Outage Probability of Dual-Hop CSI-assisted Relay Systems over Rayleigh / Nakagami-m Fading Channels with Interferences at the Relay

Dual-hop relaying technology is a well-known technique that has a number of advantages when compared to traditional communication networks. This technology is frequently used when the direct link between the source terminal and the destination terminal is in deep fade. Dualhop transmission systems, depending on the nature and complexity of the relays used for system nodes, can be classified into two dominant categories: regenerative or decode-and-forward (DF) and nonregenerative or amplifyand-forward (AF) systems [1]. Regenerative systems have nodes that use relays when decoding the signal that propagates through the first hop, retransmitting decoded version into the second hop. Nonregenerative systems have nodes with relays which simply amplify and forward the incoming signal to the next node without performing any decoding at all. There are two types of AF relays: channel state information (CSI)-assisted relays and fixed-gain relays. The CSI-assisted relays have variable gain and require knowledge of instantaneous CSI from the previous hop to produce their gain leading to a power control of the retransmitted signal. Fixed-gain relays only require longterm statistics of the channel, which introduce a fixed gain and a variable signal power at the output, but lower complexity compared to CSI-assisted relays [1, 2]. Co-channel interference (CCI) is an important issue and should be taken in consideration. Consideration of CCI is necessary because of the aggressive reuse of frequency channels for high spectrum utilization in cellular systems [3–5]. In few published works, the impact of interference on the AF and the DF relaying performance have been investigated either at the relay(s) and/or the destination(s) [6–8]. In [6], the performance of a two hop CSI-assisted AF system with CCI at the relay over Rayleigh fading was analyzed. Analytical closed-form expressions for outage probability of dual-hop AF and DF systems over channel where relay is effected by an additive white Gaussian noise (AWGN) and destination by CCI were derived in [7]. The paper [8] studies the outage probability of both types of the AF relays over Rayleigh fading channels in an interference-limited environment (the relay and destination nodes are corrupted by CCI). In this paper, we focus on dual-hop AF relay transmission systems and study their performance over mixed Rayleigh and Nakagami-m fading channels in the presence of co-channel interferences at the relay. In practice, different links in relay networks can experience separate fading conditions. Base station-relay link is considered as Rayleigh, while the relay-mobile link is observed as Nakagami-m link because of a better fading condition. In the following analysis, we assume that there are multiple Nakagami-m interferers at the relay node independent of the desired signal. Closed-form expression for the outage probability of the end-to-end signal-tointerference and noise ratio (SINR) for CSI-assisted relayed systems is derived for integer values of Nakagamim fading parameter on the second hop.


Introduction
Dual-hop relaying technology is a well-known technique that has a number of advantages when compared to traditional communication networks.This technology is frequently used when the direct link between the source terminal and the destination terminal is in deep fade.Dualhop transmission systems, depending on the nature and complexity of the relays used for system nodes, can be classified into two dominant categories: regenerative or decode-and-forward (DF) and nonregenerative or amplifyand-forward (AF) systems [1].Regenerative systems have nodes that use relays when decoding the signal that propagates through the first hop, retransmitting decoded version into the second hop.Nonregenerative systems have nodes with relays which simply amplify and forward the incoming signal to the next node without performing any decoding at all.There are two types of AF relays: channel state information (CSI)-assisted relays and fixed-gain relays.The CSI-assisted relays have variable gain and require knowledge of instantaneous CSI from the previous hop to produce their gain leading to a power control of the retransmitted signal.Fixed-gain relays only require longterm statistics of the channel, which introduce a fixed gain and a variable signal power at the output, but lower complexity compared to CSI-assisted relays [1,2].
Co-channel interference (CCI) is an important issue and should be taken in consideration.Consideration of CCI is necessary because of the aggressive reuse of frequency channels for high spectrum utilization in cellular systems [3][4][5].In few published works, the impact of interference on the AF and the DF relaying performance have been investigated either at the relay(s) and/or the destination(s) [6][7][8].In [6], the performance of a two hop CSI-assisted AF system with CCI at the relay over Rayleigh fading was analyzed.Analytical closed-form expressions for outage probability of dual-hop AF and DF systems over channel where relay is effected by an additive white Gaussian noise (AWGN) and destination by CCI were derived in [7].The paper [8] studies the outage probability of both types of the AF relays over Rayleigh fading channels in an interference-limited environment (the relay and destination nodes are corrupted by CCI).
In this paper, we focus on dual-hop AF relay transmission systems and study their performance over mixed Rayleigh and Nakagami-m fading channels in the presence of co-channel interferences at the relay.In practice, different links in relay networks can experience separate fading conditions.Base station-relay link is considered as Rayleigh, while the relay-mobile link is observed as Nakagami-m link because of a better fading condition.In the following analysis, we assume that there are multiple Nakagami-m interferers at the relay node independent of the desired signal.Closed-form expression for the outage probability of the end-to-end signal-tointerference and noise ratio (SINR) for CSI-assisted relayed systems is derived for integer values of Nakagamim fading parameter on the second hop.

System model
We consider a dual-hop system, as shown in Fig. 1.Transmission from the source terminal S to the destination terminal D is assisted by a nonregenerative CSI-assisted relay.The relay terminal R is corrupted by co-channel interferences and AWGN while destination terminal is only perturbed by an AWGN.
We assume that terminal S transmits a desired symbol, s 0 , with an average power > @ 0 2 0 E P s (E[.] is the expectation operator).The level of co-channel interference at the relay is high enough compared to the level of thermal noise, so the thermal noise can be neglected as in all interference-limited fading environments.
The received signal at relay terminal R, in interference-limited fading environment, can be written as where h SR is the fading amplitude of the channel between terminals S and R, ^`N i i h 1 are amplitudes of the interferers at the input of R and ^`N i i s 1 are interfering symbols with an average power P i each of them.In nonregenerative systems, the signal r R is then multiplied by the gain G of terminal R and retransmitted to terminal D effected by an AWGN.The received signal at terminal D can be presented as where h RD is the fading amplitude of the channel between terminals R and D, and n D is the AWGN at the The overall SINR at the receiving end can be expressed as [6] where P R is the power of the transmitted signal at the output of the relay.
When terminal R has available instantaneous CSI from the first hop, the gain G is given by In this case instantaneous end-to-end SINR can be obtained by substituting (4) in (3) and can be written as 1 where If a link experiences Nakagami-m fading, J 2 are Gamma distributed by probability density function (PDF) given by where is the average SNR per hop of RíD channel.We assume that co-channel interference fading amplitudes are also modeled as Nakagami-m random processes.When all N interferers are identical, J 3 has the PDF where , i=1,2,...N, is the average power of each CCI.For the calculation of overall SINR is necessary to know the CDF of J 1

Outage probability
Outage probability is one of the accepted performance measures for wireless systems over fading channels.This performance measure is very useful in communication system design, especially in the cases where co-channel interference is present.Roundly speaking for this case, outage probability is defined as probability that the instantaneous equivalent SINR, falls below a predetermined protection ratio.Above this protection value, the quality of service is satisfactory.
In the case of CSI-assisted relay transmission, the outage probability of instantaneous end-to-end SINR is given by [4] Substituting ( 7), ( 8) and ( 9) in ( 10) the outage probability is To evaluate the integration of (11) we assumed integer fading parameter on the second hop, m 2 , and we derived closed-form analytical expression for the outage probability of SINR.For solving the integral (11) in closed-form it is necessary that the parameter m 2 has integer values which allows us to use the series representation of binomial formula [9, eq. 1.111].For non integer values of m 2 , outage probability can be calculated from (11) Eq. ( 12) can be reduced to the previously published result presented in [6] for the case of Rayleigh fading channels.Substituting the parameters m 2 =m 3 =1 in (12), we get (13) in [6].

Numerical results
Outage probability, as a function of average SNR of RíD channel 2

J
for various values of U, where 3 1 / J J U , is presented in Fig. 2. for different outage threshold.It is observed that as J th increases, the outage probability also increases.Improving the second hop condition by increasing average SNR, does not contribute to performance gain above some particular values of average SNR.For high second hop SNR, there are outage floors depending on outage threshold values.Analytical -open marks Simulation -filled marks J th =-5 dB

Outage probability
Second hop average SNR (dB) outage probability decreases as m 2 increases.The improvement in performance is the greatest when Rayleigh fading (m 2 =1) changes in Nakagami-m fading, with parameter m 2 =2.It is noticeable that for particular values of average SNR, values of the outage probability tend to irreducible outage floor.We can also see that outage floor does not depend on fading parameter of the second hop, but only on the first hop average SIR.Increasing the SNR value of the second hop does not contribute reducing outage probability at high range of average SNR.and it is easily recognized that there is an excellent match between them.
Due to the outage floor we can conclude that the increasing relay power does not always have impact to the reduction of the outage probability.This results can be used in design of a cellular mobile system to determine optimal values of the outage threshold and interference suppression in order to achieve reasonable outage performance.

Conclusions
We have derived the closed-form expression for the outage probability of the instantaneous SINR for dual-hop transmission with CSI-assisted relays operating over Rayleigh and Nakagami-m fading channels.Effects of the outage threshold, co-channel interferers and various values of Nakagami-m fading parameter on the performance gain were presented.This performance analysis and results can be used in design of a cellular mobile system to determine optimal values of system parameters in order to achieve reasonable influence of interferers and noise on the outage.
fading scenario of the SíR and Nakagami-m fading scenario RíD links.If a link experiences Rayleigh fading, J 1 are exponential distributed by probability density function (PDF) given by 1 1 1

Fig. 2 .
Fig. 2. Outage probability for various values of outage threshold Fig. 3. depicts the outage performance for various values of the second hop Nakagami-m fading parameter.This fading parameter affects the outage performance i.e.

Fig. 3 .Fig. 4 .
Fig. 3. Outage probability for various fading parameter Fig. 4. shows the outage performance for different number of interferences.As the number of interference increases, outage probability increases, which degrades the system performance.The largest performance degradation is present when the number of CCI increases from one to two.At lower values of average second hop SNR, outage probability decreases with increasing SNR.But, above 10 dB of average SNR, further improvement of SNR does not affect the system performance.

Fig. 4 .
Fig. 4. Outage probability for various number of co-channel interferencesNumerical results obtained by the analytical approach are confirmed by simulation results.Monte Carlo simulations for Nakagami-m fading channels is assisted on paper[10].The values of the outage probability are calculated based on over 10 7 Nakagami-m fading samples.Fig.2-Fig.4containboth analytical and simulation results,