# Performance analysis of amplify-and-forward relay system in Hoyt fading channels with interference at relay/Stiprinanciuju ir tiesioginiu reliniu perdavimo Hoito slopinimo kanalais sistemu nasumo analize.

IntroductionDiversity at the receiver is a well-known promising avenue for improving mean signal strength and reducing signal level fluctuations in fading channels. Performance improvement using diversity reception is considered in [1, 2, 5, 6, 13-15]. The effect of cooperative diversity on the system performance is analyzed in [3, 4] and [16]. In paper [7] diversity techniques operating over shadowed fading channel was presented, but influence of interference was not analyzed.

Relay communications as a means to improve the range and link reliability has recently rekindled enormous interest in the context of user-cooperative communications. Relay processing can be classified as either amplify-and-forward (AF) or decode-and-forward (DF). There are two types of AF relaying schemes considering two different power constraints at the relay: fixed-gain and channel state information (CSI)-based.

Hoyt distribution is commonly used to describe the short-term signal variation of certain wireless communication systems subject to fading [9] and that distribution is normally observed on satellite links subject to strong ionospheric scintillation. Specifically, the Hoyt channel model has been applied in satellite-based cellular communications to characterize more severe fading conditions than those modelled by Rayleigh [9]. Although considerable attention has been paid to outage probability analysis, few published results for Hoyt fading channels are found in the literature, mainly due to reasons of mathematical tractability. Recently, exact closed-form results for the outage probability of interferencefree Hoyt fading channels were published in [10]. It is shown that this model is applicable for describing the statistics of the fading envelope of real-world mobile radio channels.

Few works that have studied the impact of interference on the AF and DF relaying performance have assumed interference either at the relay(s) or the destination(s). Nevertheless, co-channel interference (CCI) is an important issue. Consideration of CCI is necessary because of the aggressive reuse of frequency channels for high spectrum utilization in cellular systems. It has a very long history for investigating the performances of wireless systems in the presence of CCI. It was shown in [8] that the interference can cause a severe performance degradation. Recently, in [11] authors studied the outage probability and the average bit error rate (BER) of the CSI-assisted AF protocol with interference at the relay in Rayleigh fading channel.

Performance analysis of a amplify and forward relay system, with co-channel interference at relay in Hoyt fading environment is presented in this paper. We will consider a single interferer scenario at relay and derive the outage probability and the average BER expressions. We will consider 4-QAM modulation format, but the results may be easily extended for any other modulation scheme.

System Model

In this paper we consider a communication between source S and destination D using relay R where S does not have a direct link to D [11]. All nodes are equipped with a single antenna. The communication in the system is divided into two orthogonal time intervals. In the first time interval, S sends its symbol s0 to R which is supposed to operate in an interference limited environment. Received signal, in the presence of single interference at relay R, can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [h.sub.sr] is the complex channel between S and R with average fading power [[OMEGA].sub.sr], [P.sub.s] is the transmit power, [h.sub.j] is the channel from interference to R with average fading power [[OMEGA].sub.j] independent of [h.sub.sr], [P.sub.j] is interference average power and [n.sub.r] is the AWGN at R with variance [[sigma].sup.2].sub.r]. All links are assumed to be subject to Hoyt fading. Transmitted symbols [s.sub.0] and interfering symbols [s.sub.j] are assumed to have zero mean and unit variance.

Relay R amplifies signal [y.sub.r] with gain G which is, in the presence of interference, equal to [8]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

In the second time interval R forwards [y.sub.r] to D. The received signal at D is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [h.sub.rd] is the complex channel between R and D with average fading power [[OMEGA].sub.rd], independent of [h.sub.sr] and [h.sub.j], and [n.sub.d] is the AWGN at D with variance [[sigma].sup.2].sub.d].

Signal-to-interference plus noise ratio (SINR) of the decision variable can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

Since R is interference limit (the effect of [n.sub.r] is negligible), Eq. (4) becomes [11]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Performance analysis

In this section we analyze important system performance measures such as the outage probability and average BER.

The outage probability, [P.sub.out] is defined as the probability that [[gamma].sub.eq1] drops below an acceptable threshold [[gamma].sub.th]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where Pr(*) denotes probability and [F.sub.[[gamma].sub.eq1]] (x) is the cumulative distribution function (cdf) of [[gamma].sub.eq1] which is [11]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where [f.sub.[[gamma].sub.2]] (x) and [f.sub.[gamma]INF] (x) are probability density functions (pdf) of [[gamma].sub.2] and [[gamma].sub.INF], respectively. Since [h.sub.sr], [h.sub.rd], and [h.sub.j] are Hoyt random variables, [[gamma].sub.1], [[gamma].sub.2] and [[gamma].sub.INF] are random variables with the following pdfs:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], while [q.sub.1], [q.sub.2] and [q.sub.INF] are fading parameters. The cdf of [[gamma].sub.1] is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

The cdf [F.sub.[[gamma].sub.1]] (x) may be written as [10]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where Q(x,y) is the Marcum Q function and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

After substituting (7)-(13) in (6), the outage probability is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

The average BER, derived using 4-QAM modulation format, is equal [12]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

where Q(*) is the Gaussian Q-function. Because of easier mathematical operations, [[gamma].sub.eq1] will be replaced by

[Y.sub.eq2] = min ([[[gamma].sub.1]]/[[[gamma].sub.INF]], [[gamma].sub.2]), (16)

as in [8]. Using [[gamma].sub.eq2,] the average BER may be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

where [F.sub.[[gamma].sub.eq2]] 2 (x) is the cdf of [[gamma].sub.eq2], which is equal to [11]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are complementary cdfs of [[gamma].sub.1] / [[gamma].sub.INF] and [[gamma].sub.2], respectively. The pdf of [[gamma].sub.1]/ [[gamma].sub.INF] is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

The complementary cdfs of [[gamma].sub.1]/ [[gamma].sub.INF] and [[gamma].sub.2] are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

After substituting (18), (20), and (21) in (17), by numeric integration we get the average BER.

Numerical results

Fig. 1, Fig. 2 and Fig. 3 show results from (14), with assumption [q.sub.1] = [q.sub.2] = [q.sub.INF] = q. The strength of the interference is studied using signal-to-interference ratio (SIR) [rho] = [[bar.[gamma]].sub.1]/ [[bar.[gamma]].sub.INF] .

[FIGURE 1 OMITTED]

Fig. 1. shows the [P.sub.out] as a function of q, with p and [[bar.[gamma]].sub.2] as a parameters. It can be seen that q has stronger influence on the [P.sub.out] for higher values of [rho]. Also, the [P.sub.out] changes more rapidly for smaller values of q. Signal-to-noise ratio (SNR) [[bar.[gamma]].sub.2] at R has the same influence on the [P.sub.out] for any considered q.

The [P.sub.out] as function of [[gamma].sub.th] is shown in Fig. 2. The outage probability threshold [[gamma].sub.th] has stronger impact on the [P.sub.out] for lower values of [[gamma].sub.th] and for higher values of q.

Fig. 3 shows the [P.sub.out] as a function of [[bar.[gamma]].sub.2], with q and [rho] as parameters. It can be seen that there is the outage probability threshold for higher values of [[bar.[gamma]].sub.2] because of the influence of interference.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The average BER as a function of [[bar.[gamma]].sub.2], with q and p as parameters, is shown in Fig. 4. Due to impact of interference there is BER floor for higher values of [[bar.[gamma]].sub.2]. Considering case of no interference, it can be seen that the interference may cause a significant performance loss for higher values of SNR.

Conclusions

Performance of an amplify-and-forward relay system with co-channel interference at relay in Hoyt fading environment are presented in this paper. We consider 4-QAM modulation format. The results show that the outage probability is more influenced by the Hoyt fading parameter q for higher SIR. In the presence of interference there is a BER floor for higher SNR. Acceptable threshold [[gamma].sub.th] has stronger impact on the outage probability for lower values of [[gamma].sub.th].

Acknowledgements

This paper was supported by the Serbian Ministry of Education and Science (project III44006).

Received 2011 07 16

Accepted after revision 2012 01 02

References

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H. Stefanovic, I. Petrovic

College of Electrical Engineering and Computing Applied Science, Vojvode Stepe 283, 11000 Belgrade, Serbia, phone: + 38112471099, e-mail: stefanovic.hana@yahoo.com

R. Bojovic

Faculty of Technical Sciences, University of Pristina, Kneza Milosa 7, 38220 K. Mitrovica, Serbia, phone: +38128425320, e mail: risto.bojovic@yahoo.com

http://dx.doi.org/10.5755/j01.eee.121.5.1649

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Title Annotation: | TELECOMMUNICATIONS ENGINEERING/TELEKOMUNIKACIJU INZINERIJA |
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Author: | Stefanovic, H.; Petrovic, I.; Bojovic, R. |

Publication: | Elektronika ir Elektrotechnika |

Article Type: | Report |

Date: | May 1, 2012 |

Words: | 2154 |

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