^{1}

^{2}

^{1}

^{*}

To enhance the reliability of long wireless link, a relay is placed between transmitter and receiver which break the link into two parts: transmitter to relay called 1st hop and relay to receiver called 2nd hop; such arrangement is called two hop wireless links. In two-hop wireless communication sometimes 1st and 2nd hops are affected by different types of fading called asymmetric fading environment. In this paper we consider four different combinations of Rayleigh and Nakagami-m fading on 1st and 2nd hop to observe the profile of combined pdf (probability density function) and cdf (cumulative distribution function). With the help of cdf we determine the variation of outage probability of mixed fading. Finally we plot the SER (symbol error rate) against the SNR (signal to noise ratio) of the 2nd hop for all possible combinations of the two fading taking the SNR of 1st hop as a parameter. Although recent literature deals with asymmetric fading environment but in this paper instead of details statistical model of such fading we provide the relative scenario of mixed fading on 2-hop wireless link.

Performance of wireless communication suffers from different fading effects and these effects can be reduced by using multiple-input multiple-output (MIMO), or relayed transmission technique. Consequently, this leads to a great research interest in the MIMO and the relayed communications techniques. In amplify-and-forward (AF) relayed transmission technique, a wireless link has been established between the source and the destination via the relay. Here the source is transmitting a signal to the relay (known as 1^{st} hop S-R) and relay detects the signal with amplification sending it to the destination (known as 2^{nd} hop R-D) [

In present days the research interest on relay network over asymmetric fading channels has been increased and some recent examples of that are [

In this paper, we assume dual hope AF relay network over symmetric and asymmetric fading channels and study the performance of the relay network by evaluating the closed form expressions for outage probability, average SER by using cdf and ergodic capacity by using pdf. We plot the analytical results for the variation of combined cdf and pdf against the instantaneous SNR considering different symmetric (Nakagami-Nakagami, Releigh-Rayleigh) and asymmetric (Nakagami-m-Rayleigh, Rayleigh-Nakagami-m) fading channels for a relay network. Finally, the effects of these fading channels on the relay network are shown by considering the variation of SER against SNR of the 2^{nd} hop. It is to be mentioned here that in two-hop wireless link, there is a good possibility of experiencing different fading environments in first and second hop. Most of the papers claim their contribution in deriving the expression of SER and Outage probability in closed forms from different angles, where the expressions become very complicated. Here, we are only interested to find the solution in a simpler method.

The paper is organized as follows: Section 2 provides the theoretical analysis in determination of the combined pdf and cdf of 2-hop wireless link along with SER, Section 3 deals with the results based on analysis of Section 2 and finally Section 4 concludes the entire analysis.

In a 2-hop wireless link sometimes the 1^{st} hop (S-R) and the 2^{nd} hop (R-D) experience different types of fading called asymmetric or mixed fading environment as discussed in [

of 1^{st} hop is ^{nd} hop is

corresponding links. The cdf of the combined link is expressed [

where

and

Equation (1) can then be written as

where ^{st} link.

If S-R link is under Nakagami-m fading then its pdf

Based on [

From Equations (2) and (4),

If the R-D link is under Rayleigh fading then,

From Equations (5) and (6), we have

From [

Putting

The BER can be determined according to [

where the magnitude of

The 2^{nd} formula for SER is

The 3^{rd} formula for SER [

It is to be mentioned here that, for M-ary-QAM

The variation of combined cdf and pdf against the instantaneous SNR are shown in Figures 1-4 (four combinations of fading) taking average SNR (absolute) of the 1^{st} hop and the 2^{nd} hop as a parameter. Both cdf and pdf are found stepper for lower values of SNR-1 and SNR-2 for all the four combinations of fading. The profile of pdf and cdf are all exponential but the pdf of Nakagami-Nakagami and Nakagami-Rayleigh combinations at higher average SNR provides pdf like Poisson’s pdf is shown in ^{nd} hop is shown in ^{st} hop of 5 dB, m_{1} = 2, and m_{2} = 4. The performance is found the best for Nakagami-Nakagami combination and worst for Rayleigh-Rayleigh combination. In Nakagami-m fading, there are m direct link between transmitter and receiver hence the results of ^{st} hop stronger taking SNR of 1^{st} hop of 12 dB, m_{1} = 2, and m_{2} = 4. The corresponding profile of SER is shown in ^{st} hop is more prominent than that of 2^{nd} hop.

Finally, the performance of mixed 2-hop (1^{st} hop is Nakagami-m, m = 4 and 2^{nd} hop is Rayleigh) wireless link is shown in ^{nd} hop. The performance of the communication system enhances with increments of average SNR of 2^{nd} hop and with the decrement of the threshold SNR of 1^{st} hop is visualized from

In this paper we deal with the performance of 2-hop wireless link under asymmetric fading environment. Here, we have implemented the analytical model of asymmetric fading in a simpler way. We have combined the pdf of fading and the environment of AWGN to get the SER and Outage probability under asymmetric fading condition. Major applications of such network lie in: wireless ad-hoc network, wireless sensor network and virtual MIMO of 5G network. Here entire analysis is done under single antenna case. The work can be enhanced with multiple antennas on transmitting or receiving end; even on both sides. In this case we can apply the technique of TAS (transmitting antenna selection) on transmitting side or combining scheme on receiving side. Still we can apply zero forcing equalization technique or match filter on receiving end to improve the received SNR.

SarwarJahan,Md ImdadulIslam,Mohamed RuhulAmin, (2015) Performance Evaluation of Two-Hop Wireless Network under Asymmetric Fading Environment. Journal of Computer and Communications,03,21-27. doi: 10.4236/jcc.2015.312003