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Performance evaluation of cognitive multi-relay networks with multi-receiver scheduling

TL;DR: This paper investigates the performance of cognitive multiple decode-and-forward relay networks under the interference power constraint of the primary receiver wherein the cognitive downlink channel is shared among multiple secondary relays and secondary receivers.
Abstract: In this paper, we investigate the performance of cognitive multiple decode-and-forward relay networks under the interference power constraint of the primary receiver wherein the cognitive downlink channel is shared among multiple secondary relays and secondary receivers. In particular, only one relay and one secondary receiver which offers the highest instantaneous signal-to-noise ratio is scheduled to transmit signals. Accordingly, only one transmission route that offers the best end-to-end quality is selected for communication at a particular time instant. To quantify the system performance, we derive expressions for outage probability and symbol error rate over Nakagami-m fading with integer values of fading severity parameter m. Finally, numerical examples are provided to illustrate the effect of system parameters such as fading conditions, the number of secondary relays and secondary receivers on the secondary system performance.

SummaryĀ (1 min read)

Introduction

  • Nowadays, the increasing demand on high data rate services leads to exhausted frequency resources.
  • Techniques for adjusting secondary transmit powers to meet the interference power constraint of the primary receiver in underlay CRNs are presented in [5] while collaborative spectrum sensing techniques for interweave CRNs are studied in [6].
  • Only one relay and one secondary receiver which offer the highest instantaneous SNR is scheduled for transmission.
  • To quantify the system performance, the authors derive expressions for outage probability and symbol error rate (SER) in case of Nakagami-š‘š fading with integer fading severity parameter š‘š.

II. SYSTEM AND CHANNEL MODEL

  • Consider the downlink of a cognitive CCRN with underlay spectrum access that is subject to the interference power constraint š‘„ of a primary receiver PURX over independent and identically distributed (i.i.d.).
  • Due to shadowing, the authors assume that the direct link between the secondary transmitter and receiver is absent.
  • Specifically, only one relay and one secondary receiver which offer the highest instantaneous signal-to-noise ratio (SNR) is scheduled for transmission.
  • Then, the received signal at the š‘™š‘”ā„Ž relay, SUR,š‘™, is expressed as š‘¦š‘…,š‘™ = ā„Ž1,š‘™š‘„+ š‘›š‘…,š‘™ (1) where š‘›š‘…,š‘™ is the additive white Gaussian noise (AWGN) at SUR,š‘™ with zero mean and variance š‘0.

III. END-TO-END PERFORMANCE ANALYSIS

  • In order to obtain the outage probability and SER of the system, the authors must derive an expression for the CDF of the instantaneous SNR š›¾š· of the system.
  • Then, the authors obtain š¹š›¾2,š‘™(š›¾) as the expectation of š¹š›¾2,š‘™ (š›¾āˆ£š‘‹4,š‘™) over the distribution of š‘‹4,š‘™.

IV. NUMERICAL RESULTS

  • The authors provide numerical results to illustrate the system performance for various scenarios.
  • For the case that the system operates in a moderate environment with less scattering and multi-path effect, the fading severity parameter is set as š‘š = Furthermore, it can be observed from Fig. 4 and Fig. 5 that outage probability decreases as the number of secondary relays and receivers increases.
  • This, in turn, results in a potentially higher end-to-end SNR at the selected secondary destination.

V. CONCLUSIONS

  • The authors have conducted a performance analysis for a CCRN with multi-receiver scheduling.
  • Specifically, only one relay and one secondary receiver which offer the highest instantaneous signal-to-noise ratio is scheduled to transmit signals at a particular time instant.
  • The authors deploy multiple DF relays to assist the secondary transmitter in communicating with multiple secondary receivers.
  • Furthermore, the authors have investigated system performance by deriving expressions for outage probability and SER over Nakagami-š‘š fading.
  • Numerical results are also provided to illustrate the effects of fading conditions, the number of relays and secondary receivers on the secondary system performance.

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Performance Evaluation of Cognitive Multi-Relay
Networks with Multi-Receiver Scheduling
Thi My Chinh Chu
ā€ 
, Hans-J
ĀØ
urgen Zepernick
ā€ 
, and Hoc Phan
āˆ—
ā€ 
Blekinge Institute of Technology, Karlskrona, Sweden, E-mail: {thi.my.chinh.chu, hans-jurgen.zepernick}@bth.se
āˆ—
University of Reading, RG6 6AY, UK, E-mail: h.phan@reading.ac.uk
Abstractā€”In this paper, we investigate the performance of
cognitive multiple decode-and-forward relay networks under the
interference power constraint of the primary receiver wherein the
cognitive downlink channel is shared among multiple secondary
relays and secondary receivers. In particular, only one relay and
one secondary receiver which offers the highest instantaneous
signal-to-noise ratio is scheduled to transmit signals. Accordingly,
only one transmission route that offers the best end-to-end quality
is selected for communication at a particular time instant. To
quantify the system performance, we derive expressions for
outage probability and symbol error rate over Nakagami-š‘š
fading with integer values of fading severity parameter š‘š.
Finally, numerical examples are provided to illustrate the effect
of system parameters such as fading conditions, the number
of secondary relays and secondary receivers on the secondary
system performance.
I. INTRODUCTION
Nowadays, the increasing demand on high data rate services
leads to exhausted frequency resources. Despite this shortage,
radio spectrum is still under-utilized [1] which has fostered
studies to improve spectrum efļ¬ciency. Speciļ¬cally, cognitive
radio (CR) has emerged as a promising approach to improve
spectrum utilization [2]ā€“[5]. The studies of [2], [3] discussed
crucial requirements of CRs such as spectrum hole detection,
channel state estimation, interference temperature estimation,
transmit power control, and dynamic spectrum access. In
general, there are three spectrum access strategies for cog-
nitive radio networks (CRNs), i.e., the overlay, underlay,
and interweave schemes. Techniques for adjusting secondary
transmit powers to meet the interference power constraint
of the primary receiver in underlay CRNs are presented
in [5] while collaborative spectrum sensing techniques for
interweave CRNs are studied in [6]. Dealing with the overlay
scheme, the authors of [7] proposed a power allocation for
CRNs to achieve maximum rate whereas a hybrid scheme was
deployed in [8] to inherit the beneļ¬ts of the interweave and
underlay schemes.
Cooperative communications has been recognized as a
powerful technique to provide transmission reliability and
to extend radio coverage. This technique deploys one or
multiple relay nodes between the transmitter and receiver to
forward the source signals to the destination. In traditional
relay communication, the system is concerned with point-
to-point links each of which has a single source and a
single destination [9]. However, in environments with severe
shadowing between the transmitter and receiver, point-to-point
communication has difļ¬culties to provide high data rates for
the secondary transmission. This typically occurs in underlay
CRNs where the transmit powers are strictly controlled by the
interference power constraints imposed by primary networks.
In this case, cooperative communications can be used for
the cognitive downlink to improve the quality of service of
CRNs. The works of [10], [11] proposed relaying policies to
select a suitable relay among relay candidates based on the
received signal-to-noise ratio (SNR) of an underlay cognitive
cooperative radio network (CCRN). However, all the works of
[10], [11] performed a transmission from a single secondary
transmitter to a signal secondary receiver.
Hence, the objective of this paper is to investigate the per-
formance of a CRN which jointly includes multiple relaying
and scheduling transmission for multiple secondary receivers.
In this network, only one relay and one secondary receiver
which offer the highest instantaneous SNR is scheduled for
transmission. We utilize the decode-and-forward (DF) relaying
scheme since it is able to cancel the noise at the relays.
This advantage is crucial in underlay cognitive radio networks
where transmit powers of the secondary network are often
kept rather low to satisfy the interference power constraint of
the primary receiver [5]. To quantify the system performance,
we derive expressions for outage probability and symbol error
rate (SER) in case of Nakagami-š‘š fading with integer fading
severity parameter š‘š. Based on our analysis, the impact of
the fading conditions, the number of secondary relays and
secondary receivers on outage probability and SER is revealed.
Notation: This paper uses the following notations. The prob-
ability density function (PDF) and the cumulative distribution
function (CDF) of a random variable (RV) š‘‹ are denoted
as š‘“
š‘‹
(ā‹…) and š¹
š‘‹
(ā‹…), respectively. The gamma function [12,
eq. (8.310.1)] is presented by Ī“(š‘›). Furthermore, š‘ˆ (š‘Ž, š‘; š‘„)
is the conļ¬‚uent hypergeometric function [12, eq. (9.211.4)]
and šø{ā‹…} stands for the expectation operator. Finally, š¶
š‘›
š‘˜
=
š‘›!
š‘˜!(š‘›āˆ’š‘˜)!
is the binomial coefļ¬cient.
II. S
YSTEM AND CHANNEL MODEL
Consider the downlink of a cognitive CCRN with underlay
spectrum access that is subject to the interference power
constraint š‘„ of a primary receiver PU
RX
over independent and
identically distributed (i.i.d.) Nakagami-š‘š fading channels.
The CCRN consists of a secondary transmitter SU
TX
, which
is scheduled to transmit signals to š¾ secondary receivers,
SU
RX,1
,...,SU
RX,š¾
, through the support of šæ DF relays,
978-1-4799-4912-0/14/$31.00
c
ī˜„ 2014 IEEE

Fig. 1. System model of a cognitive multi-relay network with multi-receiver
scheduling.
SU
R,1
,...,SU
R,šæ
, as depicted in Fig. 1. In this ļ¬gure, ā„Ž
1,š‘–
,
š‘– =1,...,šæ, is the channel coefļ¬cient of the link from SU
TX
to SU
R,š‘–
. Furthermore, ā„Ž
2,š‘™š‘˜
is the channel coefļ¬cient of the
link from SU
R,š‘™
, š‘™ =1,...,šæ,toSU
RX,š‘˜
, š‘˜ =1,...,š¾.Next,
ā„Ž
3
is the channel coefļ¬cient of the link SU
TX
to PU
RX
. Finally,
ā„Ž
4,š‘–
, š‘– =1,...,šæ, is the channel coefļ¬cient of the link from
SU
R,š‘–
to PU
RX
. Due to shadowing, we assume that the direct
link between the secondary transmitter and receiver is absent.
In this system, time division multiple access (TDMA) is
used to share the downlink channel among š¾ secondary
receivers. Speciļ¬cally, only one relay and one secondary
receiver which offer the highest instantaneous signal-to-noise
ratio (SNR) is scheduled for transmission. This means that
the transmission route that has the most favorable end-to-
end quality is selected for communication. Furthermore, it
is assumed that relaying transmission is performed in half-
duplex mode, i.e., the communication period is divided into
two consecutive time slots. In the ļ¬rst time slot, the secondary
transmitter sends a signal to the selected relay. Let š‘„ be
the transmit signal at SU
TX
. The average transmit power at
the secondary transmitter must be controlled to satisfy the
interference power constraint š‘„ of the primary receiver PU
RX
,
i.e., š‘ƒ
š‘ 
= šø{āˆ£š‘„āˆ£
2
} = š‘„/āˆ£ā„Ž
3
āˆ£
2
. Then, the received signal at
the š‘™
š‘”ā„Ž
relay, SU
R,š‘™
, is expressed as
š‘¦
š‘…,š‘™
= ā„Ž
1,š‘™
š‘„ + š‘›
š‘…,š‘™
(1)
where š‘›
š‘…,š‘™
is the additive white Gaussian noise (AWGN)
at SU
R,š‘™
with zero mean and variance š‘
0
. As a result, the
instantaneous SNR at the š‘™
š‘”ā„Ž
relay, SU
R,š‘™
, is obtained as
š›¾
1,š‘™
= š›½š‘‹
1,š‘™
/š‘‹
3
(2)
where š›½ is determined as š›½ = š‘„/š‘
0
. Further, š‘‹
1,š‘™
= āˆ£ā„Ž
1,š‘™
āˆ£
2
and š‘‹
3
= āˆ£ā„Ž
3
āˆ£
2
are the channel power gains of the links
SU
TX
ā†’ SU
R,š‘™
and SU
TX
ā†’ PU
RX
, respectively.
In the second time slot, the relay decodes the received signal
and sends the resulting signal š‘„
š‘™
to the š‘˜
š‘”ā„Ž
selected secondary
receiver, SU
RX,š‘˜
. The average transmit power at SU
R,š‘™
must be
regulated as š‘ƒ
š‘™
= šø{āˆ£š‘„
š‘™
āˆ£
2
} = š‘„/āˆ£ā„Ž
4,š‘™
āˆ£
2
. Then, the received
signal at SU
RX,š‘˜
from SU
R,š‘™
is given by
š‘¦
š·,š‘™š‘˜
= ā„Ž
2,š‘™š‘˜
š‘„
š‘™
+ š‘›
š·,š‘˜
(3)
where š‘›
š·,š‘˜
is the AWGN at SU
RX,š‘˜
with zero mean and
variance š‘
0
. Thus, the instantaneous SNR at the š‘˜
š‘”ā„Ž
secondary
receiver, SU
RX,š‘˜
, is obtained as
š›¾
2,š‘™š‘˜
= š›½š‘‹
2,š‘™š‘˜
/š‘‹
4,š‘™
(4)
where š‘‹
2,š‘™š‘˜
= āˆ£ā„Ž
2,š‘™š‘˜
āˆ£
2
and š‘‹
4,š‘™
= āˆ£ā„Ž
4,š‘™
āˆ£
2
are the channel
power gains of the links SU
R,š‘™
ā†’ SU
RX,š‘˜
and SU
R,š‘™
ā†’ PU
RX
,
respectively.
Among the š¾ secondary receivers, the destination which
obtains the highest instantaneous SNR from the respective
selected relay is selected for communication, i.e., the in-
stantaneous SNR from the selected relay to the š‘˜
š‘”ā„Ž
selected
secondary receiver is obtained as
š›¾
2,š‘™
=max
1ā‰¤š‘˜ā‰¤š¾
(š›¾
2,š‘™š‘˜
) (5)
Since DF is utilized at SU
R,š‘™
, the end-to-end SNR at the š‘˜
š‘”ā„Ž
secondary receiver is found as min (š›¾
1,š‘™
,š›¾
2,š‘™
) [13]. Further-
more, the relay SU
R,š‘™
will be selected for communication only
if the transmission through this relay offers the highest SNR
among all the possible routes. Thus, the end-to-end SNR from
SU
TX
to the selected secondary receiver is obtained as
š›¾
š·
=max
1ā‰¤š‘™ā‰¤šæ
ī˜‚
min
ī˜ƒ
š›¾
1,š‘™
, max
1ā‰¤š‘˜ā‰¤š¾
(š›¾
2,š‘™š‘˜
)
ī˜„ī˜…
(6)
As such, we can rewrite š›¾
š·
as
š›¾
š·
=max
1ā‰¤š‘™ā‰¤šæ
[min (š›¾
1,š‘™
,š›¾
2,š‘™
)] = max
1ā‰¤š‘™ā‰¤šæ
(š›¾
š‘™
) (7)
where š›¾
š‘™
is deļ¬ned as
š›¾
š‘™
=min[š›¾
1,š‘™
, max
1ā‰¤š‘™ā‰¤š¾
(š›¾
2,š‘™š‘˜
)] (8)
Before further analyzing the system performance, we need to
provide the CDF and PDF of the channel power gain of a
Nagakami-š‘š fading channel with integer fading severity š‘š
š‘–
and channel mean power Ī©
š‘–
as
š¹
š‘‹
š‘–
(š‘„)=1āˆ’ exp (āˆ’š›¼
š‘–
š‘„)
š‘š
š‘–
āˆ’1
ī˜†
š‘–=0
š›¼
š‘–
š‘–
š‘„
š‘–
š‘–!
(9)
š‘“
š‘‹
š‘–
(š‘„)=
š›¼
š‘š
š‘–
š‘–
Ī“(š‘š
š‘–
)
š‘„
š‘š
š‘–
āˆ’1
exp (āˆ’š›¼
š‘–
š‘„) (10)
where š›¼
š‘–
= š‘š
š‘–
/Ī©
š‘–
.
III. E
ND-TO-END PERFORMANCE ANALYSIS
In order to obtain the outage probability and SER of the
system, we must derive an expression for the CDF of the
instantaneous SNR š›¾
š·
of the system. As can be seen from
(7), š›¾
š·
is expressed as a function of š›¾
1,š‘™
,š‘™āˆˆ{1,...,šæ}.
From (2), all š›¾
1,š‘™
contain the same variable š‘‹
3
which leads to
statistical dependence among š›¾
1,š‘™
with š‘™ āˆˆ{1,...,šæ}. Thus,
we ļ¬rst calculate š¹
š›¾
š·
(š›¾āˆ£
š‘‹
3
), then, we obtain š¹
š›¾
š·
(š›¾) as the
expectation of š¹
š›¾
š·
(š›¾āˆ£
š‘‹
3
) over the PDF of š‘‹
3
. Based on the
order statistics theory, the CDF of š›¾
š·
conditioned on š‘‹
3
can

be found from (7) as
š¹
š›¾
š·
(š›¾āˆ£š‘‹
3
)=[š¹
š›¾
š‘™
(š›¾āˆ£š‘‹
3
)]
šæ
(11)
From (8), š¹
š›¾
š‘™
(š›¾āˆ£š‘‹
3
) can be calculated as
š¹
š›¾
š‘™
(š›¾āˆ£š‘‹
3
)=1āˆ’
ī˜‡
1 āˆ’ š¹
š›¾
1,š‘™
(š›¾āˆ£š‘‹
3
)
ī˜ˆī˜‡
1 āˆ’ š¹
š›¾
2,š‘™
(š›¾)
ī˜ˆ
(12)
With the assumption of independent and identically distributed
(i.i.d.) fading channels of the ļ¬rst hop from the secondary
transmitter to any secondary relay, we also obtain š¹
š›¾
1,š‘™
(š›¾āˆ£š‘‹
3
)
from (2) and (9) as
š¹
š›¾
1,š‘™
(š›¾āˆ£
š‘‹
3
)=1āˆ’ exp(āˆ’š›¼
1
š›¾š‘„
3
/š›½)
š‘š
1
āˆ’1
ī˜†
š‘”=0
š›¼
š‘”
1
š‘”!
š›¾
š‘”
š‘„
š‘”
3
š›½
š‘”
(13)
where š‘š
1
and Ī©
1
are the fading severity and channel mean
power of the link from SU
TX
to SU
R,š‘™
, respectively. Further,
š›¼
1
is deļ¬ned as š›¼
1
= š‘š
1
/Ī©
1
.
Now, we need to calculate the CDF of š›¾
2,š‘™
. As can be
seen from (5), š›¾
2,š‘™
is a function of random variables š›¾
2,š‘™š‘˜
,
š‘˜ āˆˆ{1,...,š¾}. In addition, all š›¾
2,š‘™š‘˜
with š‘˜ āˆˆ{1,...,š¾}
expressed in (4) have the same variable š‘‹
4,š‘™
, such that they
are mutually dependent. Thus, we ļ¬rst calculate the CDF of
š›¾
2,š‘™
conditioned on š‘‹
4,š‘™
. Then, we obtain š¹
š›¾
2,š‘™
(š›¾) as the
expectation of š¹
š›¾
2,š‘™
(š›¾āˆ£š‘‹
4,š‘™
) over the distribution of š‘‹
4,š‘™
.
From (5), we have
š¹
š›¾
2,š‘™
(š›¾āˆ£š‘‹
4,š‘™
)=
ī˜‰
š¾
š‘˜=1
š¹
š›¾
2,š‘™š‘˜
(š›¾āˆ£š‘‹
4,š‘™
)=
ī˜‡
š¹
š›¾
2,š‘™š‘˜
(š›¾āˆ£š‘‹
4,š‘™
)
ī˜ˆ
š¾
(14)
Assume that the fading channels from SU
R,š‘™
to any secondary
receiver are i.i.d. with fading severity š‘š
2,š‘™
and channel mean
power Ī©
2,š‘™
. From (4) and (9), š¹
š›¾
2,š‘™š‘˜
(š›¾āˆ£š‘‹
4,š‘™
) is given by
š¹
š›¾
2,š‘™š‘˜
(š›¾āˆ£
š‘‹
4,š‘™
)=1āˆ’ exp
ī˜Š
āˆ’
š›¼
2,š‘™
š›¾š‘„
4,š‘™
š›½
ī˜‹
š‘š
2,š‘™
āˆ’1
ī˜Œ
š‘–=0
š›¼
š‘–
2,š‘™
š‘–!
š›¾
š‘–
š‘„
š‘–
4,š‘™
š›½
š‘–
(15)
where š›¼
2,š‘™
= š‘š
2,š‘™
/Ī©
2,š‘™
. Substituting (15) into (14), we have
š¹
š›¾
2,š‘™š‘˜
(š›¾āˆ£
š‘‹
4,š‘™
)=
ī˜
1 āˆ’ exp
ī˜Š
āˆ’
š›¼
2,š‘™
š›¾x
4,š‘™
š›½
ī˜‹
š‘š
2,š‘™
āˆ’1
ī˜Œ
š‘–=0
š›¼
š‘–
2,š‘™
š‘–!
š›¾
š‘–
š‘„
š‘–
4,š‘™
š›½
š‘–
ī˜Ž
š¾
(16)
By using the binomial expansion in [12, Eq. (1.111)], we can
rewrite š¹
š›¾
2,š‘™š‘˜
(š›¾āˆ£š‘‹
4,š‘™
) as
š¹
š›¾
2,š‘™š‘˜
(š›¾āˆ£š‘‹
4,š‘™
)=1+
š¾
ī˜†
š‘—=1
š¶
š¾
š‘—
(āˆ’1)
š‘—
exp(āˆ’š‘—š›¼
2,š‘™
š›¾š‘„
4,š‘™
/š›½)
Ɨ
ī˜
ī˜
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–=0
š›¼
š‘–
2,š‘™
š‘–!
š›¾
š‘–
š‘„
š‘–
4,š‘™
š›½
š‘–
ī˜‘
ī˜’
š‘—
(17)
Using the identity product, we obtain š¹
š›¾
2,š‘™š‘˜
(š›¾āˆ£š‘‹
4,š‘™
) as
š¹
š›¾
2,š‘™š‘˜
(š›¾āˆ£
š‘‹
4,š‘™
)=1+
š¾
ī˜†
š‘—=1
š¶
š¾
š‘—
(āˆ’1)
š‘—
exp(āˆ’š‘—š›¼
2,š‘™
š›¾š‘„
4,š‘™
/š›½)
Ɨ
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
š‘—
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
1
š‘—
ī˜‰
š‘¤=1
š‘–
š‘¤
!
š›¾
āˆ‘
š‘—
š‘¤=1
š‘–
š‘¤
š›¼
āˆ‘
š‘—
š‘¤=1
š‘–
š‘¤
2,š‘™
š‘„
āˆ‘
š‘—
š‘¤=1
š‘–
š‘¤
4,š‘™
š›½
āˆ‘
š‘—
š‘¤=1
š‘–
š‘¤
(18)
Therefore, š¹
š›¾
2,š‘™
(š›¾) is obtained as
š¹
š›¾
2,š‘™š‘˜
(š›¾)=
ī˜—
āˆž
0
š¹
š›¾
2,š‘™š‘˜
ī˜˜
š›¾āˆ£
š‘‹
4,š‘™
ī˜™
š‘“
š‘‹
4,š‘™
(š‘„
4,š‘™
) š‘‘š‘„
4,š‘™
(19)
Substituting (10) and (18) into (19), and then, applying [12,
Eq. (3.381.4)] to calculate the resulting integral, we ļ¬nally
obtain š¹
š›¾
2,š‘™š‘˜
(š›¾) as
š¹
š›¾
2,š‘™š‘˜
(š›¾)=1+
š¾
ī˜†
š‘—=1
š¶
š¾
š‘—
(āˆ’1)
š‘—
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
š‘—
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
š›½
š‘š
4,š‘™
š›¼
š‘š
4,š‘™
4,š‘™
š‘—
ī˜‰
š‘¤=1
š‘–
š‘¤
! š›¼
š‘š
4,š‘™
2,š‘™
Ɨ
Ī“(š‘š
4,š‘™
+
ī˜Œ
š‘—
š‘¤=1
š‘–
š‘¤
)
š‘—
š‘š
4,š‘™
+
š‘—
āˆ‘
š‘¤=1
š‘–
š‘¤
Ī“(š‘š
4,š‘™
)
š›¾
āˆ‘
š‘—
š‘¤=1
š‘–
š‘¤
(š›¾ + š›¼
4,š‘™
š›½/(š‘—š›¼
2,š‘™
))
š‘š
4,š‘™
+
š‘—
āˆ‘
š‘¤=1
š‘–
š‘¤
(20)
where š‘š
4,š‘™
and Ī©
4,š‘™
are, respectively, fading severity and
channel mean power of the link from SU
R,š‘™
to the primary
receiver and š›¼
4,š‘™
= š‘š
4,š‘™
/Ī©
4,š‘™
. By substituting (20) and (13)
into (12), we obtain š¹
š›¾
š‘™
(š›¾āˆ£
š‘‹
3
) as
š¹
š›¾
š‘™
(š›¾āˆ£
š‘‹
3
)=1+exp
ī˜š
āˆ’
š›¼
1
š›¾š‘„
3
š›½
ī˜›
š‘š
1
āˆ’1
ī˜†
š‘”=0
š›¼
š‘”
1
š‘”!
š›¾
š‘”
š‘„
š‘”
3
š›½
š‘”
š¾
ī˜†
š‘—=1
š¶
š¾
š‘—
Ɨ (āˆ’1)
š‘—
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
š‘—
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
1
ī˜‰
š‘—
š‘¤=1
š‘–
š‘¤
!
š›½
š‘š
4,š‘™
š›¼
š‘š
4,š‘™
4,š‘™
š‘—
š‘š
4,š‘™
+
āˆ‘
š‘—
š‘¤=1
š‘–
š‘¤
š›¼
š‘š
4,š‘™
2,š‘™
Ɨ
Ī“(š‘š
4,š‘™
+
ī˜Œ
š‘—
š‘¤=1
š‘–
š‘¤
)š›¾
āˆ‘
š‘—
š‘¤=1
š‘–
š‘¤
Ī“(š‘š
4,š‘™
)(š›¾ + š›¼
4,š‘™
š›½/(š‘—š›¼
2,š‘™
))
š‘š
4,š‘™
+
āˆ‘
š‘—
š‘¤=1
š‘–
š‘¤
(21)
Substituting (21) into (11) and then applying the identity
product, we obtain š¹
š›¾
š·
(š›¾āˆ£š‘‹
3
) as in (22). Therefore, š¹
š›¾
š·
(š›¾)
can be calculated as
š¹
š›¾
š·
(š›¾)=
ī˜—
āˆž
0
š¹
š›¾
š·
(š›¾āˆ£
š‘‹
3
) š‘“
š‘‹
3
(š‘„
3
) š‘‘š‘„
3
(23)
Finally, substituting (22) and (10) into (23) together with the
help of [12, Eq. (3.38.4)], we obtain an expression of š¹
š›¾
š·
(š›¾)
as in (24), where š‘š
3
and Ī©
3
are, respectively, fading severity
and channel mean power of the link from the secondary
transmitter to the primary receiver and š›¼
3
= š‘š
3
/Ī©
3
.
A. Outage Probability Performance
Outage probability is deļ¬ned as the probability that the
instantaneous SNR falls below a predeļ¬ned threshold š›¾
š‘”ā„Ž
.
Therefore, outage probability of the system can be obtained
by using š›¾
š‘”ā„Ž
as the argument of š¹
š›¾
š·
(š›¾) in (24) as š¹
š›¾
š·
(š›¾
š‘”ā„Ž
).
B. Symbol Error Rate
As reported in [14], SER can be directly expressed in terms
of the CDF of the instantaneous SNR š›¾
š·
as follows:
š‘ƒ
š‘’
=
š‘Ž
āˆš
š‘
2
āˆš
šœ‹
ī˜—
āˆž
0
š¹
š›¾
š·
(š›¾)š›¾
āˆ’
1
2
exp(āˆ’š‘š›¾)š‘‘š›¾ (25)
where š‘Ž and š‘ are modulation parameters, i.e., for š‘€-PSK,
š‘Ž =2,š‘=sin
2
(šœ‹/š‘€ ). In order to compute the SER, we

š¹
š›¾
š·
(š›¾āˆ£
š‘‹
3
)=1+
šæ
ī˜†
š‘™=1
š¶
šæ
š‘™
exp
ī˜š
āˆ’
š‘™š›¼
1
š›¾š‘„
3
š›½
ī˜›
š‘š
1
āˆ’1
ī˜†
š‘”
1
=0
...
š‘š
1
āˆ’1
ī˜†
š‘”
š‘™
=0
ī˜“ ī˜”ī˜• ī˜–
š‘™
1
ī˜‰
š‘™
š‘=1
š‘”
š‘
!
1
(Ī“(š‘š
4,š‘™
))
š‘™
š›¼
āˆ‘
š‘™
š‘=1
š‘”
š‘
1
š›¼
š‘™š‘š
4,š‘™
4,š‘™
š›¼
š‘™š‘š
4,š‘™
2,š‘™
š›½
āˆ‘
š‘™
š‘=1
š‘”
š‘
āˆ’š‘™š‘š
4,š‘™
š›¾
āˆ‘
š‘™
š‘=1
š‘”
š‘
š‘„
āˆ‘
š‘™
š‘=1
š‘”
š‘
3
Ɨ
š¾
ī˜†
š‘—
1
=1
š¶
š¾
š‘—
1
(āˆ’1)
š‘—
1
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(1)
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(1)
š‘—
1
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
1
...
š¾
ī˜†
š‘—
š‘™
=1
š¶
š¾
š‘—
š‘™
(āˆ’1)
š‘—
š‘™
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(š‘™)
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(š‘™)
š‘—
š‘™
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
š‘™
ī˜“ ī˜”ī˜• ī˜–
š‘™
š‘™
ī˜‰
š‘˜=1
Ī“
ī˜Š
š‘š
4,š‘™
+
ī˜Œ
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
ī˜‹
ī˜‰
š‘™
š‘˜=1
ī˜‰
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
!
1
ī˜‰
š‘™
š‘˜=1
š‘—
š‘š
4,š‘™
+
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
š‘˜
Ɨ
š›¾
āˆ‘
š‘™
š‘˜=1
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
ī˜‰
š‘™
š‘˜=1
ī˜Š
š›¾ +
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
ī˜‹
š‘š
4,š‘™
+
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
(22)
š¹
š›¾
š·
(š›¾)=1+
šæ
ī˜†
š‘™=1
š‘š
1
āˆ’1
ī˜†
š‘”
1
=0
...
š‘š
1
āˆ’1
ī˜†
š‘”
š‘™
=0
ī˜“ ī˜”ī˜• ī˜–
š‘™
Ī“(š‘š
3
+
š‘™
ī˜Œ
š‘=1
š‘”
š‘
)
Ī“(š‘š
3
)
š‘™
ī˜‰
š‘=1
š‘”
š‘
!
š¶
šæ
š‘™
š›½
š‘š
3
š›¼
š‘š
3
3
š‘™
š‘š
3
+
š‘™
āˆ‘
š‘=1
š‘”
š‘
š›¼
š‘š
3
1
š¾
ī˜†
š‘—
1
=1
š¶
š¾
š‘—
1
(āˆ’1)
š‘—
1
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(1)
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(1)
š‘—
1
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
1
...
š¾
ī˜†
š‘—
š‘™
=1
š¶
š¾
š‘—
š‘™
(āˆ’1)
š‘—
š‘™
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(š‘™)
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(š‘™)
š‘—
š‘™
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
š‘™
ī˜“ ī˜”ī˜• ī˜–
š‘™
Ɨ
š›½
š‘™š‘š
4,š‘™
š›¼
š‘™š‘š
4,š‘™
4,š‘™
ī˜‰
š‘™
š‘˜=1
Ī“
ī˜Š
š‘š
4,š‘™
+
ī˜Œ
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
ī˜‹
š›¼
š‘™š‘š
4,š‘™
2,š‘™
(Ī“(š‘š
4,š‘™
))
š‘™
ī˜‰
š‘™
š‘˜=1
ī˜‰
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
!
1
ī˜‰
š‘™
š‘˜=1
š‘—
š‘š
4,š‘™
+
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
š‘˜
š›¾
āˆ‘
š‘™
š‘˜=1
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
āˆ‘
š‘™
š‘=1
š‘”
š‘
ī˜Š
š›¾ +
š›½š›¼
3
š‘™š›¼
1
ī˜‹
š‘š
3
+
āˆ‘
š‘™
š‘=1
š‘”
š‘
ī˜‰
š‘™
š‘˜=1
ī˜Š
š›¾ +
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
ī˜‹
š‘š
4,š‘™
+
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
(24)
ļ¬rst substitute the CDF of the instantaneous SNR š›¾
š·
in (24)
into (25) along with applying [12, eq. (3.381.4)] to calculate
the ļ¬rst integral, after some algebraic modiļ¬cations, we can
rewrite (25) as
š‘ƒ
šø
=
š‘Ž
2
+
šæ
ī˜†
š‘™=1
š‘š
1
āˆ’1
ī˜†
š‘”
1
=0
...
š‘š
1
āˆ’1
ī˜†
š‘”
š‘™
=0
ī˜“ ī˜”ī˜• ī˜–
š‘™
Ī“
ī˜Š
š‘š
3
+
ī˜Œ
š‘™
š‘=1
š‘”
š‘
ī˜‹
Ī“(š‘š
3
)
ī˜‰
š‘™
š‘=1
š‘”
š‘
!
š¶
šæ
š‘™
š›½
š‘š
3
š›¼
š‘š
3
3
š‘™
š‘š
3
+
š‘™
āˆ‘
š‘=1
š‘”
š‘
š›¼
š‘š
3
1
Ɨ
š¾
ī˜†
š‘—
1
=1
š¶
š¾
š‘—
1
(āˆ’1)
š‘—
1
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(1)
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(1)
š‘—
1
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
1
...
š¾
ī˜†
š‘—
š‘™
=1
š¶
š¾
š‘—
š‘™
(āˆ’1)
š‘—
š‘™
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(š‘™)
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(š‘™)
š‘—
š‘™
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
š‘™
ī˜“ ī˜”ī˜• ī˜–
š‘™
Ɨ
ī˜‰
š‘™
š‘˜=1
Ī“
ī˜Š
š‘š
4,š‘™
+
ī˜Œ
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
ī˜‹
Ī“
š‘™
(š‘š
4,š‘™
)
ī˜‰
š‘™
š‘˜=1
ī˜‰
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
!
š›½
š‘™š‘š
4,š‘™
š›¼
š‘™š‘š
4,š‘™
4,š‘™
ī˜‰
š‘™
š‘˜=1
š‘—
š‘š
4,š‘™
+
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
š‘˜
š›¼
š‘™š‘š
4,š‘™
2,š‘™
Ɨ
āˆž
ī˜—
0
š›¾
āˆ‘
š‘™
š‘˜=1
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
āˆ‘
š‘™
š‘=1
š‘”
š‘
āˆ’
1
2
exp(āˆ’š‘š›¾)
ī˜Š
š›¾ +
š›½š›¼
3
š‘™š›¼
1
ī˜‹
š‘š
3
+
š‘™
āˆ‘
š‘=1
š‘”
š‘
š‘™
ī˜‰
š‘˜=1
ī˜Š
š›¾ +
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
ī˜‹
š‘š
4,š‘™
+
š‘—
š‘˜
āˆ‘
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
š‘‘š›¾
(26)
Utilizing [12, Eq. (2.102)] to transform the integral expression
of (26) into tabulated forms, then, we apply [15, Eq. (2.3.6.9)]
Fig. 2. Outage probability of the cognitive multiple relay system versus š‘„/š‘
0
for various fading severity parameters š‘š.
to calculate the resulting integrals which leads to an expression
for the SER of the system as in (27). The partial fraction
coefļ¬cients šœ’
š‘Ÿ
and šœ…
(š‘˜)
š‘ž
š‘˜
in (27) are deļ¬ned as (28).
IV. N
UMERICAL RESULTS
In this section, we provide numerical results to illustrate the
system performance for various scenarios. The SNR threshold

š‘ƒ
šø
=
š‘Ž
2
+
šæ
ī˜†
š‘™=1
š‘š
1
āˆ’1
ī˜†
š‘”
1
=0
...
š‘š
1
āˆ’1
ī˜†
š‘”
š‘™
=0
ī˜“ ī˜”ī˜• ī˜–
š‘™
Ī“(š‘š
3
+
š‘™
ī˜Œ
š‘=1
š‘”
š‘
)
Ī“(š‘š
3
)
š‘™
ī˜‰
š‘=1
š‘”
š‘
!
š¶
šæ
š‘™
š›½
š‘š
3
š›¼
š‘š
3
3
š‘™
š‘š
3
+
š‘™
āˆ‘
š‘=1
š‘”
š‘
š›¼
š‘š
3
1
š¾
ī˜†
š‘—
1
=1
š¶
š¾
š‘—
1
(āˆ’1)
š‘—
1
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(1)
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(1)
š‘—
1
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
1
...
š¾
ī˜†
š‘—
š‘™
=1
š¶
š¾
š‘—
š‘™
(āˆ’1)
š‘—
š‘™
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(š‘™)
1
=0
...
š‘š
2,š‘™
āˆ’1
ī˜†
š‘–
(š‘™)
š‘—
š‘™
=0
ī˜“ ī˜”ī˜• ī˜–
š‘—
š‘™
ī˜“ ī˜”ī˜• ī˜–
š‘™
Ɨ
ī˜‰
š‘™
š‘˜=1
Ī“
ī˜Š
š‘š
4,š‘™
+
ī˜Œ
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
ī˜‹
ī˜‰
š‘™
š‘˜=1
ī˜‰
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
!
š›½
š‘™š‘š
4,š‘™
š›¼
š‘™š‘š
4,š‘™
4,š‘™
Ī“
š‘™
(š‘š
4,š‘™
)
ī˜‰
š‘™
š‘˜=1
š‘—
š‘š
4,š‘™
+
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
š‘˜
š›¼
š‘˜š‘š
4,š‘™
2,š‘™
ī˜‚
š‘š
3
+
āˆ‘
š‘™
š‘=1
š‘”
š‘
ī˜†
š‘Ÿ=1
šœ’
š‘Ÿ
Ī“
ī˜œ
š‘™
ī˜†
š‘˜=1
š‘—
š‘˜
ī˜†
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
š‘™
ī˜†
š‘=1
š‘”
š‘
+
1
2
ī˜
Ɨ
ī˜š
š›½š›¼
3
š‘™š›¼
1
ī˜›
š‘™
āˆ‘
š‘˜=1
š‘—
š‘˜
āˆ‘
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
š‘™
āˆ‘
š‘=1
š‘”
š‘
+
1
2
āˆ’š‘Ÿ
š‘ˆ
ī˜œ
š‘™
ī˜†
š‘˜=1
š‘—
š‘˜
ī˜†
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
š‘™
ī˜†
š‘=1
š‘”
š‘
+
1
2
,
š‘™
ī˜†
š‘˜=1
š‘—
š‘˜
ī˜†
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
š‘™
ī˜†
š‘=1
š‘”
š‘
+
3
2
āˆ’ š‘Ÿ, š‘
š›½š›¼
3
š‘™š›¼
1
ī˜
+
š‘™
ī˜†
š‘˜=1
š‘š
4,š‘™
+
š‘—
š‘˜
āˆ‘
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
ī˜†
š‘ž
š‘˜
=1
Ɨ šœ…
(š‘˜)
š‘ž
š‘˜
Ī“
ī˜œ
š‘™
ī˜†
š‘˜=1
š‘—
š‘˜
ī˜†
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
š‘™
ī˜†
š‘=1
š‘”
š‘
+
1
2
ī˜
ī˜š
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
ī˜›
š‘™
āˆ‘
š‘˜=1
š‘—
š‘˜
āˆ‘
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
š‘™
āˆ‘
š‘=1
š‘”
š‘
+
1
2
āˆ’š‘ž
š‘˜
š‘ˆ
ī˜š
š‘™
ī˜†
š‘˜=1
š‘—
š‘˜
ī˜†
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
š‘™
ī˜†
š‘=1
š‘”
š‘
+
1
2
,
š‘™
ī˜†
š‘˜=1
š‘—
š‘˜
ī˜†
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
+
š‘™
ī˜†
š‘=1
š‘”
š‘
+
3
2
āˆ’ š‘ž
š‘˜
,š‘
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
ī˜›ī˜…
(27)
šœ’
š‘Ÿ
=
1
ī˜Š
š‘š
3
+
ī˜Œ
š‘™
š‘=1
š‘”
š‘
āˆ’ š‘Ÿ
ī˜‹
!
š‘‘
š‘š
3
+
āˆ‘
š‘™
š‘=1
š‘”
š‘
āˆ’š‘Ÿ
š‘‘š›¾
š‘š
3
+
āˆ‘
š‘™
š‘=1
š‘”
š‘
āˆ’š‘Ÿ
ī˜
ī˜ž
ī˜ž
ī˜
1
ī˜‰
š‘™
š‘˜=1
ī˜Š
š›¾ +
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
ī˜‹
š‘š
4,š‘™
+
āˆ‘
š‘—
š‘˜
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
ī˜‘
ī˜Ÿ
ī˜Ÿ
ī˜’
š›¾=āˆ’
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
šœ…
(š‘˜)
š‘ž
š‘˜
=
1
ī˜š
š‘š
4,š‘™
+
š‘—
š‘˜
ī˜Œ
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
āˆ’ š‘ž
š‘˜
ī˜›
!
š‘‘
š‘š
4,š‘™
+
š‘—
š‘˜
āˆ‘
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
āˆ’š‘ž
š‘˜
š‘‘š›¾
š‘š
4,š‘™
+
š‘—
š‘˜
āˆ‘
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
āˆ’š‘ž
š‘˜
ī˜
ī˜ž
ī˜ž
ī˜ž
ī˜ž
ī˜ž
ī˜
ī˜Š
š›¾ +
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
ī˜‹
š‘š
4,š‘™
+
š‘—
š‘˜
āˆ‘
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
ī˜Š
š›¾ +
š›½š›¼
3
š‘™š›¼
1
ī˜‹
š‘š
3
+
š‘™
āˆ‘
š‘=1
š‘”
š‘
š‘™
ī˜‰
š‘˜=1
ī˜Š
š›¾ +
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
ī˜‹
š‘š
4,š‘™
+
š‘—
š‘˜
āˆ‘
š‘¤
š‘˜
=1
š‘–
(š‘˜)
š‘¤
š‘˜
ī˜‘
ī˜Ÿ
ī˜Ÿ
ī˜Ÿ
ī˜Ÿ
ī˜Ÿ
ī˜’
š›¾=āˆ’
š›¼
4,š‘™
š›½
š‘—
š‘˜
š›¼
2,š‘™
(28)
for calculating the outage probability is ļ¬xed as š›¾
š‘”ā„Ž
=3
dB for all the examples. Let the normalized distances of the
links SU
TX
ā†’ SU
R,š‘™
,SU
R,š‘™
ā†’ SU
RX,š‘˜
,SU
TX
ā†’ PU
RX
,
and SU
R,š‘™
ā†’ PU
RX
be denoted as š‘‘
1
,š‘‘
2
,š‘‘
3
, and š‘‘
4
,re-
spectively. We assume that the summation of the transmission
distances from secondary transmitter to relay and from the
relay to receiver is normalized to unity, i.e., š‘‘
1
+ š‘‘
2
=1.
Assume that the channel mean powers are mainly effected by
path loss and shadowing, i.e., all channel mean powers are
attenuated according to the exponential decaying model with
path loss exponent of š‘›, i.e., Ī©
š‘™
= š‘‘
āˆ’š‘›
š‘™
. Based on empirical
measurements in [16], depending on the outdoor propagation
environment, š‘› can assume a value from the set {1, 2, 3, 4}.In
our numerical examples, we select š‘› =4for highly shadowed
urban environment and the transmission distances are chosen
as š‘‘
1
= š‘‘
2
=0.5 and š‘‘
3
= š‘‘
4
=1.0.
Fig. 2 and Fig. 3 plot outage probability and SER versus
interference power-to-noise ratio š‘„/š‘
0
. The examined net-
work has 3 relays, šæ =3, and 5 secondary receivers, š¾ =5.
The fading severity parameters are selected to be the same as
š‘š
1
= š‘š
2
= š‘š
3
= š‘š
4
= š‘š, i.e., š‘š =1for the scenario that
the system operates in a densely populated area with the most
severe multi-path effect. For the case that the system operates
in a moderate environment with less scattering and multi-path
effect, the fading severity parameter is set as š‘š =2. Finally,
š‘š =3is selected for the situation that the system operates in
a dominant line-of-sight environment. As expected, the best
performance is obtained for the case of š‘š =3and the outage
probability and SER are highest in the case of š‘š =1.
Fig. 4 and Fig. 5, respectively, examine the impact of
the number of secondary relays and secondary receivers on
outage probability and SER. To make a fair comparison, fading
severity parameters are ļ¬xed as š‘š
1
= š‘š
2
= š‘š
3
= š‘š
4
=2
for all examined examples. In these ļ¬gures, as the interference
power-to-noise ratio š‘„/š‘
0
increases, the outage probability
and SER performance are improved. Furthermore, it can be

References
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Frequently Asked Questions (1)
Q1. What contributions have the authors mentioned in the paper "Performance evaluation of cognitive multi-relay networks with multi-receiver scheduling" ?

In this paper, the authors investigate the performance of cognitive multiple decode-and-forward relay networks under the interference power constraint of the primary receiver wherein the cognitive downlink channel is shared among multiple secondary relays and secondary receivers.Ā