Open access peer-reviewed chapter

Outage Performance Analysis of Underlay Cognitive Radio Networks with Decode‐and‐Forward Relaying

By Mustafa Namdar and Arif Basgumus

Submitted: September 5th 2016Reviewed: April 14th 2017Published: July 5th 2017

DOI: 10.5772/intechopen.69244

Downloaded: 1430


In this chapter, we evaluate the outage performance of decode‐and‐forward relaying in cognitive radio networks over Rayleigh fading channels, subject to the relay location for a secondary user. In particular, we obtain the optimal relay location in wireless communications systems for the cognitive radio networks, using differential evolution optimization algorithm. Then, we investigate the optimal transmission rate of the secondary user. We present the numerical results to validate the proposed theoretical analysis and to show the effects of the Rayleigh fading channel parameters for the whole system performance.


  • cognitive radio networks
  • decode‐and‐forward relaying
  • differential evolution optimization algorithm
  • optimal relay location
  • outage probability

1. Introduction

Cognitive radio (CR) is a new approach for wireless communication systems to utilize the existing spectrum resources efficiently. Spectrum utilization can be increased by opportunistically allowing the unlicensed secondary user (SU) to utilize a licensed band in the absence of the primary user (PU) [14]. The ability of providing awareness about the usage of the frequency spectrum or the detection of the PU in a desired frequency band lets the SU access the radio communication channel without causing harmful interference to the PU [58].

Cooperative wireless communications, which depend on cooperation among distributed single‐antenna wireless nodes, have emerged recently as an alternative to multi‐antenna systems to obtain spatial diversity [913]. In a wireless communication system, when the source terminal does not have a good‐enough link with the destination one, cooperative relaying can be utilized to improve spectral efficiency, combat with the effects of the channel fading and to increase the channel capacity. There are various cooperative relaying schemes and two of the most widely studied in the literature are amplify‐and‐forward (AF) and decode‐and‐forward (DF) protocols. Between them, the DF cooperation protocol is considered in this chapter, in which the relay terminal decodes its received signal and then re‐encodes it before transmission to the destination [14]. In order to achieve higher outage performance, we investigate the DF relaying in CR networks over Rayleigh fading channels, subject to the relay location for a SU. Then, we obtain the optimal relay location for the CR networks and optimal transmission rate of the SU using the differential evolution (DE) optimization algorithm [1517].

Most of the previous publications have studied the performance of cooperative communications techniques over different fading channels and under different constraints [1826]. In [18], the authors derive the analytical error rate expressions to develop power allocation, relay selection and placements with generic noise and interference in a cooperative diversity system employing AF relaying under Rayleigh fading. Woong and Liuqing [19] address the resource allocation problem in a differentially modulated relay network scenario. It is shown to achieve the optimal energy distribution and to find optimal relay location while minimizing the average symbol error rate. The effect of the relay position on the end‐to‐end bit error rate (BER) performance is studied in [20]. Furthermore, Refs. [2126] investigate the relay node placements minimizing the outage probability where the performance improvement is quantified. Although cooperative transmissions have greatly been considered in the above manuscripts, to the best of the our knowledge, there has not been any notable research for the relay‐assisted CR networks based on the DE optimization algorithm. As far as we know, DE optimization algorithm has not been applied for obtaining the optimal location of the relaying terminal in CR networks over Rayleigh fading channels.

In summary, to fill the above‐mentioned research gap, we here provide an optimization analysis yielding the optimal location of the relaying terminal for the SU in CR networks. Furthermore, we analyse the transmission rate for the SU over Rayleigh fading channels using DE optimization algorithm. As far as we know, DE optimization algorithm has not been applied for obtaining the optimal location of the relaying terminal and the transmission rate in CR networks over Rayleigh fading channels.

The rest of the chapter is organized as follows: the system model and performance analysis are described in Section 2 presenting the relay‐assisted underlay cognitive radio networks. The numerical results and simulations are discussed in Section 3 with the DE optimization approach. Finally, Section 4 provides the concluding remarks.


2. System model and performance analysis

This section presents the system model for the CR networks with DF cooperative relaying protocol shown in Figure 1. We consider the method developed in [27] that the transmission links between the source‐to‐relay and relay‐to‐destination are subject to Rayleigh fading. In the system model for the cooperative relaying, we have both PUand SU, each with a source (PUsand SUs) and destination (PUdand SUd) nodes. Besides, the relay (r)is located in the same line between SUsand SUd. We assume that PUsonly transmits to the PUdand SUsutilize a two‐phase cooperative transmission protocol causing interference to PU within a tolerable level. We also assume that equal‐time allocation is implemented in the relayed transmission. In the first phase, SUstransmits the signal to r. In the second phase of this transmission, rdecodes its received signal and retransmits (forwards) it to the SUd[27]. We denote the distance between the secondary source SUsand the relay ras dsr, the distance between the secondary source SUdand the primary destination PUdas dsp, the distance between the secondary source SUsand the secondary destination SUdas dsdand finally, the distance between the relay rand the primary destination PUdas drp. We have


Figure 1.

System model for cooperative relaying in cognitive radio networks [27].

where the cosine theorem is used. Here, θis the angle between the horizontal axis and the line connecting the PUdand SUsnodes.

In a cognitive radio network, the transmission of a primary user has to be protected from the interference caused by either a secondary user or a relay. The level of the interference induced on the primary user (P0)must be kept below a maximum tolerable level. On the other hand, when the level of interference from the secondary user’s activity in the first phase or the relay transmission in the second phase exceeds the prescribed limit of P0, this situation results in a corruption in the transmission of the primary user. Thus, the transmitting power levels of the primary user and relay have to be controlled and must not exceed P0. Also, the outage probability of the primary destination during the source and relay transmission phases must be equal to a certain predetermined value such as εP. As the maximum transmitting power levels depends on the location of the relay, SUsand εP, on the other hand, to maximize the data rate at the destination subject to the outage probability constraints, εsis evaluated by the secondary user.

Here, we consider the worst case channel conditions, namely, Rayleigh fading, might cause some signal power loss between the SUsrand rSUdlinks, also assuming N0, power spectral density for the background noise is similar in the whole environment for the presented system model. In the literature, the outage probabilities for the PUdduring the source and the relay transmission phase are respectively given by Pout,source=exp(Po/Psdsp–α)and Pout,relay=exp(Po/Prdrp–α)where Psis the transmit power of the SUsand Pris the transmit power of the relay, r[27]. It is assumed that these equations are equal to one another in order to maximize the transmission rate, and thus, the transmit powers for the secondary user and the relay are given as


respectively [27]. Here, αis the path loss exponent, and ln(.)is the natural logarithm operator.

In this study, it is aimed to minimize the outage probability of the secondary user for the DF relaying scheme and to maximize the transmission rate, Rsubject to the outage constraints of the primary user. The main objective of the proposed optimization algorithm is to find the optimal relay location on the direct link between SUsand SUdterminals. The outage probability of the secondary user for the DF relaying can be expressed as follows [27]:

Pout = (1exp(g(R)2γ¯sd))(1exp(g(R)γ¯sr))+(1(γ¯sdγ¯sdγ¯rdexp(g(R)γ¯sd)+γ¯rdγ¯rdγ¯sdexp(g(R)γ¯rd)))exp(g(R)γ¯sr)E4

where Ris the transmission rate for SUsand g(R) = 22 R1. We have


Here, the outage probability for the secondary user is given by εs = (1γ¯sr+1γ¯rd)12γ¯sdg(R)2. The average signal‐to‐noise ratios in the links PUsto PUd, SUsto r, and rto SUdare given by γ¯sd = μ(dsd/dsp)α, γ¯sr = μ(dsr/dsp)α, and γ¯rd = μ(drd/drp)α. We have μ = P0/(N0ln(εp)).

For the optimization problem, a function is employed to minimize the outage probability and maximize the transmission rate for the DF relay‐assisted CR system. DE optimization algorithm results show that the system performance can be significantly improved for the optimal value of the system parameters, seen in the following section.

3. Numerical results and simulations

In this section, the numerical results are illustrated through the performance analysis curves of the proposed underlay cognitive radio networks with DF relaying. The detailed optimization results with the DE algorithm for DF relaying scheme are listed in Table 1. Here, the results for the optimal transmission distances, between secondary user source to relay (SUsr), dsroptare provided with different θvalues, while dsp=dsd, dsp=2dsdand dsp=5dsd. Besides, the maximum transmission rate values (Rmax)for the secondary user, SUs, are also illustrated in the same table. The results demonstrate that maximum transmission rate performance of the considered system increases while θand dspincreases.

dsp = dsddsp = 2dsddsp = 5dsd

Table 1.

Optimization results for DF relaying with different θvalues for dsp=dsd, dsp=2dsd, and dsp=5dsd.

The outage probability (Pout)performance of the considered system is illustrated in Figure 2 with varying θvalues when (Po/N0)=10 dB, α=4, εS=0.1, εp=0.05, dsp=2dsdand dsr=dsd/2. It can be observed from the simulation results in Figure 2 that the optimal θangle can be calculated, where the best minimum of Poutis achieved.

Figure 2.

Poutfor the considered underlay CR network with DF relaying under differentθvalues.

Figure 3 shows the transmission rate over Rayleigh fading channel versus (Po/N0)when α=4, εS=0.1, εp=0.05, θ = π/2, dsp=2dsdand dsr=dsd/2. The results clearly show that Rincreases with the increase of the (Po/N0).

Figure 3.


The transmission rate (R)of the considered system for the SUsrlink with the normalized dsddistance is illustrated in Figure 4 when (Po/N0)=10 dB, α=4, εS=0.1, εp=0.05, θ = π/2and dsp=2dsd. Figure 4 indicates that the maximum transmission rate is achieved when the optimal transmission distances are used.

Figure 4.

Rvs.(dsr/dsd)for(Po/N0)=10 dB.

Figure 5 depicts the outage probability performance as a function of (dsr/dsd). Here, (Po/N0)=10 dB, α=4, εS=0.1, εp=0.05, θ=π/2and dsp=2dsd. The results obtained in Figure 4 closely match with the results in Figure 5. Therefore, it can be deduced that the optimal placement of the relay terminal can be performed based on (dsr/dsd)=0.5, which leads to the midpoint of the transmission link of SUsSUdas the optimal position.

Figure 5.

Poutfor varying(dsr/dsd)with(Po/N0)=10 dB.

In Figure 6, the transmission rate for the PUdSUslink is monitored for the normalized dsddistance over Rayleigh fading channel while (Po/N0)=10 dB, α=4, εS=0.1, εp=0.05, θ = π/2and dsr=dsd/2. In addition, Poutperformance analysis is also studied for the transmission link for PUd SUswith the normalized distance of dsdand demonstrated in Figure 7 using the same parameters in Figure 6.

Figure 6.

Rvs.(dsp/dsd)over Rayleigh fading channel while(Po/N0)=10 dB.

Figure 7.

Poutperformance with varying(dsp/dsd)while(Po/N0)=10 dB.

The normalized dsrdistance varying with the transmission rate Rover Rayleigh fading channel for different θvalues and transmission links, dsp = dsd, dsp = 2dsdand dsp = 5dsdare shown in Figure 8. Besides, in Figure 9, dsr/dsdnormalized distances are calculated for the different θangles with varying dspvalues. Here, both figures are plotted for the values of (Po/N0)=10 dB, α = 4, εS = 0.1and εp = 0.05.

Figure 8.

(dsr/dsd)vs.Rover Rayleigh fading channel with differentθvalues for(Po/N0)=10 dB,dsp = dsd,dsp=2dsdanddsp=5dsd.

Figure 9.

(dsr/dsd)vs.θvalues fordsp = dsd,dsp = 2dsdanddsp = 5dsdwhile(Po/N0)=10 dB.

The maximum transmission rate varying with different θvalues for dsp = dsd, dsp = 2dsdand dsp = 5dsd, while (Po/N0)=10 dBis depicted in Figure 10. The figure demonstrates the effect of dspwith varying θangles. The results show that the maximum transmission rate of the considered system increases while θand dspincreases.

Finally, the maximum transmission rate, varying with the normalized distance for different dspvalues, is depicted in Figure 11. It is seen that while the drp/dsdincreases, the system performance also increases when θis in the interval of [π]. In other words, these results also prove that the Rperformance is directly related with the PUd SUstransmission link. While in case of dspdistance is increased, the maximum transmission is achieved.

Figure 10.

Maximum transmission rate varying with differentθvalues fordsp = dsd,dsp = 2dsdanddsp = 5dsdwhile(Po/N0)=10 dB.

Figure 11.

Maximum transmission rate varying withdrpvalues normalized withdsd, for differentPUdSUsdistance whiledsr=dsd/2and(Po/N0)=10 dB.

4. Conclusions

In this chapter, we present a comprehensive performance analysis of the outage probability (Pout)and transmission rate (R)of the underlay cognitive radio networks with decode‐and‐forward relaying over Rayleigh fading channel. We provide a rigorous data for the optimal locations of the relay terminal using differential evolution optimization algorithm. We investigate the maximum transmission rate of the secondary user, and the outage probability subject to the distance of dsp, dsr, drp, normalized with dsdbetween PUdSUs, SUsrand PUdrtransmission links, respectively. We then present the effect of the θangle, between PUdSUslink and the horizontal axis, on the Poutand Rperformance. The numerical results, validates the theoretical analysis, show that dspdistance and θangle, which is in the interval of [0π], have significant performance improvement on the transmission rate and the outage probability.


This work was supported in part by the Research Fund of Dumlupinar University under Scientific Research Project BAP/2016‐84.

© 2017 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Mustafa Namdar and Arif Basgumus (July 5th 2017). Outage Performance Analysis of Underlay Cognitive Radio Networks with Decode‐and‐Forward Relaying, Cognitive Radio, Tonu Trump, IntechOpen, DOI: 10.5772/intechopen.69244. Available from:

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