Cooperative Spectrum-Sharing with Two-Way AF Relaying in the Presence of Direct Communications

In this paper, we investigate a three-phase two-way (TW) amplify-and-forward (AF) relaying for cognitive radio networks. By utilizing the direct communications, the end user can employ diversity combining techniques, i.e., maximal ratio combining (MRC) and selection combining (SC), to achieve the full diversity. We derive the closed-form and asymptotic expressions for user and system outage probabilities which allows us to highlight the advantage of cooperative cognitive communications. The numerical results, obtained through compact forms of these outage probabilities, yield that the cognitive TW AF relaying scheme can significantly enhance the reliability of unlicensed networks in which the transmit power at secondary users is strictly governed.


Introduction
With a tremendous growth of wireless multimedia services and the number of customers, it has been an enormous pressure on available frequency bands and spectrum allocation policies.However, most of frequency bands are under-utilization according to the report of Federal Communication Commission (FCC).To get around this troublesome, cognitive radio (CR) technique has been proposed to allow the unlicensed user can utilize the licensed spectrum band [1].The principal idea of CR networks is that the secondary users (SUs) is able to use the spectrum bands of primary users (PUs) provided that the quality of service (QoS) of licensed networks is not compromised.Several CR schemes have been introduced in the literature to implement the CR network.In particular, for interweave paradigm, the unlicensed users is not allowed to occupy the spectrum bands if PU activities are detected.As such, the transmission of CR network strictly relies on the primary system.On the other hand, the underlay spectrum-sharing paradigm allows SUs to transmit its information simultaneously with PUs as long as the maximal interference does not exceed the predefined threshold.For this approach, it ensures the stable transmission for SUs at an expense of limited coverage area and low QoS.
One efficient way to alleviate the disadvantages of CR underlay scheme is to combine CR with relay networks [2,3], where the latter is know as an efficient approach for combating the effect of fading channels and expanding the communication range through the assistance of third party named relay.In particular, relay node helps source node to transmit its signal by adopting one of relaying techniques, i.e., amplify and forward (AF) and decode and forward (DF) [4].At destination, multiple replicas of source's message via relaying and direct links are combined by applying various diversity combining schemes, such as, maximal ratio combining (MRC) and selection combining (SC) to obtain a full diversity gain in a distributed fashion.
Although the one-way cognitive relay network can overcome both the impact of fading channels and the drawbacks of underlay scheme, the spectral efficiency of this system is still constrained by multiple timeslots owing to half-duplex relaying protocol [5].More recently, two-way relaying (TWR) technique has drawn a lot of attention due to fully compensating this loss by permitting two users concurrently transmit its signal to each other with the help of half-duplex relays [6].Despite getting higher spectral efficiency than the traditional cognitive one-way relay networks, only few works investigated the performance of twoway counterpart [7][8][9][10][11][12].The performance of two-way relaying with single and multiple relays has been reported in [7] and [9], respectively.In [9], the exact outage probability of opportunistic two-way relaying with spectrum-sharing has been presented.Moreover, it has been proved that system performance largely depends on the number of relay nodes and the location of relay nodes together with primary user.In [10], the tight lower bound of user outage performance of in multiple primary users environment has been obtained in two cases, i.e., two users and two group of users.The optimal relay selection for two-way cognitive relay networks has been discussed in [11,12].In addition, relay selection combined with power allocation for two-way relaying in the presence of imperfect channel state information (CSI) were studied in [13,14].It is important to note that all of these previous works have only considered DF relaying and neglected the impact of direct communication.
Different from the above works, in this paper, we investigate the two-way AF relaying for underlay spectrum-sharing with the existence of the direct link between two users.Generally, there are two distinct two-way relaying schemes depending on the number of required time-slots to complete the communication [15]: i) time division broadcast (TDBC) or threephase two-way relay (3P-TWR) and ii) multiple access broadcast (MABC) or two-phase TWR (2P-TWR) [16].For CR networks, the performance of SU is limited due to the fact that its transmit power is governed by the maximal allowable interference power constraint at PU.As such, in this paper, we exploit the direct link in 3P-TWR where the communication reliability is enhanced via diversity combining between the direct and relaying links.Our considered scheme can enhance both spectral efficiency for cognitive relay networks while keeping the desired QoS of secondary networks satisfactorily.Our main contribution in this paper is summarized as follows: • We consider the cognitive two-way relay networks in the presence of direct communication under the peak interference power constraint impinged on the licensed user.
• We investigate the spatial diversity gain for cognitive two-way relay networks by employing MRC and SC techniques between relaying and direct links.
• We characterize the statistics for the end-to-end SNR of cognitive two-way AF relay networks with MRC and SC by deriving the exact cumulative distribution function (CDF).Utilizing this result, the exact closed-form expressions for both user and system outage probability

System Model
We consider a CR network in which two secondary users (S 1 and S 2 ) exchange information with each other with the help of a non-regenerative relay R as shown in Fig.
Two-way relaying in cognitive cooperative communications.
On the other hand, owing to adopting underlay approach, the transmit power of secondary users could not exceed the maximal tolerable interference level I p .Mathematically, we have The communication between S 1 and S 2 is taken over three phase.In the first phase, user S 1 transmits its modulated signal x 1 to user S 2 and relay R. Followed by, S 2 send its signal x 2 to user S 1 and relay R in the second phase.The received signal at relay R and user S j in i-phase (i, j ∈ {1, 2} , i j) is given by where n is a circular symmetric complex Gaussian random variable with zero mean and variance N 0 .Finally, in the third phase, relay R broadcasts the scaling version of two previous received signals as where Signal is received by user S j in the third phase after canceling self-interference term is given as follows:

Maximal Ratio Combining
For MRC technique, two end-users will combine two links, namely, direct and indirect link, linearly.The end to end signal to noise ratios (SNRs) at user S j denoted as γ ij is obtained as The upper bound of equation ( 5) is given by

User Outage Probability (UOP).
In this subsection, we study the outage probability (OP) of each user with MRC is used at the secondary users.OP at user S j occurs when the information flow from node i → j is below the target rate R. Mathematically, we have where γ th = 2 3R − 1. Due to sharing the same variable, i.e., |f i | 2 the direct and indirect link are not independent.As a result, ( 7) is rewritten as As can be observed in (8), we need to find out the cumulative distribution function (CDF) of two links before evaluating the user outage probability.The CDF of indirect link under condition |f i | 2 is given as After some manipulations with the help of [17, Eq. 354.4], we get (10) as shown in the top of this page.In (10), γ = I p N 0 denotes as an average SNRs of system and E 1 (x) is exponential integral function, defined in [17,Eq. 8.211].
The probability density function (PDF) of |f i | 2 and γ 0 |f i | 2 are given as Finally, the outage probability at user S j is given in equation ( 13) at the top of next page. Here where and 2 and ; n 1 (15) Here a N , a I , b n and b i are calculated similar in [18].The remain UOP at S i gets easily by applying the similar steps.

System Outage Probability (SOP).
The system outage probability (SOP) appears when one of two user's data is under the threshold, γ th .Mathematically, we have Equation ( 19) is bounded by the following expression SOP MRC = Pr min P i , P j |h 0 | 2 + P r 2P r + max P i , P j min By using the same approach as UOP, the CDF of indirect links of Ω i is given in equation ( 22) at the next page.After that we get Ω i which is offer in equation ( 23) at the next page.Here where and K 1 = 2 , and where (3−u)  dy On the other hand, due to the symmetric between Ω 1 and Ω 2 , we solely need to obtain Ω 1 then taking similar steps to find out Ω 2 .Cooperative Spectrum-Sharing with Two-Way AF Relaying in the Presence of Direct Communications ) Finally, the SOP MRC is performed as follows: Asymptotic System Outage Probability (ASOP).In this subsection, we derive the asymptotic system outage probability (ASOP) for discovering the system diversity.
As this case, we assume that γ → ∞ and using the fact that Here AUOP i MRC , i ∈ {1, 2}, is the asymptotic of i-th user outage probability.By using binomial expansion [17, Eq. 1.110] and vanishing the second term, the asymptotic OP of S i is given in expression (30) at next page.Here Moreover, the AUOP of S j is obtained by applying the similar approach.Finally, the ASOP of MRC is obtained by substituting equation (30) into (29).
As can be seen in ( 30), the diversity gain of consider system with MRC technique is equal to 2.

Selection Combining
For SC, the upper bound of γ ij is given as User Outage Probability.For this technique, the user outage event occurs when the largest link between direct and indirect links is below the predefined threshold γ th and it is given as follows: Here H = the assistance of [17, 6.228.2].
System Outage Probability.The SOP with SC at the terminal can be bounded as follows: π 1 is obtained by taking the average of direct and indirect links over the interference links and given at the next page.
Finally, the SOP SC is given as Asymptotic System Outage Probability (ASOP).For SC, the ASOP is calculated directly from equation ( 36) and (37) and given as follows: Here 2 F 1 (a, b; c; z) is gaussian hypergeometric function which is defined in [17, Eq. 9.100] and X = ω i (ω j ) 2 (ω i +ω j ) 3 1 − 2 F 1 1, 1; 2; From (38), it is clear that the diversity gain of SC combining has the same order with MRC.In addition, although two techniques have the same diversity gain, they are quite different in coding gain as can be observed in equation ( 30) and (38).

Numerical Results
Let us consider our simulation model in twodimensional plane in which user S 1 and S 2 locate at (0,0) and (1,0), respectively.Whereas, the position of relay and primary user are (x R , y R ) and (x PU , y PU ), successively.Furthermore, only the location of relay and PU is changeable when two users situation is fixed throughout this section.The channel gain λ m and ω n are calculated by a simplified path loss model, i.e., λ 1 = d η S 1 R , with d ij is distance from node i to j, η is path loss exponent.
Fig. 2 and Fig. 3 plot UOP and SOP of MRC and SC combining with the location of relay and PU are (0.4,0.2) and (0.8,0.8), respectively.As can be seen in Fig. 2, our analyses absolutely match with simulation results.Moreover, the SOP curve is equal to the curve Cooperative Spectrum-Sharing with Two-Way AF Relaying in the Presence of Direct Communications In addition, the ASOP also has the same value with exact curve in high SNRs regime.Fig. 3 presents all of outage probability in case SC combining instead of MRC combining.Similar to MRC circumstances, the SOP of SC combining is constrained by the UOP of the weaker rate.
Fig. 4 illustrates a comparison between two diversity combining.It has proven our above analyses that two schemes have the same diversity gain but different in coding gain.More precisely, the MRC combining is only better than SC about 1 dB in high SNRs regime.Fig. 5 plots the OP versus x R where y R = 0, and PU = (0.8,0.8).As we can be seen that when x R is quite small or it is close to the S 1 , the UOP of S 1 is outperform than S 2 and vice versa.In addition, the SOP only leans on the weaker rate while the relative position between relay node and primary user is sufficient large, whereas it has a little gap with the weaker rate.Once again, the MRC technique only get a bit better than SC in all of OP curves.Fig. 6 illustrates the impact of PU position on the performance of consider system.Particularly, the location of PU is changing from (0,1) to (1,1), it means only the x-axis is vary.In this figure, we see that when the PU is proximity to S 1 or x PU is tiny, the SOP is limited by UOP1 curve and vice versa.It can be explained that the transmit power of a specific user is approach to zero when the PU is quite closely.Thereby, it easily go into outage events.

Conclusions
In this paper, outage performance has been studied in TW cognitive spectrum sharing in the presence of the direct link.In particular, the closed-form and asymptotic expression for both user and system OP have been addressed in basically tractable functions.Furthermore, it is proven that full diversity is got by adopting diversity combining techniques (MRC and SC) at two end users.The correctness of our analysis is verified by a number of simulations based on Monte Carlo method.It shows that the numerical results exactly agree with our expressions.

n 1 ,
n 2 are roots of S − Q, n 3 , n 4 are roots of Q, n 5 , n 6 are roots of S and J 7 (a, b, c, n) = c 0 log (a − y) (y − b) n dy = W (a) − W (a − c) .(27) Here W is calculated with the support of [17, 2.727.1].