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 Outage Performance Analysis of Underlay Cognitive Radio Networks with Decode‐and‐Forward Relaying http://dx.doi.org/10.5772/intechopen.69244 27

Figure 1. System model for cooperative relaying in cognitive radio networks [27].

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

Most of the previous publications have studied the performance of cooperative communications techniques over different fading channels and under different constraints [18–26]. 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. [21–26] 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

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

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.

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

the differential evolution (DE) optimization algorithm [15–17].

fading channels.

26 Cognitive Radio

Rayleigh fading channels.

Finally, Section 4 provides the concluding remarks.

2. System model and performance analysis

system model for the cooperative relaying, we have both PU and SU, each with a source (PUs and SUs) and destination (PUd and SUd) nodes. Besides, the relay rð Þ is located in the same line between SUs and SUd. We assume that PUs only transmits to the PUd and SUs utilize a twophase 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, SUs transmits the signal to r. In the second phase of this transmission, r decodes its received signal and retransmits (forwards) it to the SUd [27]. We denote the distance between the secondary source SUs and the relay r as dsr, the distance between the secondary source SUd and the primary destination PUd as dsp, the distance between the secondary source SUs and the secondary destination SUd as dsd and finally, the distance between the relay r and the primary destination PUd as drp. We have

$$\mathbf{d}\_{\rm rp}^2 = \mathbf{d}\_{\rm sp}^2 + \mathbf{d}\_{\rm sr}^2 - 2\mathbf{d}\_{\rm sp}\mathbf{d}\_{\rm sr}\cos\theta \tag{1}$$

where the cosine theorem is used. Here, θ is the angle between the horizontal axis and the line connecting the PUd and SUs nodes.

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 Pð Þ<sup>0</sup> 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, SUs and εP, on the other hand, to maximize the data rate at the destination subject to the outage probability constraints, ε<sup>s</sup> is evaluated by the secondary user.

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 are respectively given by Pout;source <sup>¼</sup> exp �Po=Psd– <sup>α</sup> sp � � and Pout;relay <sup>¼</sup> exp �Po=Prd– <sup>α</sup> rp � � where Ps 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 transmit powers for the secondary user and the relay are given as

$$P\_s = \frac{P\_0 \mathbf{d}\_{sp}^\alpha}{-\ln\left(\varepsilon\_\mathbb{P}\right)}\tag{2}$$

$$\mathbf{P\_r} = \frac{\mathbf{P\_0 d\_{rp}^{\alpha}}}{-\ln\left(\varepsilon\_\mathbf{p}\right)}\tag{3}$$

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

$$\begin{split} P\_{\rm out} &= \left( 1 - \exp\left( -\frac{\mathbf{g}(\mathbf{R})}{2\overline{\mathcal{V}}\_{\rm sd}} \right) \right) \left( 1 - \exp\left( -\frac{\mathbf{g}(\mathbf{R})}{\overline{\mathcal{V}}\_{\rm sr}} \right) \right) \\ &+ \left( 1 - \left( \frac{\overline{\mathcal{V}}\_{\rm sd}}{\overline{\mathcal{V}}\_{\rm sd} - \overline{\mathcal{V}}\_{\rm rd}} \exp\left( -\frac{\mathbf{g}(\mathbf{R})}{\overline{\mathcal{V}}\_{\rm sd}} \right) + \frac{\overline{\mathcal{V}}\_{\rm rd}}{\overline{\mathcal{V}}\_{\rm rd} - \overline{\mathcal{V}}\_{\rm sd}} \exp\left( -\frac{\mathbf{g}(\mathbf{R})}{\overline{\mathcal{V}}\_{\rm rd}} \right) \right) \right) \exp\left( -\frac{\mathbf{g}(\mathbf{R})}{\overline{\mathcal{V}}\_{\rm sr}} \right) \end{split} \tag{4}$$

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

$$R = \frac{1}{2} \log\_2 \left( 1 + \mu \sqrt{\varepsilon\_s} \sqrt{\left( \left( \frac{\mathbf{d\_{sd}}}{\mathbf{d\_{sp}}} \right)^{-a} \left( \frac{\mathbf{d\_{rd}}}{\mathbf{d\_{sp}}} \right)^{-a} \left( \frac{\mathbf{d\_{sr}}}{\mathbf{d\_{sp}}} \right)^{-a} \right)} \right) \Big/ \left( \left( \frac{\mathbf{d\_{rd}}}{\mathbf{d\_{rp}}} \right)^{-a} + \left( \frac{\mathbf{d\_{sr}}}{\mathbf{d\_{sp}}} \right)^{-a} \right) \right). \tag{5}$$

Here, the outage probability for the secondary user is given by <sup>ε</sup><sup>s</sup> <sup>¼</sup> <sup>1</sup> γsr þ 1 γrd � � <sup>1</sup> 2γsd <sup>g</sup>ð Þ <sup>R</sup> <sup>2</sup> . The average signal-to-noise ratios in the links PUs to PUd, SUs to r, and r to SUd are given by <sup>γ</sup>sd <sup>¼</sup> <sup>μ</sup> dsd=dsp � ��<sup>α</sup> , <sup>γ</sup>sr <sup>¼</sup> <sup>μ</sup> dsr=dsp � ��<sup>α</sup> , and <sup>γ</sup>rd <sup>¼</sup> <sup>μ</sup> drd=drp � ��<sup>α</sup> . We have μ ¼ P0= �N0ln ε<sup>p</sup> � � � � .

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.
