3. Numerical results and simulations

Here, we consider the worst case channel conditions, namely, Rayleigh fading, might cause some signal power loss between the SUs � r and r � SUd links, 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 PUd during the source and the relay transmission phase

> sp � �

> > sp �ln ε<sup>p</sup>

> > rp �ln ε<sup>p</sup>

is the transmit power of the SUs and Pr is 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

Ps<sup>¼</sup> P0d<sup>α</sup>

Pr<sup>¼</sup> P0d<sup>α</sup>

respectively [27]. Here, α is the path loss exponent, and lnð Þ: 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, R subject 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 SUs and SUd terminals. The outage probabil-

γsr

<sup>þ</sup> <sup>γ</sup>rd γrd � γsd exp � <sup>g</sup>ðR<sup>Þ</sup> γrd

> drp � ��<sup>α</sup>

þ dsr dsp

γsr þ 1 γrd � �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� ��<sup>α</sup>

dsp

� � � ��<sup>α</sup> ! s

ity of the secondary user for the DF relaying can be expressed as follows [27]:

exp � <sup>g</sup>ðR<sup>Þ</sup> γsd � �

where <sup>R</sup> is the transmission rate for SUs and gð Þ¼ <sup>R</sup> <sup>2</sup>2 R � 1. We have

dsd dsp

Here, the outage probability for the secondary user is given by <sup>ε</sup><sup>s</sup> <sup>¼</sup> <sup>1</sup>

� ��<sup>α</sup>

value of the system parameters, seen in the following section.

� ��<sup>α</sup> drd

<sup>1</sup> � exp � <sup>g</sup>ðR<sup>Þ</sup>

� � � �

� � � � � �

drp

� ��<sup>α</sup> dsr

average signal-to-noise ratios in the links PUs to PUd, SUs to r, and r to SUd are given by

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

, and γrd ¼ μ drd=drp

� � � ��<sup>α</sup> . drd

and Pout;relay <sup>¼</sup> exp �Po=Prd– <sup>α</sup>

� � <sup>ð</sup>2<sup>Þ</sup>

� � <sup>ð</sup>3<sup>Þ</sup>

exp � <sup>g</sup>ðR<sup>Þ</sup> γsr

> 1 2γsd <sup>g</sup>ð Þ <sup>R</sup> <sup>2</sup>

. We have μ ¼ P0= �N0ln ε<sup>p</sup>

� � <sup>ð</sup>4<sup>Þ</sup>

: ð5Þ

. The

� � � � .

rp � �

where Ps

are respectively given by Pout;source <sup>¼</sup> exp �Po=Psd– <sup>α</sup>

28 Cognitive Radio

<sup>P</sup>out <sup>¼</sup> <sup>1</sup> � exp � <sup>g</sup>ðR<sup>Þ</sup>

<sup>R</sup> <sup>¼</sup> <sup>1</sup> 2

γsd ¼ μ dsd=dsp

� ��<sup>α</sup>

� � � �

<sup>þ</sup> <sup>1</sup> � <sup>γ</sup>sd

log2 <sup>1</sup> <sup>þ</sup> <sup>μ</sup> ffiffiffiffi

2γsd

γsd � γrd

εs p

, γsr ¼ μ dsr=dsp

transmit powers for the secondary user and the relay are given as

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 SUð Þ <sup>s</sup> � r , dsropt are provided with different θ values, while dsp ¼ dsd, dsp ¼ 2 dsd and dsp ¼ 5 dsd. Besides, the maximum transmission rate values ð Þ 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 θ and dsp increases.

The outage probability Pð Þ out performance of the considered system is illustrated in Figure 2 with varying θ values when Pð Þ¼ <sup>o</sup>=N<sup>0</sup> 10 dB, α ¼ 4, ε<sup>S</sup> ¼ 0:1, ε<sup>p</sup> ¼ 0:05, dsp ¼ 2 dsd and dsr ¼ dsd=2. It can be observed from the simulation results in Figure 2 that the optimal θ angle can be calculated, where the best minimum of Pout is achieved.


Table 1. Optimization results for DF relaying with different θ values for dsp ¼ dsd, dsp ¼ 2 dsd, and dsp ¼ 5 dsd.

Figure 2. Pout for the considered underlay CR network with DF relaying under different θ values.

Figure 3 shows the transmission rate over Rayleigh fading channel versus Pð Þ <sup>o</sup>=N<sup>0</sup> when α ¼ 4, ε<sup>S</sup> ¼ 0:1, ε<sup>p</sup> ¼ 0:05, θ ¼ π=2, dsp ¼ 2 dsd and dsr ¼ dsd=2. The results clearly show that R increases with the increase of the Pð Þ <sup>o</sup>=N<sup>0</sup> .

The transmission rate ð Þ R of the considered system for the SUs � r link with the normalized dsd distance is illustrated in Figure 4 when Pð Þ¼ <sup>o</sup>=N<sup>0</sup> 10 dB, α ¼ 4, ε<sup>S</sup> ¼ 0:1, ε<sup>p</sup> ¼ 0:05, θ ¼ π=2 and dsp ¼ 2 dsd. Figure 4 indicates that the maximum transmission rate is achieved when the optimal transmission distances are used.

Figure 3. R vs. ð Þ Po=N<sup>0</sup> .

Outage Performance Analysis of Underlay Cognitive Radio Networks with Decode‐and‐Forward Relaying http://dx.doi.org/10.5772/intechopen.69244 31

Figure 4. R vs. ð Þ dsr=dsd for ð Þ¼ Po=N<sup>0</sup> 10 dB.

Figure 3 shows the transmission rate over Rayleigh fading channel versus Pð Þ <sup>o</sup>=N<sup>0</sup> when α ¼ 4, ε<sup>S</sup> ¼ 0:1, ε<sup>p</sup> ¼ 0:05, θ ¼ π=2, dsp ¼ 2 dsd and dsr ¼ dsd=2. The results clearly show that R

Figure 2. Pout for the considered underlay CR network with DF relaying under different θ values.

The transmission rate ð Þ R of the considered system for the SUs � r link with the normalized dsd distance is illustrated in Figure 4 when Pð Þ¼ <sup>o</sup>=N<sup>0</sup> 10 dB, α ¼ 4, ε<sup>S</sup> ¼ 0:1, ε<sup>p</sup> ¼ 0:05, θ ¼ π=2 and dsp ¼ 2 dsd. Figure 4 indicates that the maximum transmission rate is achieved when the

increases with the increase of the Pð Þ <sup>o</sup>=N<sup>0</sup> .

30 Cognitive Radio

optimal transmission distances are used.

Figure 3. R vs. ð Þ Po=N<sup>0</sup> .

Figure 5. Pout for varying ð Þ dsr=dsd with ð Þ¼ Po=N<sup>0</sup> 10 dB.

Figure 5 depicts the outage probability performance as a function of dð Þ sr=dsd . Here, Pð Þ¼ <sup>o</sup>=N<sup>0</sup> 10 dB, α ¼ 4, ε<sup>S</sup> ¼ 0:1, ε<sup>p</sup> ¼ 0:05, θ ¼ π=2 and dsp ¼ 2 dsd. 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 dð Þ¼ sr=dsd 0:5, which leads to the midpoint of the transmission link of SUs � SUd as the optimal position.

In Figure 6, the transmission rate for the PUd � SUs link is monitored for the normalized dsd distance over Rayleigh fading channel while Pð Þ¼ <sup>o</sup>=N<sup>0</sup> 10 dB, α ¼ 4, ε<sup>S</sup> ¼ 0:1, ε<sup>p</sup> ¼ 0:05, θ ¼ π=2 and dsr ¼ dsd=2. In addition, Pout performance analysis is also studied for the transmission link for PUd � SUs with the normalized distance of dsd and demonstrated in Figure 7 using the same parameters in Figure 6.

Figure 6. <sup>R</sup> vs. <sup>d</sup>sp=dsd over Rayleigh fading channel while ð Þ¼ <sup>P</sup>o=N<sup>0</sup> 10 dB.

Figure 7. <sup>P</sup>out performance with varying <sup>d</sup>sp=dsd while ð Þ¼ <sup>P</sup>o=N<sup>0</sup> 10 dB.

Figure 8. ð Þ dsr=dsd vs. R over Rayleigh fading channel with different θ values for ð Þ¼ Po=N<sup>0</sup> 10 dB, dsp ¼ dsd, dsp ¼ 2 dsd and dsp ¼ 5 dsd.

Outage Performance Analysis of Underlay Cognitive Radio Networks with Decode‐and‐Forward Relaying http://dx.doi.org/10.5772/intechopen.69244 33

Figure 9. ð Þ dsr=dsd vs. θ values for dsp ¼ dsd, dsp ¼ 2 dsd and dsp ¼ 5 dsd while ð Þ¼ Po=N<sup>0</sup> 10 dB.

Figure 6. R vs. dsp=dsd

32 Cognitive Radio

Figure 7. Pout performance with varying dsp=dsd

and dsp ¼ 5 dsd.

over Rayleigh fading channel while ð Þ¼ <sup>P</sup>o=N<sup>0</sup> 10 dB.

Figure 8. ð Þ dsr=dsd vs. R over Rayleigh fading channel with different θ values for ð Þ¼ Po=N<sup>0</sup> 10 dB, dsp ¼ dsd, dsp ¼ 2 dsd

while ð Þ¼ <sup>P</sup>o=N<sup>0</sup> 10 dB.

The normalized dsr distance varying with the transmission rate R over Rayleigh fading channel for different θ values and transmission links, dsp ¼ dsd, dsp ¼ 2 dsd and dsp ¼ 5 dsd are shown in Figure 8. Besides, in Figure 9, dsr=dsd normalized distances are calculated for the different θ angles with varying dsp values. Here, both figures are plotted for the values of Pð Þ¼ <sup>o</sup>=N<sup>0</sup> 10 dB, α ¼ 4, ε<sup>S</sup> ¼ 0:1 and ε<sup>p</sup> ¼ 0:05.

The maximum transmission rate varying with different θ values for dsp ¼ dsd, dsp ¼ 2 dsd and dsp ¼ 5 dsd, while Pð Þ¼ <sup>o</sup>=N<sup>0</sup> 10 dB is depicted in Figure 10. The figure demonstrates the effect of dsp with varying θ angles. The results show that the maximum transmission rate of the considered system increases while θ and dsp increases.

Finally, the maximum transmission rate, varying with the normalized distance for different dsp values, is depicted in Figure 11. It is seen that while the drp=dsd increases, the system performance also increases when θ is in the interval of 0½ � � π . In other words, these results also prove that the R performance is directly related with the PUd � SUs transmission link. While in case of dsp distance is increased, the maximum transmission is achieved.

Figure 10. Maximum transmission rate varying with different θ values for dsp ¼ dsd, dsp ¼ 2 dsd and dsp ¼ 5 dsd while ð Þ¼ Po=N<sup>0</sup> 10 dB.

Figure 11. Maximum transmission rate varying with drp values normalized with dsd, for different PU<sup>d</sup> � SU<sup>s</sup> distance while dsr ¼ dsd=2 and ð Þ¼ Po=N<sup>0</sup> 10 dB.

#### 4. Conclusions

In this chapter, we present a comprehensive performance analysis of the outage probability Pð Þ out and transmission rate ð Þ 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 dsd between PUd � SUs, SUs � r and PUd � r transmission links, respectively. We then present the effect of the θ angle, between PUd � SUs link and the horizontal axis, on the Pout and R performance. The numerical results, validates the theoretical analysis, show that dsp distance and θ angle, which is in the interval of 0½ � � π , have significant performance improvement on the transmission rate and the outage probability.

#### Acknowledgements

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

#### Author details

Mustafa Namdar\* and Arif Basgumus

\*Address all correspondence to: mustafa.namdar@gmail.com

Department of Electrical and Electronics Engineering, Dumlupinar University, Kutahya, Turkey
