
time-frequency channels. Another approach is to con-
sider independent receive channels for signals coming
from the users and the relay, also resulting in a total of
four independent channels either in time or frequency. It
should be especially noted that, although it is possible to
extend half-duplex two-time slot Amplify-and-Forward
schemes to MARC scenarios [19], the extension of De-
tect-and-Forward schemes to MARC requires the use of
complex superposition-type multiuser coding strategies,
so that the relay is able to detect multiple sources over
the same multiple access channel [8,19,20,21].
The scheme proposed in this paper does not rely on
any special coding scheme, since the users transmit to
the relay over orthogonal channels. Our analysis will be
focused on examining the error performance of the
MARC scenario in the case of full multiplexing gain
(two independent sources transmitting simultaneously in
the same time slot), where diversity gain improvement
can be verified through the slope of error probability
curve as a function of received SNR in a log-log scale.
As will be shown, by using the proposed frequency-
switching channel assignment scheme at the relay (Fig-
ure 1), the signal model will be transformed from two
independent scalar channels into a 2×2 Multiple-Input
Multiple-Output (MIMO) model [22]. Consequently,
Maximum Likelihood (ML) detection performed over
the received vector will provide an overall diversity or-
der of two for each user.
The structure of the paper is organized as follows. In
Section 2, the signal model and the channel assignment
scheme will be presented. In addition to Amplify-and-
Forward scheme, Detect-and-Forward structure and its
corresponding ML detector will be proposed. In Section 3,
analytic probability of error computations for both AF and
DF schemes will be derived. In Section 4, simulation re-
sults for both AF and DF mechanisms for different relay
locations will be presented and compared with the analy-
sis. As shown in these results, the DF approach outper-
forms the AF scheme, especially as the relay gets closer
to the destination. Finally, Section 5 concludes the paper.
2. Signal Model
In this paper, we will assume the case of two independ-
ent and identically distributed (i.i.d.) random sources S1
and S2 which generate binary symbols b1 and b2 (b1, b2∈
{-1,1}), respectively. Those symbols are transmitted in
a wireless environment to the same destination. In be-
tween these sources and the destination a single dual-
frequency relay is located. The distance between sources
and destination is normalized to one, and the location of
the relay is denoted as d (0<d<1). The channel is as-
sumed to be block Rayleigh fading, i.e. the channel is
assumed to be fixed within a block and varies independ-
ently from block to block. In addition to this Rayleigh
model, a propagation loss as a function of distance is
considered. This loss is a basic exponential model with
exponent n=2, hence the power attenuation is assumed to
be equal to K/d2 at a distance d, where K is the propaga-
tion constant [23]. The channel state information (CSI) is
only assumed to be known at the receiver locations (i.e.
both relay and destination), whereas the transmitters are
not assumed to have any knowledge of their forward
transmission channels. Both users transmit their signals
at two different frequency channels f1 and f2, respec-
tively.
Instead of forwarding each received signal over the
same incoming frequency channel, the relay of our pro-
posed dual-frequency channel assignment switches the
frequencies between the two transmitted signals. The
proposed structure is shown in Figure 1, where the
source S1 transmits at frequency channel f1, and the relay
retransmits the same signal over frequency channel f2.
Similarly, the frequency channel of source S2 is switched
at the relay before retransmission to the destination. It
can be easily verified that, without such frequency
switching at the relay, no additional diversity can be
achieved without resorting to delay diversity schemes,
since the two signals coming from the source and the
relay at each frequency are simultaneously combined at
the receiver. As will be subsequently shown, the pro-
posed channel assignment scheme will transform two
independent scalar channels into a two dimensional vec-
tor channel which achieves a diversity of order two.
Figure 1. The proposed switched frequency assignment at
the relay (the number over each link denotes the
corresponding frequency c hannel used).

J. DEL SER ET AL. 594
3
It should be noted that in the proposed scheme, the re-
lay should perform in a full-duplex mode for each trans-
mission path. In other words, two transceivers should
operate simultaneously in the same time slot at the relay.
However, since these two transceivers can be stationed
separately in hardware and the input carrier frequency of
each board is different from its output carrier frequency,
the hardware complexity will be significantly less than
the traditional full-duplex transceivers that operate on the
same carrier frequency for both their input and output
signals. In addition, the aforementioned assumption
would lead to echo-interference in case of highly asym-
metric receive and transmit power. Such an issue could
be overcome by applying preprocessing and postproc-
essing techniques as done, for instance, in [24]. Never-
theless, the echo interference will be assumed to be neg-
ligible at the relay, since its suppression falls out of the
scope of our contribution.
In the next subsections we present the two previously
mentioned relaying schemes, DF and AF, particularized
for our proposed setup.
2.1. Mplify-and-Forward ML Detector at the
Relay
Assuming that signals transmitted by each source are
denoted by b1 and b2, and that all information symbols
from source and relay stations reach the common desti-
nation in the same time slot (as done, for instance, in [25,
5]), the received signal for each frequency will be given
by
Frequency channel f1:

111 25216
=
y
bhb hnhn   
(1)
Frequency channel f2:

224 12123
=4
y
bhbh nh n   
(2 )
where h1 and h4 denote the channel coefficients between
sources S1 and S2 and the destination, h2 and h5 denote
channel taps between sources S1 and S2 and the relay, and
h3 and h6 denote the channel weights between relay and
destination at the two transmit frequencies f1 and f2, cor-
respondingly. All channel coefficients are mod-
eled as complex Gaussian random variables with zero
mean and variance per dimension equal to K/d2 (due to
the propagation loss at the distance d). In addition, com-
plex circularly symmetric zero mean additive white
Gaussian noise are assumed for receive inputs at
both relay and destination, with variance per dimension
6
=1
{}
ii
h
4
=1
{}
ii
n
20
=2
N

. Also, the quantities γ1 andγ2 denote the gain
of the relay for each frequency channel f1 and f2, whose
values are chosen such that the relay transmits with unit
average power.
A closer look at the above equations reveals that, by
the proposed switching algorithm at the relay, the chan-
nel is transformed into a 2×2 MIMO channel model as
given by
115611
223 422
16 23
2314
=hhhyb
hh hyb
hn n
hn n




  
  
  








3
(3)
As is well-known in MIMO literature, the above
model can be solved in the context of standard spatial
multiplexing MIMO systems, where the detection based
on the Maximum Likelihood (ML) criterion yields a di-
versity of order two [26]. Consequently, in our approach
we use a ML detector at the destination that will jointly
estimate b1 and b2 from the received signals y1 and y2. It
should also be observed that in our model, some entries
of the channel matrix shown in Equation (3) are multi-
plications of Rayleigh variables, and therefore the re-
sulting model is not roughly in the conventional form
spatial multiplexing models. Nevertheless, the obtained
results show that an increased diversity gain of order
close to two will still be achieved for both users in the
DF approach.
2.2. Detect-and-Forward ML Detector at the
Relay
Instead of just amplifying and forwarding each signal, in
this case the relay detects the source symbol from the
received signal before retransmitting it. Consequently, in
the DF approach the received signal at destination will be
given by
Frequency channel f1:
111216
ˆ
=
y
bh b hn 

 (4)
Frequency channel f2:
224123
ˆ
=4
y
bhb hn 

 (5)
where and denote the output of the detector at
the relay for sources S1 and S2, respectively.
1
ˆ
b2
ˆ
b
It should be noted that in this case, the maximum like-
lihood detector at the destination should also consider the
effect of detection errors at the output of the relay. Such
errors are mainly due to fading events in the source-relay
links: when one of these links is affected by a deep fade,
the detection errors committed at the relay are propa-
gated to the destination. In order to account for both
source-relay and relay-destination links, an end-to-end
ML detector should be utilized. The associated end-to-
end search criterion can be derived by first modeling the
source-relay link as a binary symmetric channel (BSC)
with probability of error equal to

J. DEL SER ET AL. 595
12
||
=
e
h
PQ






(6)
25
||
=
e
h
PQ






|,
(7)
where Q(·) denotes the standard Q-function. The esti-
mated b1 and b2 values at the final destination, denoted
by and , are then computed by maximizing the
likelihood function
1
b

2
b

121 212
,{ 1,1}
12
12 121212 12
,{1,1}
ˆˆ
, 12 12
(, )=(,|, )
argmax
ˆˆ ˆˆ
=(,|,,,)(,
argmax
bb
bb bb
bbpy ybb
p
yybb bbpbbbb

 

(8)
where
12 12
12
112 2
12
112 2
12
112 2
12
112 2
ˆˆ
(,| ,)
ˆˆ
(1)(1)= ,=.
ˆˆ
(1),= .
=ˆˆ
(1)= ,.
ˆˆ
,.
ee
ee
ee
ee
pb bb b
PPifbbbb
PP ifbbbb
PPifb bbb
PPifbb bb







(9)
It should also be remarked that, since the proposed
scheme is working on a single-slot basis, it is assumed
that the decoding delay at the relay is negligible with
respect to symbol time intervals. Therefore, the relay is
able to start the retransmission of the detected symbol
after some small delay during the same time slot.
3. Analysis
In the following section a detailed derivation of the ana-
lytic probability of error for both schemes is provided.
We begin by analyzing the AF approach.
3.1. Analysis of Amplify-and-Forward ML
Detector at the Relay
In order to compute the analytic probability of error for
the AF approach, we first rewrite Equation (3) as the sum
of a signal term u and a noise term w, i.e. y=u+w, where
u is given by
111562
223142
=hbh h b
hhbhb







u


(10)
and the noise term w will be zero mean with a covariance
expressed as1

1 *
2
0
=0
N
N



wwE (11)
where 2
2
10 16
(1 )NN h   and 2
2
20 23
(1 )NN h  .
Since the two terms of the noise vector w do not present
the same variance, we will employ a scaling matrix M so
as to transform w into a unit variance vector '=
M
ww
such that


*
22
'' =

EwwI , yielding
1
2
10
=.
(12)
1
0
N
M
N







As previously mentioned, the values of the relay gains
γ1 and γ2 are set such that the average relay transmit
power is normalized to one, yielding
2 2
25
1
=
hh


(13)
We will henceforth denote the received vector corre-
sponding to 12 (, )=(1,1)
A
bb  x by uA. Similarly, vec-
tors uB, uC, and uD correspond to ,
(1,1)
B
x
(1, 1)
C


x and (1,1)
D


x, respectively. Assum-
ing that the possible transmit vectors (b1,b2) are
equiprobable, the total probability of error is thus given
by


12
12
12
12
12
=
1
=Pr{error| (,)
4
=}Pr{error|(,)
=}Pr{error|(,)
=}Pr{error|(,)=}
1
=Pr{error|(,)
4
=}.
e
A
B
CD
D
iA
i
Pbb
bb
bb
bb
bb








x
x
xx
x
(14)
Let us consider the error term corresponding to .
Given a set of channel coefficients , we will use
the union bound to compute the probability of error when

A
x
6
1=
}{ii h

A
x was sent, resulting in





6
12 =1
6
=1
6
=1
6
=1
Prerror| (,)=,{}
Pr|{ }
Pr|{ }
Pr|{ }
Aii
ABii
ACii
ADii
bb h
h
h
h




x
xx
xx
xx
(15)
where


6
=1
Pr|{}
ijii
hxx denotes the probability that,
given a set of channel coefficients , xi is transmit-
ted and xj is detected at the receiver. Let us consider the
6
1=
}{ ii h
term


6
=1
Pr|{}
ABii
hxx . This pairwise probabil
1 denotes mathematical expectation of a random variable. {}Eity of

J. DEL SER ET AL. 596
n be obtained by userror caing the transformation in Ex-
pression (12), yielding

6
=1
222 2
23 1
12
Pr |{
iji
hxx }
||() ||
=2
|||| ||
=2
i
AB
M
Q
hh h
QNN

 











uu (16)
where denotes the Frobenius norm. Consequently,
other terms in Expressi
|||| 
ionthe un bound for the probability of error

12
Prerror| (,)=A bb  x can be computed by adding the
on (15) and taking the expectation
over channel coefficients hi, i.e.

12
Prerror| (,)=A bb 
22 2 2
23 1
12
222 2
56 4
12
22
156 423
12
|| || ||
2
|||| ||
2
||| |
2
hi
hh h
QNN
hh h
QNN
hh
hh hh
QNN









































E
(17)
Finally, it can be easily verified that the other terms in
Exp
x
ression (14) can be upper-bounded by a similar ex-
pression to that corresponding to

12
Prerror| (,)=A bb

x.
Therefore, the overall probability
by

12
=Prerror| (,)=
eA
Pbb

x, i.e. the same bound
givealso be valid for the
end-to-end probability of error Pe. As verified by our
simulation results, this expression results in a tight up-
per-bound of the end-to-end probability of error for the
AF approach.
.2. Analysis
of error will be given
n in Equation (17) will
of Detect-and-Forward ML
qua at the analysis of the DF
3Detector at the Relay
tions (4) and (5) show thE
method is quite different than that of the AF approach. In
the DF case we have complex Gaussian noise of the
same variance for both components of the received vec-
tor y and, since 1,1}{
ˆ
,
ˆ21bb, the relay gain factor is set
to 2
1, which istion of channel variables.
However, the computation of the analytic probability of
error for the former is more complicated since the de-
tected bit values of 1
ˆ
b and 2
ˆ
b at the relay are random
variables that depend on the condition of the channel
from the sources to the relay. In fact, when the vector
(1,1)=

A
x is transmitted from the sources, the noise-free
signal uA received at the destination may be any of the
g set with the corresponding probability,
16 1
11
,{= }=(1)(1
not a func
followin
2
)
43
16 12
22
43
16 12
33
43
16 12
44
43
,{ = }=(1)
,{= }=(1)
,{=}=
A
Aee
hh PrP P
hh



 

uuu

AA ee
AAee
AAee
hh Pr P P
hh
hh PrP P
hh
hh PrPP
hh








 



 








uuu
uuu
uuu



A













u
where P
respectively. Si
th
(18)
and are given in Expressions (6) and (7),
larly, if the transmit vector
2
1
e
2
e
P
mi 1,1)(= 

B
x
is sent, e possible received signal set will be
16 1
11
,{=} =(1)(1
43
16 12
22
43
16 12
33
43
16 12
44
43
)
,{= }=(1)
,{= }=(1)
,{= }=
BB ee
BBee
BBee
P
hh PrP P
hh
hh PrP P
hh
hh PrP P
hh









 



 








uuu
uuu
uuu



BBe
hh Pr P
hh


 
 

uuu
e
(19)
the above definitions, the probability that xA is
ted and xB is detected will be then given by the
ility of error for the case when xA is sent, i.e.
A













u
From
transmit
probability that one of the four signals corresponding to
xA is transmitted and one of the signals corresponding to
xB is detected. Since we have four different transmit pairs
(b1,b2) (each of which can be transmitted in four different
ways from the relay), an exact computation of the prob-
ability of error at the destination will involve complex
scenarios of non-uniform vector constellations with non-
uniform probabilities. To simplify this computation, we
will derive an approximate probability of error by solely
accounting for the most probable error events in our
scenario.
Having said this, we will consider two main terms in
the probab


12
error| (,)=A bbPr

x. The first component, denoted by
,e
P
, corresponds to th case that no error has occurred at
e the signal uA1 with probability
1
= }
AA
uu is transmitted among all the points asso-
ciated to uA. We will then compute the probability that
detected erroneously as one of the three
most likely points associated to uB (i.e. ignoring the point
uB4 with much smaller probability 4 Pr{ =}
BB
uu).
e
, and therefor
al is
the relay
Pr{
this sign

J. DEL SER ET AL. 597
Consequently, ,e
P◇ can be approximated as
22
13
,1
|| ||
{P }}
eA
hh
PQ




1
2
2
1
22
2*
36
11 6
1
3
22
2*
36
116
2
Pr{=}
ln Pr{=}
2| |
|| ||2()
2
Pr{ =}
ln Pr{ =}
|| ||
2|2 ()
2
A
B
A
B
Q
h
hh
hh h
Q
hh
hhh























2
1
r{ =
||
||
|
h


















uu
uu
uu
uu
(20)
where for the real part of a complex value,
and σ2notesriance per dimension of the noise
u
stands
the va
u
◇EE
)(
de
(n3,nterm n=4)T at the destination. Observe that the addi-
tional factors 1
2
Pr{=}
ln Pr{ =}
A
B
uu
uu and 1
3
Pr{=}
ln Pr{ =}
A
B
uu
uu in
the second and tdue
to the non-equaon-
stellation vectors uA1, uB2 and uB3.
The second main component of the proposed ap-
proximation for

12
Prerror| (,)bb
hird
l
u
21
|| >
AB
u
nt pr
jection
terms of the above equation are
probabilities of occurrence of the c
, denoted as
1A
(21)
The above joiobability can be computed by
sidering the pros of the noise term n on the two
di
=A x
es (–1,1) correspondin
,e, is related to the case when the relay has wrongly
detected the bit valg to the point
Therefore, we must compute the probability that this
signal, which belongs to the set associated to XA, is erro-
neously detected as XB at destination. In this case, such
an error probability can be approximated by the prob-
ability that this signal is transmitted by the relay and is
detected as the point uB1, which presents the highest
probability among all the points associated to uB. In other
words, an error event will occur if the received signal
y=uA2+n is more likely to be detected as uB1 instead of
uA2 or uA1. At this point it should be noted that, since we
assume that the signal uA2 is transmitted from the relay,
the probability of detecting the less probable constella-
tion points uA3 and uA4 is negligible in comparison with
the above mentioned probabilities. Thus the second error
term ,e P can be approximated by
 
22
,21
Pr||()||>|| ()||,
eAB
P unu unu
E
P
uA2.


2
22
22
|| ( )||( )||
A
A A
 un unu
con-
rections uB1–uA1 and uB1–uA2, and integrating over the
joint probability distribution of these two projection
terms. Let us denote the correlation factor of these two
noise terms as
1211
12 11
2
1
22 2
11 3
,
||
BABA

|| ||||
4||
=,
2| |2| |||
BA BA
h
hh h 

uuuu


uu uu
(22)
where



, denotes the inner product of two vectors.
With this definition, Expression (21) reduces to [27]
22
(2 )
2
2(1 )
1
xxyy 

 
 
,2
21
eab
Pedxdy












E (23)
where the integration limits a and b are obtained by
computing the distance of the received signal from the
decision boundaries between uB1 and uA1 and between
uB2 and uA2, respectively. Further geometric manipula-
tions lead to
22
1
|| |||| ||2< ,>
=BA a uu uuu
1211
11
22 222
13 3
22 2
13
2|
| ||
|| ||4||
=
2||||
AAB
BA
hh h
hh





uu
(24)
21 2
21 1
2
12
21
1
||||{ =}
=ln
2|| ||{=
|| Pr{=}
=ln.
Pr{=}
2| |
AB A
AB B
A
B
Pr
bPr
h
h






uu uu
uu uu
uu
uu
}
(25)
It should be noted that, when computing , the
value
ba
,e
P◇
obta
he r
of 2
Pr{=} =(1)
Bee
PPuu should be ined
sed on channel values that cause errors at telay.
Analogousl
12
y, ,e P

should be computed by averaging
over all values of h2 that cause such errors at the relay,
and not over thhole range of h2. Finally, the approxi-
mate end-to-end probability of error Pe for the DF
scheme can be obtained by adding these two main error
terms, i.e.
,,ee e
PP P ◇ (26)
which, as
e w
shown in next section, i
the Monte Carlo simulation results.
onte Carlo simulation results
r the proposed algorithm in comparison with the pre-
s in close match with
4. Simulation Results
In this section we provide M
fo
viously derived analytic approximations. The simulations

J. DEL SER ET AL. 598
R ratio at
tw
have been performed assuming BPSK signaling (i.e. b1,b2
∈{–1,1}). The transmitted signals at the sources and the
relay are assumed to be of unit average power. Flat
Rayleigh fading coefficients were generated based on a
complex Gaussian distribution with variance per 2 di-
mensions equal to one. As mentioned earlier, an addi-
tional signal power attenuation equal to K/d2 was as-
sumed for signal propagation over a distance equal to d,
where K is the propagation factor (set to 10–4 in our
simulations). Fading coefficients have been assumed to
be constant over a block of 100 samples, and are inde-
pendently generated over different blocks. The Signal to
Noise Ratio (SNR) is defined as the ratio of the average
received power of the direct source-destination path of
one of the sources (where average transmit power is as-
sumed to be equal to one) to the noise variance per di-
mension. The noise variance used for computing the
SNR has been assumed to be the same at the relay and
destination sites. Furthermore, the relay gains γ1 and γ2
have been chosen such that average transmit power of
the relay is also normalized to one. Finally, in order to
investigate the effect of the relay location on the per-
formance of the different considered schemes, the loca-
tion of the relay varies over a range of d=0 to d=1. The
results for d=0.1 (relay close to sources) and d=0.9 (relay
close to destination) are shown in these plots.
Figure 2 depicts the probability of symbol error of the
proposed DF and AF algorithms versus the SN
o different relay locations. First notice that in both
approaches the obtained analytic approximation for the
probability of error is in close match with the corre-
sponding simulated curves. Also observe that the per-
formance of the DF approach even improves slightly as
the relay position is changed from a location close to
sources (d=0.1) to a location close to the destination
(d=0.9). However, the performance degrades considera-
bly for the AF scheme as the distance between the relay
and the sources increases. Based on these results it is
foreseen that, in scenarios where the relay is close to the
destination, the use of the proposed switched-frequency
Figure 2. Analytic and simulated probability of symbol
error for the proposed frequency switching AF and DF
schemes at two different relay positi ons.
ance of a novel commu-
ser single-relay multiple
art by the Spanish Ministry
through the CONSOL-
ldsmith, “Capacity and coopera-
,” in Proceedings of Information
Theory and Applications (ITA) Workshop, February
E Transactions on Information Theory, January
on Information Theory, Vol. 53, No. 4, pp.
ings of IEEE International Con-
on Wireless Ad Hoc and Sensor
d turbo equalization in
mul
DF scheme will yield a significant performance en-
hancement (around 10 dB in our proposed setup) at the
cost of a minor complexity increase.
5. Concluding Remarks
In this paper, the error perform
ication scheme for the two-un
access channel has been proposed, which achieves a di-
versity of order two by using only two frequency chan-
nels over all the links. The main advantage of the pro-
posed scheme is to obviate the requirement of complex
superposition-type coding schemes in Detect-and-For-
ward scenarios. The effect of the relay location for both
AF and DF schemes has also been investigated, con-
cluding in a superior performance of the DF scheme as
the relay gets closer to the destination.
6. Acknowledgements
This work was supported in p
f Science and Innovationo
IDER-INGENIO 2010 programme (CSD2008–00010,
www.comonsens.o rg ), and by the Basque Government
through the Future Internet project (ETORTEK pro-
gramme).
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