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ARTICLE IN PRESS

JID: CAEE [m3Gsc; December 1, 2016;5:8 ]

Computers and Electrical Engineering 0 0 0 (2016) 1–20

Contents lists available at ScienceDirect

Computers and Electrical Engineering

journal homepage: www.elsevier.com/locate/compeleceng

Incremental relaying cooperative networks with dual transmit

diversity

�

Mahmoud Khodeir a , ∗, Ali Hayajneh

a , Mahsa Pourvali b , Nasir Ghani b

a Department of Electrical Engineering, Jordan University of Science and Technology, Irbid, Jordan b Department of Electrical Engineering, University of South Florida, Florida, USA

a r t i c l e i n f o

Article history:

Received 11 December 2014

Revised 9 November 2016

Accepted 10 November 2016

Available online xxx

Keywords:

Incremental-relaying

Maximal ratio combining

Error performance

Outage probability

Space time block coding

Rayleigh fading

a b s t r a c t

This paper studies the performance of cooperative wireless networks using incremental-

relaying and dual transmit diversity with the simple orthogonal space time block coding

(OSTBC) scheme. The proposed model is studied by utilizing different relaying schemes

including decode and forward (DF), amplify and forward (AF), and adaptive incremental-

relaying (i.e., best relay selection) with DF relaying. In particular, upper-bounded expres-

sions are derived for the average bit error rate (BER), signal to noise ratio (SNR) outage prob-

ability, average achievable rate, and normalized throughput. Detailed results show that the

dual transmit diversity approach outperforms the regular incremental relaying coopera-

tive diversity scheme in terms of transmission power and channel efficiency for the same

transmit power. Moreover, best relay selection with multiple relaying nodes outperforms

fixed incremental DF relaying, especially for lower transmitted SNR values.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Wireless networks continue to experience high demand and growth with the constant emergence of new user services

and applications. As a result, there is a continual need to improve channel utilization and achieve higher data transmission

rates. Along these lines, a range of cooperative diversity techniques have been proposed to overcome common impairments

found in wireless channels, e.g., such as fading and path-loss attenuation. Namely these methods use relaying techniques to

transmit multiple copies of a signal over independent channels in order to improve transmission capacity and bit error rate

(BER) performance. Overall, diversity techniques can exploit three different transmission dimensions, i.e., frequency, time,

space. Furthermore, other virtual diversity techniques have also been developed [1] .

In general, cooperative diversity schemes can result in increased resource usage in wireless networks, i.e., via increased

power consumption from relaying. As a result, further incremental-relaying techniques have been introduced to improve

channel utilization and power efficiency in cooperative networks [1–4] . Indeed, these strategies provide some of the most

effective means of improving relaying performance in modern wireless communication systems. However, existing studies

on incremental-relaying in cooperative networks have only looked at simpler single input single output (SISO) communication

methods. For example, this includes work on the performance of incremental-relaying cooperative diversity over Rayleigh

� Reviews processed and approved for publication by Editor-in-Chief. ∗ Corresponding author.

E-mail addresses: [email protected] (M. Khodeir), [email protected] (A. Hayajneh), [email protected] (M. Pourvali),

[email protected] (N. Ghani).

http://dx.doi.org/10.1016/j.compeleceng.2016.11.013

0045-7906/© 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: M. Khodeir et al., Incremental relaying cooperative networks with dual transmit diversity, Com-

puters and Electrical Engineering (2016), http://dx.doi.org/10.1016/j.compeleceng.2016.11.013


http://www.ScienceDirect.com

http://www.elsevier.com/locate/compeleceng

mailto:[email protected]






2 M. Khodeir et al. / Computers and Electrical Engineering 0 0 0 (2016) 1–20

ARTICLE IN PRESS


fading channels [1] , the performance of decode and forward (DF) incremental-relaying cooperative diversity over Rayleigh

fading channels [2] , the performance of selective DF multi-node incremental-relaying with maximal ratio combining (MRC)

[3] , and also the performance of incremental best relay amplify and forward (AF) techniques [4] .

In light of the above, there is a further need to extend this body of work and evaluate incremental-layering schemes in

more complex network settings. Hence this paper analyzes incremental-relaying with dual transmit diversity, i.e., multiple

input single output (MISO) techniques. In particular, the performance of the orthogonal space-time block code (OSTBC) scheme

is evaluated for three different relaying strategies, i.e., AF, DF, and best relay selection (adaptive DF). The dual transmit

diversity approach is chosen here in order to improve overall performance by adding transmit diversity gain to the existing

virtual diversity gain achieved in [1] . Various performance metrics are also analyzed here, including average BER, outage

probability, average achievable rate (Shannon capacity), throughput, and channel re-use factors.

Overall, this paper is organized as follows. First Section 2 presents a survey of some existing work on incremental-

layering schemes and motivates the effort. Section 3 then analyzes incremental cooperative relaying for the AF scheme using

simple dual transmit diversity. Upper-bounded expressions for average error rate, outage probability, average achievable rate,

and throughput are also derived here. Similarly, Section 4 studies incremental cooperative relaying for the DF scheme using

simple dual transmit diversity (and also compares findings with the AF scheme). Finally, Section 5 analyzes adaptive DF

relaying, i.e., best relay selection, for the simple OSTBC technique. Further comparisons are also made with the incremental

(AF, DF) relaying schemes. Finally, Section 6 presents detailed performance evaluation results for all three schemes, followed

by conclusions in Section 7 .

2. Background and motivations

The concept of cooperation in wireless networks was first introduced in [5] and [6] , where the authors studied a simpli-

fied three-terminal communication problem for discrete memoryless channels. The findings here confirmed the effectiveness

of using a relaying node (between the source and destination) to improve data transmission rates and channel efficiency. In

general, these initial contributions provided a strong basis from which to develop more advanced cooperative strategies. For

example, [7] presented an efficient protocol for realizing cooperative diversity in wireless networks, i.e., where users had

the option of selecting between several actions such as continuing data transmission in the next transmit phase or relay-

ing other user signals to the destination. This work also incorporated network outage probabilities for both the AF and DF

relaying schemes. Meanwhile, results from other studies [8–10] also showed an increase in achievable throughput rates for

networks using cooperation techniques.

Building on the above, [11,12] presented more advanced distributed space-time-coded protocols for wireless networks

using cooperative diversity. Namely, these solutions leveraged spatial diversity (with multiple relay terminals) to allow des-

tination nodes to average fading effects. However the analyses here assumed that source signals were received and re-

transmitted by all relay nodes, i.e., no uniquely identifiable relay. Nevertheless, this setup still achieved full diversity order

and hence higher spectral efficiency. Meanwhile, the authors in [13] studied outage behaviors for networks running coopera-

tive diversity and proposed some efficient relaying protocols for both the AF and DF strategies. Overall findings here showed

that all cooperative diversity protocols (except those using DF) were efficient and achieved full diversity order. However

spectral efficiency was lower due to the use of half-duplex relaying.

Furthermore, [14] and [15] studied the performance of cooperative diversity schemes and developed some new theoret-

ical models for multi-hop relaying with fading channels. In particular, closed-form expressions for the average BER and the

SNR outage probability were derived. Similarly, [16,17] analyzed the end-to-end performance of relay-based transmission

systems for Rayleigh fading channels. Meanwhile [18–20] looked at relay node selection in cooperative diversity networks

and proposed several strategies for the destination nodes. These proposed methods achieved full diversity order and out-

performed fixed relaying schemes in terms of BER, SNR outage probability, and average achievable rate. Carefully note that

relaying is a dependent process, i.e., since it mandates the destination to request re-transmission (when the received SNR

is below a pre-defined threshold or based upon some other trigger). Therefore, the authors in [1–3] also presented novel

closed-form derivations for incremental-relaying cooperative networks based upon the results in [14,15] . This work assumed

a simple single input single output (SISO) transmission model and analyzed the AF and DF relaying methodologies. Findings

revealed that regular incremental cooperative diversity achieved superior channel utilization compared to regular coopera-

tive diversity. Subsequently, [3,4] also studied best relay selection for incremental-relaying to achieve full virtual diversity

order and improve channel utilization. Overall, findings here confirmed that incremental best relay selection gave better

performance than regular fixed incremental-relaying.

In light of the above, this effort studies the performance of simple dual transmit diversity methods in incremental-

relaying cooperative wireless networks. The system model assumes independent and non-identical Rayleigh slow-flat fading

channels with simple binary phase shift keying (BPSK) modulation and MRC at the receivers. Furthermore, each transmitter

has two properly-spaced antennas to achieve independent fading channels, i.e., Alamouti scheme [21,22] . Note that this

setup can also provide added transmit diversity gain beyond the achievable virtual diversity gain [1] . Overall, three relaying

schemes are analyzed here. The first method uses AF relaying to amplify and re-transmit source signals to the destination

without any decoding, i.e., non-regenerative relays. Here, re-transmission is done whenever the received SNR falls below a

pre-defined threshold (in response to a destination request). Note that simple transmit diversity does not require perfect

channel state information at the transmitter (CSIT). Meanwhile, the second method uses DF relaying, i.e., to decode source




M. Khodeir et al. / Computers and Electrical Engineering 0 0 0 (2016) 1–20 3

ARTICLE IN PRESS


Fig. 1. Incremental-relaying cooperative diversity networks model using dual transmit diversity.

signals at the relay and then re-encode/re-transmit them to the destination. Finally, the third approach uses (adaptive)

DF relaying with best relay selection, i.e., the destination node selects the best relay based upon received SNR. Note that

adaptive relay selection has been widely used to improve diversity order in terms of error rate, outage probability, and

outage capacity. Detailed analyses are now presented.

3. Amplify and forward (AF) scheme

The AF relaying scheme uses a Gaussian parallel relay network [7,23] and is a well-studied approach in cooperative

wireless networks. Overall, conventional AF with incremental-relaying gives relatively better resource utilization and power

saving versus regular cooperative networks [1,14,15] . Hence in this section, this scheme is combined with simple OSTBC

[21] and then analyzed. Namely, the transmitted signal coming from the source is amplified and re-transmitted to the

destination (i.e., without any decoding) when the received SNR is below a pre-defined threshold. Furthermore, note that

there is no need for perfect CSIT with this simple transmit diversity scheme.

3.1. System model

The proposed model is shown in Fig. 1 and assumes Rayleigh slow-flat fading channels for all pairs of source-destination

and source-relay paths. Thus, one can obtain the Rayleigh fading coefficients ( h S, D, 1 , h S, D, 2 , h S, R, 1 , h S, R, 2 , h R, D ), which are

independent and non-identical to each other. Now, the relay is placed between the information source and the destination,

i.e., in order to re-transmit a copy of the original signal if the received SNR at the destination is below the threshold SNR.

Furthermore, all links ( S → D, R → D, S → R ) are assumed to have additive white Gaussian noise (AWGN) terms with equal

variances N ◦. Furthermore, the Alamouti model is assumed with no CSIT, and two symbols s 1 (t) and s 2 (t) are transmitted

from the source antennas using two allocated timeslots. Hence, the received signals at the destination can be written as

follows [22] :

y 1 = h 1 s 1 + h 2 s 2 + n 1 (1)

y ∗2 = −h 1 s ∗2 + h 2 s

∗1 + n 2 (2)

where { h i = r i e jθi } 2

i = 1 are the complex Gaussian channel gains for the two antenna, { n i } 2 i = 1 are the AWGN terms of the

received Alamouti symbols, and { s i } 2 i = 1 are the transmitted Alamouti symbols. Furthermore, the received signals vector can

be expressed as:

Y = [ y 1 y 2 ] T =

[h 1 h 2

h

∗2 −h

∗1

][s 1 s 2

]+

[n 1

n 2

](3)

Now in order to decouple the received symbols, the receiver has to compute the vector Z = [ z 1 z 2 ] T , where the elements of

Z correspond to the transmitted symbols s 1 ( t ) or s 2 ( t ). Hence, one can write [22] :

Z = H

H A Y (4)

where

z 1 = (| h

2 1 | + | h

2 2 | ) s 1 +

˜ n 1 (5)

z 2 = (| h

2 1 | + | h

2 2 | ) s 2 +

˜ n 2 (6)

Here, { ̃ n i } 2 i =1 is the AWGN terms after decoupling the received signals, and H is the channel transition matrix. Finally, one

can write the equivalent received SNR for any of the OSTBC symbols as follows:

γ� =

(| h

2 1 | + | h

2 2 | ) E s

2 N

(7)
o




ARTICLE IN PRESS


where E s is the symbol energy. Note that the above expressions will be used to find the probability density function (PDF) of

the equivalent received SNR for the symbols s 1 ( t ) or s 2 ( t ). Furthermore, the analysis will only be done for one symbol (due

to similarity between the two).

Overall, communication between the source and destination nodes in Fig. 1 occurs in two phases, each of which is

partitioned into two OSTBC timeslots [9,21] . In the first phase, the source sends signals using the two transmit antennas,

and the faded versions of these signals are received by both the relay node and the destination. Based upon the received

SNR at the destination, the receiver then decides whether or not the relay should re-transmit a copy of the signal (already

stored at the relay node). This decision depends upon the threshold assigned by the destination. To summarize, the timing

model of the system is divided into two phases, i.e., the first phase involves direct transmission to the destination and the

second phase involves the relaying process. As per above, each phase is further divided into two timeslots, where each

timeslot is defined as an Alamouti timeslot. Hence the received signals at the destination and at the relay node can be

written as follows:

y S, D , 1 (t) = h S, D , 1

√

E s / 2 x (t) + n 1 (t) (8)

y S, D , 2 (t) = h S, D , 2

√

E s / 2 x (t) + n 2 (t) (9)

y S, R , 1 (t) = h S, R , 1

√

E s / 2 x (t) + n 3 (t) (10)

y S, R , 2 (t) = h S, R , 2

√

E s / 2 x (t) + n 4 (t) (11)

y R , D (t) = h R , D

√

E s x r (t) + n r (t) (12)

where { n i (t) } 4 i = 1 are the AWGN terms, { y S, D , i ( t ) } 2 i = 1 are the received signals at the destination coming from the first and the

second source antennas at the first and the second OSTBC timeslots, respectively; { y S, R , i ( t ) } 2 i = 1 are the received signals at the

relay coming from the first and the second source antennas at the first and the second OSTBC timeslots, respectively; y R, D ( t )

is the received signal at the destination coming from the relay; x ( t ) is the transmitted symbol with unit energy; E s is the

overall transmitted signal energy; x r ( t ) is the transmitted signal coming from the relay to the destination; and finally, n r ( t )

is an amplified version of the AWGN terms such that n r (t) = G × { n i (t) } 4 i = 1 where the factor G is the amplification factor.

Carefully, note that the above equations only correspond to one of the OSTBC symbols, and similar expressions can be also

be written for the second symbol.

Moreover, in order to capture the effects of path loss on the overall performance of the proposed model, some additional

statistical averaging operators are also defined here, i.e., E

(h 2

S, D , 1

)= E

(h 2

S, D , 2

)= 1 , E

(h 2

S, R , 1

)= E

(h 2

S, R , 2

)=

(d S, D

d S, R

)α

, E

(h 2 R , D

)=(

d S, D

d R , D

)α

, where E ( ·) is the statistical average operator, α is the path loss, and d i, j is the distance between nodes i and j [12] .

3.2. Error performance analysis

To analyze the error performance of the proposed model, one must determine the error probability of the combined

signal at the receiver using the AF technique. Hence the total BER, P(e) , is defined as the sum of all error sources along the

multi-hop transmission path, i.e., written as follows [1] :

P ( e ) = P r ( γS,D, � ≤ γo ) ×P div ( e ) + (1 − P r (γS,D, � ≤ γo )) × P direct (e ) (13)

where γ S, D, � is the instantaneous equivalent SNR of the sum of the two signals coming from the two antennas at the

source (from both Alamouti symbol periods); P div ( e ) is the average probability of error in the combined destination signal

due to transmission via the relay; P direct ( e ) is the probability of error at the destination due to the direct path transmission

(i.e., holding the signal at the relay when γ S, D, � ≤ γ o ); and P r ( γ S, D, � ≤ γ o ) is the probability that the combined received

signal along the direct paths is less than the threshold SNR. Furthermore, the received signal at the destination (from the

relay) can be expressed as follows [1] :

x r (t) = G × x (t) (14)

where G =

√

1

0 . 5 E s h 2 S, R , 1 + N o =

√

1

0 . 5 E s h 2 S, R , 2 + N o =

√

1

0 . 5 E s h 2 S, R + N o is a normalizing factor to achieve unity transmission energy [16] .

Note that this equation is only valid for the Alamouti model when the transmitted signal powers are equal and the channels

are independent and identically distributed ( i.i.d ). Hence every Alamouti symbol will see the same amplification factor.

Next, consider the general expression for the bit error probability for the AF relaying scheme. If needed, the relay will

re-transmit a second version of the original signal using two new OSTBC timeslots. Hence in order to find the end-to-end





ARTICLE IN PRESS


PDF of the equivalent fading channel at the destination for any of these OSTBC signals, one can write the following [1,24] :

γS, R , D =

γR , D h

2 S, R

E S 2 N ◦

γR , D + h

2 S, R

E S 2 N ◦

+ 1

(15)

where γS, R , D is the end-to-end SNR for any of the Alamouti symbols signals in one of the OSTBC timeslots. Now given the

complexity involved in computing the PDF, a well-known upper-bound for γS, R , D is used here instead [1,24] :

γS, R , D ≤ γ = min

(γR , D ,

h

2 S, R E S

2 N ◦

)(16)

Assuming Rayleigh fading channels, the above expression reduces to an exponentially-distributed random variable [1] , i.e.,

f γ (γ ) =

1

γe −

γγ (17)

where the end-to-end average SNR, γ , can be written as [1,24] :

γ =

γ R , D E

(h

2 S, R

)E S

2 N ◦

γ R , D + E

(h

2 S, R

)E S

2 N ◦+ 1

(18)

Furthermore, the PDF of the combined Alamouti symbol SNR, γ S, R, D, � , at the destination (from all relayed versions of

the orthogonal signals in the two timeslots) can be written akin to Eq. (7) as [25] :

f γS,R,D, �(γ ) = f γ (γ ) � f γ (γ ) =

1

γ 2 γ e −

γγ (19)

Next, P r ( γ S, D, � ≤ γ o ) in Eq. (13) can also be written as:

γS,D, � =

(| h

2 S,D, 1 | + | h

2 S,D, 2 | ) E s

2 N o (20)

Now since the fading channel parameters, h S, D, 1 and h S, D, 2 , are Rayleigh-distributed random variables, the distribution of

γ S, D, � can be written as:

f γS,D, �(γ ) =

1

γ 2 S, D

γ e − γ

γ S, D (21)

where γ S, D = E

(h 2

S, D , 1

)E S

2 N ◦ = E

(h 2

S, D , 2

)E S

2 N ◦ . Hence, the probability of a relay re-transmission request is given by [24] :

P r ( γS,D, � ≤ γo ) =

∫ γo

0

1

γ 2 S, D

γ e − γ

γ S, D d γ = 1 −(

1 +

γo

γ S, D

)e

− γo γ S, D (22)

Furthermore, P direct ( e ) can be re-written as [24] :

P direct ( e ) =

∫ ∞

0

P ( e/γ ) × f γS,D, �(γ / γS,D, � > γo ) dγ (23)

where P ( e / γ ) is the conditional error probability and f γS,D, �(γ / γS,D, � > γo ) is the conditional PDF of γ S, D, � , given by γ S, D, �

> γ o at the destination. After some manipulation [24] , P direct ( e ) can be re-written as:

P direct ( e ) =

0 . 5 × exp

(γo

γ S, D

)γ 2

S, D ×(

1 +

γo

γ S, D

) ×(

γ S, D

μ√

π( γ S, D + 1)

[(γ S, D

√

γo exp

(

−(γ S, D + 1

)γo

γ S, D

)

−√

πexp

(− γo

γ S, D

)×

(erfc (

√

γ0 ) ×(γ S, D + 1

)(γ S, D + γo

)))

−√

π(γ S, D +

3

2

)× γ S, D erf ( μ

√

γo )

]−

γ S, D 2 (3 + 2 γ S, D

)μ( γ S, D + 1)

)(24)

where μ=

√

( γ S, D +1) / γ S, D .

Overall, Eq. (24) indicates that P direct ( e ) will decrease if γ o increases. Hence the relay node will be used more often.

An expression for P div ( e ) is now derived for use in Eq. (13) to resolve P ( e ). Here, γ S, D, � is distributed as per Eq. (21) and

the h R, D parameter is assumed to be a Rayleigh random variable. Now assuming a MRC technique to combine multiple

(relay, direct path) signals at the recevier, the total destination SNR is given by:

γAF = γS,R,D, � + γS,D, � (25)





ARTICLE IN PRESS


Further applying some convolutions and taking into account the integration bounds, one gets [24] :

f γAF (z) =

1

γ 2 S,D γ

2 ×

{ ∫ z 0

(zy + y 2

)e

− z+ β y γ S,D dy if z ≤ γo . ∫ z

z−γo

(z y + y 2

)e

− z+ β y γ S,D dy if z > γo .

(26)

where β =

γ S, D −γ

γ . After some manipulation, f γAF (z) can be re-written as follows:

f γAF (z) =

⎧ ⎪ ⎪ ⎪ ⎨

⎪ ⎪ ⎪ ⎩

σ γ SD β z e − z ( 1+ β)

γ SD + 2 σ γ 2 S, D e

− z ( 1+ β) γ S, D

+ σ γ S, D β z e − z

γ S, D − 2 σ γ 2 S, D e

− z γ S, D if z ≤ γo .

σ γ S, D β z e − z ( 1+ β)

γ S, D − σ(γ S, D β − β2 γo

)e

β γo γ S, D e

− z ( 1+ β) γ S, D

+2 σ γ 2 S, D

2 e

− z ( 1+ β) γ S, D − σ ηe

β γo γ S, D e

− z ( 1+ β) γ S, D if z > γo .

(27)

where η =

(2 γ SD

2 − 2 γ SD β γ0 + β2 γ0 2 )

and σ =

1

γ 2 β3 γ SD

. Assuming BPSK modulation, completing the analysis gives:

P div ( e ) =

1

2

∫ ∞

0

f γAF ( z/ γS,D, � ≤ γo ) erfc ( √

z ) dz (28)

Also, the conditional PDF of γ AF has the following distribution:

f γAF ( z/ γS,D, � ≤ γo ) =

f γAF ( z )

F γS,D, �(γo )

=

f γAF ( z )

1 −(

γo

γ S,D + 1

)exp

(− γo

γ S,D

) (29)

Hence, P div ( e ) can be written as follows:

P di v ( e ) =

0 . 5

1 −(

γo

γ S,D + 1

)exp

(− γo

γ S,D

) ×[�

(0 , γo , σ γ SD β,

β + 1

γ S,D

)+ �

(0 , γo , 2 σ γ 2

S,D , β + 1

γ S,D

)

+ �

(0 , γo , σ γ SD β,

1

γ S,D

)− �

(0 , γo , 2 σγ 2

S,D , 1

γ S,D

)+ �

(γo , ∞ , σ γ S, D β,

β + 1

γ S,D

)

−�

(γo , ∞ , σ

(γ S, D β − β2 γo

)e

β γo γ SD ,

β + 1

γ S,D

)+ �

(γo , ∞ , 2 σ γ 2

S,D , β + 1

γ S,D

)

−�

(γo , ∞ , σηe

β γo γ SD ,

β + 1

γ S,D

)](30)

where �( A, B, ω, λ) and �( A, B, ω, λ) are auxiliary functions (see Appendix A ). Finally, by substituting Eqs. (30) and (24) into

Eq. (13) , one can obtain the upper-bound expression for the overall BER performance for the simple OSTBC AF incremental-

relaying scheme.

3.3. Outage probability

Now consider the outage probability for AF relaying technique. Here, given the dual transmit diversity model, the SNR

outage probability can be written as [1] :

P out = P r(γS,D, � ≤ γo ) P r(γAF ≤ γo /γS,D, � ≤ γo )

= P r(γAF ≤ γo ) (31)

After some manipulation, the above expression can be simplified to (see [24] ):

P out = 1 +

1

( γ − γ S, D ) 3

×[ γ S, D

(γ 2

S, D −(

3 γ − γo

)γ S, D − γ γo

)e

− γo γ S, D

−γ((

− 3 γ − γo

)γ S, D + γ

(γo + γ

))e −

γo γ

] (32)

3.4. Average achievable rate

Next, consider the average achievable rate in the Shannon sense (assuming errors are recoverable). Here the average

achievable rate can be defined as follows [1] :

C a v g = P r ( γS,D, � ≤ γo ) ×C di v + (1 − P r (γS,D, � ≤ γo )) × C direct (33)





ARTICLE IN PRESS


where C div is the average achievable rate due to the total received signal at the destination. Furthermore, the average achiev-

able rate achieved using the direct path only, i.e., no relay, is termed as C direct and can be expressed as follows:

C direct = BW

∫ ∞

0

log 2 (1 + γ ) × f γS,D, �(γ / γS,D, � > γo ) dγ (34)

where BW is the available bandwidth. After some manipulation, the above can be written as:

C direct =

BW

ln (2) (

1 +

γo

γ S, D

)exp

(− γo

γ S, D

)[ln ( γo + 1 ) e

−γo γ S, D +

γo

γ S, D

ln ( γo + 1 ) e −γo γ S, D

+ e 1

γ S, D E 1

(γo

γ S, D

+ γ S, D −1

)+ e

−γo γ S, D − e γ S, D

−1

γ S, D

E 1

(γo

γ S, D

+ γ S, D −1

)](35)

where E 1 (.) is the exponential integral. Furthermore, the average achievable rate for the total received signal, C div , can also

be written as follows:

C div =

BW

2

∫ ∞

0

log 2 (1 + z) × f γAF (z/ γS,D, � ≤ γo ) dz (36)

where the factor of 1/2 accounts for the two transmission timeslots. After some manipulation, the above equation can be

re-written as follows:

C div =

0 . 5 BW

1 −(

γo

γ S, D + 1

)exp

(− γo

γ S, D

) ×[�c

(0 , γo , σ γ SD β,

β + 1

γ S, D

)+ θc

(0 , γo , 2 σ γ 2

S, D , β + 1

γ S, D

)

+ �c

(0 , γo , σ γ SD β,

1

γ S, D

)− θc

(0 , γo , 2 σγ 2

S, D

1

γ S, D

)+ �c

(γo , ∞ , σ γ S, D β,

β + 1

γ S, D

)

+ θc

(γo , ∞ , 2 σ γ 2

S, D , β + 1

γ S, D

)− θc

(γo , ∞ , σηe

β γo γ SD ,

β + 1

γ S, D

)

− θc

(γo , ∞ , σ

(γ S, D β − β2 γo

)e

β γo γ SD ,

β + 1

γ S, D

)](37)

where �c ( A, B, ω, λ) and �c ( A, B, ω, λ) are auxiliary functions (defined in Appendix B ). Finally, by substituting Eqs. (37) and

(35) in Eq. (33) , gives an upper-bound for the total average achievable rate for incremental-relaying with the simple OSTBC

scheme.

3.5. Throughput analysis

The normalized throughput for incremental-relaying is also analyzed here. In particular, incremental-relaying uses the

second timeslot to re-transmit the symbol based upon a (re-transmission) request from the destination, i.e., when γ S, D, � <

γ o . Hence re-transmission implies that the total channel throughput will depend on the desired value of the threshold SNR.

Now throughput is defined as the amount of data transmitted successfully per unit time [26] . Hence, the expected time for

a successful transmissionis given by [1] :

E (T ) = 1 × P r (T = 1 ) + 2 × P r (T = 2 ) (38)

where P r (T = 1) and P r (T = 2) are the probabilities of using one or two timeslots, respectively. Based on Eq. (38) , the ex-

pression for the normalized throughput is:

T hroughput =

R

E(T) (39)

where R is the transmission rate in bits · Hz/sec. Furthermore, the probability that one or two timeslots are used is equivalent

to the usage of only one direct transmission path or both direct and indirect transmission paths, respectively. Based upon

[1] , this gives:

P r (T = 1) =

(1 +

γo

γ S, D

)e

− γo γ S, D (40)

P r (T = 2) = 1 − P r (T = 1) (41)

from which Eq. (39) becomes:

T hroughput =

R

1 × P r (T = 1) + 2 × P r (T = 2)

=

R

− γo γ S, D

γo − γo γS, D

(42)
2 − e − γS, D
e





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4. Decode and forward (DF) scheme

This section presents the regenerative DF incremental-relaying scheme for cooperative networks with simple OSTBC.

Namely, Alamouti signals are decoupled and detected in the first timeslot by the relay node. These regenerated symbols are

then transmitted to the destination if the received SNR is below the pre-defined threshold (in response to a possible request

from the destination).

4.1. System model

The system here also assumes a Rayleigh slow-flat fading channel, i.e., as per AF model in Section 3 . Hence the received

relay signal at the destination can be written as:

y R,D (t) = h R,D

√

E s x r (t) + n (t) (43)

where n ( t ) is the AWGN term, and y R, D ( t ) and x r ( t ) are defined in Section 3 . Moreover, all the statistical average operators

are also the same as those defined in Section 3 .


To analyze the BER for the proposed model, one must determine the error probability for the combined signal at the

receiver. Now the total BER, P(e) , is the sum of all error sources along the multi-hop transmission path, see Eq. (13) . Hence

the general expression for BER can be derived for the DF relaying scheme, i.e., where the relay signal x r ( t ) is detected in

the first timeslot and then regenerated/re-transmitted if the received SNR is below the threshold γ o . Note that the error

probability can also be affected by erroneous decoding decisions. Hence P div ( e ) can be expressed as [1,27] :

P di v (e ) = P S,R, �(e ) × P x (e ) + (1 − P S,R, �(e )) × P com

(e ) (44)

where P S, R, �( e ) is the probability of a decision error at the relay; P x ( e ) is the probability of error at the destination given

the relay has erroneous decoding [28] ; and P com

( e ) is the probability of error at the destination given the relay decodes

correctly. Note that P x ( e ) is the value of propagation error and is bounded by P x ( e ) < 0.5. Next, assuming DF relaying, P div ( e )

can be derived and substituted into Eq. (13) to find P ( e ). Also, the h R, D parameter is assumed to be a Rayleigh random

variable, and γ R,D is the average SNR at the relay where:

γ S,R, 1 = γ S,R, 2 = E

(h

2 S,R, 1

) E S 2 N ◦

= γ S,R (45)

γS,R, � = γS,R, 1 + γ S,R, 2 (46)

f γS,R, �(γ ) =

1

γ 2 S,R

γ e − γ

γ S,R (47)

Using the above equations, an upper-bound for the probability of error at the relay is [29] :

P S,R, �(e ) =

∫ ∞

0

f S,R, �(γ ) ×P ( e/γ ) dγ =

[ 1 −

(1 +

3 2 γ S,R

)−3 / 2

√

1 +

1 γ S,R

] 2

(48)

Furthermore, since the MRC technique is used to combine the received signals, γ com

can be used to represent the instanta-

neous SNR as follows:

γcom

= γS,D, � + γR,D = z (49)

while

f γR,D (γ ) =

1

γ R,D

e − γ

γ R,D (50)

f γcom (γ ) = f γS,D, �

(γ ) ∗ f γR,D (γ ) (51)





ARTICLE IN PRESS


Hence by solving the above equation and taking into account the bounds on γ (and also assuming α = 1 / γ R,D −1 / γ S,D )

one can write the following [25,30] :

f γcom ( z ) =

⎡

⎣

exp

(− z

γ S,D

)γ 2

S,D γ R,D α2

⎤

⎦ ×{

[ exp ( −αz ) + αz − 1 ] if z ≤ γo .

αγo exp ( αγo ) −exp ( αγo ) +1 exp ( αz )

if z > γo . (52)

Finally, the exact expression for the conditional error probability at the destination P com

( e ) for BPSK modulation can be

written as:

P com

( e ) =

1

2

∫ ∞

0

f γcom ( z/ γS,D, � ≤ γo ) × erfc ( √

z ) dz (53)

Furthermore, the conditional PDF of γ com

is distributed as:

f γcom ( z/ γS,D, � ≤ γo ) =

f γcom ( z )

F γS,D, �(γo )

=

f γcom ( z )

1 −(

γo

γ S,D + 1

)exp

(− γo

γ S,D

) (54)

Hence, P com

( e ) can be written as:

P com

( e ) =

1

2

[( (γ 2

S,D γ R,D α2 )−1 (

1 −(

γo

γ S,D + 1

)exp

(− γo

γ S,D

) ))

×(

�

(0 , γo , 1 , α +

1

γ S,D

)+ �

(0 , γo , α,

1

γ S,D

)− �

(0 , γo , 1 ,

1

γ S,D

)

+

�(γo , ∞ , 1 , α +

1 γ S,D

)( γo exp ( αγo ) − exp ( −αγo ) + 1 )

−1

)](55)

where �( A, B, ω, λ) and �( A, B, ω, λ) are auxiliary functions (defined in Appendix A ). From the above, the total BER, P(e) ,

can be computed by substituting Eqs. (55) and (48) into Eq. (44) , and then by substituting Eqs. (44) , (24) , and (22) into Eq.

(13) .


The SNR outage probability for the DF incremental-relaying scheme can also be written as follows [1] :

P out = P r ( γS,R, � ≤ γo ) P r ( γS,D, � ≤ γo ) + ( 1 − P r ( γS,R, � ≤ γo ) ) P r ( γcom

≤ γo ) (56)

Using the previous definitions, the above equation can be re-written as:

P out =

(1 −

(γo

γ S,R

+ 1

)exp

(− γo

γ S,R

) )×

(1 −

(γo

γ S,D

+ 1

)exp

(− γo

γ S,D

) )

+

((γo

γ S,R

+ 1

)exp

(− γo

γ S,R

) )×

(1

γ 2 S,D γ R,D α

2

)

×((

αγ 2 S,D − γ S,D

)−

(αγ S,D γo + αγ 2

S,D − γ S,D

)exp

(− γo

γ S,D

)+ γ R,D

(− exp

(− γo

γ R,D

)))(57)


The performance of the average achievable rate in the Shannon sense is now considered. In particular, leveraging the

average rate expressions in Eqs. (33) , (35) and (36) from Section 3 , one can represent the total achievable rate as [1] :

C avg = P r ( γS,D, � ≤ γo ) ×C div + (1 − P r (γS,D, � ≤ γo )) × C direct (58)

Furthermore the average achievable rate for the combined signal at the destination can be written as:

C div =

BW

2

∫ ∞

0

log 2 (1 + z) × f γcom (z/ γS,D, � ≤ γo ) dz (59)





ARTICLE IN PRESS


Fig. 2. Incremental-relaying in cooperative diversity networks model using dual transmit diversity and multiple relay selection.

Fig. 3. Ordering process of the SNRs as random variables.

Hence, substituting Eq. (52) into Eq. (54) and then substituting the result into the above yields:

C di v =

BW

2

[( (γ 2

S,D γ R,D α2 )−1 (

1 −(

γo

γ S,D + 1

)exp

(− γo

γ S,D

) ))

×(

�c

(0 , γo , 1 , α +

1

γ S,D

)+ �c

(0 , γo , α,

1

γ S,D

)− �c

(0 , γo , 1 ,

1

γ S,D

)

+

�c

(γo , ∞ , 1 , α +

1 γ S,D

)( γo exp ( αγo ) − exp ( −αγo ) + 1 )

−1

)](60)

where �c ( A, B, ω, λ) and �c ( A, B, ω, λ) are auxiliary functions (defined in Appendix B ). Finally, one can obtain the total

average achievable rate, C avg , by substituting Eqs. (60) and (35) into Eq. (58) .

5. Best relay selection

This section extends the study of the DF incremental-relaying scheme with adaptive relaying geometry. In particular,

the selection combining diversity technique is used at the receiver in order to achieve full diversity order. Furthermore, a

new relaying scheme using both simple dual transmit diversity and incremental-relaying is also used to achieve the same

diversity order as the selection combining technique, i.e, increase the SNR at the destination antenna.

5.1. System model

The performance of adaptive relaying network geometry is studied by adding multiple relays between the source and

destination nodes and selecting the best one. Fig. 2 shows a model of this multi-relay network setup. Here, L relays are

deployed in the network, and all the relays are assumed to operate using the DF scheme. By utilizing dual transmit diversity,

every relay has the ability to decouple the Alamouti received signals, decode and re-encode these signals, and then re-

transmit them to the destination. Hence the destination requests re-transmission from the best relay if the received SNR on

the direct path is below the pre-defined SNR threshold. The selected relay then re-transmits the encoded signals, adding

further virtual diversity gain to that achieved in the aforementioned relaying schemes.

In general, the received signal at any cooperating relay can be expressed as follows:

y S,R,i (t) = h S,R,i

√

E s / 2 x (t) + n i , i = 1 , 2 , 3 , . . . , L (61)

where L is the number of the cooperating relays, y S, R, i is the received signal at the i th relay (from the source), h S, R, i is the

channel coefficient between the source and the i th relay, x ( t ) is the transmitted symbol (from the source) with unit energy,

and n i is the AWGN term. Hence the received signal at the destination from the i th relay is:

y R,D,i (t) = h R,D,i

√

E s x r (t) + n i , i = 1 , 2 , 3 , . . . , L (62)

where h R, D, i is the channel coefficient between the i th relay and the destination and x r ( t ) is the signal transmitted from the

relay. Now the actual selection of the best relay is a routing protocol problem. Namely, the best relay can be selected as the

one with the highest received SNR ( Fig. 3 ):

γ ∗R,D = max

i =1 , 2 , 3 , ... ,L { γR,D,i } (63)





ARTICLE IN PRESS


Note that all channel coefficients are assumed to have non-identical Rayleigh fading channels.

Now in order to select the best relay, it is necessary to have knowledge of the ordered statistics of the received sig-

nal. These values relate to the PDFs of the received signals, and it is assumed that the routing protocol can order the re-

ceived signal realizations from their SNR values. In this regard, [18,31,32] have proposed some unified approaches to resolve

the PDF of the ordered statistics of i.i.d random variables with common PDF expressions. Moreover, these realizations are

ranked starting from the one with the largest received SNR down to the smallest one, i.e., γ1: L ≥ γ2: L ≥ . . . ≥ γL −1: L ≥ γL : L .

Furthermore, the relay with the best SNR value is denoted by γ 1: L , i.e., for simplicity (and without loss of general-

ity) assume γ ∗R,D = γ1: L = γ ∗. Hence assuming a mean for all SNR PDF expressions, the PDF of γ ∗

R,D can be written as

f γ ∗R,D

(γ ) = 2 L f γR,D (γ )[1 − F γR,D

(γ )][2 F γR,D (γ ) − (F γR,D

(γ )) 2 ] L −1 . Now for a Rayleigh fading channel, the PDF of γ R, D, i has an

exponential distribution defined as follows [27] :

f γR,D,i (γ ) =

1

γ R,D,i

e − γ

γ R,D,i (64)

Given common mean assumption, the above simplifies to a single PDF as follows:

f γR,D (γ ) =

1

γ R,D

e − γ

γ R,D (65)

Hence the received signal corresponding to the best relay has the following PDF [18] , [27] :

f γ ∗R,D

(γ ) =

L ∑

i =1

(−1) i −1

(L

i

)2 i

γ R,D

e −i 2 γ

γ R,D (66)

Finally, statistical average operators [12] can also be defined to capture the effect of path loss, i.e., E

(h 2

S,D

)= 1 , E

(h 2

S,R,i

)=(

d S,D d S,R

)α

, E

(h 2

R,D,i

)=

(d S,D d R,D

)α

.


Now consider the error probability of a combined signal at the receiver, i.e., Eq. (13) . Here the total SNR of the signal at

the receiver is the sum of the SNR of two signals, i.e., direct path and relay path signals, i.e.,

γtot = γ ∗R,D + γS,D, � = Z (67)

Moreover, the PDF of the total received signal can be written as the convolution of the two random variables f γ ∗R,D

(γ ) and

f γS,D, �(γ ) , as [33] :

f γtot (z) =

1

γ 2 S,D

∫ ∞

0

L ∑

i =1

(−1) i −1

(L

i

)λi × e −λi γ (z − γ ) e

− z−γγ S,D dγ (68)

where λi =

2 i γ R,D

. After some manipulation, the above equation reduces to:

f γtot (z) =

⎧ ⎨

⎩

1

γ 2 S,D

∫ z 0

∑ L i =1 (−1) i −1

(L i

)λi e

−λi γ (z − γ ) e − z−γ

γ S,D dγ if z ≤ γo .

1

γ 2 S,D

∫ z z−γ o

∑ L i =1 (−1) i −1

(L i

)λi e

−λi γ (z − γ ) e − z−γ

γ S,D dγ if z > γo . (69)

and this can be further simplified as follows:

f γtot (z) =

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

1

γ 2 S,D

∑ L i =1

(−1) i −1 ( L i ) λi

( λi γ S,D −1 ) 2 ×

[γ 2

S,D e −λi z + γ 2

S,D λi z e − z

γ S,D − γ 2 S,D e

− z γ S,D − γ S,D z e

− z γ S,D

]if z ≤ γo .

1

γ 2 S,D

∑ L i =1

(−1) i −1 ( L i ) λi

( λi γ S,D −1 ) 2 ×

[γ 2

S,D e λi γo λi γo e

− γo γ S,D e −λi z

+ γ 2 S,D e

−λi z − γ 2 S,D e

λi γo e − γo

γ S,D e −λi z − γ S,D e λi γo γo e

− γo γ S,D e −λi z

]if z > γo .

(70)

Finally, to compute the average BER (for BPSK modulation), one must resolve P div ( e ), i.e., the error from the combined signal

at the destination. This value is computed as:

P di v (e ) = P ∗S,R, �(e ) × P x (e ) + (1 − P ∗S,R, �(e )) × P tot (e ) (71)

where P tot ( e ) is the BER of the combined signal (i.e., direct path and best relay), and P ∗S,R, �

(e ) is the probability of a decision

error at the best relay. Hence to complete the analysis of best relay selection with OSTBC, P tot ( e ) can be written as follows:

P tot ( e ) =

1

2

∫ ∞

f γtot ( z/ γS,D, � ≤ γo ) erfc ( √

z ) dz (72)
0




ARTICLE IN PRESS


Further simplifying Eq. (72) , gives [27] :

P tot (e ) =

1

2 γ 2 S,D

(1 −

(γo

γ S,D + 1

)exp

(− γo

γ S,D

) ) ×L ∑

i =1

(−1) i −1 (

L i

)λi (

λi γ S,D − 1

)2

[�(0 , γo γ

2 S,D , λi )

+ �

(0 , γo , γ

2 S,D λi ,

1

γ S,D

)− �

(0 , γo , γ

2 S,D ,

z

γ S,D

)− �

(0 , γo , γ S,D ,

z

γ S,D

)+ �( γo , ∞ , η, λi )

](73)

where η = γ 2 S,D + γ 2

S,D e λi γo λi γo e

− γo γ S,D − γ 2

S,D e λi γo e

− γo γ S,D − γ S,D e

λi γo γo e − γo

γ S,D , and �( A , B, ω , λ) and �( A , B, ω , λ) are auxiliary

functions (defined in Appendix A ). Assuming dual transmit diversity with BPSK modulation over Rayleigh fading channels,

the probability of decision error at the best relay (in decoding the Alamouti signals) can be written as follows:

P ∗S,R, �(e ) =

∫ ∞

0

f S,R, �(γ ) ×P ( e/γ ) dγ P ∗S,R, �( e ) =

[ 1 −

(1 +

3 2 γ S , R

)−3 / 2

√

1 +

1 γ S , R

] 2

(74)

Finally, substituting Eqs. (74) and (72) into Eq. (71) , and then substituting the result into Eq. (13) , gives an upper-bound for

the total average BER using the incremental-relaying technique (with best relay selection and simple STBC scheme).


The BER can also be used to evaluate the performance of the SNR outage probability for the DF scheme. Namely, the

total SNR outage probability for the total received signal (best relay) can be written as [1] :

P out = P ∗r ( γS,R, � ≤ γo ) P r ( γS,D, � ≤ γo ) + ( 1 − P ∗r ( γS,R, � ≤ γo ) ) P r ( γtot ≤ γo ) (75)

where P ∗r (γS,R, � ≤ γo

)is the outage probability at the best relay, P r ( γ S, D, � ≤ γ o ) is the outage probability if only the

direct path is used, and P r ( γ tot ≤ γ o ) is the outage probability when both the direct path signal and the relayed signal are

combined at the destination. Note Eq. (75) can also be used to evaluate the outage probability of the regular incremental-

relaying scheme with OSTBC [25] . Hence by applying the previous definitions, P ∗r (γS,R, � ≤ γo

)can be written as follows:

P ∗r ( γS,R, � ≤ γo ) =

∫ γo

0

1

γ 2 S,R

γ e − γ

γ S,R dγ = 1 −(

1 +

γo

γ S,R

)e

− γo γ S,R (76)

From this, the SNR outage probability from the combined destination signal can be written as:

P r ( γtot ≤ γo ) =

∫ γo

0

f γtot (γ ) dγ

=

1

γ 2 S,D

L ∑

i =1

(−1) i −1 (

L i

)λi (

λi γ S,D − 1

)2

[(γ 2

S,D γo − γ 3 S,D λi γo − γ 4

S,D λi + 2 γ 3 S,D

)e

− γo γ S,D

− γ 2 S,D

λi e λi γo +

γ 2 S,D

λi

+ γ 4 S,D λi − 2 γ 3

S,D

](77)

Finally, by substituting Eqs. (77) and (76) into Eq. (75) gives an upper-bound for the SNR outage probability for incremental-

relaying.


The average achievable rate (in the Shannon sense) is now analyzed to evaluate the system for recoverable errors. In

particular, for best relay selection, one can write the following:

C a v g = P r ( γS,D, � ≤ γo ) × C tot + (1 − P r (γS,D, � ≤ γo )) × C direct (78)

where C tot is the average achievable rate for the combined signal. Now in order to resolve Eq. (78) , the average achievable

rate for the combined signals, C tot , can be written as:

C tot =

BW

2

∫ ∞

0

log 2 (1 + z) × f γtot (z| γS , D , � ≤ γo ) dz (79)





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Fig. 4. (a) Average BER versus normalized distance from source to relay for E s /N o = 15 dB. (b) Average BER versus the forwarding threshold SNR value, γ o ,

for d S,R = 0 . 42 and E s /N o = 15 dB for incremental cooperative diversity with dual transmit diversity. (c) Average BER versus SNR of transmitted signal for

d S,R = 0 . 42 .

After some manipulation, C tot can be written as:

C tot =

BW

2 γ 2 S,D

(1 −

(γo

γ S,D + 1

)exp

(− γo

γ S,D

) )×

L ∑

i =1

(−1) i −1 (

L i

)λi (

λi γ S,D − 1

)2

[�c

(0 , γo γ

2 S,D , λi

)+ �c

(0 , γo , γ

2 S,D λi ,

1

γ S,D

)

−�c

(0 , γo , γ

2 S,D ,

z

γ S,D

)− �c

(0 , γo , γ S,D ,

z

γ S,D

)+ �c ( γo , ∞ , η, λi )

](80)

where �c ( A, B, ω, λ) and �c ( A, B, ω, λ) s auxiliary functions (defined in Appendix B ). Finally, substituting Eqs. (80) and

(35) into Eq. (78) , gives an upper-bound for the total average achievable rate for incremental best relay selection.

6. Numerical results

Numerical results are now presented for the three proposed system models. In particular, the bit error rate, outage

probability, average achievable rate, and the normalized throughputs are plotted versus the SNR of the transmitted signal,

( E s / N o ).

6.1. Amplify and forward (AF) scheme

Here the relay is assumed to have a variable location between the source and destination. Furthermore, the distance

between the relay and the source node is denoted by d = d S, R , and the distance between the source and destination nodes

is normalized to unity. Moreover, the path loss exponent, α, is set to 3, as per [1] . First, results for the average BER versus

distance the between the relay node and the source are shown in Fig. 4 (a). These findings indicate that the average BER

decreases and achieves an optimal value of γ ∗o = 8 . 8 dB around d S, R = 0 . 42 . Moreover, increasing γ o flattens the average BER

curve, and this supports asymptotic error performance when P r ( γ S, D, � ≤ γ o ) → 0. Furthermore, when γo = 0 dB (direct

transmission) there is no need to use the relay, and hence the BER is not affected by its location. However, these results also

show that there is an optimal relative distance between the source and the relay. In particular, when the threshold SNR is

8 dB, this value is d S, R = 0 . 42 , i.e., similar to the results shown in [1] .

Next, Fig. 4 (b) plots the BER versus γ o for AF incremental-relaying with simple STBC. These results indicate that there is

a maximum value for γ o (i.e., γ ∗o = 8 . 8 dB) after which the BER levels off. Moreover, this relaying scheme achieves better

BER performance and saves more power versus the regular relaying scheme. In particular, the BER performance (when γ o

is greater than 8.8 dB) is similar to the asymptotic performance, i.e., γ o → ∞ dB. Also Fig. 4 (c) plots the average BER

performance versus SNR for both the single and dual transmission schemes. The findings here indicate that incremental-

relaying cooperative diversity with dual transmit diversity outperforms SISO incremental-relaying for all values of E s / N o

(these results also hold for different values of γ o ). For instance, when d S, R = 0 . 42 and γo = 4 dB, incremental-relaying with

simple OSTBC requires a SNR value 8 dB below that for regular incremental-relaying to achieve the same BER ( 10 −5 ). Also,

γo = 0 dB is equivalent to direct transmission (i.e., relay does not send original transmission), whereas γo = ∞ dB is equiva-

lent to regular cooperative AF operation. Furthermore, the proposed model also achieves an optimal threshold value when

γ ∗o = 8 . 8 dB, which gives the best error performance. Carefully note that there is no need to use larger thresholds, i.e., above





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Fig. 5. (a) Outage probability versus SNR of transmitted signal for d S,R = 0 . 42 . (b) Average achievable rate versus SNR of transmitted signal for d S,R = 0 . 42

for AF incremental-relaying. (c) Normalized throughput versus SNR of transmitted signal.

Fig. 6. (a) Expected timeslots versus SNR of transmitted signal. (b) Average BER versus forwarding threshold SNR value, γ o , for E s /N o = 15 dB and

d S,R = 0 . 56 for incremental cooperative diversity with dual transmit diversity. (c) Average BER versus normalized distance from source to relay, d S, R , for

incremental cooperative diversity with dual transmit diversity with E s /N o = 15 dB.

γ ∗o = 8 . 8 dB, since incremental-relaying will function as per the regular cooperative case, i.e., since the relay will help all

the time. Additionally, for small SNR thresholds the simple transmit scheme outperforms the case for large SNR thresholds.

Next, Fig. 5 (a) plots the outage probability, P out , versus SNR. These results show improved (virtual) diversity array gain

and better SNR outage probability performance with the proposed AF incremental-relaying scheme. Fig. 5 (b) also compares

the average achievable rate (versus the SNR) for the two schemes, i.e., regular incremental-relaying and AF-incremental-

relaying (with simple OSTBC). Here both schemes give similar results, and the findings also show improved efficiency (versus

regular cooperative networks) with incremental-relaying in general, i.e., in terms of transmit power and achievable rate.

Next, Fig. 5 (c) shows the normalized throughput of the proposed incremental-relaying scheme. Here, the dual transmit

diversity scheme outperforms regular incremental-relaying. For example, when γo = 4 , incremental-relaying with simple

OSTBC achieves a throughput of 0.9 with an SNR 3 dB lower than that required for regular incremental-relaying. This

improvement is due to the added transmit diversity gain, i.e., since the throughput expression does not depend upon the

relayed signal. Moreover, the normalized throughput is unity for large values of E s / N o , i.e., the network needs less assis-

tance from the relay, and most likely the second timeslot is not required for re-transmission either. Hence the normalized

throughput equals 50%, implying that the destination regularly requests assistance from the relay. Finally, Fig. 6 (a) plots the

expected number of timeslots required for successful transmission. These results show that OSTBC incremental-relaying out-

performs regular incremental-relaying. The duality between the normalized throughput and expected number of timeslots

is also obvious, i.e., fewer timeslots are needed for larger SNR values (direct path reception). Namely, as the SNR increases

(due to increase in transmitted signal power), the network will tend to use the direct path more often.

6.2. Decode and forward (DF) scheme

Results for DF incremental-relaying cooperative diversity (with dual transmit) are now presented. Again, the same geom-

etry is assumed as in case of the AF relaying case ( Section 3.1 ). First, Fig. 6 (b) plots the average BER performance versus the

distance between the relay and the source nodes, i.e., to capture the effects of relay location. Note that as γ o decreases, the

shape of the average BER curve becomes more flat and this supports asymptotic error performance when P r ( γ S, D, � ≤ γ o )





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Fig. 7. (a) Average BER versus SNR of transmitted signal when d S,R = 0 . 56 for the incremental cooperative diversity with dual transmit diversity. (b) Outage

probability versus SNR of the transmitted signal for d S,R = 0 . 56 for incremental cooperative diversity with dual transmit diversity. (c) Average achievable

rate versus SNR of transmitted signal for d S,R = 0 . 42 with DF relaying scheme.

Fig. 8. (a) Average BER versus SNR of transmitted signal for best relay selection for γo = 5 dB and d S,R = 0 . 4 . (b) Average BER versus SNR of transmitted

signal for the relay selection for γo = 8 dB and d S,R = 0 . 4 . (c) Average BER versus SNR of transmitted signal for best relay selection for L = 1, L = 3, γo = 8 dB

and d S,R = 0 . 4 .

→ 0. Furthermore, when γo = 0 dB, transmission occurs without relaying, and hence the BER is not affected by the location

of the relay. Also, Fig. 6 (c) plots the BER versus γ o , indicating an optimum value of γ ∗o = 8 . 85 dB. Hence the DF scheme

achieves better BER performance and saves more power versus regular relaying.

Meanwhile, Fig. 7 (a) gauges the average BER versus the transmitted SNR. This plot shows that OSTBC incremental-

relaying cooperative diversity gives better error performance for all values of E s / N o and different values of γ o . Again note

that γo = 0 dB is equivalent to direct transmission case [21] , whereas, γ o = ∞ dB is equivalent to the regular cooperative

network case for DF relaying. Clearly, based upon the results in Fig. 6 (b), there is no need to increase the threshold beyond

the optimum value of γ ∗o = 8 . 85 . Next, Fig. 7 (b) plots P out versus the SNR of the transmitted signal for both the incremen-

tal cooperative diversity scheme (with dual transmit diversity, i.e, MISO) and regular incremental cooperative diversity (i.e,

SISO). These results show that the proposed model achieves good virtual diversity array gain and better SNR outage prob-

ability performance. Moreover, increasing γ o reduces P out and yields better overall performance. Finally, Fig. 7 (c) shows the

average achievable rate performance versus transmitted SNR for both the OSTBC incremental cooperative diversity and reg-

ular incremental cooperative diversity schemes. These result shows that the former method gives slightly lower average

channel capacity overheads/usage. Nevertheless, the associated gains in terms of BER and SNR outage probability are still

very notable here.

6.3. Best relay selection

Results are also presented for the incremental best relay selection scheme, i.e., capture the effects of the number of

relays and the geometry of the network in terms of the distance between the source and the relay. First, Figs. 8 (a) and (b)

plot the BER versus transmitted SNR for the proposed model with multiple relay counts ( d S,R = 0 . 4 , γo = 5 dB, and path

loss exponent α = 3 ). Obviously, incremental best relay selection (i.e., L > 1) with dual transmit diversity outperforms both

fixed incremental-relaying and one-hop transmission (i.e., γ o → 0 dB). For example, when d S,R = 0 . 4 , γo = 8 dB, and L = 2

relays, OSTBC incremental best relay selection requires 4 dB lower SNR than fixed incremental-relaying ( L = 1) to achieve





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Fig. 9. (a) Average BER versus number of relays for best relay selection for γo = 8 dB and d S,R = 0 . 4 . (b) Average BER versus threshold SNR for best relay

selection for E s /N o = 10 dB and d S,R = 0 . 4 . (c) Outage probability versus SNR of transmitted signal for best relay selection for γo = 5 dB and d S,R = 0 . 4 .

a BER of 10 −6 . Depending upon the value of γ o , incremental best relay selection also outperforms fixed relaying for small

values of ( E s / N o ). Hence the proposed model requires more assistance from the relays. In fact using more relays can add

more diversity order and enhance the BER to some extent. Therefore selecting from more than three relays will not add

perceptible enhancement, i.e., this resembles the conventional selection mechanisms in one-hop receive diversity.

Next, Fig. 8 (c) plots the BER versus transmitted SNR for both fixed incremental-relaying ( L = 1) and OSTBC incremental

best relay selection with L = 3 and varying γ o . Here results show that the latter scheme clearly outperforms the former

albeit, increasing γ o requires more relay assistance. Note that OSTBD incremental best relay selection will also increase

diversity order and enhance BER performance. For example, for d S,R = 0 . 4 , γo = 8 dB, and L = 3, this approach requires

about 5 dB lower SNR versus the fixed incremental-relaying scheme ( L = 1) to achieve a BER of 10 −5 . Also, Fig. 9 (a) shows

the average BER versus the number of the relays for two values of E s / N o ( d S,R = 0 . 4 , γo = 8 dB). Clearly, increasing the

number of the relaying nodes here yields more diversity order and better overall error performance. However this result

does not hold for any arbitrary number of relays, e.g., E s /N o = 5 dB, there is a sharp improvement in the overall BER (up to

L = 5 ). Subsequently no further improvement is seen for L > 5. In general, increasing the number of relays improves BER

performance for lower transmitted SNR values, E s / N o . However negligible improvement is seen for relay counts greater than

L = 3 and E s /N o = 10 dB (similar to the case L > 5 for E s /N o = 5 dB).

Furthermore Fig. 9 (b) also plots BER versus γ o for best relay selection. Here it is clear that there is a maximum value

of γ o for which the minimum BER is achieved. Moreover the incremental best relay selection scheme also gives better

BER performance and more power savings. However the maximum value of γ o also depends upon the number of relaying

nodes. For example, with one relay ( L = 1 ) and d S,R = 0 . 4 and E s /N o = 10 dB, the maximum γ o value is γ ∗o = 6 dB. This value

increases to 8.5 dB with L = 3 relays. Note that if the destination uses a threshold above these values, the resultant system

is equivalent to the regular cooperation model (i.e., the relay will assist all the time). In particular, the BER performance for

γ o > 8.5 dB will approach asymptotic performance (i.e., γ o → ∞ dB). Hence the key motivation behind using incremental-

relaying will be lost since resource utilization will not be optimum.

Meanwhile, Fig. 9 (c) plots P out versus transmitted SNR for incremental best relay selection. The results here show im-

provement over fixed incremental-relaying and show higher values for both virtual diversity array gain and transmit diver-

sity gain (as well as SNR outage probability). In particular, for d S,R = 0 . 4 , γo = 5 dB, and L = 2 relays, the proposed model

requires 6 dB lower SNR than that for fixed incremental-relaying to achieve the same outage probability ( P out = 10 −6 ). Fur-

thermore, increasing the number of relays also lowers the outage probability to an extent. Meanwhile Fig. 10 (a) plots the

outage probability, P out , for different numbers of relay nodes and threshold values. The findings here show that incremen-

tal best relay selection outperforms fixed incremental-relaying and hence can achieve higher diversity order. Hence as γ o

increases, the proposed model needs more assistance from the relaying nodes, i.e., P out decreases with increasing L . In par-

ticular, smaller when γo = 6 dB.

Finally, Fig. 10 (b) presents average achievable rate performance versus transmitted signal SNR for both incremental coop-

erative diversity (with best relay selection) and regular OSTBC cooperative diversity (with different numbers of relay nodes).

These results show that using OSTBC incremental-relaying improves spectral efficiency with regards to average channel ca-

pacity as compared to regular cooperative relaying (i.e., γ o → ∞ dB). However increasing the number of relaying nodes

yields better channel utilization (i.e., slight increase in the overall average achievable rate). Regardless, the improvements in

terms of the BER and the SNR outage probability are notable here.

6.4. Models comparison

Finally, some overall comparisons are also made between the three different relaying schemes, i.e., AF, DF and adaptive

DF. Foremost, Fig. 10 (c) plots the BER versus transmitted SNR for all schemes. These results show that best relay incremental





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Fig. 10. (a) Outage probability versus number of relays for different values of γ o for d S,R = 0 . 4 . (b) Average achievable rate versus SNR of transmitted signal

for best relay selection for d S,R = 0 . 42 and γo = 4 dB. (c) Bit error rate versus SNR of transmitted signal for three models for d S,R = 0 . 42 and γo = 8 . 85 dB.

Fig. 11. Outage probability versus SNR of transmitted signal for three models for d = 0 . 42 and γo = 8 . 85 dB.

DF and incremental DF outperform the incremental AF scheme. Also, the performance of best relay selection is always the

same as the fixed incremental DF scheme when L = 1 . This is expected since the model will always choose the single

achievable relay node. Next, Fig. 11 plots results for outage probability, P out , versus transmitted SNR. Here incremental best

relay selection outperforms both the AF and DF schemes. However, all of these models give very close performance in terms

of average achievable rate, i.e., see results in Figs. 5 (b), 7 (c), and 10 (b). Furthermore, the normalized throughput for all three

schemes is also the same since it depends upon the direct path.

7. Conclusions

This paper studies the performance of incremental-relaying in cooperative wireless networks using dual transmit diver-

sity with different relaying schemes. In particular, the amplify and forward (AF) incremental-relaying scheme is analyzed first

using simple orthogonal space time block coding scheme (OSTBC), i.e., Alamouti scheme. Results confirm that this approach

outperforms both regular incremental-relaying and direct path transmission in terms of average bit error rate, signal to noise

ratio, outage probability, and average achievable rate. Furthermore, using dual transmit diversity also gives better channel

utilization and reduced power consumption. Subsequently, a decode and forward (DF) incremental-relaying scheme using

dual transmit diversity is also investigated. Related findings show that this method also outperforms regular incremental-

relaying and direct path transmission. This approach also gives improved performance over regular cooperative networks

(i.e., in terms of channel utilization, power savings) for mid-to-large values of predefined signal-to-noise ratio thresholds.

The incremental-relaying scheme (with simple OSTBC) also outperforms regular fixed relaying schemes to achieve full di-

versity order. Finally, throughput analysis confirms that incremental-relaying gives lower normalized throughput than di-

rect path transmission. However this behavior is asymptomatic to the direct transmission case for all values of transmitted

signal-to-noise ratio.

Appendix A

Several auxiliary expressions are derived in order to reduce the number of terms in the derivations presented in

Sections 2 and 4 . In particular consider the following definitions:

�(A, B, ω, λ) =

∫ B

ω z e −λ z er f c (√

z )dz

A





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=

ω

√

πλ2 ( 1 + λ) 3 / 2

[ ( −3 / 2 λ − 1 )

√

πerf

(√

1 + λ√

z

)

+

√

1 + λ(

e −λ z √

π(−1 + erf

(√

z ))

( 1 + λ) ( λ z + 1 )

)+ λ

√

z e −( 1+ λ) z ] B

A

(A.1)

�(A, B, ω, λ) =

∫ B

A

ω e −λ z er f c (√

z )dz

= ω

[− e −λ z

λ+

erf (√

z )

λe λ z −

erf (√

1 + λ√

z )

λ√

1 + λ

]B

A

(A.2)

Appendix B

Log function integrals are commonly used to evaluate the average achievable rate. Based on this some appropriate aux-

iliary functions are also:

�c (A, B, ω, λ) =

∫ B

A

ω z e −λ z log 2 ( z + 1 ) dz

=

[− ω ( 1 + λ z ) e −λ z ln ( 1 + z )

ln ( 2 ) λ2 − ω e −λ z

ln ( 2 ) λ2 +

ω e λE 1 ( λ + λ z )

ln ( 2 ) λ− ω e λE 1 ( λ + λ z )

ln ( 2 ) λ2

]B

A

(B.1)

�c (A, B, ω, λ) =

∫ B

A

ω e −λ z log 2 ( z + 1 ) dz

=

[− ω e −λ z ln ( 1 + z )

ln ( 2 ) λ− ω e λE 1 ( λ + λ z )

ln ( 2 ) λ

]B

A

(B.2)

where E 1 ( . ) is the exponential integral.

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Mahmoud Khodeir is an assistant professor in the Electrical Engineering Department at Jordan University of Science and Technology. Currently he isinvolved in a wide range of research activities in the areas of wireless communications, wireless and computer networks, cognitive radio, cooperative

networks, and game theory applications. He received the Ph.D. degree in electrical engineering from the University of New Mexico.

Ali Hayajneh is currently pursuing the Ph.D. degree in the electronics and electrical engineering (EEE) school in the University of Leeds, UK. His currentresearch interests include drone assisted wireless communications, public safety communication networks, stochastic geometry, device-to-device (D2D)

and machine-to-machine (M2M) communications, modeling of heterogeneous networks, cognitive radio networks and cooperative relaying networks. Hereceived his MSc and Bachelor of Engineering degrees from the Electrical Engineering Department at Jordan University of Science and Technology, Jordan.

Mahsa Pourvali is a Ph.D-degree student in the Electrical Engineering Department at the University of South Florida. Her research interests include network

virtualization, cloud computing, disaster recovery, and wireless networks. She received her MSc degree in computer engineering from Ferdowsi Universityof Mashhad and her BS degree in computer engineering from Azad University of Lahijan.

Nasir Ghani is a professor in the Electrical Engineering Department at the University of South Florida and Research Liaison for the Florida Center for

Cybersecurity. Currently he is involved in various research activities in the areas of cyber-infrastructure networks, cyber-security, cloud computing, disasterrecovery, and cyber-physical systems. He received the Ph.D. degree in computer engineering from the University of Waterloo.



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Incremental relaying cooperative networks with dual transmit …eng.usf.edu/~nghani/papers/cee2016.pdf · 2017. 9. 21. · Note that simple transmit diversity does not require perfect