Performance Evaluation of Two-Hop Wireless Link under Nakagami-m Fading

Now-a-days, intense research is going on two-hop wireless link under different fading conditions with its remedial measures. In this paper work, a two-hop link under three different conditions is considered: (i) MIMO on both hops, (ii) MISO in first hop and SIMO in second hop and finally (iii) SIMO in first hop and MISO in second hop. The three models used here give the flexibility of using STBC (Space Time Block Coding) and combining scheme on any of the source to relay (S- R) and relay to destination (R-D) link. Even incorporation of Transmitting Antenna Selection (TAS) is possible on any link. Here, the variation of SER (Symbol Error Rate) is determined against mean SNR (Signal-to-Noise Ratio) of R-D link for three different modulation schemes: BPSK, 8-PSK and 16-PSK, taking the number of antennas and SNR of S-R link as parameters under Nakagami -m fading condition.


I. INTRODUCTION
Most common protocols used in wireless networks are the decode-and-forward (DF) and amplify-and-forward (AF) methods [1]. AF protocol used the knowledge of the instantaneous channel state information (CSI) of the source to relay (S-R) channel to control the gain by the relay [2]. The CSI assisted relay may also use the knowledge of the CSI of the S-R channel in the gain; we refer to this as CSI-assisted AF (CSIAF). When the direct link between source and destination is neglected, this is referred to a two-hop network. Two-hop relay networks, where the channel from source to destination (S-D) is split into two possibly shorter links using a relay, are attractive when the direct link between the source and destination is in deep fading. The performance analysis of the two-hop relay network has gained a lot of attention [3]. The two-hop relaying techniques are one of the promisingwireless technologies that have been kindling an enormous interest from the wireless community in the last decade [4]. To achieve higher reliability and throughput for wireless networks, half-duplex two-way relaying system has attracted much research interest [5]. Two-hop relaying communication has a number of advantages over direct-link transmission in terms of connectivity, power saving and channel capacity for the high data-rate coverage required for future cellular and ad-hoc networks [6]. Relaying is a convenient solution to satisfy the requirements of the next generation wireless communication systems, such as: high data rates and large coverage areas [7].
Multiple-antenna systems, also known as multiple-input multiple-output (MIMO) radio, can improve the capacity and reliability of radio communication. In this system, the multiple antenna elements are at both the transmitter and the receiver [8]. They were first investigated by computer simulations in the 1980s [9], and later papers explored them analytically. Since that time, interest in MIMO systems has exploded. The multiple antennas in MIMO systems can be exploited in two different ways. One is the creation of a highly effective antenna diversity system; the other is the use of the multiple antennas for the transmission of several parallel data streams to increase the capacity of the system. The multiple antennas also increase the average SNR seen at the combined output [10]. Antenna diversity is used in wireless systems to combat the effects of fading. If multiple independent copies of the same signal are available, we can combine them to a total signal with high quality, even if some of the copies exhibit low quality.
Deploying multiple antennas in wireless relay networks, referred to as MIMO relaying, has been identified as a promising technique to combat fading and increase transmission reliability [11]- [12]. Transmit antenna selection (TAS) with receive maximal-ratio combining (MRC) in MIMO relaying was proposed in [13]. In TAS/MRC relaying, a single antenna is selected at the transmitters and all the antennas at the receivers are MRC combined [14]. In [15], authors presented a framework for the comparative analysis of TAS/MRC and TAS with receive selection combining (TAS/SC) in a two-hop AF relay network. TAS/MRC and TAS/SC are two attractive MIMO protocols. This paper presents the performance of a two-hop link where the number of antennas and SNR of S-R as parameters is evaluated under Nakagami-m fading environment separately for BPSK, 8-PSK and 16-PSK modulation schemes. The objective of the paper is to observe the relative impact of Nakagami-m fading environment on the two above mentioned modulation schemes under three different conditions; MIMO on the both hop, MISO in the first hop and SIMO in the second hop, SIMO in the first hop and MISO in the second hop. Though Nakagami-m fading affects the two-hop link, hence some additional techniques like: adaptive equalization, combining scheme of MIMO, incorporation of space-time block code (STBC) etc. are recommended to enhance the performance of such links. www.ijacsa.thesai.org The rest of the paper is organized as follows. Section II describes the system model under consideration. In section III, performance analysis and results from the system model are presented. Finally, section IV concludes the paper.

II. SYSTEM MODEL
We consider a two-hop wireless network as shown in Fig.  1, where the source node S, communicates with the destination node D, through the relay node R and they equipped with N S , N R , N D antennas respectively. There is no direct link between S and D and the communication can be performed only through the relay R. This introduces fixed gain on the received signal regardless of the amplitude on the first hop, hence in an output signal with variable power, this type of fixed gain relay is cost effective to implement. Here, space diversity technique is used. Space diversity technique employs multiple transmit or receive antennas having some separation between the adjacent antennas [16]. Various techniques are available to combine the signals from multiple diversity branches. As has been mentioned in the introduction that MRC scheme is one of them. MRC represents a theoretically optimal combiner over fading channels as a diversity scheme in a communication system. Theoretically, multiple copies of the same information signal are combined so as to maximize the instantaneous SNR at the output [17]. Here N S = i, N R = j and N D = k where i = 1,2,…n; j = 1,2,…n; and k = 1,2,…n. Let Γ 1 and Γ 2 are the random variables representing the SNRs of link S-R and R-D. Then, the equivalent SNR will be Let the individual probability density function (PDF) and cumulative distribution function (CDF) of S-R and R-D links are fΓ γ1), FΓ γ1), fΓ γ2), FΓ γ2) respectively. Then, the CDF of the equivalent link will be [18] F Γ ( ) = eq 2 } fΓ ( 2 ) For the condition, when 2 > , we have 1 ≤ ; the range of 2 will be [ , ] Again, when 2  , 1 ≥ ; the range of 2 will be [o, ] From (1), Or, F Γ ( ) = I 1 + I 2 Where I1 = 1 ≥ 2} fΓ ( 2) 2 and I2 = 1 2} fΓ ( 2) 2 We know, the cdf will be and, Pr {x ≤ r} = F x (r) Then, I1 = 1 ≥ 2} fΓ ( 2) Using (6), (9) and (10), we can write The symbol error rate (SER) [15] will be PSER = . FΓ ( ) Where, a and b are the constellation-specific constants.
In the following, we have considered three cases depending on the number of antenna of source, relay and destination.

A. Case A: Mimo on Both Hops
In the case A, we consider a distributed wireless network where node S is equipped with a multiple transmitting antennas S 1 , S 2 and S 3 and node D is equipped with a multiple receiving antennas D 1 , D 2 and D 3 whereas the relay has three antennas R 1 , R 2 and R 3 in Fig. 2. These three antennas R 1 , R 2 and R 3 play the role of receiving antennas when they receive signals from the transmitting antennas S 1 , S 2 and S 3 . These three antennas R 1 , R 2 and R 3 also play the role of transmitting antennas when they transmit signals to the receiving antennas D 1 , D 2 and D 3 .

B. Case B: MISO in the First Hop and SIMO in the Second Hop
In the case B, node S is equipped with a multiple transmitting antennas S 1 , S 2 and S 3 and node D is equipped with a multiple receiving antennas D 1 , D 2 and D 3 whereas the relay has a single antenna R 1 in Fig. 3. The antenna R 1 plays the role of receiving antenna when it receives signals from the transmitting antennas S 1 , S 2 and S 3 . The antenna R 1 also plays the role of transmitting antenna when it transmits signals to the receiving antennas D 1 , D 2 and D 3 . Therefore, from the path S to R, space diversity is used as there are three transmitters and one receiver. Now, from R to D, the method of MRC is used as there are only one transmitter and three receivers.

C. Case C: SIMO in the First Hop and MISO in the Second Hop
In the case C, node S is equipped with a single transmitting antenna S 1 and node D is equipped with a single receiving antenna D 1 whereas the relay has three antennas R 1 , R 2 and R 3 in Fig. 4. These three antennas R 1 , R 2 and R 3 play the role of receiving antennas when they receive signals from the transmitting antenna S 1 . These three antennas R 1 , R 2 and R 3 also play the role of transmitting antennas when they transmit signals to the receiving antenna D 1 . Therefore, from the path S to R, the method MRC is used as there are only one transmitter and three receivers; from R to D, orthogonal scheme is used as there are three transmitters and one receiver. The impact of number of antennas is visualized from Fig.  6. Similar to the previous case like Fig. 5, it is observed that the SER decreases with the mean SNR. Here, the parameter of the curves is the number of antennas of MIMO link. Incorporation of a signal antenna at each step increases the performance of the SER tremendously. The impact of the number of antennas is more prominent of BPSK scheme than the other two modulation schemes. Fig.6.
Impact of Modulation Scheme and the number of antennas Next, we use MISO technique in the first hop and SIMO technique in the second hop so that the space diversity can be applied at the first hop and MRC can be used at the second hop. In this case, performance is heavily improved with the incorporation of one additional antenna at the source and the destination as shown in Fig. 7. But the overall performance of such a scheme is inferior to the MIMO case. Fig.7.
Impact of Modulation Scheme, numbers of transmitting and receiving antennas Finally, we use single antenna at both the source and the destination but multiple antennas on the relay, hence MRC and orthogonal scheme can also be applied in this case. Fig. 8 shows the performance of the scheme for N R = 2 and N R = 4 cases. This scheme gives marginally better performance than that of the case of Fig. 7 for the same number of antennas and modulation schemes. The finding of the paper is that, instead of using multiple antennas at the sender and the receiver one can use multiple antennas only on the relay but single antenna at the sender and the receiver. Therefore, SIMO in the first hop and MISO in the second hop is better scheme than MISO in the first hop and SIMO in the second hop case. Although, MIMO on the both hops is better than anyone of above model. But if we use SIMO-MISO scheme, cost could be minimized. So, SIMO-MISO combination is the best in context of SER and cost. We have used this technique only for Nakagami-m fading. In future, the above phenomenon can also be observed for Rayleigh, Rician and K-fading cases. Furthermore, equalizer could be used to improve the overall system performance. This work is under investigation and will be reported soon in future.