Adaptive power allocation and outage performance of cognitive best relay cooperation systems with multiple primary transceiver pairs and direct path between cognitive source and destination
© Jia et al.; licensee Springer. 2014
Received: 3 October 2013
Accepted: 14 July 2014
Published: 23 July 2014
Based on decode-and-forward (DF) protocol, this work focuses on the adaptive power allocation and outage performance of underlay cognitive radio and opportunistic relaying (UCR-OR) systems with direct path between cognitive source and destination. The UCR-OR systems suffer from the interference of multiple primary user (PU) pairs. Under the outage constraint of PUs and the cognitive peak transmit power limit, we first obtain the adaptive power allocation schemes for secondary transmitters. Secondly, we obtain the exact closed-form expression to the outage probability of UCR-OR systems by using appropriate mathematical proof. Finally, to obtain a clear insight and to highlight the effect of system parameters on the performance of UCR-OR systems, the asymptotic closed-form expression of outage probability is achieved with the assumption of high cognitive transmit power. The presented simulations show that, due to the adaptive power allocation employed, the outage probability of UCR-OR systems is decreasing with PUs' transmit power P p when P p is less than a specific value . Only when the value of P p is greater than the outage probability is increasing gradually with the increase of P P . When the transmit power of PUs is very high, the outage probability of UCR-OR systems tends to one. That is to say, in this case, the increase of PUs' transmit power degrades severely the performance of UCR-OR systems. Besides this, it is also found that the diversity gain of UCR-OR systems is proportional to the number of cognitive relays. The parameters of PUs only affect the coding gain of UCR-OR but not the diversity gain.
Since the electromagnetic spectrum is becoming more and more scarce, improving spectrum efficiency is becoming extremely important for the sustainable development of wireless communication systems and service. However, under the current command-and-control spectrum management policy, spectrum resource is not utilized sufficiently as reported by the Federal Communications Commission  and becomes crowded due to the increasing number of various bandwidth-consuming wireless applications. Recently, cognitive radio (CR) has been proposed as an effective solution to deal with these problems by allowing the access of unlicensed secondary users (SUs) to the frequency band that is allowed to licensed primary users (PUs), in a way that does not affect the quality of service (QoS) of the licensed primary systems [2, 3]. In general, there are three main CR paradigms: interweave, overlay, and underlay . Among the three paradigms, the underlay paradigm has been considered as a promising solution due to the high spectrum efficiency and has become the hot topic of wireless communications [5–7]. The basic idea of underlay CR is that SUs are allowed to share the spectrum with PUs so long as the interference they create on PUs remains below a specific threshold. This results in the improvement on spectrum efficiency. The underlay paradigm is also called spectrum-sharing paradigm [8, 9].
However, due to the stringent interference constraint, very low transmit power level is often allowed for the secondary transmitters, and this would significantly degrade the QoS of cognitive systems and reduce the coverage of cognitive networks. One efficient method to improve the performance of cognitive systems is to employ the cooperative communication techniques [10, 11]. Cooperative communications allow different users in a wireless network to collaborate and share each other’s resource; thus, a particular user may transmit data of its own or assist another user through forwarding the received message by acting as a relay. Cooperation among the users helps in generating diversity and enhancing communication coverage [12–14]. Aiming at such improvements, so far, various cooperation schemes have been proposed in literature. Among them, opportunistic relaying (OR) has been shown simple but achieving near optimal outage performance with full diversity. In , authors have found that OR schemes can obtain the same diversity order as obtained by the complex distributed space-time code ones. The multi-user multi-relay scenarios have been considered in . The results in  showed that the employment of multi-relay can enhance the diversity gain such that the system performance can be improved greatly. Thus, the combination of underlay CR and OR (UCR-OR) can not only undoubtedly inherit the advantages of the two techniques but also shed new light on high performance. For example,  is a very important work about cognitive radio with relay cooperation. In this work, authors have presented an exact outage performance analysis for the rates of a decode-and-forward cooperative network where a source communicates with its destination using the well-known repetition-based relaying scheme or using the single best relay, i.e., selection cooperation. Closed-form expressions have been obtained for independent Rayleigh fading channels. The obtained results in  indicated that selection cooperation exhibits lower outage probabilities compared to the repetition-based scheme.
Currently, the cognitive radio relay cooperation systems have been investigated widely in literature, see, e.g., [18–23] and references therein. A typical CR relay system consists of a secondary system and a primary system. The primary system includes a pair of primary source and primary destination, while the secondary system includes a secondary source, a secondary destination, and a secondary relay. In such scheme, besides the interference at primary receiver created by SUs, the primary transmitter’s interference to the secondary relay and destination cannot be neglected, too. From the viewpoint of SUs, the interference from PUs has severe impact on system performance; thus, it is not ignored and must be considered. With the consideration, based on such system schemes, in [18, 19], authors have investigated the outage performance of underlay CR systems with interference from PUs, where the conventional amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols have been employed, respectively. Though in [18, 19] the impact of the primary user's interference on the secondary users for the cognitive systems with single relay has been investigated, the corresponding results for the underlay CR systems with multiple relays have not been presented. That is to say, in the two works, the outage performance of cognitive best relay selection systems has not been studied. Moreover, in [18, 19], the direct path transmission between secondary source and destination has been neglected. Thus, in , the outage performance of cognitive best relay selection system with primary user interference has been investigated. In particular, authors have obtained the closed-form expression for outage probability. The obtained results show that, though the interference from PUs badly degrades the performance of SUs, an increase of relays can compensate the loss. However, the drawback of the work is that the direct path between secondary source and destination has been ignored. In practice, for such scheme investigated in , the performance can be further improved by exploiting the direct path between cognitive source and destination. With this consideration, in , the outage performance of UCR-OR systems with direct path has been achieved. Though the schemes considered in [20, 21] outperform the one in [18, 19], the drawback of the schemes in [20, 21] is that the maximal transmit power limits at secondary users have been ignored. That is to say, in [20, 21], the transmit powers of secondary transmitters were determined only by the interference power constraint at PUs. The available maximal transmit power was assumed to be large enough. However, in practical implementation, the transmitters are maximal power-limited.
In , a more general cognitive relay system with primary users' interference has been investigated. In , authors have considered a system where the primary system consists of multiple transceiver pairs. This is a realistic consideration in large-scale cognitive systems where the SUs transmit over long distance and may suffer from the interference signals created by multiple primary users. For the scheme, the exact and asymptotic expressions to outage probability were obtained . Obviously, in the systems with multiple primary transceivers, the interference at SUs from PUs is increasing with the number of primary transmitters, which degrades greatly the performance of cognitive systems. To compensate the performance loss caused by primary users' interference, as investigated in [20, 21], the opportunistic relay schemes should be employed. Therefore, in , the outage performance of UCR-OR with multiple primary transceivers has been investigated under imperfect channel state information (CSI). Similarly, as stated in previous, although exploiting the direct path transmission can effectively compensate the performance loss of secondary systems caused by multiple primary users' interference, in , the direct link between cognitive source and destination was neglected.
The aforementioned literature review shows that the UCR-OR with multiple primary transceivers is very realistic cognitive radio schemes in large-scale cognitive networks. One example of such cognitive systems is wireless regional area network (WRAN) systems covering a suburb college tower and rural areas. In this case, the cognitive systems would maybe contain multiple PUs and suffer from the interference from multiple PUs. This would degrade greatly the performance of cognitive systems . Therefore, for overcoming this problem, it is an effective solution to compensate the loss by exploiting the multiple relay schemes and the direct path between cognitive source and destination. However, to the best of our knowledge, in existing work about cognitive radio systems, the problem has not been resolved. This paper aims at filling this gap. Particularly, for the UCR-OR systems with multiple primary transceivers and direct path transmission between cognitive source and destination, the peak transmit power constraint and the peak interference power constraint are existent simultaneously. The peak transmit power is the available maximum power of SUs, which is determined by the battery capacity of SUs. In contrast, the peak interference power is the permissible maximum transmission power of SUs in order to guarantee the QoS of primary users. Under the peak interference power constraint, the secondary transmitters should always maintain their transmission power below a predetermined threshold. Obviously, in time-varying channels, it is impossible to satisfy this peak power constraint at all times. For this reason, in this paper, we first consider a constraint based on a stochastic concept instead of the strict peak interference power constraint. The primary systems should be allowed a certain percentage of outage so long as the outage probability of primary systems maintains below a predetermined outage constraint.
The remainder of this paper is organized as follows. In Section 2, the system model and the assumptions are presented. Based on the concept of outage constraint, by using minimum signal-to-interference-plus-noise ratio (SINR) criterion, we present the adaptive power allocation schemes for SUs in Section 3. Section 4 is the outage performance analysis. To highlight the impact of system parameters on performance of UCR-OR systems, in Section 5, the asymptotic outage probability is also derived under the case where the adaptive power allocation is not employed. The simulated results are presented in Section 6. Section 7 is the conclusions.
2 System model
It is assumed that all primary and secondary terminals are equipped with single omni-antenna and work on half-duplex mode by using time division multiple access (TDMA). The channel coefficients (or link gains) of SS − SD, SS − SR k , SR k − SD, and PS m − PD m communication links are denoted as ϕ, g k , h k , and θ m , respectively. Furthermore, the channel coefficients of the SS − PD m and SR k − PD m interference links are β sm and , and the ones of the PS m − D and PS m − SR k interference links are α Dm and . We also assume that all channels in each link experience independent and identically distributed (i.i.d) Rayleigh fading. This indicates that for a given link gain X, it obeys exponential distribution with hazard rate 1/ω X , denoted by X ~ Υ(1/ω X ). Accordingly, as shown in Figure 1, the mean channel powers of ϕ, g k , h k , θ m , β sm , , , and are ω ϕ , ω g , ω h , ω θ , , , , and , respectively. At each receiver node, the received signals are affected by symmetry Gaussian additive noise with identical variance N0. Note that, for simplicity, we assume that the transmit power of all primary users is P p , the one of all secondary relays is P R , and the one of secondary source is P s . The peak transmit power constraints of secondary source and relays are and , respectively.
where b is defined by Equation 4.
3 Outage constraint and adaptive power allocation
where X P is defined by Equation 17.
Therefore, by using Equations 16 and 20, the transmit powers P s and P R can be determined. Due to the fact that the DF protocol is employed, the power allocation for P s and P R is manipulated separately. For P s , the secondary relays and the primary destination send the local CSIs to the secondary source firstly by using feedback links. After collecting the CSIs from the secondary relays and the primary destination, with Equation 16 the transmit power P s of the secondary source can be determined. For P R , in our scheme, a distributed scheme is employed, which combines the best relay selection and adaptive power allocation. The basic idea is that each relay sets up an internal timer which triggers transmission. Assuming synchronization among the secondary relays, all secondary relays start their timer simultaneously, whose initial values are inversely proportional to the corresponding SINR given by Equation 5. Since the cognitive destination has the local channel state information (CSI), it can send feedback to the secondary relays. The best relay is the one with its timer reduced to zero first. When the timer of best relay has expired, the relay is expected to broadcast a ‘flag’ message to neighboring nodes to prevent other relays from transmission. Then, by using the collected CSI from the secondary destination and the primary destination, the selected best relay calculates the transmit power P R according to Equation 20. Obviously, due to the distributed scheme employed, the implementation complexity of the scheme is lower than the centralized scheme.
4 Exact outage performance analyses
where the direct link SINR γSD is given by Equation 2, and is the outage threshold at cognitive destination.
In the following subsection, we would derive the closed-form expressions to and .
4.1 Detailed analyses to
4.2 Detailed analysis to
Combining Equations 44 and 48, the result for can be obtained. Then, by substituting Equations 36 and 33 into Equation 22, we can obtain the closed-form solution to that is outage probability of DF UCR-OR systems when the decoding subset is not empty.
5 Asymptotic outage performance analyses
Although in Section 4 we obtain the exact closed-form expression of outage probability for the considered UCR-OR systems, the derivations are computationally complicated and do not offer insight into the impact of system parameters on system performance. Therefore, in practice, some simplified expressions are required. To this end, we now derive the asymptotic closed-form expressions of outage probability by using the assumption that the value of the transmit power P s is high. At the same time, for simplicity, we also assume P R = λP S . Then, from the asymptotic results in high transmit power P s , the diversity and coding gains can be achieved.
Note that here, we employ the fact 1 − Δ ≈ 1 in high P s .
It can be observed from Equations 60 and 61 that the diversity gain of the considered UCR-OR systems is determined by the number of relays, i.e., G d = K + 1. The parameters of primary system only affect the coding gain, not the diversity gain. This is due to the fact that the key idea of relay cooperation is that multiple single antenna relays work together and form virtual multiple-input and multiple-output (MIMO) systems. In such virtual MIMO systems, the number of the available source-relay or relay-destination transmissions dominates the diversity gain. However, from Equation 3 to 7, we can find that the mutual interference between PUs and SUs only affects the equivalent SINR of each single path signal but not cause the increase or decrease in the number of the available source-relay or relay-destination transmissions. That is to say, the number of multiple path signals is still K + 1. Therefore, we have the result that the diversity gain of the UCR-OR systems is K + 1.
6 Simulation results and performance comparison analyses
In previous sections, we obtain the adaptive power allocation schemes of cognitive transmitters for the considered UCR-OR systems under outage and peak transmit power constraints. Based on the results, we achieve the exact evaluation to the outage probability of UCR-OR systems with the multiple PU pairs and the direct path transmission between cognitive source and destination. At the same time, to obtain the insight about the effect of system parameters on outage performance, with the assumption of high transmit power P s , the asymptotic closed-form expression of outage probability is derived too. With these derivations, the simulated and numerical results are presented in this section, which is used to validate the derivations and to obtain the acknowledgement about the impact of system parameter on the UCR-OR systems. During the analyses, we use MATLAB to build simulations. In all case, the channels are generated by using MATLAB toolbox ‘Rayleigh’, which makes a fading channel. Specially, the following system parameters are employed: number of the cognitive relays K = 10, PUs' outage threshold , mean power of PUs channels ω θ = 2, peak transmit power constraints at SUs , and noise variance N0 = 1. Note that, for the clarity of comparison analyses, in the sequence discussion, the outage probabilities of the UCR-OR systems with and without direct path are presented simultaneously, which are marked by ‘Dir link’ and ‘No-dir link’, respectively.
For the impact of the direct link, we can find that the systems with direct link outperform the ones without direct link. With the increase of the direct link mean power ω ϕ , the gap between the outage probabilities of the two systems is increasing. For example, when ω ϕ = 0.05, we can find the gap of outage probabilities is very little and can be ignored. Whereas, when ω ϕ = 1.5, the outage performance of UCR-OR systems is improved greatly. In this case, the direct link between cognitive source and destination should be considered, which results in the enhancement of communication reliability.
In Figure 3b, by using ω ϕ = 0.5 and , we investigate the impact of the outage threshold of the first hop. In the figure, we take , respectively. It can be clearly seen that the outage probability of the UCR-OR systems is decreasing with the decrease of the outage threshold . This is due to the fact that the number of relays in the decoding subset DS is increased as the outage threshold of the first hop is decreased. As a result, the outage performance of the UCR-OR systems is improved. At the same time, it can be also seen that the gap of the outage probabilities between the two UCR-OR systems (with and without direct path) is increasing with the decrease of the outage threshold . The observation is explained as follows. As aforementioned, the number of relays in the decoding subset DS is increased as the outage threshold of the first hop is decreased. This yields that the outage performance of the UCR-OR systems is improved greatly and is dominated by the relay link. The gap is increasing with the number of relays in the decoding subset DS.
In this work, we investigate the UCR-OR systems in terms of transmission power allocation and outage performance. Specially, we consider a system in which there are multiple primary user pairs and the direct path between cognitive source and destination. Under primary outage constraint and cognitive peak transmit power limit, the adaptive power allocation schemes for secondary users are achieved firstly. Then, we obtain the exact closed-form expression to the outage probability of UCR-OR systems with direct path transmission and multiple PUs' interference. Finally, to obtain the insight into the impact of system parameters on the performance of UCR-OR systems, by using the approximation of the high transmit power of SUs, the asymptotic closed-form expression of outage probability is achieved. The asymptotic results show that the diversity gain of the considered UCR-OR systems is determined by the number of relays. The parameters of primary systems only affect the coding gain but not the diversity gain. Simulated results validate the derivations firstly. At the same time, we investigate the impact of system parameters on outage performance such as the peak power P P of primary users, the mean power ω ϕ of cognitive direct path, and the number M of primary user pairs. Specially, for the impact of ω ϕ and M, the simulations show that the direct path transmission can improve the performance of UCR-OR systems, and the number of primary users has very severe impact on the UCR-OR system's performance.
The authors would like to thank the editors and the anonymous reviewers for their constructive comments and suggestions, which helped to improve the quality of this paper. This work was supported by the Natural Science Foundation of China under Grant 61261015, the 973 project 2013CB329104, the Natural Science Foundation of China under Grant 61372124, 61363059, and 61363059, the projects BK2011027, the Natural Science Foundation of Gansu Province for Distinguished Young Scholars (1308RJDA007), the China Postdoctoral Science Foundation 2012 M521105, and by the project 11KJA510001.
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