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Outage performance of fixedgain and variablegain AF fullduplex relaying in nonidentical Nakagamim fading channels
EURASIP Journal on Wireless Communications and Networking volume 2017, Article number: 110 (2017)
Abstract
We investigate outage performance of fixedgain and variablegain amplifyandforward (AF) fullduplex (FD) relaying systems under residual loopinterference (LI) in nonidentical Nakagamim fading channels. New exact outage probability expressions are derived analytically in a singleintegral form by using the cumulative distribution function approach. Moreover, tight lowerbound and asymptotic outage probability expressions are derived in closedform for the evaluated systems. It is shown that the fixedgain AFFD relaying outperforms the variablegain AFFD relaying when LI power and/or signaltonoise ratio increase. The analytical results are verified by MonteCarlo simulations.
1 Introduction
FullDuplex (FD) communication allows receiving and transmitting the signal at the same time interval using the same frequency band, hence it improves the spectral efficiency and reduces endtoend delay with respect to the conventional halfduplex communication [1]. Additionally, the FD communication improves the network secrecy by means of the mixed signals during the simultaneous transmission [1]. Therefore, it has recently gained great attention as a potential candidate for the next generation wireless communication systems [2]. Although FD communication causes loopinterference (LI) (or selfinterference) at the receiver antenna, the recent developments on antenna technology and signal processing techniques make it feasible by applying LI cancellation techniques, e.g., antenna separation, analog cancellation and digital cancellation [3–5]. The practical implementations in [4] shows that although the LI power can be decreased 74 dB on average, it cannot be completely removed, even with complex cancellation processes [4–6]. Moreover, the experimental studies as in [4] demonstrate that it is convenient to model the residual LI channel with Rician or Nakagamim fading due to the multipath signal propagation and lineofsight (LOS) component between the transmitter and the receiver.
Cooperative communication with relaying has also attracted considerable attention in recent years since it provides coverage extension, capacity, outage, and error performance enhancement [7]. Amplifyandforward (AF) and decodeandforward (DF) are the most popular signal forwarding methods used at the relays [7]. In the AF method, the amplifying process may be based on the partial or full channel state information of the sourcerelay channel, namely fixedgain [8] and variablegain [9] AF relaying, respectively. The conventional cooperative communication systems suffer from spectral efficiency loss due to halfduplex relaying. In order to improve the spectral efficiency, FD communication is utilized at the relays [10]. In the literature, several papers investigate performance of the AFFD relaying. In [11], optimal power allocation (PA) problem and capacity of the variablegain AFFD relaying are investigated. In [12], outage probability of the variablegain AFFD relaying system with direct link between source and destination is investigated in Rayleigh fading channels and shown that the direct link provides diversity gain. The outage probability of the variablegain AFFD relaying system with direct link is derived for Rayleigh fading channels in [13] under processing delay and residual LI. Note that the sourcerelay link is assumed fadingfree in [13]. In [14], optimal PA problem based on statistical and instantaneous channel state information for the variablegain AFFD relaying system with direct link is investigated for Rayleigh fading under total source and relay power constraint. In that paper, minimum outage probability expressions are derived and comparisons with the DFFD relaying are also presented. An optimal PA analysis based on minimizing the pairwise error probability is carried out for the fixedgain AFFD relaying in [15] and shown that unequal PA presents better error performance than those using equal power in the transmitters. In [16], error performance and diversity of uncoded and coded fixedgain AFFD relaying with direct link are investigated. AFFD relaying is applied to the systems with multiple relays (e.g. in [17–19]) and shown that the performance can be enhanced significantly by using all the relays or the selected relay. The outage performance of variablegain AFFD relaying over Nakagamim channel is recently analyzed in [20] and the exact outage probability expression is derived in terms of extended generalized bivariate MeijerG function (EGBMGF). In [20], an approximate outage performance expression is also obtained in closedform by ignoring additive noise in the sourcerelay channel. Besides, the asymptotic outage probability, asymptotic ergodic capacity and ergodic capacity lowerbound expressions are presented. In [21], the outage performance of the fixedgain AFFD relaying is investigated and compared with the variablegain AFFD relaying over Rayleigh fading channels where the exact outage probability expression is obtained in a singleintegral.
In this paper, we derive exact outage probability expressions for both fixedgain and variablegain dualhop AFFD relaying where all channels are modeled as Nakagamim fading channel including the residual LI channel. The outage probability expressions are obtained by using cumulative distribution function (CDF) of the endtoend signaltointerferenceplusnoise ratio (SINR). Our results in the fixedgain and variablegain AFFD relaying are both in a singleintegral form. To the best of our knowledge, there is no outage performance investigation in the literature for the fixedgain AFFD relaying systems over nonidentical Nakagamim fading channels. Also, our exact outage performance result for the variablegain AFFD relaying can be easily calculated numerically in comparison to the exact outage probability expression in terms of EGBMGF given in [20] which is based on double MellinBarnes type integrals. Furthermore, there is no restriction on the m parameter of the relaydestination link in our analyses. We also present tight lowerbound and asymptotic outage probability expressions of the considered systems in closedform. The theoretical results are validated by computer simulations.
The main contributions of our paper can be summarized as follows:

All of the channels are modeled as Nakagamim fading channels including the residual LI channel at the relay node which makes the analyses more accurate for practical purposes.

The exact outage probability expressions of the fixedgain AFFD and variablegain AFFD systems are derived in singleintegral forms which can be easily evaluated by using common mathematical package programs.

For both of the considered systems, the exact outage performance analyses are supported with the lowerbound and asymptotic outage probability expressions obtained in closedform.

The advantages of the fixedgain AFFD relaying with respect to the variablegain AFFD relaying in terms of outage performance are presented. We demonstrate that the system has lower error floor when the fixedgain AFFD relaying is deployed.

It is shown that m parameter of the residual LI channel has dominant effect for the performance limitation in the fixedgain AFFD systems. On the other hand, the dominant m parameter of the variablegain AFFD systems belongs to the sourcerelay link channel for the error floor.
The remainder of the paper is organized as follows. In Section 2, the system model for AFFD relaying is introduced and the SINR expressions are derived for the fixedgain and variablegain relays. The exact outage probability expressions of the proposed systems are given in Section 3. Then, the lowerbound and asymptotic outage probability analyses are given in Section 4. The theoretical and simulation results for different scenarios are demonstrated in Section 5. Finally, Section 6 concludes the paper.
2 System model and endtoend SINR
We consider a dualhop network as in Fig. 1 where the source (S) and the destination (D) both have single antenna. Source and destination communicate with each other through an AFFD relay (R) and there is no direct link between the source and destination. The relay is equipped with one receive and one transmit antenna. In the figure, h _{ SR } and h _{ RD } are complex channel coefficients between SR and RD links, respectively and h _{ LI } is the complex residual LI term. Their envelopes (h _{ SR },h _{ RD },h _{ LI }) are assumed to be independent and nonidentically Nakagamim distributed. When the unitpower signal x(t) is transmitted from the source, the signal received at the receive antenna of the relay is expressed as
where s(t)=β r(t−τ) is the signal transmitted by the relay at the same time. P _{ S } and P _{ R } are the transmission powers at the source and relay, respectively and n _{ R }(t) is the complex noise with zero mean and variance \(\sigma _{R}^{2}\). β is the amplification factor and τ is the processing delay at the relay. By recursively using (1), the transmitted signal s(t) can be rewritten as
where \(g\left (t \right) = {h_{SR}}\sqrt {{P_{S}}} x\left (t \right) + {n_{R}}\left (t \right)\). Finally, the received signal at the destination can be given by \(y(t) = {h_{RD}}\sqrt {{P_{R}}} s(t) + {n_{D}}(t)\) where n _{ D }(t) is the complex noise with zero mean and variance \(\sigma _{D}^{2}\). By analyzing (2), one can easily show that stability of the relay is guaranteed and oscillations are prevented, if the β ^{2}<1/(P _{ R }h _{ LI }^{2}) condition is satisfied [3]. In that case, the instantaneous transmission power at the relay and the instantaneous endtoend signaltointerferenceplusnoise ratio (SINR) at the destination are, respectively, given as [3]
where 〈.〉 represents the time average over one symbol duration, \({\gamma _{SR}}={P_{S}}{h_{SR}}{^{2}}/\sigma _{R}^{2}\), \({\gamma _{RD}} = {P_{R}}{h_{RD}}{^{2}}/\sigma _{D}^{2}\) and \({\gamma _{LI}} = {P_{R}}{h_{LI}}{^{2}}/\sigma _{R}^{2}\). By defining \({\bar \gamma _{SR}} = {P_{S}}{\Omega _{SR}}/\sigma _{R}^{2}\), \({\bar \gamma _{RD}} = {P_{R}}{\Omega _{RD}}/\sigma _{D}^{2}\), \({\bar \gamma _{LI}} = {P_{R}}{\Omega _{LI}}/\sigma _{R}^{2}\) and Ω _{ A }=E[ h _{ A }^{2}] with A∈{SR,RD,LI}, probability density function (PDF) and CDF of these random variables can be given, respectively, by \({p_{{\gamma _{A}}}}(x) = {{\mu _{A}^{m_{A}}}{x^{{m_{A}}  1}} \over {\Gamma ({m_{A}})}}{e^{ x{\mu _{A}}}}\) and \({F_{{\gamma _{A}}}}(x) = {{\gamma ({m_{A}},x{\mu _{A}})} \over {\Gamma ({m_{A}})}}\) with \({\mu _{A}} = {m_{A}}/{\bar \gamma _{A}}\). Here, Γ(.) and γ(.,.) are the Gamma ([22] eq.(8.310.1)) and the lower incomplete Gamma ([22] eq.(8.350.1)) functions.
2.1 Fixedgain relaying
By choosing the amplification factor \({\beta = 1/\sqrt {{P_{S}}{\Omega _{SR}} + {P_{R}}{\Omega _{LI}} + \sigma _{R}^{2}}}\), the instantaneous SINR is obtained as [21]
with \(C = {\bar \gamma _{SR}} + {\bar \gamma _{LI}} + 1\). Here, γ _{ LI }<C is obtained from the condition β ^{2}<1/(P _{ R }h _{ LI }^{2}) given before. Note that when the condition β ^{2}<1/(P _{ R }h _{ LI }^{2}) is not satisfied, i.e., when \({\gamma _{LI}} \geqslant C\), then γ _{ end }=0 since the power of the interference goes to infinity.
In order to make a fair comparison, average power consumption of the fixedgain AFFD relays should be taken into account. By using (3) and β, the average transmission power at the relay is given by
By using the independence property of γ _{ SR } and γ _{ LI }, the average power consumption can be obtained as
Although the instantaneous transmission power at the relay varies for the fixedgain AFFD relaying, the average value is set to P _{ R } due to the selected β. It is important to note that we assume the dynamic range of the power amplifier at the relay is unrestricted for the fixedgain AFFD systems similar to [8] and [21].
2.2 Variablegain relaying
In order to assure the instantaneous transmission power as P _{ R }, the amplification factor is set to \({\beta =1/\sqrt {{P_{S}}{h_{SR}}{^{2}} + {P_{R}}{h_{LI}}{^{2}} + \sigma _{R}^{2}}}\). Please note that the same amplification factor is commonly used in the FD literature such as in [12, 14, 18–20]. Although the amplification factor changes with the instantaneous value of residual LI channel coefficient, which is an unknown for the relay, h _{ LI }^{2} can be obtained by using the energy detection techniques as mentioned in [14]. Then, the instantaneous SINR becomes
where X _{1}=γ _{ SR }/(γ _{ LI }+1). Note that the condition β ^{2}<1/(P _{ R }h _{ LI }^{2}) given before is always satisfied for the variablegain relaying. By substituting β into (3), the instantaneous transmission power for the variablegain AFFD relaying can be easily given by [3]
which also shows that the average transmission power of the relay for both the fixedgain and variablegain AFFD relaying are the same and equal to P _{ R }.
3 Exact outage probability analysis
In this section, exact outage probabilities of the considered FD systems are analyzed by using the CDFs of γ _{ end } given in (5) and (8). The exact outage probability equals \(\phantom {\dot {i}\!}{P_{out}} = {F_{{\gamma _{end}}}}({\gamma _{th}})\) where \({F_{{\gamma _{end}}}}(.)\) is CDF of γ _{ end } and γ _{ th } is a threshold SINR.
3.1 Fixedgain relaying
The CDF expression for the SINR given in (5) can be expressed as
where \(P({\gamma _{LI}}<C) = {F_{{\gamma _{LI}}}}(C) = \frac {{\gamma ({m_{LI}},{\mu _{LI}}C)}}{{\Gamma ({m_{LI}})}}\) and therefore \(P({\gamma _{LI}} \geqslant C) = 1 {F_{{\gamma _{LI}}}}(C)\) for nonidentical Nakagamim fading channels. In (10), the conditional CDF \({F_{{\gamma _{end}}}}(x\left  {{\gamma _{LI}} \geqslant C} \right.) = P({\gamma _{end}} < x\left  {{\gamma _{LI}} \geqslant C} \right.) = 1\) since γ _{ end }=0 when \({\gamma _{LI}} \geqslant C\). Hence, we obtain
where the conditional CDF \({F_{{\gamma _{end}}}}({\gamma _{th}}\left  {{\gamma _{LI}} < C} \right.)\) can be given by
In the above integral, the probability term can be written as
By substituting (13) into (12), \({F_{{\gamma _{end}}}}(x\left  {{\gamma _{LI}} < C} \right.)\) is rewritten as
where \({\bar F_{{\gamma _{SR}}}}(.) = 1  {F_{{\gamma _{SR}}}}(.)\). So, \({F_{{\gamma _{end}}}}(x\left  {{\gamma _{LI}} < C} \right.)\) is written as
In the above equation, the first integral term I _{1} can be simply solved as
The second integral term I _{2} can be calculated as
For integer values of m _{ SR }, by using ([22] eq. (8.352.6)), I _{2} can be rewritten as
By using the binomial equation for the term shown in the square brackets the above equation, we obtain
By using ([22] eq. (3.471.9)), the integral term I _{3} is solved as
where \({K_{{m_{RD}}  i}}(.)\) is the (m _{ RD }−i)^{th} order modified Bessel function of second kind ([22] eq. (8.407.1)). Using (20) in (19) gives
To the best of authors’ knowledge, there is no closedform solution for the above expression. By substituting (15), (16) and (21) into (11), P _{ out } for the fixedgain AFFD relaying can be evaluated by using numerical integration and it is rewritten as
The above expression is in a singleintegral form. Therefore, it can be easily and efficiently evaluated with common mathematical software packages such as MATLAB, MATHEMATICA or MAPLE.
3.2 Variablegain relaying
The CDF expression for the SINR given in (8) is given by
By using ([18] eq. (13)), \({F_{{\gamma _{end}}}}(x)\) can be rewritten as
where \({\bar F_{{X_{1}}}}(.) = 1  {F_{{X_{1}}}}(.)\). Again by using ([18] eq. (14)),
can be obtained. For integer values of m _{ SR }, by using ([22], eq. (8.352.6)), ([23] eq. (8)) and also the binomial expansion,
can be obtained. Now substituting (26) into (24), P _{ out } for the variablegain AFFD relaying is
The above expression is in singleintegral form as well. Hence, it can be also easily and efficiently evaluated with common mathematical software packages such as MATLAB, MATHEMATICA, or MAPLE. As mentioned in the Introduction, outage performance of the variablegain AFFD relaying systems in Nakagamim fading channels is also independently evaluated in [20]. On the other hand, the exact outage probability expression given in ([20] eq. (16)) is written in terms of EGBMGF which contains MellinBarnes type doublecontourintegration ([24] Table I). Although, MATHEMATICA implementation of the EGBMGF function has been provided in ([24] Table II), the builtin function is not available for EGBMGF to the best of our knowledge. Also, different from [20], our result is valid for both integer and noninteger m _{ RD } values.
4 Lowerbound and asymptotic outage probability analyses
In this section, both the lowerbound and asymptotic outage probability of the fixedgain and variablegain AFFD systems are investigated.
4.1 Fixedgain relaying
4.1.1 Lowerbound
In the previous section, the exact outage probability of the fixedgain AFFD relaying is derived in a singleintegral form and given in (22). One can show that the integral term at (21) can be upperbounded when C−z(γ _{ th }+1) term inside the integration is replaced with C−z term. This leads to a lowerbound of the outage probability which can be given by
By applying the variable transformation as \(t = \frac {Cz}{C}\) and using the binomial expansion, the above integral I _{4} is expressed as
Then, the power series and the binomial expansions are used respectively as follows
where I _{5} can be easily solved as
By combining (28), (30), and (31), we obtain the lowerbound expression for the fixedgain AFFD systems in closedform as
4.1.2 Asymptotic outage probability
When signaltonoise ratio (SNR) goes to infinity, i.e., when P _{ S },P _{ R }→∞ for the finite \(\sigma _{R}^{2}\) and \(\sigma _{D}^{2}\), the instantaneous SINR in (5) becomes
The asymptotic expression for the outage probability of the fixedgain AFFD systems can be obtained from (11). One can easily show that γ(m _{ LI },μ _{ LI } C) goes to γ(m _{ LI },m _{ LI }(η+1)) for P _{ S },P _{ R }→∞ where \(\eta = {\bar {\gamma }_{SR}}/\bar {\gamma }_{LI}\). The conditional CDF term in (11) is obtained for the asymptotic SINR as
By substituting (34) in (11), the asymptotic outage probability is obtained in closedform as
As seen, \(P_{out}^{\infty } \) for the fixedgain case is a constant and therefore leads to zero diversity order at high SNR and does not depend on m _{ SR }, m _{ RD } and Ω _{ RD } parameters.
4.2 Variablegain relaying
4.2.1 Lowerbound
In order to obtain a lowerbound for the variablegain AFFD relaying systems, we use the property of γ _{ end } < X _{1} γ _{ RD }/(X _{1}+γ _{ RD }) < min(X _{1},γ _{ RD }) where the instantaneous SINR for variablegain relaying is given in (8). So, the lowerbound can be expressed as
where \(\bar {F}_{X_{1}}\left (.\right) \) was already found in (26). Therefore, we can easily derive the lowerbound expression in closedform as
4.2.2 Asymptotic outage probability
When P _{ S },P _{ R }→∞, the instantaneous SINR in (8) becomes
In that case, the corresponding asymptotic CDF can be given by \(F_{{\gamma _{end}}}^{\infty } \left (x \right) = P({\gamma _{SR}}/{\gamma _{LI}} < x) = \int \limits _{0}^{\infty } {{F_{{\gamma _{SR}}}}\left ({xy} \right)} {p_{{\gamma _{LI}}}}\left (y \right)dy.\) For integer values of m _{ SR } by using ([22] eq. (8.352.6)), the asymptotic CDF expression is rewritten as
The above integral can be easily solved by using ([22] eq. (3.351.3)). At the end, we obtain the asymptotic outage probability in closedform as
As seen, \(P_{out}^{\infty } \) for the variablegain case is also a constant, hence leads to zero diversity order at high SNR. In addition, it does not depend on m _{ RD } and Ω _{ RD } parameters. Note that similar expression was also obtained independently in ([20] eq. (22)). Here, we provide (40) for the sake of consistency.
5 Numerical results
The theoretical (numerical) and MonteCarlo simulations outage performance results of the fixedgain and variablegain AFFD systems are shown in this section. During the outage performance analyses, we assume that \(\sigma _{D}^{2} = \sigma _{R}^{2}\) for all the scenarios and Ω _{ SR }=Ω _{ RD }=1, P _{ S }=P _{ R } unless otherwise stated. Moreover, the residual LI power, apart from Fig. 6, is chosen in the range of 0.01 and 0.1 (−20 and −10 dB) as in [12, 14, 18–20].
Figure 2 plots the outage probability results of the fixedgain AFFD relaying versus \({P_{S}}/\sigma _{D}^{2}\) for two different LI powers, Ω _{ LI }={0.05,0.1}, and various m values. The threshold SINR was set to γ _{ th }=3 for these scenarios. As seen from the curves, the outage probability decreases as Ω _{ LI } decreases, i.e., efficiency of the loopinterference cancellation process increases. As seen, the exact analytical results obtained from (22) perfectly overlap with the simulation results for all \({P_{S}}/\sigma _{D}^{2}\) values, verifying the accuracy of our analyses. Moreover, the error floors monitored in simulations are consistent with the asymptotic expression for the fixedgain AFFD relaying given in (35). We see that the dominant m parameter on the asymptotic performance is m _{ LI } and other m parameters have no effect on the error floor for the fixedgain AFFD relaying.
The outage probability results of the variablegain AFFD relaying for Ω _{ LI }={0.01,0.05}, γ _{ th }=1 and various m values are demonstrated by Fig. 3. The simulation results are perfectly matched with both the analytical exact and the asymptotic outage results given by (27) and (40), respectively. Different from the fixedgain AFFD relaying, we see that the parameter m _{ SR } has more dominant effect than the other m parameters on the asymptotic performance in the case of variablegain AFFD relaying.
Figure 4 compares the outage performance for the fixedgain and variablegain AFFD systems for Ω _{ LI }=0.06, γ _{ th }=2 and various m values. As seen, the fixedgain AFFD relaying provides better outage performance than the variablegain AFFD relaying at moderate and high SINR regions since the LI effect decreases due to the fixed amplification factor. We also present the asymptotic outage results and observe that the error floor occurs for both systems even at moderate values of \({P_{S}}/\sigma _{D}^{2}\) due to the residual LI at the relay. The variablegain AFFD relaying has much higher error floor and reaches to the error floor at lower \(P_{S}/\sigma _{D}^{2}\) values compared to the fixedgain AFFD relaying.
In Fig. 5, the consistency of the lowerbound analyses for both the fixedgain and variablegain AFFD relaying are demonstrated where the system parameters are chosen as 2P _{ S }=3P _{ R }, Ω _{ SR }=1, Ω _{ RD }=2, Ω _{ LI }=0.025, m _{ SR }=4, m _{ RD }=2.5, m _{ LI }=1 and γ _{ th }=4. It is observed that the exact outage probability of the fixedgain AFFD systems is tightly lowerbounded by the expression given in (32). For instance, there is only 0.38 dB difference between the lowerbound and the exact outage probability curves when the outage probability equals to 10^{−4}. In addition, the lowerbound overlaps with the exact outage probability at the error floor. For the variablegain AFFD relaying, the lowerbound results obtained from (37) are close to the exact outage performance, e.g., the gap between the lowerbound and exact outage probability curves is approximately 1.4 dB at 2×10^{−2}. As in the fixedgain AFFD relaying, the lowerbound reaches to the exact performance at the error floor.
Figure 6 indicates the outage probability versus Ω _{ LI } for \({P_{S}}/\sigma _{D}^{2}\) values of 10 dB, 20 dB and 30 dB with m _{ SR }=3, m _{ RD }=m _{ LI }=2.5 and γ _{ th }=2. It is seen that the fixedgain AFFD relaying achieves better outage performance as long as Ω _{ LI } and \({P_{S}}/\sigma _{D}^{2}\) increases. On the other hand, the variable gain AFFD relaying has lower outage probability for the small values of Ω _{ LI }, e.g., when Ω _{ LI } is smaller than approximately −2, −16 and −24 dB for \({P_{S}}/\sigma _{D}^{2}\) equals to 10 dB, 20 dB and 30 dB, respectively. Moreover, it is observed that the outage probability values for both the fixedgain and variablegain AFFD systems are higher than 5×10^{−1}, even for the high SNR values, e.g., \({P_{S}}/\sigma _{D}^{2} = 30\) dB, when Ω _{ LI } is set to Ω _{ SR }=Ω _{ RD }=1. This example clearly presents the importance of the LI cancellation in the FD transmission.
In Fig. 7, by using the consistency of asymptotic outage probability expressions given in (35) and (40) with the error floors for the fixedgain and variablegain AFFD systems, respectively, the error floors are represented versus P _{ S }/P _{ R } for Ω _{ SR }=1.2, Ω _{ RD }=0.8, Ω _{ LI }={0.02,0.06,0.1}, m _{ SR }=2, m _{ RD }=1.4, m _{ LI }=1.9 and γ _{ th }=5. We observe that the error floors decrease as long as the P _{ S }/P _{ R } ratio increases for both systems. Actually, this is a predictable outcome because both the endtoend SINR expressions given in (33) and (38) for P _{ S },P _{ R }→∞ are directly proportional to P _{ S } and inversely proportional to P _{ R }. Similar to the previous observations, it is also shown that the fixedgain AFFD relaying systems has considerably lower error floors. Also, the error floor for the fixedgain AFFD relays decreases more sharply in comparison with the variablegain AFFD relays, when P _{ S }/P _{ R } increases.
6 Conclusions
New exact outage probability expressions for the fixedgain and variablegain AFFD relaying systems were presented over nonidentical Nakagamim fading channels. The outage probabilities were obtained from CDF of the endtoend SINR at the destination and verified through MonteCarlo simulations. Our results show that the fixedgain AFFD relaying provides much better outage performance than the variablegain AFFD relaying when the power of the residual LI and SNR increase. We have also presented tight lowerbound and asymptotic outage performance results for both fixedgain and variablegain AFFD relaying. It was observed that the fixedgain AFFD relaying has much lower error floor with respect to the variablegain AFFD relaying. We have shown that m _{ LI } and m _{ SR } are dominant m parameters on the asymptotic outage performance of the fixedgain and variablegain AFFD relaying, respectively.
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The authors would like to thank the editor and anonymous reviewers for their constructive comments which helped to improve the technical quality of this paper.
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Koç, A., Altunbaş, İ. & Yongaçoğlu, A. Outage performance of fixedgain and variablegain AF fullduplex relaying in nonidentical Nakagamim fading channels. J Wireless Com Network 2017, 110 (2017). https://doi.org/10.1186/s1363801708881
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DOI: https://doi.org/10.1186/s1363801708881