Variable packet splitting transmission in multi-relay cooperative communications with DF and DAF for SC-FDMA

In recent years, cooperative communications are widely studied. Cooperative communications can obtain the space diversity as multiple-input multiple-output (MIMO) systems. In cooperative communications, the relay method is important as decode-and-forward (DF) and decode-amplify-forward (DAF). The multi-relay cooperative communications can improve the system performance. In the multi-relay cooperative communications, the optimum packet splitting method is effective. Moreover, the multi-relay cooperative communications can more improve the system performance by using the power allocation (PA). However, the PA method requires large feedback information (FBI). To solve this problem, in this article, we propose the optimum packet splitting method based on the time domain channel state information (CSI) in the multi-relay cooperative communication with DF and DAF.


Introduction
As the next generation standard of the mobile communications, a long-term evolution (LTE)-Advanced is standardized [1]. LTE-Advanced supports broadband data services with the maximum transmission rate of about 0.1-1 Gbps. In a LTE-Advanced, single carrier frequency division multiple access (SC-FDMA) has been adopt in the uplink communication, and orthogonal frequency division multiple access (OFDMA) has been adopt in the downlink communication [2]. SC-FDMA can achieve a low peak average power ratio (PAPR) compared with OFDMA [3][4][5]. Since a low PAPR of SC-FDMA can reduce the cost and the power consumption of communication, SC-FDMA is suitable transmission method for the uplink communication.
In recent years, cooperative communications are widely studied [6][7][8][9]. Cooperative communications use the relay node except the source and destination nodes. By using the relay node, cooperative communications can obtain the space diversity as multiple-input multiple-output (MIMO) systems. For the problem of PAPR, the signals of each antenna have to process in the same device for MIMO systems. As a result, MIMO systems increase PAPR. On the other hand, the signals process in the independent device as the relay node for cooperative communications. Therefore, cooperative communications mitigate the problem of PAPR compared with MIMO systems [10,11]. In cooperative communications, the relay method is important as amplify-and-forward (AF), decode-and-forward (DF), and decode-amplifyforward (DAF) [12][13][14][15][16][17][18][19][20][21]. AF is the simplest method. This is because it is only adjust the amplitude of the signal in the relay node [12][13][14]. However, since AF is poor in a frequency selective fading environment, the system performance is significantly degraded. To solve this problem, DF and DAF have been proposed [15][16][17][18][19][20][21]. DF and DAF detect the received signal in the relay node. As a result, DF and DAF are strong in a frequency selective fading environment. For the deference of DF and DAF, DF detects the received signal by using the hard decision [15,16]. On the other hand, DAF detects the received signal by using the soft decision [17][18][19][20][21]. In this article, we use DF and DAF, and compare their performances. http://jwcn.eurasipjournals.com/content/2013/1/64 In cooperative communications, the multi-relay cooperative communications have been proposed [22]. This system can improve the system performance to obtain more strong diversity by using several relay nodes. However, if the channel condition of relays is bad, the system performance is degraded. To solve this problem, the optimum packet splitting has been proposed in MIMO systems [23]. The optimum packet splitting method splits the packet by considering the channel condition and sends from each transmit antenna. As a result, the optimum packet splitting method can improve the system performance. However, the optimum packet splitting is not considered in the multi-relay cooperative communications. Therefore, in this article, we propose the optimum packet splitting in the multi-relay cooperative communication systems. Cooperative communications can improve the system performance by using the power allocation (PA) [24][25][26][27][28]. This method is also effective in the multi-relay cooperative communications [26]. Therefore, [27] has adopt the waterfilling power allocation (WF/PA) method. The WF/PA method mitigates the deep faded channel by using the optimum power [24][25][26][27]. However, the PA method requires large feedback information (FBI) since it has to feedback the channel state information (CSI) of each sampling point in a frequency domain. To solve these problems, in this article, we propose the optimum packet splitting method based on the time domain CSI in the multi-relay cooperative communication with DF and DAF.

System model
In this article, we assume the multi-relay cooperative communications as shown in Figure 1. Here, we define the notation as follows.
• SD is the link between the source and destination nodes. • SR is the link between the source and relay nodes.
• RD is the link between the relay and destination nodes. • SRD is the link between the source, relay, and destination nodes.

Channel model
We assume that a propagation channel consists of L discrete paths with different time delays. The impulse response h n (τ , t) for the nth node is represented as where h n,l , τ n,l are the complex channel gain and the time delay of the lth propagation path for the nth node, and

Source node
The source node block diagram of the proposed system is shown in Figure 2a. Firstly, the coded data is modulated, and is performed with interleaving. After the N c points IFFT operation, the time domain transmitted signal for the nth node s n (t) can be expressed as where N c is the number of sampling points, T s is the effective symbol length, and E s is the average transmission power, respectively. For Equation (3), by using the N c points FFT operation, the frequency domain signal u n (k) is given by where d n (t) is the original signal for the nth node. From Equation (3), the proposed method splits the packet as http://jwcn.  shown in Figure 3. Here, the number of total data symbols N d is defined as where N D is the number of data symbols for SD, N i,R is the number of data symbols for ith SRD, and N is the number of relay nodes, respectively. In this article, since we assume the multi-relay cooperative communications, we define N D ≥ 1 and N i,R ≥ 1. For the proposed packet splitting method, we explain in the next section. In general, the guard interval (GI) is inserted in order to eliminate the inter-symbol interference (ISI) due to a multipath fading, and hence, we have where T g is the GI length.

Relay node
The relay node structure is illustrated in Figure 2b. The received signal for the nth relay noder n (t) can be expressed aŝ Direct Relay #0 Relay #N-1 where n n (t) is additive white Gaussian noise (AWGN) with a single sided power spectral density of N 0 . After removing the GI, by using the N c points FFT operation, Equation (7) is rewritten aŝ wheren n (k) is AWGN noise with zero-mean and a variance of 2N 0 /T s . By using the minimum mean square error (MMSE) equalization, the detected signal of Equation (8) u n (k) is given bŷ where ω n,sr (k) is the MMSE weight. After the detection, the detected signalû n (k) is also modulated and transmits to the destination node by using decode-and-forward (DF) or decode-amplify-forward (DAF).

Destination node
The destination node structure is illustrated in Figure 2c. The received signal r(t) can be expressed as where r 0 (t) is the received signal for SD, r n (t) is the nth received signal for RD, and n(t) is AWGN, respectively. http://jwcn.eurasipjournals.com/content/2013/1/64 After removing the GI, by using the N c points FFT operation, Equation (10) is rewritten as wheren(k) is AWGN noise. By using the MMSE equalization, the detected signal of Equation (11)ũ n (k) is given bỹ where ω sd (k) and ω n,rd (k) are the MMSE weights for SD and nth RD, respectively. Finally, by using the N c points IFFT operation, the desired signald n (t) is given bỹ

MMSE equalization
In this article, we assume the perfect channel estimation. The MMSE weight ω n (k) is given by where σ 2 n is the noise power [29].

Proposed variable splitting method
In this section, we explain the waterfilling power allocation (WF/PA) method and the proposed variable splitting method.

Waterfilling power allocation (WF/PA)
The waterfilling power allocation (WF/PA) method has been proposed to improve the system performance [24][25][26][27]. The WF/PA method mitigates the deep faded channel by using the optimum power assignment. The optimum power of the kth sampling point for the nth node P n (k) is given by where the cutoff SNR revel μ n is From Equation (15), the WF/PA method can improve the system performance. However, the WF/PA method requires large feedback information (FBI). To mitigate this problem, we propose the variable splitting method.

Proposed variable splitting method
The proposed variable splitting method is performed based on the time domain CSI. For the time domain CSI, the amplitudes are constant. From this characteristic, since FBI of the proposed method becomes only one, the proposed method can reduce FBI compared with the WF/PA method. Next, we explain the proposed method. The output signal X due to a Rayleigh fading is expressed as where X c is a real part and X s is a imaginary part, respectively [30]. From Equation (17), the amplitude of X is given by By using Equation (18), the proposed method is performed. First, we define the amplitude for each propagation. The amplitude for SD (λ D ) is expressed as where X SD is the output signal due to a Rayleigh fading for SD. Also, the amplitude for the ith SRD (λ i,R ) is expressed as where X i,SR and X i,RD are the output signals due to a Rayleigh fading for ith SR and ith RD, and α is the selection parameter for SRD, respectively. Then, we decide the number of data symbols for SD (N D ) and the number of data symbols for ith SRD (N i,R ). Firstly, the proposed method decides the number of data symbols for SD (N D ) as where γ is the selection parameter for SD and SRD, and x stands for the integer and closer to x, respectively. For the parameters α and γ , we decide them by using the computer simulation for DF and DAF in the next section. After choosing N D , the proposed method decides the number of data symbols for ith SRD (N i,R ). The number of data symbols for ith SRD (N i,R ) is given by By using Equations (21) and (22), the proposed method can achieve the optimum packet splitting.

Computer simulation results
In this section, we show the performance of the proposed method. In our simulation, we have used MATLAB simulation. For increasing the simulation accuracy, we consider the Monte Carlo method for computer simulation. Figure 2 shows a simulation model of the proposed http://jwcn.eurasipjournals.com/content/2013/1/64 system. On the source node, the data stream is encoded.
Here, convolutional codes (rate R = 1/2, constrain length K = 7) with interleaving are used. The coded bits are QPSK modulated. After serial to parallel (S/P) converted, the FFT spreading operation is performed. By using the IFFT operation, the SC-FDM time domain signal is generated and is inserted a guard interval (GI). The SC-FDM time domain signal is split based on Equations (21) and (22), and is transmitted to the relay and destination nodes.
In this simulation, we assume that the channel estimation is the perfect. Moreover, the SC-FDM symbol period is 2 μs, the GI length is 125 ns, the path separation is T path = 37 ns, and the maximum Doppler frequency is 5 Hz. In the relay node, the received signal is detected as Equation (9). After the detection, the detected signal is modulated again, and is transmitted to the destination node. For the relay method, in this article, we assume the decoded-and-forward (DF) and the decode-amplifyforward (DAF). In the destination node, all received signals are combined, and are S/P converted. After removing the GI, the parallel sequences are passed to the FFT operator and convert the signal back to the frequency domain. The frequency domain data signal is detected by using the MMSE equalization. After the detection, the detected signal is converted to the time domain signal by the IFFT operation. And then, the total bits are decoded by using the Viterbi soft decoding algorithm. The packet consists of N d = 80 data symbols. Table 1 shows the simulation parameters. First, we decide the optimum value of the parameters α and γ for DF. Figure 4 shows the BER versus the parameter α for γ = 0.1, 1, 2, 3, and 4 with E b /N 0 = 20 dB at Doppler frequency of 5 Hz. From the simulation result, when α is small and γ is large, the proposed method shows the good BER performance. Moreover, when α = 0.1 and γ = 4, the proposed method shows the best BER performance. Figure 5 shows the BER versus the parameter γ for α = 0, 0.1, 0.2, 0.3, and 0.4 with E b /N 0 =  5, we decide the parameters as α = 0.1 and γ = 4 for DF. Next, we decide the optimum value of the parameters α and γ for DAF. Figure 6 shows the BER versus the parameter α for γ = 0.1, 1, 2, 3, and 4 with E b /N 0 = 20 dB at Doppler frequency of 5 Hz. From the simulation result, when α is small and γ is large, the proposed method shows the good BER performance. Moreover, when α = 0.4 and γ = 3, the proposed method shows the best BER performance. Figure 7 shows the BER versus the parameter γ for α = 0, 0.1, 0.2, 0.3, and 0.4 with E b /N 0 = 20 dB at Doppler frequency of 5 Hz. From the simulation result, when α is small and γ is large, the proposed method shows the good BER performance as same Figure 5. Moreover, when α = 0.4 and γ = 3.5, the proposed method shows the best BER performance. On the other hand, when γ is greater than 3.5, the proposed method shows the bad BER performance. From Figures 6  and 7, we decide the parameters as α = 0.4 and γ = 3.5 for DAF.
Finally, we show the BER performance of the proposed method. Figure 8 shows the BER of the conventional and proposed methods at Doppler frequency of 5 Hz. First, the BER of the conventional method N D = 40 and N i,R = 20 shows about 4 dB gain compared with N = 0, where i = 1, 2. This is because the conventional method of N D = 40 and N i,R = 20 obtains the strong space diversity by using two relay nodes. Next, the BER of WF/PA shows about 2 dB gain compared with N D = 40 and N i,R = 20. This is because the WF/PA method mitigates the deep faded channel by using the optimum power assignment. However, the WF/PA method requires large FBI. The proposed method reduces FBI compared with the WF/PA method. Moreover, the BER of the proposed method shows about 2 dB gain compared with the WF/PA method. This is because the proposed method obtains the space diversity and coding gains by using the optimum packet splitting. Finally, we compare the BER performance for DF and DAF. For the conventional and proposed methods, the BER of DAF shows the good BER performance compared with DF. This is because the signal with DAF can obtain the more accurate detected signal compared with DF in the relay node. Moreover, the BER of the proposed method for DAF shows about 1.5 dB gain compared with DF. Therefore, the proposed method for DAF is effective, and shows the best BER performance.

Conclusion
In this article, we have proposed the variable packet splitting method in the multi-relay cooperative communications with DF and DAF. The proposed method obtains the space diversity by using the multi-relay cooperative communications. Moreover, since the proposed method uses the error correcting code and interleaving, obtains also the coding gain. However, if the channel condition of relays is bad, the system performance is degraded. Therefore, the proposed method splits the packet to obtain the space and coding gains. Moreover, the proposed method uses the selection parameters α and γ to obtain the maximum gains. As a result, the proposed method obtains the maximum coding gain due to the space diversity. From the simulation results, the proposed method has decided the optimum value of selection parameters α and γ , and achieved the best BER performance. Moreover, the proposed method of DAF has shown the good BER performance compared with DF.